As a mathematician stumbling on this video, to my mind, “logic” and “reasoning” are completely distinct concepts in my mind. The latter is a cognitive activity tantamount to usefully processing data about the world, and the former is a formal system-no different than a game of chess or a computer program. In that sense, I think my initial objection to the notion of logical normativity can probably be reasonably dismissed as semantics/trivial; “logic” is just symbol-pushing and doesn’t make external claims about anything. And, of course, “reasoning” is only a useful emergent physical phenomenon-and probably just illusory in the final empirical analysis. This doesn’t seem to be what people mean by “logic” either. (It’s just a physical phenomenon. E.G., is photosynthesis normative?) However, I think what’s actually being asked is whether or not “the systematic philosophical study of correct/useful reasoning” makes normative claims. Framed this way, I think the answer is *obviously* yes: we need to choose what we mean by correct/useful! As I said, this isn’t my field and I’m just an amateur. Feedback appreciated! (Please let me know all the dumb mistakes I’ve made.)
I'm a mathematician too (not a logician though). I used to think that (mathematical) logic was just a formal/mathematical model for human rigorous rational reasoning (whatever the latter means). This is in line with the fact that there are different logics: classical, modal, aletheic, ... : different models describe different aspects of human reasoning; like different physical theories (classical mechanics, quantum mechanics, general relativity,... ) describe different aspects of physical reality [Not that I think that mental activity is non-physical; rather, it's more emergent than fundamental physics]. And that's all. But now I've seen the title of this video and it instilled quite some doubt in me: why *should* people adhere to principles of logic when they attempt to talk about the world in a rational way? Does logic (which is a piece of syntax, hence of language) somehow reflect the objective structure of the world?
But do we actually have a choice about what we mean by correct/useful? What would a different choice look like, and what would be its consequences? There is a model of language, that allows for unsolved contradictions, and it will be usually employed in poetry. There is no absolute norm, to never employ poetic language, this kind of language will just not be very useful in solving a whole lot of problems, which makes the normativity of reasoning purely conditional: If you want to solve a problem of this given type, reasoning gives you the best chances of success.
@@rv706 I've been dealing with Lean and computer proof assistants a lot recently, and it has become clear to me that it's actually an issue among mathematicians that we frequently delude ourselves into thinking that we're engaging in "logical" thinking when, much of the time, we're really reasoning via all manners of non-logical means with the implicit understanding that "certain moves" are, in principle, translatable back to formalistic foundations. I think that basic human reasoning is just something that we have to accept as an empirical fact--much like human language; it probably has history in evolutionary time, and I think our formal logics are just useful tools to translate some of its nuance into a formal language. That is, their utility as a means of facilitating "reasoning-computations" is a result of their design to capture the essence of human reasoning. When it comes down to it, I don't think we can rule out gaps in which 1) our logical systems don't capture bits of human reasoning, or 2) human reasoning fails to be an effective method for processing information about the world.
@@stefanb6539 I think that human reasoning isn't perfectly captured via, e.g., classical first-order logic. Even ignoring issues of expressibility (we probably want higher-order logics, which come at the cost of worse proof theories), take, for instance, the issue of credence vs belief. You can give propositions A, B, C, ..., Z high enough credence individually that you believe each of them, but then we understand that their conjunction "A and B and C and ... and Z" may well have very low credence, and we probably wouldn't believe that. This aspect of human reasoning is not captured in propositional logic--or even first order logic (by itself). That kind of thing comes up all the time when we're designing plans. Of course, each of the steps 1,2,3,...,n seems like they ought to work (in fact, it's not clear how they wouldn't work!)... but we're still going to make a back up plan because they're *definitely* not all going to work together--at some point, *something* will go wrong and we'll need to fall back on a backup plan. You might choose a formal logical framework which takes that into account, but then you'll probably miss something else. If you *do* have a complete formal description of how humans make "intelligent decisions," then I think Google and Tesla would be willing to pay you a lot of money; it's not so easy, and we usually still need to add more stuff in. Even probability theory--undergirded by the full power of modern mathematical analysis--leaves a lot to be desired, despite being sufficient for machine learning applications. And that's missing the point that humans generically (and infamously) don't reason probabilistically. Our reasoning is a lot more flexible and a lot more general--unfortunately, it's also a lot less precise. We can choose which aspects of our reasoning we want to encode into a formal language (which, in this context, we call "logic"), but it's ultimately still a choice of where to stop because we don't understand human reasoning well enough to encode *everything*.
I think what you call "logic" here is "formalism". We can make arbitrary formalisms, not unlike arbitrary games. The word "logic" in ordinary language means a variety of reasoning. So, formal logic is a subset of formalisms constrained by norms of reasoning. At least in my view.
Math is a language for describing relationships (between what and what is irrelevant). What you care about in logic is the relationship between elements and propositions on those elements. Logic really says nothing about truth or falsehood outside 'true' and 'false' being elements of a proposition. Everything else is interpretation. There are an uncountable number of logical statements which are perfectly valid logical statements but for which any interpretation would be ludicrous. Math is a game whose interpretation is sometimes useful in explaining how things in the real world relate within given bounds.
@@victor.sannier Interesting. What point am I being naïve on? There is more than one type of logic math. I have a big textbook on Fuzzy Set Theory and Fuzzy logic which is very useful for designing AI and Expert systems. In Fuzzy logic you have many more outcomes than just true or false. When you are trying to solve a problem in reality, you have options on which math to use or which game to play and how to interpret it. Much of the craziness in modern physics isn't the math but the interpretation. Pretending that math somehow IS reality is an extremely dangerous delusion which our society admittedly often falls into.
@@victor.sannier Studying the "consequences of a certain choice of axioms and rules of deduction" is more about the philosophy of mathematics. The problem with thinking that logic includes its own interpretation is a real problem. What does "true" actually mean? In Fuzzy logic what does "25% true" actually mean? When you do the math, true and false are just game outcomes. How you apply those outcomes is something completely different. As for axioms, it is true that insanity resides not in the logic, which is often valid, but in the initial assumptions or axioms you start with. If you assume that someone is out to get you then paranoid behavior is completely rational.
Yes, "explore" is a better word especially when you consider mathematics/logic as a game where you can play with the knobs and see what happens. Just don't assume that the results says anything about reality. In particular, while mathematically anything can be reduced to bits (see Information Theory), reality itself is not Boolean.
The purpose of logic is to reveal "good" vs "bad" reasoning. It cannot tell us what we should or should not believe, but it can help us think clearly and consistently. It can also not tell us what is true or not true, because the terms within logical arguments (by terms I mean the claims or premises, etc.), can be true or false. Logic is, then, a tool to guide thinking, not belief or truth.
saying something is good or bad is an evaluative statement, but you are the one putting normative weight on the logical valuations. Logic doesnt tell us what is good or bad reasoning on its own, theres some hidden non-logic evaluative standard youre appealing to.
@@DoomKaiserGliders "saying something is good or bad is an evaluative statement, but you are the one putting normative weight on the logical valuations." No. This makes no sense. I am not putting any weight on anything. I did not invent logic. Logic is largely discovery and development over time. Things like Modus Ponens, or the law of non-contradiction are not invented, but are observed relationships in reality. Violating reality in argumentation is bad reasoning. " Logic doesnt tell us what is good or bad reasoning on its own, theres some hidden non-logic evaluative standard youre appealing to." No. I think you don't actually understand logic or the concept of reasoning. It seems like you're trying to fight over nothing.
@@droe2570 I think he's trying to make the distinction between "Good/bad" and "correct/incorrect" you can have a logical argument which is invalid, but only the norm that "being invalid is bad" makes it a "bad argument". see: (6:19) You could change your premise to: "The purpose of logic is to reveal "good" vs "bad" reasoning, when combined with norms of what logical qualities are "good" vs "bad"." And I think he'd agree with that. There is a semantic difference between "good/bad" and "true/false", and the difference between them is the hidden premise in most philosophical debate that "we ought to believe true things, and ought not to believe false things". "logic" and "norms on how to use logic" are different concepts, and a certain kind of logical anti-normativists base belief is that "norms on how to use logic" are *not a part of* "logic".
@@haph2087 To determine good vs bad reasoning , we require rules (norms) that allow us to determine "good" vs "bad". Without logic rules, in this case, then we can never determine good or bad reasoning. I did not discuss this because I thought it was self-evident.
@@droe2570 Cool, I understand why you didn't say it cause generally it's self-evidence means we don't need to mention these norms, but... In the specific conversation of logical normativity, the main difference between the logical normativists and (some of) the logical anti-normativists is that the logical normativists define logic to *include* these logic-adjacent norms, while a certain kind of logical anti-normativists do not.
Excellent video! This was one of the few topics that I couldn't even fathom how someone could argue that logic isn't normative, but I must say, you gave some really good arguments that changed my mind on this
this video is awesome because i’ve always just taken it for granted that logic is descriptive and had no idea that anyone thought it was normative, let alone that this was apparently the dominant view lol
@@captainbeefheart5815This seems more like a play on words, unless you really mean e.g. bad reasoning is unethical in itself, i.e. ignoring its consequences.
@@pwhqngl0evzeg7z37 Not all normativity falls under the branch of ethics. Normativity is about evaluation. Some of our evaluations are ethical evaluations and some are not.
There's two kinds of statements: "is" statements and "ought" statements. They do not naturally interact. In order to bridge the gap between them, you must at some point introduce a moral assumption. P, P -> Q |= Q doesn't say that an observer Ought to Believe Q, it says that P is true, that If P is true then Q is true, and therefore Q is true. To get from Is to Ought, you have to introduce the moral assumption that you Ought to value believing in true things. Without that bridging tactic, it isn't possible to have any sort of meaningful conversation about either morality or logic. Therefore, they aren't at odds with one another; they're companions.
Thank you, I found this very interesting. I was really absorbed in the preface paradox, never having encountered this before, but it seems that there is a very simple way out of this paradox, by saying "I believe P" is really a shorthand for "I believe P is *likely* ." Indeed, we may find that we accept P, Q, and P conjunction Q in some subset of our beliefs-- maybe if we assign "Triangles have three sides" and "Squares have four sides", for example-- when we have beliefs that we find *perfectly* likely. It also seems like it would be worthwhile to examine in more detail exactly what normativity *is*, and exactly what the significance of logic (or other rules of reasoning) being normative would be. We can describe many moral precepts in ways less normative: if you kill somebody, you will go to jail; if you kill somebody, that will make other people sad. We can describe logical rules in similar ways: if you simultaneously accept P and not P, you will starve. But these descriptions don't capture the entirety of how we seem to feel about morality: when we say that lying is wrong, and that affirming the consequent is wrong, we don't really behave the same way in response to that wrongness, and it makes me think that this is a case where "wrong" is being given two different and relatively distinct meanings, more distinct than when we compare the wrongness of lying with the wrongness of pedophilia, where the difference feels like a difference in degree rather than quality.
I think that at least in most cases normative statements don't even function as claims, but partially unconscious social signals between us social animals, signals that persists because they have social utility, that is, they give a tribe of people an evolutionary advantage. I may go as far as to say they aren't claims at all. What the heck is the definition of "ought"?
These are good ideas. I think saying "if X is true, then Y is true" like a language, is logic, and there's no "ought to" about it but there is "it doesn't follow the language" about it. and the decision to translate observations into premises and translate conclusions into assumptions is like a separate attachment to logic, and there is "ought to" about that choice, and also "ought to" about which logic language you choose for translation
The way I understand it, logic/reason in itself is consequence and pattern-ness which everything follows, even competing logics. Individual formal logics are strict formulations which are allowed to follow the patterns of reason. This way we can more precisely study of more complex things because we can define them through this strict vigorous system. Like if one wants to study circles, there are competing views of what a circle is which makes them difficult to study. If you define a circle using geometry which is built from formal logic, you can make specific deductions (A circle is set of points of equal distance from a center, and from this you can make deductions about its area, circumference etc. You cannot do this if the object circle is not strictly defined using geometry) So individual logics are kind of like lego blocks we use to make bigger and more complex structures. But logic itself is like the principle which allows any kind of blocks to be connected in certain ways and form these larger structures.
Having some basic probability theory intuition, I found the preface paradox really interesting. It makes sense that you consider your beliefs to have a small error probability, and "rolling the dice" for every individual belief is likely to show "no error", but considering the conjunction of all beliefs, the probability of "error" is almost surely 1. Or I might just be connecting random dots :D
If logic is normative and I think the sense which includes telling us to reject inconsistency is normative, this normative aspect is an axiom that is not part of logic. It is outside the logical system but necessary for the practice of logic.
The problem of belief in P1, P2 etc but not in the conjunction of P1& P2 etc goes away if you think of beliefs (at least your empirical beliefs) as Bayesian.
Category theory offers a systematic exploration of the issues you raise in the second half. Categorical logic is a complete answer to the question of when a formal system should be considered a logical system. LEM can be seen as a special axiom which is not needed for general topos theory.
i feel there are a lot of recurring principles when you introduce a dialogue between a realism and anti-realism in a given field. do you think it is possible to talk about realism and anti-realism generally or is it the case that we need to see these types of positions in conversation in a more local context like logical realism or moral realism etc.?
Interesting. This seems to be a conversation about whether a thing is real, or is it a representation of something else that's real. Or perhaps an emergent description of something else that's going on. Maybe I'm wrong, but the realist position seems to want to take many things at face value, as obvious. The anti realist shows reasons why the obvious thing may be more complex than what has been given credit for by the realist. This could be very interesting to explore
@@saimbhat6243 i guess im wondering can we meaningfully debate these two positions at such a high level of generality. like i said i see a lot of recurring themes, arguments, beliefs, and principles between the various realist and antirealist positions i have seen in Kane B's videos. this leads me instinctually to wonder if we can abstract these recurring things from a specific field and consider them on a structural level. but also instinctually im skeptical that this level of generality would afford anything remotely like what we discover in the proverbial trenches when we walk through concrete arguments.
@@uninspired3583 "Maybe I'm wrong, but the realist position seems to want to take many things at face value, as obvious Realism is the metaphysical proposition that "things" are mind-independent. That is, the state of affairs of the universe is independent of human understanding or perception. These things may not always be obvious. For instance, we can use observations to make inferences that are unobservable. The realist can believe that these unobservables are true, or could be true. An anti-realist would not take such a position, but might say that the unobservables seem empirically adequate based on our observations. An example of this in physics today is something like string theory or dark matter/energy. This might seem somewhat academic, or one position might seem more "rational" to you than the other, but here's the rub: these two different positions can have huge ethical ramifications. Take, for example, the question of God. Let's say we can infer that God exists from a wide range of observations. A realist might then believe there is a God, which indicates certain necessary ethical ramifications. An agnostic might conclude there might be a God, but not believe in God. This also has serious necessary ethical ramifications.
33:32 Incorrect. actually classical logic can handle future contingent propositions. Your example of a many-valued logic was a particular 3-state logic, which throws away a number of logical rules from classical logic. I propose the 4-state _classical_ logic. Let there be 4 values, T, F, X, and Y. Basically, T and F are still the respective identities and annihilators for conjunction and disjunction, X and Y are negations of each other, and you'd want to keep that A * A = A + A = A for any A, as well as A * ¬A = F and A + ¬A = T. Implication can be defined in terms of disjunction. As I suggested earlier, this logic follows all classical rules. You have modus ponens, double negation elimination, absurdity, excluded middle, explosion, and whatever other inferrences you would expect a classical logic to have. This 4-valued logic gives you an interesting property: it is classical, and yet you may have a proposition A such that you cannot derive that A is true, and yet you cannot derive that ¬A is true (for example, A = X). You don't actually have to stop at 4. You can actually say a proposition _is its own_ "truth value" and simply say that two propositions A and B have the same truth value if A B can be derived with classical inferrences. For example, A and (A->B)->A would have the same truth value (for any A and B). Well, classical logic does still have problems even if this isn't one of them. Sometimes you want to be a constructivist and therefore follow intuitionistic logic, or perhaps you take a look at quantum mechanics and find that actually linear logic models the way the world works better than classical logic.
great video! though you may have relied a bit too heavily in your framing of the issue on anti-normativists like gillian russell, though her work is great! frege for instance was happy to say that any descriptive theory is normative in the same hypothetical sense that logic is, but that, since logic's laws are maximally general, it has a particular place in any inquiry, namely it's laws are normative for any thought (insofar as any thought should be truth-directed) - not quite a demarcation argument, it's not quite a normative consequences argument. and you've left off the best case for categorical logical normativity, kant's! i'd look at steinberger's 2017 paper on frege and carnap, and his SEP entry is really excellent too (surprised i didnt see it in your references!), and leech's 2015 and 2017 papers on the kantian laws of thought approach.
We can create an ultimate consistency by assuming that nothing exists. Since propositions are ultimately about something, then there can be no propositions, and hence, no instances of logical applicability or normative reasoning. Thus, no contradictions can arise. In our experience we do deal with things as if they exist. The introduction of an experiential reality leads to a distinction between relative truth and ultimate truth. Nothing inherently exists on its own side, but becomes a conceptual referent in terms of its interdependent relationship with everything else, which we may designate as relative or conventional truth. All relationships change in time, and eventually everything ceases to be. The ultimate truth is that nothing inherently exists on its own side; the noun becomes an illegitimate part of speech, so propositions based on ultimate thingness cannot constitute a model of ultimate reality. Thus, systems of logic can apply only to relative truth, and not to ultimate truth.
The term "moral realist" always cracks me up ever since I first heard it. "Me? Of course I am a moral realist!!! that means my morality is the real morality. Any one who doesnt believe in my morality is a moral Fake-ist, or a moral imaginary-ist" lmao. (i know thats not the common definition but it the absurdity of the name implies something allong these lines.
One of my favorite quotations in all of philosophy is Wittgenstein's comment on FP Ramsey's statement that "logic is a normative science" (around 81 of the Investigations). Relevant bere
when wittgenstein mentions that ramsey reminded him that logic is normative, but he didn't know what ramsey meant? also like that line. remember reading that crispin wright suspected that ramsey must have put this point to wittgenstein in the context of a critique of the tractatus
@@loudmmind yes, but specifically Wittgenstein goes on to make a great articulation of the view that logic isn't a good modeling approach for natural language (semantics)
About the companion in guilt, in my humble opinion, the analogy does not tell us anything of substance. Why accept that logic is objective if you cannot accept objective morality? In my opinion, both logic and morality are inventions of human mind to interact with others, so they both aren't objective in a sense that they are divinely granted. But the morality is a complicated field which tries to answer what ought to be, yet logic is a tool to analyze statements. Just as there can be an infinite number of self contained algebras, there could potentially be an infinite number of logics, for example a logic where a false statement cannot imply a true one. Yet we stick with the one we know best because we've collectively decided it best describes what happens when people interact and seek things they agree upon.
Starting off, I believe that absolute truth is unknowable. If we grant the axioms of deductive reasoning "validity" exists but "soundness" does not, for example, because inherently knowing the "truth value" of a premise is impossible. You can only prove a premise by an argument, which must raise another premise to be valid. All "truths" are approximate truths derived from our choice of axioms, and our choices about what axioms we believe and how we interpret our experiences isn't "true" or "false", so nothing we build could be anything other than an approximation of truth. If absolute truth exists, we can't obtain it, so it's existence isn't relevant to us. With that out of the way: Whether we call logic "normative" is clearly just a semantic debate of how to define "logic". Does it include or exclude norms about how to use logic? Do we for some reason choose to define "normative" and "logic" in an (extremely unhelpful and silly) way such that errors imply logic is normative? Do we try to separate it from other disciplines, and how do we define those disciplines? Then there's the section about pluralism. I think most different "systems of logic" are just different approximations of the math behind it. They each pick different axioms, so of course they get different results. None are any truer than any other (unless they contain errors), because the axioms, (a type of belief) are inherently unknowable. Different systems of logic are useful in different situations, because in different situations, we may have already assumed/be able to derive different axioms. Just like your examples of scientific models, logical models are only useful in contexts they were designed for, with the assumptions they were built upon. Logic vs the norms of belief: Fun. My beliefs have infinite logical consequences? Of course they do! Such is the case with approximations, only certain beliefs are useful in certain contexts. Figuring out which beliefs to use at a given time is the important thing. I believe orange is a nice color, but that doesn't mean I must be happy if my hair turned orange, my belief that orange is a nice color is less relevant than my belief that my hair shouldn't change colors suddenly. "Oh, but those are non-objective beliefs" *all my beliefs are non-objective, so I don't care*. Of course, I can mix and match various beliefs which contain inconsistencies to conclude an infinite number of unhelpful things, but the only helpful thing is to find the relevant beliefs to the context and use them efficiently. There can be different ways to do that, but as they are all approximations, that is no issue. "You could then measure their predictions against the truth!" but again, I can only approximately know the truth, and I can only approximate the difference between predictions and my approximation of the truth, so there may still be multiple which end up being "useful". When the error bars overlap, then is any of them more true? Not really, they can merely be more precise by a particular metric (a particular way to measure). Muahahaha! There is no truth, because semantics can obfuscate any question, our fleshy bodies provide us with not-entirely-trustworthy data, our uncertainty about what axioms to choose, and even our uncertainty that our thoughts are rational, means we must conclude that at best, we probably have something approximating the truth.
I would be interested in a longer/more indepth discussion on whether or not "P v ~P" is actually true. In regular language, we seem to discuss partial truths all the time, even if a given statement being partially true will itself have a binary truth value. By this I mean "Statement X is partially true" can be assigned a fully true or false value. The normal language concepts of half truths and "the best lies contain elements of truths" both would violate the idea that something must be totally true or totally false, in addition to the time example you gave in the video Anyway, i found this video surprisingly interesting even if the demarcation points made me cringe. You presented it well, but God this sort of reasoning is so annoying to deal with in any question of philosophy that doesn't have the most rigidly defined lines
there is no such thing as partial truth. If we say: “A is sometimes B”, then either A is sometimes B, or the opposite. It just so happens that the opposite of the statement isn’t “A is not sometimes B”, it’s something else. So P or not P is always true. However natural language makes finding “not P” quite ambiguous
You example of "A is sometimes B" doesn't really even fit what people would usually consider a half truth, if they did exist. Using a separate false statement or providing truth without sufficient relevant context to deceive is more in line with the usual understanding of a half truth. Trying to evaluate "the sun is the center of the universe" will have completely different truth values depending on what model of the universe one contextualizes it with. But that aside, I think you just calling it "the opposite" is rather misleading since there could be several states in which A is sometimes B is denied. You may call it an issue of ambiguity in normal language but the denial of P is no more clarified in basic logic
For any given proposition P, it can be the case that P v ~P; we say that such propositions are *decidable*; if doing type theory, then we say that P is a *decidable type*. If we claim that for *any* P, P v ~P, then we are claiming LEM/AOC/etc. It is possible for LEM to be false (just pick a non-Boolean topos) but for many propositions to still be decidable! This nuance is missing in the video.
I thought for a long time that logic was normative, but not in the sense that it tells us what we ought to believe, rather as a language convention concerning what we should infer from a given assumption.
I assume that single claims on their own are not relevant in science, that what is important is the dynamic of claims and how this dynamic coincide with the real world. In that regard, the language we use can be more or less suited for describing one or another phenomenum. I would believe that different logics are different conventions for how we agree collectively to use language when trying to give a scientific description of a phenomenum.
As such, we wouldn't ought to commit to one or another logical claim, unless we want to be part of a collective attempt to describe the real world. Do you know if this view has been studied ?
With regards to the error issue - why couldnt we say - if logical laws are not about our reasoning but about truth preservation in inferences, separated from our reasoning those inferences - parallel to that - morality isnt about our actions but about goodness preservation in behavior, separated from our acting out those behaviors; and so actually people can never violate moral laws, just make errors when trying to apply them. This would be an equivalent move, and one that doesnt seem to make sense. Or maybe it does make sense, that would be Tjumps wet dream, we have found an actual way to have morality and it to be descriptive.
It surprises me that we dont suggest just rejecting the initial dichotomy. What if we suggest that Logic is just a list of rules. Its descriptive, but not of people or acts in the world or of anything in particular. Rather logic is a name applied to a list of imperative utterances. If you obey those utterances you are doing logic. If you do not, you are not. Logic is a game one does or does not play and logic itself makes no injunction to obedience Here is a list of things. If you are doing these things, then you are doing the things it says on the list. If you are doing the things it says on the list we say you are doing logic. If you arent, we say you arent. That's it.
but logic wouldn't allow you to premise your argument on {P, P->Q, ~Q}. Logic would immediately say "no, you must be wrong, because..." Sorites has a false premise. "If n is not a heap, n+1 is not a heap" is a statement about the function P(heap) = f(n). A false statement. The function f(n) is a sigmoid curve, something like -1/(1-(e^(50-(x/10)))) that crosses P=0 at just above n=0 and crawls and then curves up reaching 1 at around 500.
6:30 Łukasiewicz wrote book on that topic in 1911, its not listed in bibliography therefore I am pointing to it, because it may interest you, at least from historical point of view.
8:13 If you want to know why it is phrased: "then it is false that I have less than $15 overall" rather than: "then it is true that I have $15 overall" It is because, though they know they have $5 in one pocket and $10 in the other, it isn't specified whether they have more money in other places, such as in their shoe, which means they don't necessarily have exactly $15.
I think heaps are part of a weird category of words that I call "vibe words". The heap problem can be replicated for any situation in which there is a gradient change that isn't specifically quantified. For example, when exactly does an athlete become great? So for baseball, where is the line where one can say that according to their stats they've achieved greatness? It's going to be arbitrary no matter what, but when someone is convinced someone is great, they'll FEEL it. I FEEL that say, Derek Jeter is a great baseball player, and while I can point to various stats of his baseball career, I can't say where was the line that he crossed to qualify as a great baseball player. Perhaps heaps and other unspecified gradients like "greatness" are essentially phenomenological in character.
It seems fairly straight forward to avoid the middle third regarding eggs in the morning. If someone announces they will eggs in the morning, of course this statement will end up either true, or false. However, I think logic is really only meant to deal with facts, so if someone says something like "I will...eat eggs tomorrow" it's less of a fact and more of an announcement. The only logical fact that arises from that announcement is "So-and-so intends to have eggs tomorrow". THAT is true, but this does NOT imply that eggs will be for breakfast. Not at all, actually. Now, it may well turn out that he was right and had eggs, but by this point "I will have eggs" is off the table, now it's "I HAD eggs", which is a different statement, and the only statement between the two that is factual. So, no, the middle third is not necessary to stop bivalent analysis.
Moral realism always struck me as some particularly superficial way of thinking. Who made those laws? Who validates them? How come that people had so different ideas for a long time, we’re they all just wrong and we figured ethics out? The only thing that comes close to something existing in the real world that can serve as a basis of ethical laws is human nature. The problem is that nobody really knows what it is. All societies hitherto have declared themselves as being most in tune with human nature - and we find those claims ridiculous in retrospect. I think what’s really going on is that our understanding of human nature and ethics is and will always remain fuzzy because it’s too complex. But over time, evidence is mounting how our current understanding of ethics fails to provide social stability - which hints at a mismatch with human nature. Once that’s recognized, people will make guesses how we should change our understanding of ethics to best match human nature and then they’ll start experimenting with that. Once we hit a working formula, progress is made. Unfortunately, ever since antiquity, all societies seem to have had a ruling class: powerful individuals with interests that systematically diverge from those of the general population; their main interest is self-preservation, and that’s not due to a conspiracy or due to a problem with human nature, but it’s strictly a selection effect: those people who remain in power once they rose to power are precisely those who stick to it and won’t give it up without a fight. Those people will - purely because they’re a biased sample of the population - make very different guesses about human nature, but with dramatic consequences, as their power precisely means that they can force their views down our throat. Social stability can therefore only be accomplished once we abolish all power and all hierarchy - and we ought to abolish it all in one simultaneously, as otherwise, the remaining hierarchies will Grab total power. This means we ought to destroy the power of politicians with too limited democratic legitimization at the same time as we abolish employers, landlords and markets as such.
Evolution by natural selection is the only plausible source for a moral realism: if all members of a population act immorally, then the population goes extinct. In this sense, right makes might. For example, what if piranhas treated each other the way they treat the other animals they eat? Piranhas wouldn't be a species anymore. Piranhas not eating each other is therefore moral.
@@NoActuallyGo-KCUF-Yourself but if a moral reality existed, there would exist only one survival strategy. That’s clearly not the case. Male lions kill offspring of other male lions - and their mothers are cool with that. Male spiders get eaten after sex. I could go on and on.
30:20 I have to disagree with this particular point; you said yourself we adopt ideals in those cases either to sidestep the arbitrary or to cope with inability, but I disagree that we can infer from this that science is not set on finding the perfect model, as even though we have many models, we would use the perfect one in all areas (idealizing only when the level of specificity is arbitrarily greater than necessary). It’s human to simplify and use ideal models, but a perfect scientist would use only perfect models with full detail if ever and whenever available (science also wishes to hash out a theory of everything as well, aiming towards this) Please let me know what you think! I might be misunderstanding something
If one can’t enumerate one’s beliefs (in a practical sense I cannot), then, perhaps a quantifier would be a better way of expressing “not(all my beliefs are true)” and then this would only be an omega-inconsistency (or something like it) and not an inconsistency? Like uh, even if there is an enumeration of all my beliefs, and a statement which is a conjunction of all of them, that statement certainly isn’t a statement which I either believe or disbelieve! (For one thing, if it were a statement I believed, then the statement would be infinitely long, which is not permissible in most languages I think?) But, I think a simpler version which avoids this difficulty with self-reference, is just the lottery “paradox” showing that beliefs shouldn’t always just be completely Boolean true/false assignments? Like, if there are 100 lotto numbers, it might be that for each ticket I believe that it is not the winning ticket (suppose that I know that which ticket is the winner has already been determined, but I don’t know which one), but I believe that one of them is. This apparent paradox is just from interpreting “I believe this is not the winning ticket” as “100% sure this is not the winning ticket” instead of the actual belief which is more like “99% sure this is not the winning ticket”. Edit: ok the point about “assignment of credences is probably inconsistent” is a much stronger point. I feel like this is a much weaker and much less concerning type of inconsistency though.
Why is the set of bunched grains of sand taken to be an inductive set? The axiom of induction need not apply if the collection of n+1 grains is not obviously a "next" collection. One way in which it may not be is there are any number of ways to arrange n grains of sand, and the way they are arranged can dictate properties that are inferred about them. For instance, if you have a million grains of sand all laid out in a row or a sheet, that's not much of a heap. You can impose structural constraints on the collection method, such that enough grains will always be a heap, but then it is just not true that you can always infer the group of n+1 grains is not a heap. It's a distinct thing to say "if one grain is not a heap, then two is not a heap, and if two is not a heap then three is not a heap" and to say "if n grains is not a heap then n+1 grains is not a heap", as one is a set of entailments over specific elements of the set and the other is a general entailment, which may be false even if many instantiations of it for small values are true. I can't conclude, given floor(1/10) = 0, and floor(2/10) = 0 and floor(3/10) = 0, that floor(n/10) = 0 implies floor((n+1)/10) = 0. We need, in order to make this claim, a formal definition of the collection of grains of sand. If the way we define it then goes on to have properties that violate our intuitions, then the definition does not supply a very good model. We could just as well propose a model where the property of heap-ness is gradient, that it can take on values between 0 and 1, and this may be a fine way to represent the issue. The paradox, then, becomes an issue of an unspoken choice of definition producing counterintuitive results.
This was a lot of fun, thank you! Do you have merch?
2 года назад+1
Interesting. It seems to me that the limits of logic, the point when it becomes practical without being normative would be rationality. I would define rationality, in this context, as the averages and ratios made out of heuristics to form first principles, hence prone to error, but nevertheless presented through a conceptual framework and counter-validated by peers. Thus, although there's room for argumentum ad populum and groupthink, the model allows for a shared comprehension of reality that can be discussed and debated through logos. And since those judgments are cognitive rather than affective, we can escape normativity by instead establishing a "common sense", hence scientific reasoning. Now, of course, I am no "lover of wisdom" and, strategy obliges, thus shall live through the sharp edge of my sagacity rather than "pure reason".
12:40 is wrong. We reason about the truth, which is a real thing and which is described by logic. Stars don't have rays, yet when we look at the night sky, we see them with pointy spikes coming off of them. This mistake is due to our vision apparatus. The field that studies the vision apparatus, anatomy, describes things as they in fact behave, we recieve the light in a certain way and the images on our retinas are inaccurate in a certain way under certain circumstances. That does not mean the proposition that stars are smoothly spherical is a moral one, because astronomy still is a study of how things in fact behave. I hope this analogy is clear enough, it's the clearest way I managed to express my criticism of that gross miscategorization.
I think looking for a distinction between normative and non-normative logic can be misleading. I've defined logic as sequential reasoning, and as such we want to evaluate reason based on some sequential order; and "sequential" not by time alone, but by it's order of validity or acceptance. If we accept tinfoil as the name for foil made of aluminum based on normative standards then it can be logically argued that tinfoil is not tin foil, which can then create a false proof. Tin is not a valid name for aluminum unless we grant it as an exception, outside the use of logic, while ignoring the potential confusion or disruption to the independent development of knowledge which may arise through the use of 'gratuitous' equivocation.
The heap argument hinges on whatever is the definition of a heap. In general usage a heap may be described as an unquantified amount, if this is accepted it would explain why quantification (such as n + 1) creates a problem. Of course we could claim that all entities are capable of being quantified, in which case any heap is only contingently a heap!
I dont think that quite works. Consider 3 of something. 3 grains of sand is probably not a heap in almost any context, but 3 PhD's probably involves a heap of education. Also we could have a heap of something that does have a known quantity. The problem of heap is about relative terms, the contextual fluidity of language. I don't think it's just about quantification.
@@uninspired3583 If you qualify a heap of education as a multitude of actions or "happenings", the same is true for the grains of sand. They didn't start out as grains of sand.
@@mbbmbbmm precisely. The definition is relative to how the category is framed. The original post talked about quantifying, which isn't that far off. When something is quantified it has a discrete value, this can't be done in the same way for relative terms. Is 5 greater or less? This doesn't make any sense without a frame of reference. For heap, context gives the reference. Whether i know how many grains of sand are in my hand or not doesn't affect if it's a heap. For an ant to carry or me to fill a dump truck, now I have context to decide if that amount is a heap or not.
When you say 5+3=9 you’re only mistaken because you’re violating the laws of math-laws that are based on the laws of logic. If I run through a traffic light that doesn’t mean I’m mistaken about what the law is (even if I am) it just means that I am breaking the law. A conductive argument in court would show that. I couldn’t tell the judge and get away with it that I “was mistaken about the law”. A lot of question begging on both sides.
I’m a bit unclear on details of what it means for something to be normative. If someone attempts a calculation, and get the wrong answer, then, they have erred, and the result they got was wrong. Is saying that something was an error, isn’t that saying it should not have been done the way it was? Is that not normative? I mean, of course most wouldn’t claim that making an error in calculation is a moral error, but- well, here’s probably part of what I’m unclear on regarding what is meant by “normative”: are there any positions that aren’t moral or ethical positions, and which clearly count as “normative”? If something being normative just means that if violated, this is regarded as “an error”, or as “something a standard person would endeavor to avoid” or whatnot, then the “it is only in conjunction with the fact* that one ought to avoid believing falsehoods that you get the conclusion that one should avoid believing [P, P->Q, ~Q] simultaneously” seems maybe not super compelling because a standard person would try to avoid believing falsehoods and so avoid believing inconsistencies (by avoid I don’t mean always successfully avoid, or something that can’t be outweighed by other considerations) such as the combination of beliefs [P, P->Q, ~Q]. It has been said that in the presence of people who believe inconsistencies, it can be useful to state tautologies. This would be as a correction. It would be an attempt to bring the beliefs of those others to align more with logic. I think I’m even more unclear on what “normative” means than I thought I was. I’m not sure why it shouldn’t be that basically any claim made with the goal of others believing it, counts as normative? If you say “P” with the intent that others believe you and so come to believe that P, it would seem rather strange to, at the same time, say “but you shouldn’t believe that P.” . One might say “P, but you (currently) shouldn’t believe that P”, but presumably if doing so one either wouldn’t intend for people to believe the statement that P, or wouldn’t really believe the statement that one is telling others that they shouldn’t believe P? Well..., ok maybe one could want people to believe something, while thinking that they “shouldn’t” believe you, but still wanting them to? Uhhh... hm
It seems more and more, a concepts of uncertainty/relativity crops up again and again. We cannot know anything without creating a system for understanding. And what is knowable depends upon the axioms we put in place. This in a way defines what is possible to know. We look through the lens of our understanding, which is arbitrary. Godel's Incompleteness Theorem seems to extend to other fields which rest upon having sound logic.
I am absolutely new to such topics, so pardon my lack of knowledge/reasoning: “We look through the lens of our understanding, which is arbitrary” Is this an objective (true) statement or an arbitrary (opinion) statement?
Is there any room to assert that the normative-looking axioms of logic are really just normative statements that "these are the definitions of not, implies, etc"? In other words, if you are capable of asserting P, PimpliesQ and not(Q) then we must disagree on the definitions of either the words "imply" or "not". e.g. when contrasting constructive and classical logic, the points of disagreement occur due to differing interpretations of "not" - classically, "complementary to P" and constructively "can be proved to be incompatible with P".
33:43 it’s a crazy and strange problem! I don’t believe personally in 3 valued logic outside of paradox (you go back and kill your grandpa and end up with a paradox of whether you were born in 2 valued logic: not-true because, but also not-false because (we all know why lol)) and find that unless there’s a paradox inherent, the third value is just undetermined *currently* ie. It isn’t true of false that I’ll eat eggs tomorrow, that lemon is the best flavor, or that a virtuous man is best for society; though only because in the first assertion we have to wait until tomorrow to see if the statement was true or false, in the second we don’t have criteria, and in the third we don’t have a defined set of virtues
Do you know of any non-paradoxical issues that have three truth values which don’t fall under one of those categories? I want to avoid making an argument based on my inability to think of a point contradictory to my argument haha
only 1 min into the vid: The question of what it means to believe in something needs to be answered first. AS WELL AS the question of grammatical definition/semanitcal definition, or philosophical definition. How can you say what something is? how can you know what something is or isnt? though you may hava a logically consistant internal definition of the lines where something is or isnt. dont you have to realize that this definition is imposed becasue on a surface level the human brain operates on a binary? (Neurons either fire or they do not) (although there is still potentially quantum activity in the brain to an extent that may be relavent. Some studies on the microtubules come to mind)
Morality often contradicts logic. For example in prisoner's dilemma, the only logical behavior is to snitch, but moral behavior is to keep silence. So if we would say that we are obligated to behave morally and rationally, this would create contradictions.
This doesn't quite work as an example. 'Logical Behavior' in game theory is defined by what decision optimizes one's own outcome, and the prisoner's dilemma is described by its outcomes given the choices. If you and I sat down at a table and played the prisoner's dilemma with pen and paper with no tangible consequences (akin to playing tic-tac-toe), and I chose defect to your cooperate, it appears hard to argue that I have actually done you a moral wrong of which I should plead forgiveness for. Also, the outcomes of a game are determined by a total evaluation of everything one receives, so moral outcome is something to also be evaluated in addition to the other outcomes, and so if two people were trapped in a prisoner's dilemma when only considering physical outcomes absent morality, it's not necessarily a prisoner's dilemma when moral outcomes are considered too. For example, if myself and someone I deeply cared about played the prisoner's dilemma in real life, the emotional weight of forcing them to spend 10 years of their life just so I could be free would be hard to bare, being much more costly for me than that 1 year of prison potentially. Just from the emotional outcome included, this renders this situation a new game, and no longer the prisoner's dilemma. If the moral outcomes are of such severe consequence that one ought to choose to cooperate, this would undermine the game being a prisoner's dilemma.
Well, from the standpoint of set theory one grain of sand does make a tiny heap. Mathematical jokes aside, when dealing with blurred concepts or imprecise/irrelevant/nonsensical statements one must abandon notion of absolute unambiguous truth. Any type of logic, so to speak, has its specific terms of use.
This is like saying math is normative, which (through argument by absurdity) it isn't. Math doesn't tell you how you "should" reason, but it tells you what is good (correct) reasoning from bad (incorrect) based on a set of axioms which are taken for granted as true. Logic is the same. Whether you choose to use logic or not is up to you, nobody can tell you if you "should" or "shouldn't" use correct reasoning (or if you should or shouldn't conclude 2+2=4) but they could still evaluate your reasoning using the system of logic or math developed to formally tell correct from incorrect.
Hmm... logic and meta-physics being the same thing? I suppose it depends on the definition of meta-physics. I would argue that physics is derived from logic, but that logic is an inherently irrational imposition on the world of physics to make it necessary to perform any reasoning at all. There's probably something that does unite the meta-philosophies on some level, but we are all fairly uncertain of what that exactly is. Regardless, there's no logical necessity, nor physical necessity for logic. It seems to be more of a heuristic that we adopt to understand physics and ethics. Such that one cannot truly imagine performing any kind of study in either without it, but I don't think that there's a basis in logic for this necessity either. Meaning, there is some kind of higher meta-unification that makes the various schools of philosophy inherently contingent on each other, but I think that one could just as easily argue that meta-logic is a form of physics or ethics, as well. I would go with the classical theory of unification of the whole, given their inherent relatedness to each other, but this ultimately results in an appeal to the unknown, which I can understand bothers a great many people and probably doesn't provide any kind of answer to the problem. I just don't see a hierarchy of meta-philosophical positions on this, as they all seem equally contingent on each other in equal directions. I can't fathom how any one meta position could not rely on the others, but I'd like to hear more of a constructionist argument for meta-philosophy rather than the unknown/esoteric organic argument that I would subscribe to.
The "heap" paradox is a problem of definition. "Heap" is a recognizable structure, not a count. A million grains of sand, one grain deep, is not a heap. Many of the difficulties in this discussion seem to be of similar nature - using words without actually explaining how they are being used. Note that if there are more than one non-equivalent self-consistent logics, none of them can be generally normative. I made a comment about philosophy students in Mathematical Logic classes (taught by mathematicians) earlier today. Falling into this video was an entertaining consequence of the RUclips algorithm.
At 2:15 you say "if I deny the objectivity of logic, then I can no longer make any assessment of the rationality of any position." doesn't this statement also imply the objectivity of logic? If logic is non-normative then you wouldn't even be able to make this seemingly rational statement... so you wouldn't be able to make any logically valid statement at all... not even a statement of whether or not you can make valid statements.... I am on team normative... for now.
You here seem to be talking of 'normative' in the sense of constituting an ideal, or something to which people should strive, in their reasoning. There is a different sense in which logic can be normative, however. Logic can be normative in the same sense that a game, or language, is normative. Games, or languages, are normative in the sense that they are constituted by norms. If something fails to exemplify these norms, it does not fall short of any ideal, it just simply isn't part of that game or part of that language.
26:31 “we assume there is some logical theory that provides the correct account of logical consequence” - isnt this begging the question? Because you’re presumably also assuming that we ought to adopt such a theory, if it were found. This is a very common assumption, but couldn’t the intuitionist avoid it by saying that the best logical theory is eg the one thats easiest to work with, that allows the production of the most proofs and that doesn’t get falsified, etc etc?
I think it is a necessary assumption. If a logical system cannot consistently produce true conclusions (as determined by observation), then no one would use it, and that system or theory would go extinct. If there is no logical theory that provides correct conclusions, then making an error in reasoning or not would be based on luck or coincidence. Evidence does not support that scenario.
@@NoActuallyGo-KCUF-Yourself I see your point. But Im not sure logical statements can always be verified by observation. For example, how you do find evidence for a universally quantified proposition?
Good stuff. My view: logic is a language, languages are tools, tools can be optionally used to advance goals. Do hammers tell us how we should pound nails? No, but they can be useful to do so.
Logic _has_ a language, but is not itself a language. There is a system of definitions and notation and ground rules / axioms, but you still need some other language to communicate the actual logical values (i.e. meaning).
@@NoActuallyGo-KCUF-Yourself You are implying there is something in logic that is _a priori_ to the language. The burden is on you to explain what this is, and as it is prior to language, ideally you wouldn't use language for your explanation. In any case, can't use pragmatism to talk about idealism. The point of pragmatism is to get away from the mush that is metaphysics... just opinions and checks that can't be clearly cashed in to the state of affairs. So, I reject this. A rock can be prior to language, as it has color, shape, and mass. Logic is a mental notion, and for me, this places it in the realm of "not real outside of language".
A piece is never the whole, nor does it define the whole. Normative (relating to a social or behavioral norm) is suggesting the false dichotomy that binary states of normal and abnormal exists, when it's actually on some spectrum. There is no normal, only commonly accepted behavior in society. There is no abnormal, only rarely to unaccepted behavior in society. As for "Logic", everyone reasons what is acceptable to themselves, or objects to their reasoning..... who gives a sh#t what other people think. Morality is self-determined and sometime the majority agrees with you and sometimes it doesn't.
Is Math normative? 2+2=4? You have done a good job of making nonsense clearly nonsensical. It has become fashionable to make truth and logic and even sciences (like biology) to dismiss everything as arbitrary and oppressive.
would it not be true to say that logical laws ARE descriptive laws, just over what things are possible to cognize. When people say that 5+3=9 they don't actually think that, they are mistaken about something, they are simply ignorant over the nature of the mistake. Once the mistake is corrected then it becomes impossible for them to believe that 5+3=9. Like for example if give the formula 5+3 and the person says it equals 9, that is possible due to them not knowing they are making a mistake, but when the mistake is made clear, for example, by placing 5 and 3 coins in front of the person in a row and asking them to count. Then they will count 8, once they have counted 8 they cannot say it still equals 9. Where will they derive that number 9 from after they have finished counting all the coins? Another example is not (a and not a). You can't believe an apple exists and doesn't exist in the same place and at the same time and in the same way. When people declare similarly contradictory statements it is because they are ignorant of a mistake being made, but once the mistake is understood, it then becomes impossible to make the same previously contradictory claim (unless the mistake is once again forgotten) So the laws of logic become descriptive in a state of complete understanding, whereas violations of the laws are a result of an incomplete understanding. If we call 5+3=9, statement a, then the person that says 5+3=9 does not actually believe in statement a in other words, they think they do but that's because they don't actually understand statement a.
Is it always immoral to have slaves? One person who claimed to have slaves said that his actions are moral, because he runs a business that buys slaves in North Korea, where they have awful conditions, and uses such slaves as construction workers, giving them much better conditions, and above of that, a good amount of money. Without his business, more people would be slaves in NK, their families would have less money, so ultimately, everyone would be in a worse situation. Doesn't it imply that having slaves in his case is okay?
@14:30 I think the moral anti-realist is making the following mistake: Programming a flight computer with a slightly wrong mathematical model of reality (Newtonian mechanics) may allow the plane to fly without any problems, you could say those engineers are anti-Einsteinian-relativists. They are effectively adhering to a normative notion of reality (even if they think they are holding to a realist-Newtonian view). On a small local scale, this may not matter, but if we scale this up to interstellar flight we are going to notice our error. In the same manner, the moral anti-realist thinks the view he is holding is normative, and he can even break them (by flying a plane with a normative view or) by owning slaves, but if he was to scale that up over time we are going to notice our error. In other words.. moral reality is not about individual laws or even humans ...moral laws are simply that certain processes will provide significantly different outcomes to other processes. If you do not want to call such processes "morality" then what else do you call them? check Process Ontology -SEP
In logic if p then q is true when p is false. So if unicorns were real then they would have two horns is a true statement Unfortunately I find the above statement a violation of definition.
But the laws of physics are not descriptive, they are not a representation of reality and they are not referential. They are just tools to solve problems and explain reality. Saying that they are "descriptive" is an epistemological leap that it isn't justified nor needed for physics to "work".
Logic sets the rules for correct inference it is not concerned with the truth of the premises and the conclusions which may be correctly derived from the premises. If the premises are true, and the conclusion is correctly inferred, then we say the conclusion is correct and true. We can have correct inference but with false premises and conclusion e.g., all cows are cats but chickens are cows, therefore, chickens are cats--this is correct but false. We can also have true premises but with incorrect conclusion e.g., All cows are four footed. But carabaos are four footed. Ergo, Carabaos are cows. Here though the premises are true, yet the inference is incorrect, it is illogical. One has to make a distinction between formal and material logic. Bertrand Russel missed this distinction. Logic is normative to mean it sets rules of correct thinking which is based on the the fundamental laws of thoughts e.g. principle of contradiction, of identify, Dictum de omni and dictrum de nullo. It is not normative as far as the truth of the premise. Hence ethics applies logic assuming the premises are ethically true, and what can be inferred from these true premises correctly.
This is really funny to me, I'm only halfway through, so I'm hoping for a surprise ending, but your first argument was phenomenologically very self-aware (if you understand the simple flaw you made) and your second argument is wrong at the level of convincing. Where of course, the law of excluded middle is not implied by your construction of P1. Can't wait to see the rest!
RE: Error (12:54): (a) laws of logic, whether cardinal (mathematics, commensurable), ordinal (qualitative, comparable), operational (sequences of actions), or set (verbal) are descriptive (facts). (b) logical reducibility (generalization of a rule) of cardinal, ordinal, operational, or set statements is limited by the referrers to constant relations (nouns) or inconstant relations (verbs), paradigm (system of decidability, first principles (premises), how far they diverge from laws of nature) and information (knowledge and skill) available to the speaker. (c) especially given that existing logic (grammars of paradigms) at least as practiced in logicl and philosophy, do not adhere to the first principle of grammar, which is the requirement for continuous recursive disambiguation any statement or claim to an unambiguous identity. (d) there is a natural conflict between the search for general rules, and sufficient disambiguation to test individual cases. As such what we find is that logical claims require both a general rule AND a spectrum of claims that falsify to the limits and full accounting of the general rule (e) what we find then is that not all statements are reducible to a general rule sufficient to limit error for all possible cases within the limits of the general rule. This is the problem of logical reducibility. And this is why computation (operations, realism) has replaced mathematics (set theory, idealism) and verbal logic as the foundation of logic. ... That paragraph explains the failure of philosophy, mathematics, and mathematical experimentation in physics in the late 19th through present century. ... And we see this in all sciences. The most important of which is neuroscience, because, we do in fact, understand qualia and consciousness - and it's tragically simple. And the 'oddity' is that these solutions to ancient questions are not penetrating the discipline of philosophy. Why is that? Is it the same reason that science has not penetrated religion?
Your latest video, “Is Logic Normative” has excellent information in it. This is why I’m listening. Your last video was also dealing with an important subject, but for some reason your friend and you had to add puerile trash-talk I heard on street corners in Brooklyn NYC in the 1950s. At 75, I don’t have a woke death. For some of your listeners living is a good idea. If someone can control you friends’ mouth, you two should work together, get a producer to keep you in the real world (which existence you doubt), keep the conversation under an hour, and link up your topics. You know, today we talk about this, tomorrow we talk about that. Together the two you, spontaneity & expertise, could blow-up the internet. In other words, Kane, get a purpose and get a life. Right now, the vibe is floundering talent. Jack Cascione
I think logic is ideal, but normative? I would like to think so but it is not. People use their best idea of logic, as each person has their own idea of what is logical.
“Useful” is, in itself, a strange term to even apply to these types of discussions though, innit? The whole point is that the value of the philosophy is relativistic.
@@galahadsoundscape6365 Philosophy is supposed to be the "love of knowledge". It is not supposed to be mere mental masturbation. Relativism is self-refuting in the eyes of most philosophers and is dangerous and deadly when put into practice in the real world.
All very lucid. The normative utility of logic lies in its consistency. But disingenuously applied through various forms of rhetoric argument from authority (which branches off into deontological claims and their own special logic), two applications of logic may be valid, but inconsistent with one another as to their applicability to a case. One doing this can force facts, or draw false syllogism with horrible fallacies and sophism. They could even draw out their logic falsely on a whim as a "power play" as in the villains of 1984 or Brave New World. A sort of "arbitrary" logic where inconsistency is only someone else's problem. Extortionist psychology has a logic of its own when it comes to application. So Logic per se cocerns partly with the schema of any normative domain of thought or action, and yet doesn't in its science directly espouse any ethical use of its frames nor does it protect people from fallacies if they don't properlly train in it or have preternatural facility in it. But for people who want to be fair and just about things, consistency in logic is indispensible until a better system of cognition can be devised. I've never had a problem with Modus Ponens. Logic analyzes many subtleties of modeling that as part of various systems of logic about that thought, which represent it in different forms encompassing bare truth claims, evaluations of oughts, legal codes and procedures, protocols for every endeavor and the heuristics which devises all evaluations of problems in order to seek solutions, all investigationos and forms of engineering. An extortionist has a set of norms that forces him to leverage power over logic, to gaslight his enemies and captives. Unfortunately, there isn't much done by some logicians to learn what the "ethics of logic" might be while they were conducting a study on the logic of ethics. They caved in to the pressure and joined the open-air manhatten project. No you but there must be some. He's the "evil logician" who is duped by the supervillain and through vanity and ambition serves his evil ends with logic. That's a thought experiment . But what would the virtuous logician look like? He would use his logical mind to determine what is the best for of world into which he could participate, and seek to make that be isomorphic with the world in which he finds himself. He would determine what normative ethics is, and decide for himself what the ideal form of ethical approch he will take. Then after formulating that ethic, devise a way to ensure that it becomes permanent and ever-improving. He will develop very specialized heuristics for watching his own motivations for actions, his cognitive slips in how projecting ideas onto externals (including other people), and he will have to always be growing his general knowledge and exercising all of his other faculties and his body in a healthy way. I think Aristotle was the big heavy on the "whole body-mind" approach in his day, as was Hippocrates etc. So there are a lot of "meta"-ehtical considerations and logic is only one of them. There is a best and there is a worst, or it seems reasonable to think that. Make things better, including your logic and use of logic. So what heppens when the logical hero meets the logical villain? It's not pretty. But that's a bit into aesthetics.
More on the companions in guilt argument: ruclips.net/video/7HHBNU_gXP0/видео.html
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No, logic is not normative; though, a logic of norms is possible. Kelsen was wrong on that and so are the countless people who misinterpret Hume.
Logic is a mental machine (or better, logics are mental machines), and no machine should be allowed to be normative.
As a mathematician stumbling on this video, to my mind, “logic” and “reasoning” are completely distinct concepts in my mind. The latter is a cognitive activity tantamount to usefully processing data about the world, and the former is a formal system-no different than a game of chess or a computer program.
In that sense, I think my initial objection to the notion of logical normativity can probably be reasonably dismissed as semantics/trivial; “logic” is just symbol-pushing and doesn’t make external claims about anything.
And, of course, “reasoning” is only a useful emergent physical phenomenon-and probably just illusory in the final empirical analysis. This doesn’t seem to be what people mean by “logic” either. (It’s just a physical phenomenon. E.G., is photosynthesis normative?)
However, I think what’s actually being asked is whether or not “the systematic philosophical study of correct/useful reasoning” makes normative claims. Framed this way, I think the answer is *obviously* yes: we need to choose what we mean by correct/useful!
As I said, this isn’t my field and I’m just an amateur. Feedback appreciated! (Please let me know all the dumb mistakes I’ve made.)
I'm a mathematician too (not a logician though). I used to think that (mathematical) logic was just a formal/mathematical model for human rigorous rational reasoning (whatever the latter means). This is in line with the fact that there are different logics: classical, modal, aletheic, ... : different models describe different aspects of human reasoning; like different physical theories (classical mechanics, quantum mechanics, general relativity,... ) describe different aspects of physical reality [Not that I think that mental activity is non-physical; rather, it's more emergent than fundamental physics]. And that's all. But now I've seen the title of this video and it instilled quite some doubt in me: why *should* people adhere to principles of logic when they attempt to talk about the world in a rational way? Does logic (which is a piece of syntax, hence of language) somehow reflect the objective structure of the world?
But do we actually have a choice about what we mean by correct/useful? What would a different choice look like, and what would be its consequences?
There is a model of language, that allows for unsolved contradictions, and it will be usually employed in poetry. There is no absolute norm, to never employ poetic language, this kind of language will just not be very useful in solving a whole lot of problems, which makes the normativity of reasoning purely conditional: If you want to solve a problem of this given type, reasoning gives you the best chances of success.
@@rv706 I've been dealing with Lean and computer proof assistants a lot recently, and it has become clear to me that it's actually an issue among mathematicians that we frequently delude ourselves into thinking that we're engaging in "logical" thinking when, much of the time, we're really reasoning via all manners of non-logical means with the implicit understanding that "certain moves" are, in principle, translatable back to formalistic foundations.
I think that basic human reasoning is just something that we have to accept as an empirical fact--much like human language; it probably has history in evolutionary time, and I think our formal logics are just useful tools to translate some of its nuance into a formal language. That is, their utility as a means of facilitating "reasoning-computations" is a result of their design to capture the essence of human reasoning.
When it comes down to it, I don't think we can rule out gaps in which 1) our logical systems don't capture bits of human reasoning, or 2) human reasoning fails to be an effective method for processing information about the world.
@@stefanb6539 I think that human reasoning isn't perfectly captured via, e.g., classical first-order logic. Even ignoring issues of expressibility (we probably want higher-order logics, which come at the cost of worse proof theories), take, for instance, the issue of credence vs belief. You can give propositions A, B, C, ..., Z high enough credence individually that you believe each of them, but then we understand that their conjunction "A and B and C and ... and Z" may well have very low credence, and we probably wouldn't believe that. This aspect of human reasoning is not captured in propositional logic--or even first order logic (by itself).
That kind of thing comes up all the time when we're designing plans. Of course, each of the steps 1,2,3,...,n seems like they ought to work (in fact, it's not clear how they wouldn't work!)... but we're still going to make a back up plan because they're *definitely* not all going to work together--at some point, *something* will go wrong and we'll need to fall back on a backup plan.
You might choose a formal logical framework which takes that into account, but then you'll probably miss something else. If you *do* have a complete formal description of how humans make "intelligent decisions," then I think Google and Tesla would be willing to pay you a lot of money; it's not so easy, and we usually still need to add more stuff in.
Even probability theory--undergirded by the full power of modern mathematical analysis--leaves a lot to be desired, despite being sufficient for machine learning applications. And that's missing the point that humans generically (and infamously) don't reason probabilistically.
Our reasoning is a lot more flexible and a lot more general--unfortunately, it's also a lot less precise. We can choose which aspects of our reasoning we want to encode into a formal language (which, in this context, we call "logic"), but it's ultimately still a choice of where to stop because we don't understand human reasoning well enough to encode *everything*.
I think what you call "logic" here is "formalism". We can make arbitrary formalisms, not unlike arbitrary games. The word "logic" in ordinary language means a variety of reasoning. So, formal logic is a subset of formalisms constrained by norms of reasoning.
At least in my view.
Math is a language for describing relationships (between what and what is irrelevant). What you care about in logic is the relationship between elements and propositions on those elements. Logic really says nothing about truth or falsehood outside 'true' and 'false' being elements of a proposition. Everything else is interpretation. There are an uncountable number of logical statements which are perfectly valid logical statements but for which any interpretation would be ludicrous. Math is a game whose interpretation is sometimes useful in explaining how things in the real world relate within given bounds.
Between what? is totally relevant, it's anything you can divide into equal parts.
@@victor.sannier thats a very kind way of calling him a retard.
@@victor.sannier Interesting. What point am I being naïve on? There is more than one type of logic math. I have a big textbook on Fuzzy Set Theory and Fuzzy logic which is very useful for designing AI and Expert systems. In Fuzzy logic you have many more outcomes than just true or false. When you are trying to solve a problem in reality, you have options on which math to use or which game to play and how to interpret it. Much of the craziness in modern physics isn't the math but the interpretation. Pretending that math somehow IS reality is an extremely dangerous delusion which our society admittedly often falls into.
@@victor.sannier Studying the "consequences of a certain choice of axioms and rules of deduction" is more about the philosophy of mathematics. The problem with thinking that logic includes its own interpretation is a real problem. What does "true" actually mean? In Fuzzy logic what does "25% true" actually mean? When you do the math, true and false are just game outcomes. How you apply those outcomes is something completely different. As for axioms, it is true that insanity resides not in the logic, which is often valid, but in the initial assumptions or axioms you start with. If you assume that someone is out to get you then paranoid behavior is completely rational.
Yes, "explore" is a better word especially when you consider mathematics/logic as a game where you can play with the knobs and see what happens. Just don't assume that the results says anything about reality. In particular, while mathematically anything can be reduced to bits (see Information Theory), reality itself is not Boolean.
The purpose of logic is to reveal "good" vs "bad" reasoning. It cannot tell us what we should or should not believe, but it can help us think clearly and consistently. It can also not tell us what is true or not true, because the terms within logical arguments (by terms I mean the claims or premises, etc.), can be true or false. Logic is, then, a tool to guide thinking, not belief or truth.
saying something is good or bad is an evaluative statement, but you are the one putting normative weight on the logical valuations. Logic doesnt tell us what is good or bad reasoning on its own, theres some hidden non-logic evaluative standard youre appealing to.
@@DoomKaiserGliders "saying something is good or bad is an evaluative statement, but you are the one putting normative weight on the logical valuations."
No. This makes no sense. I am not putting any weight on anything. I did not invent logic. Logic is largely discovery and development over time. Things like Modus Ponens, or the law of non-contradiction are not invented, but are observed relationships in reality. Violating reality in argumentation is bad reasoning.
" Logic doesnt tell us what is good or bad reasoning on its own, theres some hidden non-logic evaluative standard youre appealing to."
No.
I think you don't actually understand logic or the concept of reasoning. It seems like you're trying to fight over nothing.
@@droe2570 I think he's trying to make the distinction between "Good/bad" and "correct/incorrect" you can have a logical argument which is invalid, but only the norm that "being invalid is bad" makes it a "bad argument".
see: (6:19)
You could change your premise to:
"The purpose of logic is to reveal "good" vs "bad" reasoning, when combined with norms of what logical qualities are "good" vs "bad"."
And I think he'd agree with that.
There is a semantic difference between "good/bad" and "true/false", and the difference between them is the hidden premise in most philosophical debate that "we ought to believe true things, and ought not to believe false things".
"logic" and "norms on how to use logic" are different concepts, and a certain kind of logical anti-normativists base belief is that "norms on how to use logic" are *not a part of* "logic".
@@haph2087 To determine good vs bad reasoning , we require rules (norms) that allow us to determine "good" vs "bad". Without logic rules, in this case, then we can never determine good or bad reasoning. I did not discuss this because I thought it was self-evident.
@@droe2570 Cool, I understand why you didn't say it cause generally it's self-evidence means we don't need to mention these norms, but...
In the specific conversation of logical normativity, the main difference between the logical normativists and (some of) the logical anti-normativists is that the logical normativists define logic to *include* these logic-adjacent norms, while a certain kind of logical anti-normativists do not.
Excellent video! This was one of the few topics that I couldn't even fathom how someone could argue that logic isn't normative, but I must say, you gave some really good arguments that changed my mind on this
Great video! Thanks for your hard work putting it together!
this video is awesome because i’ve always just taken it for granted that logic is descriptive and had no idea that anyone thought it was normative, let alone that this was apparently the dominant view lol
Of course logic is normative. It's a tool for evaluating "good" vs. "bad" reasoning.
@@captainbeefheart5815This seems more like a play on words, unless you really mean e.g. bad reasoning is unethical in itself, i.e. ignoring its consequences.
@@pwhqngl0evzeg7z37 Not all normativity falls under the branch of ethics.
Normativity is about evaluation. Some of our evaluations are ethical evaluations and some are not.
There's two kinds of statements: "is" statements and "ought" statements. They do not naturally interact. In order to bridge the gap between them, you must at some point introduce a moral assumption.
P, P -> Q |= Q doesn't say that an observer Ought to Believe Q, it says that P is true, that If P is true then Q is true, and therefore Q is true. To get from Is to Ought, you have to introduce the moral assumption that you Ought to value believing in true things. Without that bridging tactic, it isn't possible to have any sort of meaningful conversation about either morality or logic. Therefore, they aren't at odds with one another; they're companions.
However you made the assumption that it exists absolute logic, the "is" statements. Ans so it exists objects without a subject
Thank you, I found this very interesting.
I was really absorbed in the preface paradox, never having encountered this before, but it seems that there is a very simple way out of this paradox, by saying "I believe P" is really a shorthand for "I believe P is *likely* ." Indeed, we may find that we accept P, Q, and P conjunction Q in some subset of our beliefs-- maybe if we assign "Triangles have three sides" and "Squares have four sides", for example-- when we have beliefs that we find *perfectly* likely.
It also seems like it would be worthwhile to examine in more detail exactly what normativity *is*, and exactly what the significance of logic (or other rules of reasoning) being normative would be. We can describe many moral precepts in ways less normative: if you kill somebody, you will go to jail; if you kill somebody, that will make other people sad. We can describe logical rules in similar ways: if you simultaneously accept P and not P, you will starve. But these descriptions don't capture the entirety of how we seem to feel about morality: when we say that lying is wrong, and that affirming the consequent is wrong, we don't really behave the same way in response to that wrongness, and it makes me think that this is a case where "wrong" is being given two different and relatively distinct meanings, more distinct than when we compare the wrongness of lying with the wrongness of pedophilia, where the difference feels like a difference in degree rather than quality.
I think that at least in most cases normative statements don't even function as claims, but partially unconscious social signals between us social animals, signals that persists because they have social utility, that is, they give a tribe of people an evolutionary advantage. I may go as far as to say they aren't claims at all. What the heck is the definition of "ought"?
These are good ideas.
I think saying "if X is true, then Y is true" like a language, is logic, and there's no "ought to" about it but there is "it doesn't follow the language" about it. and the decision to translate observations into premises and translate conclusions into assumptions is like a separate attachment to logic, and there is "ought to" about that choice, and also "ought to" about which logic language you choose for translation
The way I understand it, logic/reason in itself is consequence and pattern-ness which everything follows, even competing logics. Individual formal logics are strict formulations which are allowed to follow the patterns of reason. This way we can more precisely study of more complex things because we can define them through this strict vigorous system. Like if one wants to study circles, there are competing views of what a circle is which makes them difficult to study. If you define a circle using geometry which is built from formal logic, you can make specific deductions (A circle is set of points of equal distance from a center, and from this you can make deductions about its area, circumference etc. You cannot do this if the object circle is not strictly defined using geometry)
So individual logics are kind of like lego blocks we use to make bigger and more complex structures. But logic itself is like the principle which allows any kind of blocks to be connected in certain ways and form these larger structures.
Having some basic probability theory intuition, I found the preface paradox really interesting. It makes sense that you consider your beliefs to have a small error probability, and "rolling the dice" for every individual belief is likely to show "no error", but considering the conjunction of all beliefs, the probability of "error" is almost surely 1. Or I might just be connecting random dots :D
If logic is normative and I think the sense which includes telling us to reject inconsistency is normative, this normative aspect is an axiom that is not part of logic. It is outside the logical system but necessary for the practice of logic.
This was so interesting! Glad I stumbled across it
Actually yeah, immediate sub
The problem of belief in P1, P2 etc but not in the conjunction of P1& P2 etc goes away if you think of beliefs (at least your empirical beliefs) as Bayesian.
Quite good stuff, Normativity is a gnarled thicket
Category theory offers a systematic exploration of the issues you raise in the second half. Categorical logic is a complete answer to the question of when a formal system should be considered a logical system. LEM can be seen as a special axiom which is not needed for general topos theory.
great video if you want to continue the series on logic paraconsistency might be a great topic
Great video (and a very endearing ending).
i feel there are a lot of recurring principles when you introduce a dialogue between a realism and anti-realism in a given field. do you think it is possible to talk about realism and anti-realism generally or is it the case that we need to see these types of positions in conversation in a more local context like logical realism or moral realism etc.?
Interesting. This seems to be a conversation about whether a thing is real, or is it a representation of something else that's real. Or perhaps an emergent description of something else that's going on.
Maybe I'm wrong, but the realist position seems to want to take many things at face value, as obvious. The anti realist shows reasons why the obvious thing may be more complex than what has been given credit for by the realist.
This could be very interesting to explore
Basically, your point translates to if the question,"what does it mean for something to be real?", is valid question or not.
@@saimbhat6243 i guess im wondering can we meaningfully debate these two positions at such a high level of generality. like i said i see a lot of recurring themes, arguments, beliefs, and principles between the various realist and antirealist positions i have seen in Kane B's videos. this leads me instinctually to wonder if we can abstract these recurring things from a specific field and consider them on a structural level. but also instinctually im skeptical that this level of generality would afford anything remotely like what we discover in the proverbial trenches when we walk through concrete arguments.
I am a realist. I believe in what is real. If you dont agree with me. You believe in what is fake. LMAO
@@uninspired3583 "Maybe I'm wrong, but the realist position seems to want to take many things at face value, as obvious
Realism is the metaphysical proposition that "things" are mind-independent. That is, the state of affairs of the universe is independent of human understanding or perception. These things may not always be obvious.
For instance, we can use observations to make inferences that are unobservable. The realist can believe that these unobservables are true, or could be true. An anti-realist would not take such a position, but might say that the unobservables seem empirically adequate based on our observations. An example of this in physics today is something like string theory or dark matter/energy.
This might seem somewhat academic, or one position might seem more "rational" to you than the other, but here's the rub: these two different positions can have huge ethical ramifications.
Take, for example, the question of God. Let's say we can infer that God exists from a wide range of observations. A realist might then believe there is a God, which indicates certain necessary ethical ramifications. An agnostic might conclude there might be a God, but not believe in God. This also has serious necessary ethical ramifications.
33:32 Incorrect. actually classical logic can handle future contingent propositions.
Your example of a many-valued logic was a particular 3-state logic, which throws away a number of logical rules from classical logic. I propose the 4-state _classical_ logic. Let there be 4 values, T, F, X, and Y. Basically, T and F are still the respective identities and annihilators for conjunction and disjunction, X and Y are negations of each other, and you'd want to keep that A * A = A + A = A for any A, as well as A * ¬A = F and A + ¬A = T. Implication can be defined in terms of disjunction. As I suggested earlier, this logic follows all classical rules. You have modus ponens, double negation elimination, absurdity, excluded middle, explosion, and whatever other inferrences you would expect a classical logic to have.
This 4-valued logic gives you an interesting property: it is classical, and yet you may have a proposition A such that you cannot derive that A is true, and yet you cannot derive that ¬A is true (for example, A = X). You don't actually have to stop at 4. You can actually say a proposition _is its own_ "truth value" and simply say that two propositions A and B have the same truth value if A B can be derived with classical inferrences. For example, A and (A->B)->A would have the same truth value (for any A and B).
Well, classical logic does still have problems even if this isn't one of them. Sometimes you want to be a constructivist and therefore follow intuitionistic logic, or perhaps you take a look at quantum mechanics and find that actually linear logic models the way the world works better than classical logic.
great video! though you may have relied a bit too heavily in your framing of the issue on anti-normativists like gillian russell, though her work is great! frege for instance was happy to say that any descriptive theory is normative in the same hypothetical sense that logic is, but that, since logic's laws are maximally general, it has a particular place in any inquiry, namely it's laws are normative for any thought (insofar as any thought should be truth-directed) - not quite a demarcation argument, it's not quite a normative consequences argument. and you've left off the best case for categorical logical normativity, kant's! i'd look at steinberger's 2017 paper on frege and carnap, and his SEP entry is really excellent too (surprised i didnt see it in your references!), and leech's 2015 and 2017 papers on the kantian laws of thought approach.
We can create an ultimate consistency by assuming that nothing exists. Since propositions are ultimately about something, then there can be no propositions, and hence, no instances of logical applicability or normative reasoning. Thus, no contradictions can arise. In our experience we do deal with things as if they exist. The introduction of an experiential reality leads to a distinction between relative truth and ultimate truth. Nothing inherently exists on its own side, but becomes a conceptual referent in terms of its interdependent relationship with everything else, which we may designate as relative or conventional truth. All relationships change in time, and eventually everything ceases to be. The ultimate truth is that nothing inherently exists on its own side; the noun becomes an illegitimate part of speech, so propositions based on ultimate thingness cannot constitute a model of ultimate reality. Thus, systems of logic can apply only to relative truth, and not to ultimate truth.
The term "moral realist" always cracks me up ever since I first heard it. "Me? Of course I am a moral realist!!! that means my morality is the real morality. Any one who doesnt believe in my morality is a moral Fake-ist, or a moral imaginary-ist" lmao. (i know thats not the common definition but it the absurdity of the name implies something allong these lines.
One of my favorite quotations in all of philosophy is Wittgenstein's comment on FP Ramsey's statement that "logic is a normative science" (around 81 of the Investigations). Relevant bere
when wittgenstein mentions that ramsey reminded him that logic is normative, but he didn't know what ramsey meant? also like that line. remember reading that crispin wright suspected that ramsey must have put this point to wittgenstein in the context of a critique of the tractatus
@@loudmmind yes, but specifically Wittgenstein goes on to make a great articulation of the view that logic isn't a good modeling approach for natural language (semantics)
Beware that all "normers" claim that their particular toy is normative.
About the companion in guilt, in my humble opinion, the analogy does not tell us anything of substance. Why accept that logic is objective if you cannot accept objective morality? In my opinion, both logic and morality are inventions of human mind to interact with others, so they both aren't objective in a sense that they are divinely granted. But the morality is a complicated field which tries to answer what ought to be, yet logic is a tool to analyze statements. Just as there can be an infinite number of self contained algebras, there could potentially be an infinite number of logics, for example a logic where a false statement cannot imply a true one. Yet we stick with the one we know best because we've collectively decided it best describes what happens when people interact and seek things they agree upon.
Wonderful video!
Starting off, I believe that absolute truth is unknowable. If we grant the axioms of deductive reasoning "validity" exists but "soundness" does not, for example, because inherently knowing the "truth value" of a premise is impossible. You can only prove a premise by an argument, which must raise another premise to be valid. All "truths" are approximate truths derived from our choice of axioms, and our choices about what axioms we believe and how we interpret our experiences isn't "true" or "false", so nothing we build could be anything other than an approximation of truth. If absolute truth exists, we can't obtain it, so it's existence isn't relevant to us.
With that out of the way:
Whether we call logic "normative" is clearly just a semantic debate of how to define "logic". Does it include or exclude norms about how to use logic? Do we for some reason choose to define "normative" and "logic" in an (extremely unhelpful and silly) way such that errors imply logic is normative? Do we try to separate it from other disciplines, and how do we define those disciplines?
Then there's the section about pluralism. I think most different "systems of logic" are just different approximations of the math behind it. They each pick different axioms, so of course they get different results. None are any truer than any other (unless they contain errors), because the axioms, (a type of belief) are inherently unknowable. Different systems of logic are useful in different situations, because in different situations, we may have already assumed/be able to derive different axioms. Just like your examples of scientific models, logical models are only useful in contexts they were designed for, with the assumptions they were built upon.
Logic vs the norms of belief: Fun. My beliefs have infinite logical consequences? Of course they do! Such is the case with approximations, only certain beliefs are useful in certain contexts. Figuring out which beliefs to use at a given time is the important thing. I believe orange is a nice color, but that doesn't mean I must be happy if my hair turned orange, my belief that orange is a nice color is less relevant than my belief that my hair shouldn't change colors suddenly. "Oh, but those are non-objective beliefs" *all my beliefs are non-objective, so I don't care*. Of course, I can mix and match various beliefs which contain inconsistencies to conclude an infinite number of unhelpful things, but the only helpful thing is to find the relevant beliefs to the context and use them efficiently. There can be different ways to do that, but as they are all approximations, that is no issue. "You could then measure their predictions against the truth!" but again, I can only approximately know the truth, and I can only approximate the difference between predictions and my approximation of the truth, so there may still be multiple which end up being "useful". When the error bars overlap, then is any of them more true? Not really, they can merely be more precise by a particular metric (a particular way to measure).
Muahahaha! There is no truth, because semantics can obfuscate any question, our fleshy bodies provide us with not-entirely-trustworthy data, our uncertainty about what axioms to choose, and even our uncertainty that our thoughts are rational, means we must conclude that at best, we probably have something approximating the truth.
the laws of logic are norms themselves. whether or not we violate those laws depends on the norms around that type of logic.
I would be interested in a longer/more indepth discussion on whether or not "P v ~P" is actually true. In regular language, we seem to discuss partial truths all the time, even if a given statement being partially true will itself have a binary truth value. By this I mean "Statement X is partially true" can be assigned a fully true or false value. The normal language concepts of half truths and "the best lies contain elements of truths" both would violate the idea that something must be totally true or totally false, in addition to the time example you gave in the video
Anyway, i found this video surprisingly interesting even if the demarcation points made me cringe. You presented it well, but God this sort of reasoning is so annoying to deal with in any question of philosophy that doesn't have the most rigidly defined lines
there is no such thing as partial truth.
If we say: “A is sometimes B”, then either A is sometimes B, or the opposite. It just so happens that the opposite of the statement isn’t “A is not sometimes B”, it’s something else.
So P or not P is always true.
However natural language makes finding “not P” quite ambiguous
You example of "A is sometimes B" doesn't really even fit what people would usually consider a half truth, if they did exist. Using a separate false statement or providing truth without sufficient relevant context to deceive is more in line with the usual understanding of a half truth. Trying to evaluate "the sun is the center of the universe" will have completely different truth values depending on what model of the universe one contextualizes it with. But that aside, I think you just calling it "the opposite" is rather misleading since there could be several states in which A is sometimes B is denied. You may call it an issue of ambiguity in normal language but the denial of P is no more clarified in basic logic
For any given proposition P, it can be the case that P v ~P; we say that such propositions are *decidable*; if doing type theory, then we say that P is a *decidable type*. If we claim that for *any* P, P v ~P, then we are claiming LEM/AOC/etc. It is possible for LEM to be false (just pick a non-Boolean topos) but for many propositions to still be decidable! This nuance is missing in the video.
Hey, I think you should improve the audio quality on your videos. It's really important!
n+1 is heap thingy is actual mathematical _induction_, where logic bases itself in the realm of _deduction_
The simultaneity problem of special relativity gives a good example of logical truth leading to separate branching paths.
I thought for a long time that logic was normative, but not in the sense that it tells us what we ought to believe, rather as a language convention concerning what we should infer from a given assumption.
I assume that single claims on their own are not relevant in science, that what is important is the dynamic of claims and how this dynamic coincide with the real world. In that regard, the language we use can be more or less suited for describing one or another phenomenum. I would believe that different logics are different conventions for how we agree collectively to use language when trying to give a scientific description of a phenomenum.
As such, we wouldn't ought to commit to one or another logical claim, unless we want to be part of a collective attempt to describe the real world.
Do you know if this view has been studied ?
With regards to the error issue - why couldnt we say - if logical laws are not about our reasoning but about truth preservation in inferences, separated from our reasoning those inferences - parallel to that - morality isnt about our actions but about goodness preservation in behavior, separated from our acting out those behaviors; and so actually people can never violate moral laws, just make errors when trying to apply them. This would be an equivalent move, and one that doesnt seem to make sense. Or maybe it does make sense, that would be Tjumps wet dream, we have found an actual way to have morality and it to be descriptive.
It surprises me that we dont suggest just rejecting the initial dichotomy. What if we suggest that Logic is just a list of rules. Its descriptive, but not of people or acts in the world or of anything in particular. Rather logic is a name applied to a list of imperative utterances. If you obey those utterances you are doing logic. If you do not, you are not.
Logic is a game one does or does not play and logic itself makes no injunction to obedience
Here is a list of things. If you are doing these things, then you are doing the things it says on the list. If you are doing the things it says on the list we say you are doing logic. If you arent, we say you arent. That's it.
"it's up to us!" Kane b. "The spade had turned." LW
but logic wouldn't allow you to premise your argument on {P, P->Q, ~Q}.
Logic would immediately say "no, you must be wrong, because..."
Sorites has a false premise. "If n is not a heap, n+1 is not a heap" is a statement about the function P(heap) = f(n). A false statement. The function f(n) is a sigmoid curve, something like -1/(1-(e^(50-(x/10)))) that crosses P=0 at just above n=0 and crawls and then curves up reaching 1 at around 500.
6:30 Łukasiewicz wrote book on that topic in 1911, its not listed in bibliography therefore I am pointing to it, because it may interest you, at least from historical point of view.
It would be useful if you gave an understanding of the meaning of normativity itself.
8:13 If you want to know why it is phrased:
"then it is false that I have less than $15 overall"
rather than:
"then it is true that I have $15 overall"
It is because, though they know they have $5 in one pocket and $10 in the other, it isn't specified whether they have more money in other places, such as in their shoe, which means they don't necessarily have exactly $15.
I think heaps are part of a weird category of words that I call "vibe words". The heap problem can be replicated for any situation in which there is a gradient change that isn't specifically quantified. For example, when exactly does an athlete become great? So for baseball, where is the line where one can say that according to their stats they've achieved greatness? It's going to be arbitrary no matter what, but when someone is convinced someone is great, they'll FEEL it. I FEEL that say, Derek Jeter is a great baseball player, and while I can point to various stats of his baseball career, I can't say where was the line that he crossed to qualify as a great baseball player. Perhaps heaps and other unspecified gradients like "greatness" are essentially phenomenological in character.
It seems fairly straight forward to avoid the middle third regarding eggs in the morning. If someone announces they will eggs in the morning, of course this statement will end up either true, or false. However, I think logic is really only meant to deal with facts, so if someone says something like "I will...eat eggs tomorrow" it's less of a fact and more of an announcement. The only logical fact that arises from that announcement is "So-and-so intends to have eggs tomorrow". THAT is true, but this does NOT imply that eggs will be for breakfast. Not at all, actually. Now, it may well turn out that he was right and had eggs, but by this point "I will have eggs" is off the table, now it's "I HAD eggs", which is a different statement, and the only statement between the two that is factual. So, no, the middle third is not necessary to stop bivalent analysis.
Moral realism always struck me as some particularly superficial way of thinking. Who made those laws? Who validates them? How come that people had so different ideas for a long time, we’re they all just wrong and we figured ethics out?
The only thing that comes close to something existing in the real world that can serve as a basis of ethical laws is human nature. The problem is that nobody really knows what it is. All societies hitherto have declared themselves as being most in tune with human nature - and we find those claims ridiculous in retrospect.
I think what’s really going on is that our understanding of human nature and ethics is and will always remain fuzzy because it’s too complex. But over time, evidence is mounting how our current understanding of ethics fails to provide social stability - which hints at a mismatch with human nature. Once that’s recognized, people will make guesses how we should change our understanding of ethics to best match human nature and then they’ll start experimenting with that. Once we hit a working formula, progress is made.
Unfortunately, ever since antiquity, all societies seem to have had a ruling class: powerful individuals with interests that systematically diverge from those of the general population; their main interest is self-preservation, and that’s not due to a conspiracy or due to a problem with human nature, but it’s strictly a selection effect: those people who remain in power once they rose to power are precisely those who stick to it and won’t give it up without a fight. Those people will - purely because they’re a biased sample of the population - make very different guesses about human nature, but with dramatic consequences, as their power precisely means that they can force their views down our throat.
Social stability can therefore only be accomplished once we abolish all power and all hierarchy - and we ought to abolish it all in one simultaneously, as otherwise, the remaining hierarchies will Grab total power. This means we ought to destroy the power of politicians with too limited democratic legitimization at the same time as we abolish employers, landlords and markets as such.
Evolution by natural selection is the only plausible source for a moral realism: if all members of a population act immorally, then the population goes extinct. In this sense, right makes might.
For example, what if piranhas treated each other the way they treat the other animals they eat? Piranhas wouldn't be a species anymore. Piranhas not eating each other is therefore moral.
@@NoActuallyGo-KCUF-Yourself but if a moral reality existed, there would exist only one survival strategy. That’s clearly not the case. Male lions kill offspring of other male lions - and their mothers are cool with that. Male spiders get eaten after sex. I could go on and on.
30:20 I have to disagree with this particular point; you said yourself we adopt ideals in those cases either to sidestep the arbitrary or to cope with inability, but I disagree that we can infer from this that science is not set on finding the perfect model, as even though we have many models, we would use the perfect one in all areas (idealizing only when the level of specificity is arbitrarily greater than necessary). It’s human to simplify and use ideal models, but a perfect scientist would use only perfect models with full detail if ever and whenever available (science also wishes to hash out a theory of everything as well, aiming towards this)
Please let me know what you think! I might be misunderstanding something
Descriptive laws vs. normative laws are, it seems, basically what linguists call descriptivistic rules vs. prescriptivistic rules respectively.
If one can’t enumerate one’s beliefs (in a practical sense I cannot), then, perhaps a quantifier would be a better way of expressing “not(all my beliefs are true)” and then this would only be an omega-inconsistency (or something like it) and not an inconsistency?
Like uh,
even if there is an enumeration of all my beliefs, and a statement which is a conjunction of all of them,
that statement certainly isn’t a statement which I either believe or disbelieve! (For one thing, if it were a statement I believed, then the statement would be infinitely long, which is not permissible in most languages I think?)
But, I think a simpler version which avoids this difficulty with self-reference, is just the lottery “paradox” showing that beliefs shouldn’t always just be completely Boolean true/false assignments? Like, if there are 100 lotto numbers, it might be that for each ticket I believe that it is not the winning ticket (suppose that I know that which ticket is the winner has already been determined, but I don’t know which one), but I believe that one of them is. This apparent paradox is just from interpreting “I believe this is not the winning ticket” as “100% sure this is not the winning ticket” instead of the actual belief which is more like “99% sure this is not the winning ticket”.
Edit: ok the point about “assignment of credences is probably inconsistent” is a much stronger point. I feel like this is a much weaker and much less concerning type of inconsistency though.
Why is the set of bunched grains of sand taken to be an inductive set? The axiom of induction need not apply if the collection of n+1 grains is not obviously a "next" collection. One way in which it may not be is there are any number of ways to arrange n grains of sand, and the way they are arranged can dictate properties that are inferred about them. For instance, if you have a million grains of sand all laid out in a row or a sheet, that's not much of a heap. You can impose structural constraints on the collection method, such that enough grains will always be a heap, but then it is just not true that you can always infer the group of n+1 grains is not a heap. It's a distinct thing to say "if one grain is not a heap, then two is not a heap, and if two is not a heap then three is not a heap" and to say "if n grains is not a heap then n+1 grains is not a heap", as one is a set of entailments over specific elements of the set and the other is a general entailment, which may be false even if many instantiations of it for small values are true. I can't conclude, given floor(1/10) = 0, and floor(2/10) = 0 and floor(3/10) = 0, that floor(n/10) = 0 implies floor((n+1)/10) = 0. We need, in order to make this claim, a formal definition of the collection of grains of sand. If the way we define it then goes on to have properties that violate our intuitions, then the definition does not supply a very good model. We could just as well propose a model where the property of heap-ness is gradient, that it can take on values between 0 and 1, and this may be a fine way to represent the issue. The paradox, then, becomes an issue of an unspoken choice of definition producing counterintuitive results.
This was a lot of fun, thank you! Do you have merch?
Interesting. It seems to me that the limits of logic, the point when it becomes practical without being normative would be rationality.
I would define rationality, in this context, as the averages and ratios made out of heuristics to form first principles, hence prone to error, but nevertheless presented through a conceptual framework and counter-validated by peers. Thus, although there's room for argumentum ad populum and groupthink, the model allows for a shared comprehension of reality that can be discussed and debated through logos. And since those judgments are cognitive rather than affective, we can escape normativity by instead establishing a "common sense", hence scientific reasoning.
Now, of course, I am no "lover of wisdom" and, strategy obliges, thus shall live through the sharp edge of my sagacity rather than "pure reason".
chuck some intuition in as well?
12:40 is wrong. We reason about the truth, which is a real thing and which is described by logic. Stars don't have rays, yet when we look at the night sky, we see them with pointy spikes coming off of them. This mistake is due to our vision apparatus. The field that studies the vision apparatus, anatomy, describes things as they in fact behave, we recieve the light in a certain way and the images on our retinas are inaccurate in a certain way under certain circumstances. That does not mean the proposition that stars are smoothly spherical is a moral one, because astronomy still is a study of how things in fact behave. I hope this analogy is clear enough, it's the clearest way I managed to express my criticism of that gross miscategorization.
I think looking for a distinction between normative and non-normative logic can be misleading. I've defined logic as sequential reasoning, and as such we want to evaluate reason based on some sequential order; and "sequential" not by time alone, but by it's order of validity or acceptance.
If we accept tinfoil as the name for foil made of aluminum based on normative standards then it can be logically argued that tinfoil is not tin foil, which can then create a false proof. Tin is not a valid name for aluminum unless we grant it as an exception, outside the use of logic, while ignoring the potential confusion or disruption to the independent development of knowledge which may arise through the use of 'gratuitous' equivocation.
The heap argument hinges on whatever is the definition of a heap. In general usage a heap may be described as an unquantified amount, if this is accepted it would explain why quantification (such as n + 1) creates a problem. Of course we could claim that all entities are capable of being quantified, in which case any heap is only contingently a heap!
I dont think that quite works. Consider 3 of something. 3 grains of sand is probably not a heap in almost any context, but 3 PhD's probably involves a heap of education.
Also we could have a heap of something that does have a known quantity.
The problem of heap is about relative terms, the contextual fluidity of language. I don't think it's just about quantification.
@@uninspired3583 If you qualify a heap of education as a multitude of actions or "happenings", the same is true for the grains of sand. They didn't start out as grains of sand.
@@mbbmbbmm precisely. The definition is relative to how the category is framed.
The original post talked about quantifying, which isn't that far off. When something is quantified it has a discrete value, this can't be done in the same way for relative terms. Is 5 greater or less? This doesn't make any sense without a frame of reference.
For heap, context gives the reference. Whether i know how many grains of sand are in my hand or not doesn't affect if it's a heap. For an ant to carry or me to fill a dump truck, now I have context to decide if that amount is a heap or not.
When you say 5+3=9 you’re only mistaken because you’re violating the laws of math-laws that are based on the laws of logic. If I run through a traffic light that doesn’t mean I’m mistaken about what the law is (even if I am) it just means that I am breaking the law. A conductive argument in court would show that. I couldn’t tell the judge and get away with it that I “was mistaken about the law”. A lot of question begging on both sides.
I’m a bit unclear on details of what it means for something to be normative.
If someone attempts a calculation, and get the wrong answer, then, they have erred, and the result they got was wrong.
Is saying that something was an error, isn’t that saying it should not have been done the way it was? Is that not normative?
I mean, of course most wouldn’t claim that making an error in calculation is a moral error, but-
well, here’s probably part of what I’m unclear on regarding what is meant by “normative”:
are there any positions that aren’t moral or ethical positions, and which clearly count as “normative”?
If something being normative just means that if violated, this is regarded as “an error”, or as “something a standard person would endeavor to avoid” or whatnot, then the “it is only in conjunction with the fact* that one ought to avoid believing falsehoods that you get the conclusion that one should avoid believing [P, P->Q, ~Q] simultaneously” seems maybe not super compelling because a standard person would try to avoid believing falsehoods and so avoid believing inconsistencies (by avoid I don’t mean always successfully avoid, or something that can’t be outweighed by other considerations) such as the combination of beliefs [P, P->Q, ~Q].
It has been said that in the presence of people who believe inconsistencies, it can be useful to state tautologies. This would be as a correction. It would be an attempt to bring the beliefs of those others to align more with logic.
I think I’m even more unclear on what “normative” means than I thought I was. I’m not sure why it shouldn’t be that basically any claim made with the goal of others believing it, counts as normative?
If you say “P” with the intent that others believe you and so come to believe that P, it would seem rather strange to, at the same time, say “but you shouldn’t believe that P.” . One might say “P, but you (currently) shouldn’t believe that P”, but presumably if doing so one either wouldn’t intend for people to believe the statement that P, or wouldn’t really believe the statement that one is telling others that they shouldn’t believe P?
Well..., ok maybe one could want people to believe something, while thinking that they “shouldn’t” believe you, but still wanting them to? Uhhh... hm
It seems more and more, a concepts of uncertainty/relativity crops up again and again. We cannot know anything without creating a system for understanding. And what is knowable depends upon the axioms we put in place. This in a way defines what is possible to know. We look through the lens of our understanding, which is arbitrary. Godel's Incompleteness Theorem seems to extend to other fields which rest upon having sound logic.
I am absolutely new to such topics, so pardon my lack of knowledge/reasoning:
“We look through the lens of our understanding, which is arbitrary”
Is this an objective (true) statement or an arbitrary (opinion) statement?
@@isaacnewtonbr2139 Interesting. Because either way his argument would undermine itself, leading to a non-arbitrary conclusion. Very clever
Excellent episode and a very strange idea haha
Thank you
“Ought to hold” and “ought not to hold” certain beliefs sounds like a moral statement to me
Nietzsche digged deep into this argument, I think.
I think it is just a proxy for "correctness", and hence is a moral statement only insofar as "you ought not to believe false things" is.
Depends on what "morality" means to you.
Is there any room to assert that the normative-looking axioms of logic are really just normative statements that "these are the definitions of not, implies, etc"? In other words, if you are capable of asserting P, PimpliesQ and not(Q) then we must disagree on the definitions of either the words "imply" or "not". e.g. when contrasting constructive and classical logic, the points of disagreement occur due to differing interpretations of "not" - classically, "complementary to P" and constructively "can be proved to be incompatible with P".
33:43 it’s a crazy and strange problem! I don’t believe personally in 3 valued logic outside of paradox (you go back and kill your grandpa and end up with a paradox of whether you were born in 2 valued logic: not-true because, but also not-false because (we all know why lol)) and find that unless there’s a paradox inherent, the third value is just undetermined *currently*
ie. It isn’t true of false that I’ll eat eggs tomorrow, that lemon is the best flavor, or that a virtuous man is best for society; though only because in the first assertion we have to wait until tomorrow to see if the statement was true or false, in the second we don’t have criteria, and in the third we don’t have a defined set of virtues
Do you know of any non-paradoxical issues that have three truth values which don’t fall under one of those categories?
I want to avoid making an argument based on my inability to think of a point contradictory to my argument haha
only 1 min into the vid: The question of what it means to believe in something needs to be answered first. AS WELL AS the question of grammatical definition/semanitcal definition, or philosophical definition. How can you say what something is? how can you know what something is or isnt? though you may hava a logically consistant internal definition of the lines where something is or isnt. dont you have to realize that this definition is imposed becasue on a surface level the human brain operates on a binary? (Neurons either fire or they do not) (although there is still potentially quantum activity in the brain to an extent that may be relavent. Some studies on the microtubules come to mind)
Logic is 🔴
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Morality often contradicts logic. For example in prisoner's dilemma, the only logical behavior is to snitch, but moral behavior is to keep silence. So if we would say that we are obligated to behave morally and rationally, this would create contradictions.
This doesn't quite work as an example. 'Logical Behavior' in game theory is defined by what decision optimizes one's own outcome, and the prisoner's dilemma is described by its outcomes given the choices. If you and I sat down at a table and played the prisoner's dilemma with pen and paper with no tangible consequences (akin to playing tic-tac-toe), and I chose defect to your cooperate, it appears hard to argue that I have actually done you a moral wrong of which I should plead forgiveness for. Also, the outcomes of a game are determined by a total evaluation of everything one receives, so moral outcome is something to also be evaluated in addition to the other outcomes, and so if two people were trapped in a prisoner's dilemma when only considering physical outcomes absent morality, it's not necessarily a prisoner's dilemma when moral outcomes are considered too.
For example, if myself and someone I deeply cared about played the prisoner's dilemma in real life, the emotional weight of forcing them to spend 10 years of their life just so I could be free would be hard to bare, being much more costly for me than that 1 year of prison potentially. Just from the emotional outcome included, this renders this situation a new game, and no longer the prisoner's dilemma.
If the moral outcomes are of such severe consequence that one ought to choose to cooperate, this would undermine the game being a prisoner's dilemma.
Well, from the standpoint of set theory one grain of sand does make a tiny heap. Mathematical jokes aside, when dealing with blurred concepts or imprecise/irrelevant/nonsensical statements one must abandon notion of absolute unambiguous truth. Any type of logic, so to speak, has its specific terms of use.
This is like saying math is normative, which (through argument by absurdity) it isn't. Math doesn't tell you how you "should" reason, but it tells you what is good (correct) reasoning from bad (incorrect) based on a set of axioms which are taken for granted as true. Logic is the same. Whether you choose to use logic or not is up to you, nobody can tell you if you "should" or "shouldn't" use correct reasoning (or if you should or shouldn't conclude 2+2=4) but they could still evaluate your reasoning using the system of logic or math developed to formally tell correct from incorrect.
Hmm... logic and meta-physics being the same thing? I suppose it depends on the definition of meta-physics. I would argue that physics is derived from logic, but that logic is an inherently irrational imposition on the world of physics to make it necessary to perform any reasoning at all. There's probably something that does unite the meta-philosophies on some level, but we are all fairly uncertain of what that exactly is. Regardless, there's no logical necessity, nor physical necessity for logic. It seems to be more of a heuristic that we adopt to understand physics and ethics. Such that one cannot truly imagine performing any kind of study in either without it, but I don't think that there's a basis in logic for this necessity either. Meaning, there is some kind of higher meta-unification that makes the various schools of philosophy inherently contingent on each other, but I think that one could just as easily argue that meta-logic is a form of physics or ethics, as well. I would go with the classical theory of unification of the whole, given their inherent relatedness to each other, but this ultimately results in an appeal to the unknown, which I can understand bothers a great many people and probably doesn't provide any kind of answer to the problem. I just don't see a hierarchy of meta-philosophical positions on this, as they all seem equally contingent on each other in equal directions. I can't fathom how any one meta position could not rely on the others, but I'd like to hear more of a constructionist argument for meta-philosophy rather than the unknown/esoteric organic argument that I would subscribe to.
The "heap" paradox is a problem of definition. "Heap" is a recognizable structure, not a count. A million grains of sand, one grain deep, is not a heap.
Many of the difficulties in this discussion seem to be of similar nature - using words without actually explaining how they are being used.
Note that if there are more than one non-equivalent self-consistent logics, none of them can be generally normative.
I made a comment about philosophy students in Mathematical Logic classes (taught by mathematicians) earlier today. Falling into this video was an entertaining consequence of the RUclips algorithm.
At 2:15 you say "if I deny the objectivity of logic, then I can no longer make any assessment of the rationality of any position." doesn't this statement also imply the objectivity of logic? If logic is non-normative then you wouldn't even be able to make this seemingly rational statement... so you wouldn't be able to make any logically valid statement at all... not even a statement of whether or not you can make valid statements.... I am on team normative... for now.
do P & Q exist as discrete values? do they have hard limits? are there any hard limits?
11:25
2022 noble prize goes to quantum entanglement which is faster than speed of light.
i.e the model is useful because its not a 1:1 representation of the thing, e.g map is useful because its not actually the earth.
You here seem to be talking of 'normative' in the sense of constituting an ideal, or something to which people should strive, in their reasoning. There is a different sense in which logic can be normative, however. Logic can be normative in the same sense that a game, or language, is normative. Games, or languages, are normative in the sense that they are constituted by norms. If something fails to exemplify these norms, it does not fall short of any ideal, it just simply isn't part of that game or part of that language.
Logic is rigorously discovered relationships that always replicate.
26:31 “we assume there is some logical theory that provides the correct account of logical consequence” - isnt this begging the question? Because you’re presumably also assuming that we ought to adopt such a theory, if it were found. This is a very common assumption, but couldn’t the intuitionist avoid it by saying that the best logical theory is eg the one thats easiest to work with, that allows the production of the most proofs and that doesn’t get falsified, etc etc?
I think it is a necessary assumption. If a logical system cannot consistently produce true conclusions (as determined by observation), then no one would use it, and that system or theory would go extinct.
If there is no logical theory that provides correct conclusions, then making an error in reasoning or not would be based on luck or coincidence. Evidence does not support that scenario.
@@NoActuallyGo-KCUF-Yourself I see your point. But Im not sure logical statements can always be verified by observation. For example, how you do find evidence for a universally quantified proposition?
Good stuff. My view: logic is a language, languages are tools, tools can be optionally used to advance goals. Do hammers tell us how we should pound nails? No, but they can be useful to do so.
Tool used to reach this conclusion: pragmatism.
Logic is less than language, because language can be used to make logic, but logic cannot be used to make poetry.
@@andsalomoni Yes, logic is "a language", it is not all of it.
Logic _has_ a language, but is not itself a language. There is a system of definitions and notation and ground rules / axioms, but you still need some other language to communicate the actual logical values (i.e. meaning).
@@NoActuallyGo-KCUF-Yourself You are implying there is something in logic that is _a priori_ to the language. The burden is on you to explain what this is, and as it is prior to language, ideally you wouldn't use language for your explanation. In any case, can't use pragmatism to talk about idealism. The point of pragmatism is to get away from the mush that is metaphysics... just opinions and checks that can't be clearly cashed in to the state of affairs. So, I reject this. A rock can be prior to language, as it has color, shape, and mass. Logic is a mental notion, and for me, this places it in the realm of "not real outside of language".
What is "normative"?
A piece is never the whole, nor does it define the whole. Normative (relating to a social or behavioral norm) is suggesting the false dichotomy that binary states of normal and abnormal exists, when it's actually on some spectrum. There is no normal, only commonly accepted behavior in society. There is no abnormal, only rarely to unaccepted behavior in society. As for "Logic", everyone reasons what is acceptable to themselves, or objects to their reasoning..... who gives a sh#t what other people think. Morality is self-determined and sometime the majority agrees with you and sometimes it doesn't.
i agree with pluralism
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Is Math normative? 2+2=4?
You have done a good job of making nonsense clearly nonsensical.
It has become fashionable to make truth and logic and even sciences (like biology) to dismiss everything as arbitrary and oppressive.
The bigger question: Are norms logical?
Generally no.
Of course.
would it not be true to say that logical laws ARE descriptive laws, just over what things are possible to cognize. When people say that 5+3=9 they don't actually think that, they are mistaken about something, they are simply ignorant over the nature of the mistake. Once the mistake is corrected then it becomes impossible for them to believe that 5+3=9.
Like for example if give the formula 5+3 and the person says it equals 9, that is possible due to them not knowing they are making a mistake, but when the mistake is made clear, for example, by placing 5 and 3 coins in front of the person in a row and asking them to count. Then they will count 8, once they have counted 8 they cannot say it still equals 9. Where will they derive that number 9 from after they have finished counting all the coins?
Another example is not (a and not a). You can't believe an apple exists and doesn't exist in the same place and at the same time and in the same way. When people declare similarly contradictory statements it is because they are ignorant of a mistake being made, but once the mistake is understood, it then becomes impossible to make the same previously contradictory claim (unless the mistake is once again forgotten)
So the laws of logic become descriptive in a state of complete understanding, whereas violations of the laws are a result of an incomplete understanding.
If we call 5+3=9, statement a, then the person that says 5+3=9 does not actually believe in statement a in other words, they think they do but that's because they don't actually understand statement a.
Is it always immoral to have slaves? One person who claimed to have slaves said that his actions are moral, because he runs a business that buys slaves in North Korea, where they have awful conditions, and uses such slaves as construction workers, giving them much better conditions, and above of that, a good amount of money. Without his business, more people would be slaves in NK, their families would have less money, so ultimately, everyone would be in a worse situation. Doesn't it imply that having slaves in his case is okay?
@14:30 I think the moral anti-realist is making the following mistake:
Programming a flight computer with a slightly wrong mathematical model of reality (Newtonian mechanics) may allow the plane to fly without any problems, you could say those engineers are anti-Einsteinian-relativists. They are effectively adhering to a normative notion of reality (even if they think they are holding to a realist-Newtonian view). On a small local scale, this may not matter, but if we scale this up to interstellar flight we are going to notice our error.
In the same manner, the moral anti-realist thinks the view he is holding is normative, and he can even break them (by flying a plane with a normative view or) by owning slaves, but if he was to scale that up over time we are going to notice our error.
In other words.. moral reality is not about individual laws or even humans ...moral laws are simply that certain processes will provide significantly different outcomes to other processes. If you do not want to call such processes "morality" then what else do you call them?
check Process Ontology -SEP
depends on definition 😎
In logic if p then q is true when p is false.
So if unicorns were real then they would have two horns is a true statement
Unfortunately I find the above statement a violation of definition.
But the laws of physics are not descriptive, they are not a representation of reality and they are not referential. They are just tools to solve problems and explain reality. Saying that they are "descriptive" is an epistemological leap that it isn't justified nor needed for physics to "work".
Logic sets the rules for correct inference it is not concerned with the truth of the premises and the conclusions which may be correctly derived from the premises. If the premises are true, and the conclusion is correctly inferred, then we say the conclusion is correct and true. We can have correct inference but with false premises and conclusion e.g., all cows are cats but chickens are cows, therefore, chickens are cats--this is correct but false. We can also have true premises but with incorrect conclusion e.g., All cows are four footed. But carabaos are four footed. Ergo, Carabaos are cows. Here though the premises are true, yet the inference is incorrect, it is illogical. One has to make a distinction between formal and material logic. Bertrand Russel missed this distinction. Logic is normative to mean it sets rules of correct thinking which is based on the the fundamental laws of thoughts e.g. principle of contradiction, of identify, Dictum de omni and dictrum de nullo. It is not normative as far as the truth of the premise. Hence ethics applies logic assuming the premises are ethically true, and what can be inferred from these true premises correctly.
This is really funny to me, I'm only halfway through, so I'm hoping for a surprise ending, but your first argument was phenomenologically very self-aware (if you understand the simple flaw you made) and your second argument is wrong at the level of convincing. Where of course, the law of excluded middle is not implied by your construction of P1. Can't wait to see the rest!
True
RE: Error (12:54): (a) laws of logic, whether cardinal (mathematics, commensurable), ordinal (qualitative, comparable), operational (sequences of actions), or set (verbal) are descriptive (facts). (b) logical reducibility (generalization of a rule) of cardinal, ordinal, operational, or set statements is limited by the referrers to constant relations (nouns) or inconstant relations (verbs), paradigm (system of decidability, first principles (premises), how far they diverge from laws of nature) and information (knowledge and skill) available to the speaker. (c) especially given that existing logic (grammars of paradigms) at least as practiced in logicl and philosophy, do not adhere to the first principle of grammar, which is the requirement for continuous recursive disambiguation any statement or claim to an unambiguous identity. (d) there is a natural conflict between the search for general rules, and sufficient disambiguation to test individual cases. As such what we find is that logical claims require both a general rule AND a spectrum of claims that falsify to the limits and full accounting of the general rule (e) what we find then is that not all statements are reducible to a general rule sufficient to limit error for all possible cases within the limits of the general rule. This is the problem of logical reducibility. And this is why computation (operations, realism) has replaced mathematics (set theory, idealism) and verbal logic as the foundation of logic. ... That paragraph explains the failure of philosophy, mathematics, and mathematical experimentation in physics in the late 19th through present century. ... And we see this in all sciences. The most important of which is neuroscience, because, we do in fact, understand qualia and consciousness - and it's tragically simple. And the 'oddity' is that these solutions to ancient questions are not penetrating the discipline of philosophy. Why is that? Is it the same reason that science has not penetrated religion?
Your latest video, “Is Logic Normative” has excellent information in it. This is why I’m listening. Your last video was also dealing with an important subject, but for some reason your friend and you had to add puerile trash-talk I heard on street corners in Brooklyn NYC in the 1950s. At 75, I don’t have a woke death. For some of your listeners living is a good idea. If someone can control you friends’ mouth, you two should work together, get a producer to keep you in the real world (which existence you doubt), keep the conversation under an hour, and link up your topics. You know, today we talk about this, tomorrow we talk about that. Together the two you, spontaneity & expertise, could blow-up the internet. In other words, Kane, get a purpose and get a life. Right now, the vibe is floundering talent. Jack Cascione
I think logic is ideal, but normative? I would like to think so but it is not. People use their best idea of logic, as each person has their own idea of what is logical.
Socrates is a man, All men are immortal, therefore Socrates is immortal
Destiny? That's a girl's name.
It seems that the main focus of philosophy these days is to increase doubt in the usefulness of philosophy.
Jedi mind trick
“Useful” is, in itself, a strange term to even apply to these types of discussions though, innit?
The whole point is that the value of the philosophy is relativistic.
@@galahadsoundscape6365 Philosophy is supposed to be the "love of knowledge". It is not supposed to be mere mental masturbation. Relativism is self-refuting in the eyes of most philosophers and is dangerous and deadly when put into practice in the real world.
Dang. Spock was wrong.
All very lucid. The normative utility of logic lies in its consistency. But disingenuously applied through various forms of rhetoric argument from authority (which branches off into deontological claims and their own special logic), two applications of logic may be valid, but inconsistent with one another as to their applicability to a case. One doing this can force facts, or draw false syllogism with horrible fallacies and sophism. They could even draw out their logic falsely on a whim as a "power play" as in the villains of 1984 or Brave New World. A sort of "arbitrary" logic where inconsistency is only someone else's problem. Extortionist psychology has a logic of its own when it comes to application. So Logic per se cocerns partly with the schema of any normative domain of thought or action, and yet doesn't in its science directly espouse any ethical use of its frames nor does it protect people from fallacies if they don't properlly train in it or have preternatural facility in it. But for people who want to be fair and just about things, consistency in logic is indispensible until a better system of cognition can be devised. I've never had a problem with Modus Ponens. Logic analyzes many subtleties of modeling that as part of various systems of logic about that thought, which represent it in different forms encompassing bare truth claims, evaluations of oughts, legal codes and procedures, protocols for every endeavor and the heuristics which devises all evaluations of problems in order to seek solutions, all investigationos and forms of engineering. An extortionist has a set of norms that forces him to leverage power over logic, to gaslight his enemies and captives. Unfortunately, there isn't much done by some logicians to learn what the "ethics of logic" might be while they were conducting a study on the logic of ethics. They caved in to the pressure and joined the open-air manhatten project. No you but there must be some. He's the "evil logician" who is duped by the supervillain and through vanity and ambition serves his evil ends with logic. That's a thought experiment . But what would the virtuous logician look like? He would use his logical mind to determine what is the best for of world into which he could participate, and seek to make that be isomorphic with the world in which he finds himself. He would determine what normative ethics is, and decide for himself what the ideal form of ethical approch he will take. Then after formulating that ethic, devise a way to ensure that it becomes permanent and ever-improving. He will develop very specialized heuristics for watching his own motivations for actions, his cognitive slips in how projecting ideas onto externals (including other people), and he will have to always be growing his general knowledge and exercising all of his other faculties and his body in a healthy way. I think Aristotle was the big heavy on the "whole body-mind" approach in his day, as was Hippocrates etc. So there are a lot of "meta"-ehtical considerations and logic is only one of them. There is a best and there is a worst, or it seems reasonable to think that. Make things better, including your logic and use of logic. So what heppens when the logical hero meets the logical villain? It's not pretty. But that's a bit into aesthetics.