The Laws of Logic Defended
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- Опубликовано: 19 окт 2024
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The laws of logic are constantly attacked by absolute skeptics, but their arguments are pointless in their endeavors and their reasoning is self-refuting. This video explains why.
Sources:
The Last Word - Thomas Nagel
Laws of Form - G. Spencer Brown
Philosophical Foundations for a Christian Worldview - William Lane Craig and J. P. Moreland
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Stephen Fry said something on this:
“The Laws of Logic are essentially non-negiotiable. As long as you’re not using violence or bribery, any reason that you give to convince someone that logic doesn’t exist relies on logic.”
Still, it's only if one believes the laws of logic that they will agree they are using logic.
Definitions of Identity, and contradiction vary according to the logical system used. so how are they absolute and universal if their definitions vary?
@@landgabriel we use logic to show that logic is illogical all the time... you are confusing different levels of logical inquiry.
Logically.
What is logical in a particular situation might not apply logically to a different situation. Especially when those situation involve people that arent YOU.
Neither can we defend laws of logic nor we should try to. That is because everything you say in its defense depends upon the validity of the laws of logic. Anyone who disagrees with laws of logic is as irrational as one can possibly be.
@Ruben O. There are a lot of problem building up logic from experience...
Their validity depends on what you mean with „truth“.
If „truth“ is just a symbol that is manipulated in a formal system then the laws of logic can be proven to be valid in that system by using the truth tables that are used to define the logical operators.
But if we fill the empty shell of truth with substance by connecting it with a theory of truth. Then their validity can be held accountable by our sense experience. If we could sense a state of affairs in which the sun exists and doesn’t exist at the same time or otherwise prove that there is a true contradiction. Then the law of noncontradiction can not be a universal natural law, at best it would only be a parameter dependent regularity which is sometimes valid.
@Ruben O. So... We can't prove anything you just said either? 😶
@thewanderer797
I make a difference between empty truth and substantive truth.
Empty truth does not refer to anything, it is just a sign that we connect with a proposition.
It is basically just a placeholder for a substantive truth. It is like the variable x and f(x) in mathematics. x can be used to represent something but in pure mathematics it is just a empty placeholder for a number or physical quantity.
Substantive truth may or may not be a property of the proposition, depending on the theory it can also just mean that a certain epistemic criterion has been met. And therefore T is connected with p.
To deny the laws of logic require the laws of logic. Damn some absolute skeptics are extremely delusional and are worse than flat earthers.
Kyle Alander CivilianName295 I was actually thinking the same exact thing. If you want to prove the laws of logic false, then you'd have to use something else other than the laws of logic to prove logic false. Since one needs logic to show that the laws of logic are logically untrue.... good luck.
Not necessarily, its really just a matter of taste. The laws of logic don't come from reason, they are simply axioms that can be accepted or denied. They have no proof or disproof, only personal belief.
If someone denies the axioms of logic, then there is nothing to disprove. Logic is not an established concept, rather it is presumed true.
It is NOT merely personal belief. It is in the deepest of our intuitions. Are you saying that it is mere opinion to state that A=A is true? Are you going to reduce the law of non-contradiction to a silly whim? If so you aren't even worth talking to...
Jonathon Peterson I was actually about to use the same examples you did. Notice how even he is trying to use logic to disprove logic! This is ridiculous.
Yes it is an opinion, including A=A. The Law of non-contradiction is simply an axiom which is up to an individual to believe in. Maybe A=A=B+A = fish. It may seem impossible but again if someone doesn't accept the axioms of logic, then maybe it is possible.
What I'm saying is that logic reaches its limits at our human thinking, we can't conceptualize anything beyond logic. Its not our fault, but I'm not sure that is reason enough to say we there can't be anything beyond logic.
p.s. yes you can joke and say my argument uses logic. But I believe that is irrelevent. Since logic is whats at question, there are no "rules" to follow in this discussion.
i remember nothing about my high school math
If a proposition is either true or false, then "This proposition is false" is not, by definition, a proposition. It doesn't matter that it looks like one.
Excellent point
This argument definitely does not work. The main problem these premises are making is comparing (True) vs (False). When it should be, (True) vs (Not True). And yes, there is a huge difference.
This sentence is not true.
@@jeremyhansen9197 but your sentence is in fact true tho sir
I also disagree with premise 2 in the intro, but for different reasons. “ All propositions are either true or false”. No. All propositions are either true or not true, false or not false (A or not A). Premise 5 is accidentally correct.
This would also correct the flaw in premise 3 to be: The proposition “This proposition is not true” is true. or The proposition “This proposition is true” is not true.
Apart from the points you mention, there is a linguistic problem with the sentence
"this proposition is false".
"This proposition is false" in language, is a proxy for an actual proposition
e.g(which proposition) 2 + 2 = 5.
You can't simply make something a proposition by saying it is a proposition.
similar to the fact that the sentence "My favorite color is taste" does not make taste a color unless taste is a proxy for an actual color.
thus you make the "sentence" linguistically unintelligible and thus not a sentence and not a proposition.
"This statement is not true" is it true or not true? If you say its uninteligable then it isnt true, since it cant have a truth value. If its null, same thing. If its false, its not true. And if its not true then it is true.
I would say that the laws of logic either a) arent universal. There are things that the laes of logic dont apply to and b) these things are just concepts like words, phrases, statements but not entities which exist outside the mind. So mind-independent entities cannot violate the laws of logic.
@@mothernature1755 to help you out.."this sentence" refers to a sentence in language. Since there is no established sentence. It is not referring to an actual sentence. Thus there is no sentence. Making it un intelligible.
Which is no difference to me saying ' blue oranges are faster than me...this sentence is true'
Blue oranges.....is not a sentence thus calling it a sentence does not make it one.
Try to think in terms of a logical argument and you should get it.
@@joshjeggs but when you say "this sentence" you are fereing to the everything from the start to the period, because thats what a sentence is. So i would say this sentence is not true.
@@mothernature1755 oh I see. You define a sentence as "a set of words". Which is false by the way.
The best I can do for you there is to say your "sentence" is unintelligible and thus has no truth value. A "sentence" must be intelligible to be true or false.
So you should have looked up the meaning of the word before attempting to correct someone about it.
@@joshjeggs is its true that the statement "this statement is not true" is not true? since it can be true or false, it doesnt have a truth value, therefore it cannot be true
It's frustrating to see so many theists commenters painting with a broad brush, acting like: "OMG, atheists are now trying to disprove logic! The very thing they get on our case about." The video deals with philosophy, not atheism or theism. I got the impression that the topic had more to do with objective vs subjective views of truth and reality.
Chris Collins Yeah this video addresses hard skepticism not atheism.
God is Reason. Without is madness.
With all due respect, you are presenting a wrong conception of formal logic.
1. Russel's paradox has nothing to do with invalidating logic, it shows a contradiction in naive set theory which has been solved by proposing systems such as the ZFC axioms.
2. The liar's paradox is not expressible in classical propositional logic, so it is irrelevant here.
3. It doesn't make sense to say that a logical system is either true or false, a proposition can be true or false.
You can say that a logical system is sound (everything that's provable is true), complete (everything that's true is provable) but there is no sense in which truth values can be assigned to a logical system.
4. How would you even express sentences like "Easter is the best holiday" in formal propositional logic? Or in any logical system for that manner?
5. It is possible to deny some of the laws of logic without using them.
Maybe the most popular example for this is the law of excluded middle: For al A: A or ~A.
In intuitionist logic it doesn't always hold, and the basic propositional logic taught in discrete math classes treats it as a theorem, not some metaphysical assumption.
That brings me to my next point.
6. There is no such thing as the "logical absolutes".
The law of excluded middle is an "absolute" in the same sense that 2+2=4 is an "absolute".
These propositions are true by virtue of the definitions of the terms that they refer to, they are 100% true, because they are defined this way.
It's like defining 1+1=2 and then saying that it isn't 100% true because "we can't be sure".
In short, videos on the subject of logic should advocate a more mathematical perspective of it, not this.
The „correctness“ of a law of logic depends on what you mean with „truth“.
If „truth“ is just a symbol that is manipulated in a formal system then the laws of logic can be proven to be valid in that system by using the truth tables that are used to define the logical operators.
But if we fill the empty shell of truth with substance by connecting it with a theory of truth. Then they can be held accountable by our sense experience. If we could sense a state of affairs in which the sun exists and doesn’t exist at the same time or otherwise prove that there is a true contradiction. Then the law of noncontradiction can not be a universal natural law. In other words a contradictory state of affairs can defeat the law of noncontradiction.
ZFC is a workaround. The philosophical question remains. Lord have mercy. I don’t think you understand what’s actually going on here…
This reminds me of The Poison Of Subjectivism via C.S. Lewis
Do you know what moral subjectivism is?
Absolutely, that and his work on bulverism.
This video is based on a number of outright misrepresentations or careless mistakes. Most of the people you think you're arguing against are not saying "Logic doesn't work" or "The Laws of Logic are false", or some such. Rather, they are saying that one may be mistaken about what the correct logic is (e.g. the correct inference rules, axioms, semantics, theories of the connectives, etc.) There are no "THE Laws of Logics" just as there are no "THE Laws of Math" or of science; there are axioms in particular systems of reasoning. This is just a presupposition you have and it's known to be a false one (see Intuitionistic logic, Paraconsistent Logic, Non-Reflexive Logic, etc.)
And that silly argument you gave is just... silly. It's invalid, for one. Premise 6 is a non sequitur. If it's not the case the all propositions are either true or false, that doesn't imply that some propositions are both true and false. Have you not heard of Intuitionistic Logic? Further, it's hilarious that you argue against Premise 2 seeing as that's a law in *classical* logic: The principle of Bivalence.
So wait, you accept that Classical Logic has exceptions? Then you cannot accept the "simple argument" you made in this video, since it means you reject your Premise 1. But worse, the example you gave is just bunk. An opinion like "Easter is the best holiday" does not express a proposition. Opinions are not truth-apt and thus do not fall under the purview of logic anyway.
Also, you completely misunderstood Godel's Incompleteness theorems. It's not about, as you put it, "proving all truth". It's about the ability to prove things in *mathematics*. It has nothing to do with all truths in general. Don't skim a Wiki article for this stuff anymore. The Incompleteness Theorems don't challenge Classical Logic anyway (or rather, not inherently so). After all, in reaction to these results one can simply choose to accept that not all mathematical truths are provable and get on with life.
Beyond this, the video is just waffle and I can't be bothered. Non-classical logics exist, many of which are well explored (they have their own algebras, their own proof theories, there own non-classical semantics) and are rather robust and even provide a decent challenge to the standard Classical Logic.
I have had people deny the laws of logic are objective and believe they are a human construct. Nagel talks about some who take this view in his book. And it is not just a presupposition. The laws of logic are inescapable.
Please explain how something can be true and false at the same time. I also didn't say all propositions had to be true or false so I am not sure what you are assuming. I didn't assume classical logic or argue for it. I am only attacking epistemic skeptics. Also, it depends on what you mean by a proposition. You have simply redefined the term.
Also, I really do not think you paid attention well since I never argued the Incompleteness Theorems challenge Classical Logic. Also philosophically, it has been pointed out the logic of the Incompleteness Theorems can apply to truth in general. You are really reading into this far more than you should.
It is a presupposition, because you are holding to the view that there are "the" laws of logic without justification. These so-called inescapable laws are not tautologies in numerous logics, such as the Intuitionistic Logic I mentioned, wherein Excluded Middle is not a necessary truth. Also neither you nor Nagel (as shown in the video anyway) quote your apparent targets so no one can be sure what their intended argument is. I fully admit some people make stupid arguments, but why would you target the worst version of the opposing view to your own?
You did say all propositions have to be true or false. That's literally the 2nd premise of your "simple argument": "All propositions are either true or false" (that's what you put in the video). I have not redefined the definition of a proposition. Heck, just take the SEP:
"Propositions, we shall say, are the sharable objects of the attitudes and the *primary bearers of truth and falsity*. "
Opinions aren't truth-apt. And you did argue for classical logic, you were speaking of "the laws of logic" and you were defending as inescapable those most cloesly associated with classical logic (after all, you did not mention a single non-classical logic in this video). The very first image in this video in fact shows axioms of Classical Logic; a Boolean algebra is the algebra of Classical Logic.
As for how a proposition can be true & false at the same time, well you'd have to be a dialetheist to think they can. One example is the Liar sentence: "This sentence is false". And if you think the Liar has some simple answer, you;re literally going against the last 50 years of formal logic bearing on this topic because logicians have no standard resolution; the only agreement seems to be that no one has actually solved it. A little tip would be to look up the "Revenge Paradoxes" if you think the solution is obvious, because I promise you that whatever solution you have has been tried and has been shown to either fail or to fail to cover other versions of the paradox.
You brought up Godel's Incompleteness Theorems as if they were relevant to "the" laws of logic; they aren't. And no the have nothing to do with truth in general, no one argues that because it's false. It's relatively simple to put:
The Incompleteness theorems regard formal systems (not truth in general) which are capable of expressing arithmetic. Any such system is either inconsistent (because contradictions can be proved in the system) or the system is incomplete (there are truths within the system that cannot be proven within the system). This only applies to formalisms that can express basic math, which means propositional logics (e.g. classical propositional logic, paraconsistent propositional logic, etc.) are not relevant nor affected by this theorems implications. It's not even about truth in mathematics, its about the ability to *prove* truths in mathematics.
The laws of logic do not need justified because they are inescapable. You assume them in making an argument.
Second, I said who the intended argument is, people who deny the laws of logic. That should have been obvious. Nowhere did I try to attack different views of logic. You read into what I said and heard what you wanted...To prove my point, you said, "You did say all propositions have to be true or false. That's literally the 2nd premise of your "simple argument"
What the hell are you talking about? You do realize that is the argument I said in the beginning to debunk? Did you even pay attention, kid? That is not my argument, that is the argument I am taking down... Obviously. I said You read into what I said and heard what you wanted.
Opinions are not true or false but they are expressed with truth-apt in mind. If I say the penguins are the best hockey team. I am stating an opinion, but I am stating it if it is true. They are not emotions which lack truth-apt. They are stated with a cognitivist view in mind.
Again, Where in the video did I say this was a defense of classical logic? You read into what I said and heard what you wanted.
Godel's Incompleteness Theorems, can be and have been used to relate to logic:
arxiv.org/pdf/1509.02674.pdf
mat.iitm.ac.in/home/asingh/public_html/papers/goedel.pdf
I really do not know why you are taking such an odd view...
Finally, You said, "It's not even about truth in mathematics, it is about the ability to prove truths in mathematics." No shit... Agin, did you pay attention? I went over all it shows was absolute truth will always be out of our reach... It sounds like you just read some obscure blog, which took the video out of context as well, instead of actually watching the video itself...
They are not inescapable. If they are assumed then they can be "escaped" by not assuming them.
The very first image you showed in the video when you were speaking of logic being inescapable was classical logic. I'm aware you were debunking the argument. My issue, as I stated in my initial comment, was that you say the "laws of logic are inescapable", and then you present a law of classical logic (Principle of Bivalence) and then say the principle does not hold. So, kid, either you do think the "laws of logic" are escapable (because you rejected Bivalence) or you just contradicted yourself without realizing it. I literally mentioned this in my first comment.
Opinions are not truth-apt just because they are expressed as if they are, that doesn't follow at all. "Easter is the best holiday" is understood as meaning "In my opinion, Easter is the best holiday." The latter sentence is true (trivially true), but the former cannot be given a truth-value if interpreted straight, it has no corresponding proposition because there is no state of affairs that can make it the case.
You literally showed Classical Logic's axioms at the beginning and you defend "the laws of logic" as inescapable. If you aren't going to specify what laws you think are "inescapable", there's nothing I can assume you mean other than what you, ya know, actually show onscreen (which was Classical Logic).
I know for a fact that you either didn't read those papers or you didn't understand them. Link #1 is referring to mathematical logic (the field which Godel's theorems are part of). The theorems are proved within a formal system (a logic, if you will), but the theorems are *about* formal systems capable of expressing arithmetic. Read your own link man:
"However, there is an obstruction to the TOE concept, which comes from the Goedel's
incompletness theorems (GIT) in logic, see [3]. The first incompletness theorem states that a finite
or recursive logical system, which includes arithmetics, has a finite demonstrational power. More
precisely, one can construct an undecidable statement (the Godel statement) which can not be
proven to be true or false by using the postulates of the theory"
And how I know you didn't read link #2 either is because of the following excerpt:
"Godel’s incompleteness theorems are considered as achievements of twentieth century *mathematics*. The theorems say that the natural number system, or arithmetic, has a true sentence which cannot be proved and the consistency of arithmetic cannot be proved by using its own proof system;"
Which is literally what I said. To call what I commented previously an "odd view" is just to admit you didn't read your own links.
Oh nonsense, this has nothing to do with "absolute truth" (whatever that means). Many truths in mathematics *can* be demonstrated via formal proofs. The issue is that there is always at least one truth (likely infinite, in actuality) which cannot be proven. Namely, the Godel sentence, as per Godel, "This sentence is unprovable" when converted using Godel numbering. I don't get the feeling you looked into any of these issues beyond a quick Google or Wiki glance.
You have to assume they in order to make an argument. You are doing that now… Like Nagel says, “"Claims to the effect that a type of judgment expresses a local point of view are inherently objective in intent: They suggest a picture of the true sources of those judgments which place them in an unconditional context. The judgment of relativity or conditionally cannot be applied to the judgment of relativity itself. To put it schematically, the claim "Everything is subjective" must be nonsense, for it would itself have to be either subjective or objective. But it can't be objective since in that case, it would be false if true. And it can't be subjective, because then it would not rule out any objective claim, including the claim that it is objectively false."
You want to tell me your argument is objectively right, but that is assuming objective laws of logic. Any attack on objective laws of logic has to assume they are objective, and actions speak louder than words.
Holding up an image which represents logic is all that that is. Again, where did I defend classical logic? It is an image which simply represents a form of logic. You need to take my words and not what you want to hear…
Also, now you are lying since in your previous comment you accused me of holding to P2 of the argument I am debunking. You said, “You did say all propositions have to be true or false. That's literally the 2nd premise of your "simple argument" So don’t lie.
Second, I never said all statements have to be true or false. Did you even pay attention?
“Easter is the best holiday" is understood as meaning "In my opinion, Easter is the best holiday.”- Then why is it claimed in the statement itself to be true? All you did was change the meaning by adding, ‘"In my opinion.” Opinions are expressed as truth. Two sports team fans can fight over which team is better, and both express their opinions as if they are objectively right. Opinions function with truth-aptness because people believe their opinions to be true. Just look at ESPN commentators fight over who is the best quarterback.
“Link #1 is referring to mathematical logic (the field which Godel's theorems are part of).“- Wow,, you are really not seeing it… You are trying to say GIT cannot apply to logic when they directly do that in the papers because mathematics and logic are closely tied. The fact you are trying to divorce the two is what I am aiming at. No where did I say GIT was not mathematical, but that doesn’t mean it cannot be used for logical concepts as well, since they directly refer to them as laws of logic in the papers I gave you. I really do not understand how you can think something regarding the nature of mathematics does not apply to the realm of logic. As the first paper says, “The natural laws must be mathematical because, by definition, a natural law must be expressible by a finite string of symbols obeying the laws of logic.”
Mathematics is a form of logic… You even say, “Many truths in mathematics can be demonstrated via formal proofs.” Exactly,, because mathematics is a form of logic.
Then you are so bold as to say, “The issue is that there is always at least one truth (likely infinite, in actuality) which cannot be proven. Namely, the Godel sentence, as per Godel, "This sentence is unprovable" when converted using Godel numbering.”- Okay, I don’t know what your problem is but this was exactly my point in the video when I said, “Godel’s theorems show we cannot fully prove something is true, just because it seems like it is or is consistent. All Godel did was show we are limited in having total proof of something.”So now you are attacking the video by making the video’s point. You are actually agreeing with me. Nothing I said was meant to go against this obvious claim. Again, did you pay attention to the video, or hear what you want to hear, or just take the word of a blog which misrepresented the video greatly?
Well in order to proof laws of logics false, you have to use another method than logic. Therefore whole argument melts down as IP concluded in the end.
M.H Indeed so, and this is why anyone who debate against logic, ultimate truth or even morality does not have a leg to stand on in their argument. Its easy to prove, but the argument against logic, truth and morality is not a honest one, it is more about power and will since truth and logic is not a priority. So it disguises the fact that anyone who argues against logic is essentially not attempting to be honest and so would rarely admit defeat to their argument even if proven wrong. For it is a battle of wills, not a argument about truth or evidence.
This is why it is not so tough to win or prove this argument, but it is still not likely to change much with atheists who go against it.
The truth would not really be so complicated if people were honest and not in objection to it.
But the problem is that there is too many people who care more about their pride, power and personal gain than they do about truth, love or a collective good. And to those logic means as little as dictionary definition for they will refuse to comply even if the majority agree on rules or definition.
An example of this would be with the many atheists who argue that everyone who is not a theist is a atheist. But this argument is false because the definition of belief is to be confident in something, and many atheists do not account for that belief is NOT binary like truth and that confidence can be in degrees unlike the logical truth-false arguments. So it is possible NOT to be confident about there being a God, but at the same time NOT be confident about there NOT being a God. In which case you should actually NOT be a theist or atheist.
This is logic, but good luck convincing any atheist of this despite that you can prove this with math as well ;)
Therefore many atheists will falsely argue that children are born atheists and that is nonsense.
For children have not been introduced to either theist or atheist argument and therefore can not be either until the have a reason to be convinced one way or the other. But most atheists just can't or rather won't accept this obvious logic.
Stephen Fletcher true
Well IP didn't conclude it, at least not originally and I doubt formally.
The criticism of extreme scepticism levied against logic, is it self just another logical exercise that's been around since the sixties, with precursors to the question going all of the way back to greek stoicism.
Stephen Fletcher nobody is born an atheist because babies lack the cognitive abilities to make any kind of decision about a god.
+Mike TheMonk Exactly! There is too many today who don't seem to understand what belief is and so get theism and atheism wrong for this reason. Most don't understand what truth, faith, morals, love, consciousness and many other words really is either, and this is part of the reason most arguments don't go very far. For it's often blind debating against blind.
Lool it was done and dusted when he said "You can't undermine the laws of logic themselves if you use the laws of logic"
I'm not sure if that is the case. You can use something to disprove itself. Say we have a computer program called "X" that is supposed to tell if a program is functioning properly. X accepts a computer program as input and outputs weather that program is functioning properly or not. If we give X itself as input and X says that X is not working, we have successfully used X to undermine X. In other words, this result would prove: "if X is functioning properly, X is not functioning properly". Likewise, any contradiction derived from the laws of logic would prove: "if the laws of logic are true, the laws of logic are not true".
@@jordannewberry9561 You just used the laws of logic or at least tried to use them.
@@Epicsandmore24 Yes, my use of logic was deliberate. Is anything I said not true? I can provide my argument syllogistically if you prefer.
@@jordannewberry9561
You assume that (p⇒¬p)⇒¬p is a valid argument. But if the law of noncontradiction is false then if a law of logic is self-contradictory then it doesn’t follow that it is not true.
It could still be argued that it still works against the law of noncontradiction since the argument (p⇒¬p)⇒¬p gets its validity from it. But it doesn’t work anymore against the other laws of logic.
But let’s allow true contradictions. This means that (p^¬p) and ¬(p^¬p) could both be true and false. So it is possible that the law of noncontradiction ¬(p^¬p) is both always true and false. There is nothing anymore that hold us back from trivialism which would mean that the laws of logic are both, universal laws of nature and man made fictions.
I don’t even know what “doubting the laws of logic” is supposed to mean. The laws of logic are just things we assume outright by default as a matter of axiomatic definition. They’re just ways we determine if the words we use to describe things are well-behaved and abide by our collective understanding of language. So, yes, the laws of logic are “true,” because we’ve analytically defined them as such.
uhlan30 this
What are Premise 4-6? They are contradictions in itself and still how does this lead to the conclusion.
Honestly I wouold just laugh if someone presented me an argument like this.
Atheists in the comments are hurting themselves in their confusion
I think it is the case that in logic, a proposition is something that is true or false. Many sentences are not true or false, and these are not propositions as defined in logic.
So I think the main issue with the argument is that the self referencing "proposition" is simply equivocating on "proposition" - since it is a not a proposition, clearly.
Also about your part about skepticism and particularism. I made a post somewhere about how skepticism is irrational, and it is, the only responses were that skepticism is not the same as saying you should not believe something. Most skeptics tend to equivocate on what they actually mean by skepticism when you point it is irrational to be skeptical.
Essentially, not being 100% certain about things is quite normal, but believing something is more likely one thing than another, requires meeting a burden of proof that would provide the reasons to rationally shift belief into another alternative.
Also it is pretty important to present valid arguments when producing some standard form argument, otherwise viewers have to fix the argument as they are watching and it makes it look like you do not sufficiently understand the material to be presenting a video on it.
I've been aware of this high level scepticism since school, and it only ever comes up as a primer in the exploration of 'what is scepticism?' and 'how do we know we can trust logic.'
So I'm lead to believe that the video uses special fictions in conjunction with known exercises, to indicate a point that no one really thinks about.
nunya bisnass You're forgetting about insane people like me and Albert Camus.
Atheist Monkey oh, we're all crazy if we're arguing a over whether logic is useful by using logic.
Literal pure nonsense, *no existence of sane brains detected*
This is a very silly video, and hopefully you've changed you mind by now, since it is rather old You try to defend the laws of logic by denying one of the founding principle of classical theory, namely the law of the excluded Middle. On top of that, your reasons for denying the excluded middle are terrible. No, the fact that some propositions are matters of opinion does not mean those preposition don't have truth values. The value is simply determined by whatever your opinion is. And no, epistemology has nothing to do with it. The point of the liar's sentence is not to say we do not know it's truth value. Rather, if successful, the sentence would show that we know a sentence that can't be true or false. And no, the lair's sentence is not based in Godel's thereoms. Godel's thereoms are based in the liar's sentence. You have it backwards. Finally, disproving something by first assuming that thing is a perfectly legitimate form of argumentation. It's called an argument from contradiction. As such if the skeptic first assumes the laws of logic are valid, inorder to show that the laws are contradictory, I see no problem in principle with that.
Didn’t Aristotle have this exact dialogue in his Metaphysics when debating the Sophists? The Sophists asked what if they deny the laws of Logic. Aristotle replied that to deny Logic you must use Logic, therefor contradicting the Sophist argument.
X:=(X→Y) [By Definition]
Y:=God exist [By Definition]
X→(X→Y) [Self-equivalence]
(X→(X→Y))→(X→Y) [Contraction]
(X→Y)→X [Self-equivalence]
(X→Y)^X→Y [Modus Ponens]
Y→God exist [Self-equivalence]
Here, I have proven that God exist by using pure logic. By using the rules of inference (Self-equivalence, contraction and modus ponens) and by using the definitions (X:=(X→Y) and Y:=God exist)
Thanks IP. What I don't understand is why philosophers say there are only 3 fundamental laws of logic. There are so many logical fallacies. Can all fallacies be refuted by employing these 3 laws, or some combination?
It's like when someone says "there's no such thing as truth" or "the truth is subjective" the very next thing out of your mouth should be "is that objectively true"?
I love your videos and your channel is one of the best I have ever seen, but I would like to offer a correction:
The definition of a proposition in logic is a sentence that is either true or false. There is no other option, all propositions are either true or false (or have "truth values"). The proposition "Easter is the best holiday" has a truth value - it is either true or false (since Easter either is the best holiday or Easter is not the best holiday). Even mere opinions have truth values. For example,
"I prefer chocolate ice cream over strawberry ice cream" has a truth value, because I either do prefer chocolate over strawberry or do not. And the opinion "Chocolate ice cream is better than strawberry ice cream" has a truth value too. Of course it depends on how you define "better" and "best" but so long as all of your terms in the sentence have coherent definitions then the proposition has a truth value. (1:20 - 1:45).
Therefore I don't think we can throw out premise 2. But rather I believe we should attack premise 3, because it states that there is at least one proposition that is neither true nor false. But this contradicts premise 1, which assumes that the laws of logic are true, and one of those laws is the Law of Non-Contradiction:
A always equals A: A = A
A never equals not A: ~(A = ~A)
So premise 3 is incoherent, therefore the conclusion does not follow from the premises.
Thoughts?
Yeah, your terminology is too sloppy. "Equals" is very different than "Identical". 2 strawberries can be "Equal" to 2 peaches, but (clearly) not "Identical". The "law of Identity" states; "A is IDENTICAL (not equal) to A."
The law of non-contradiction states that ~(p and ~p) is a tautology, that means that no matter what truth value you assign to p (true or false in two-valued logic).
It is not formulated with the equality sign "=", and contrary to many youtubers who talk about subjects they haven't studied, the law of non-contradiction ***doesn't*** state that "p is not non-p", if anything, this is double negation elimination/introduction at this point.
Other than that I haven't noticed anything in your message that "screams" to me like that.
@@vortigon2519 wordsalad
*Laws of Reality violated*
Comment invalidated
@@g--br1el985 I don't even understand if you are objecting to something I said or simply joking.
You're not being sufficiently precise. A logical proposition is not a statement that IS either true or false, but rather one that can only be EVALUATED as either true or false.
If the statement either (a) pro tem lacks the values of premises upon which it's based, or (b) strictly cannot be evaluated then in either case it still remains a proposition.
Russell's Teapot is an example of alternative (a). This is a consequence of empirical unfalsifiability.
The simplest example I have for alternative (b) is the proposition that some irrational number such as √2 or π does not have a particular sequence of bits in its binary expansion. This proposition, in general, is formally falsifiable but not formally provable.
At 0:44, so far, I would reject Premise 2 because of Premise 3.
X=-1/x
Taking x on other side
X²=-1
X=sqrt-1
X=i
Sike I have solved it.
Im disturbed by comments of the skeptics
and atheists here
They try to disprove logic with a formal argument?
Poor souls.
CORRECTION; a statement "all propositions.." does indeed include itself, IT IS SELF REFERENTIAL. However, using that notion that it is self-referential, as self-refuting, IS A FALLACY. THE VICIOUS CIRCLE FALLACY>.
All we can really say about the laws of logic is that they are useful and can accurately describe experience and especially future predictions.
It's like four dimensional euclidian space: We know it is possible, but we can never experience it because of our nature, we are simply limited to this 3 dimensional world. The analogy is, if there is something "weirder" , greater than logic, outside of universe, we just can't simply understand it. It's beyond our scope.
> Claims to defend the laws of logic.
> Provides a false definition of logic.
> Ignores the principle of the excluded middle and the principle of bivalence.
> Claims success.
Seems legit.
(Note that I'm not disputing the laws of logic here, merely pointing out the errors in this argument).
That is not a false definition and this was addressed: inspiringphilosophy.wordpress.com/2019/02/12/illogical-propaganda-of-martymer81/
InspiringPhilosophy Tell me then, where was this definition found? Or was it found anywhere outside your own head?
I simply put it into my own words to explain my point. It doesn't contradict any formal definition. Logic is co-extensive to all things that do exist and can exist. You have not shown what I said is incorrect.
@@InspiringPhilosophy Very well IP, I’ll show you what’s wrong with it. According to this video the term logic is defined as a description of two things, those being:
1. Everything that is by (which I assume you mean everything that exists), and
2. Everything that is possible (by which I assume you predominantly mean everything that CAN exist).
In your latest comment you claim that logic is coextensive to all things that do exist and can exist. The definitions of “coextensive” differ somewhat.
Merriam-Webster: having the same spatial or temporal scope or boundaries
Oxford: Extending over the same area, extent, or time.
Collins: of the same limits or extent.
Essentially you’re saying that logic is something that is extends over everything (which should include Yahweh, but let’s not go down that rabbit hole). But let’s assume that logic is coextensive with everything that can and does exist.
The definition of the term “description” can mean:
A spoken or written account of a person, object, or event.
A type or class of people or things.
Something that tells you what something or someone is like.
So congratulations; you’ve managed to define “logic” in such a way that it is a description of everything from microbes and amoebas to the entire universe.
Here are some actual definitions of what logic is:
Reasoning conducted or assessed according to strict principles of validity.
The formal principles of a branch of knowledge
A particular mode of reasoning viewed as valid or faulty
A method of reasoning that involves a series of statements, each of which must be true if the statement before it is true.
The systematic study of the form of valid inference and the most general laws of truth.[
A particular system or codification of the principles of proof and inference.
A science that studies the principles of correct reasoning.
So to boil it down the term “logic” refers to the study of reasoning and the system of principles on which correct inference and reasoning are based. That is not in line with your definition of the word. “The study and systematization of correct reasoning” is definitely not the same as “a description of literally everything that can and does exist”. The definition of logic in this video is far too broad and only encompasses the actual definition of logic in the loosest sense. You define logic not as the study of reasoning, but as something that tells you what reasoning; thoughts; lampposts; cities; galaxies and everything else that you can think of and more.
Just to provide a comparison, this is like saying that “evolution is a description of life”, when it’s actually the study of how living creatures changed over time, just a fair bit worse since that example was on a much smaller scale.
Really the much bigger problem is that you talk about the laws of logic without defining which laws and then ignoring some of them to prove your point, inadvertently agreeing with the “epistemic skeptics” that you claim to defend these laws from.
By the way I’ve read that blog post and it’s pretty unimpressive, to put it mildly.
"you’ve managed to define “logic” in such a way that it is a description of everything from microbes and amoebas to the entire universe. "
Yeah.. and? Logic covers all of existence, just like the laws of physics cover all descriptions within physical reality.
"Reasoning conducted or assessed according to strict principles of validity."
"A particular mode of reasoning viewed as valid or faulty"
- And? This is how logic would be talked about in epistemology. I am referring to how we talk of logic in metaphysics. This is not controversial stuff. I have no clue what you are making a fuss about.
“The study and systematization of correct reasoning” is definitely not the same as “a description of literally everything that can and does exist”
- Again, you are confusing epistemology with metaphysics.
"The definition of logic in this video is far too broad and only encompasses the actual definition of logic in the loosest sense."
- Yeah... I was simply defining it in a broad sense, and in a broad sense of what it means in metaphysics. You are wasting a lot of time for no reason. Nothing you said shows disagreement here.
"Really the much bigger problem is that you talk about the laws of logic without defining which laws"
- Yeah... again, and? That was the point. I was not defending a particular version of logic, but just logic in general from epistemic skeptics. For example, one could argue for non-cognitivism is metaethics without taking a particular non-cognitivist view. You are attacking the video for something it was never intended to be. And why? We don't even disagree.
"By the way I’ve read that blog post and it’s pretty unimpressive,"
- I don't care about your opinion. MM81 lied, and quoted mined, whether you want to admit it or not. He made a piece of propaganda to stroke his own ego.
I think you misunderstand the argument, the argument is not that 'logic is false' its simply that we cannot show it to be absolutely true -- we can only show it is apparently true. Therefore you cannot argue logic is absolutely/objectively/ontologically true.
This disproves arguments like the transcendental argument that states the laws of logic are absolutely true, therefore they need an absolute basis... because we cannot claim the laws of logic are absolute due to Tarski's undefinability theorem (not Godel)
Tarski's undefinability theorem is the proof for truth, Godel is for math.
I address that at the end what I cited Thomas Nagel. Just because we can't prove them true that doesn't mean we should not assume they are not.
I agree we should assume they are true, but not absolutely true only apparently true
Nothing can be shown to be absolutely true. But I don't think that is reason enough to doubt our intuition.
Intuition is definitely something in our heads 'man made construct built on sand' so i dont think the fact we intuitively believe something is relevant to whether or not it is absolutely true... or that we should believe it to be.
Do you think the laws of logic are not objectively true?
The law of logic still stand, even if I don’t have enough into. It’s not the jaws of logic who has a problem in that scenario, it’s like saying that a hard math problem is unsolvable and it’s the math problem that just isn’t logical since u don’t know the answer. The math problem is still correct even though some people can’t solve it.
The only reason we can’t epistemically understand the mathematical usage of i is because i is a fake number. It’s not an actual number but rather a placeholder, a concept may even be a more correct term. It’s like infinity which is a concept and not something that’s countable and real and something that regular should care about. The statement “this sentence is false” is not true and not false, and so it violated the law of excluded middle. i is an imaginary number, and “this sentence is false” is a proposition with an imaginary outcome.
There are propositions that are either true or false, such as I exist, but not every proposition is either true or false.
And using logical reasoning to prove logic false isn’t incorrect to do. It shows that there’s an internal inconsistency to logic. I can start by assuming no even numbers exist, and then start counting. After a while I’ll stumble upon an even number proving my own claim false. I’m using a claim to prove its negation true.
I like how everyone here is screaming about how it is supposedly only atheists that make this argument. At no point was it implied that criticism of logic has anything to do with atheism or theism. In fact, in my personal experience, it is always the theist that goes against the rules of logic claiming that they are "man made constructs". This compulsive need to ascribe everything you don't like to atheism despite there being no evidence to support your accusations points to a deep insecurity about one's own beliefs in my opinion. It feels like theists are just slandering atheists' beliefs to hide the glaring inconsistencies in their own belief systems and their incompatibility with scientific findings and modern secular thinking. Good luck guys!
You go way off track when you confuse the applicability of logic with the properties of things. There is no such applicability. Logic is used to evaluate propositions or statements, which can be _about_ things, of course, but _logic_ only applies to the statement or proposition. _Things_ are _not_ evaluated with, nor subject to, the laws of logic.
That is assuming reality is divorced from our language which is absurd to suggest.
It suggests, as is in fact the case, that reality is not _contingent_ on our language. "Divorced from" is an odd choice of description by which I don't know what you mean.
huh? That doesn't make any sense. Language is a way to describe reality. It doesn't not bult reality... We cannot make reality what it is by inventing words, we can only come up with words to describe things in reality.
What does not make any sense is that you would re-word what I said without altering its meaning and then claim that what we both just said makes no sense. And since you agree that reality is not contingent on our use of language, then you must also agree that is is not subject to the rules of language.
No, because the rules of language must conform to reality. That is just common sense.
If the Law Of Identity is true, Time Travel is impossible because you would be taking atoms from the future to the past where the identical atoms would already exist.
It has nothing to do with time travel.
And even if it did, all electrons are already identicle in their internal properties.
There is nothing which makes it impossible for whole atoms.
The law of identity is strictly a formal property of the equality relation, which exists only as a part of language.
@@vortigon2519 You don't understand the Law Of Identity. Even if 2 things look identical , each one is "unique" and therefore 2 unique objects cannot exist at the same time.
@@lewisner That is true, but remember I was responding to your claim that time travel would violate the law of identity.
I was using your line of reasoning.
If you put two helium atoms in a box it would be the same physical situation as taking one from the future and putting it in a box with it's past self.
Also notice I said that electrons are identical *internally*. It means that they all have the same rest mass, electric charge etc.
At 1:25, why do you ignore the definition of 'proposition' that is specific to logic? That definition is, "A statement that expresses a concept that can be true or false." Since your topic is logic, you should be using the definition that applies to that field specifically, not a more general definition.
Because I don't hold to classical logic and think all propositions are true or false.
@@InspiringPhilosophy Now I'm confused. I thought the point of your video was to defend logic, and now you seem to be rejecting it.
When you say you don't hold to classical logic, do you mean that you deny it is consistent and complete? And by classical logic do you mean the standard first-order logic, or something else?
Not all forms of logic are classical logic. I hold to Kleene's three-valued logical system: melvinfitting.org/bookspapers/pdf/papers/KleeneThree.pdf
I think logic is valuable to a certain extent. Not everything will follow the rules of logic. Sometimes there wont be any sense at all. Logic is situational. Has limited frame work , gives us a bit of an edge in any problem presented. All theory but in the real world is dfferent.
Now that i think about it, technically it could be intuition . Quantum physics, the universe is making up logic constantly its generating. Its the source. With out it, nothing would be logical. zero possibilites, no alternatives...it be a blank...just a flow of nothing
Pseudo-scientific babble
You’re self refuting argument uses the 2nd law of thought which says that A can’t be both A & ~A because that would be a contradiction (hence, self-refuting). That makes perfect sense for that system.
However, if all 3 laws of thought were done away with (including contradictions) and new laws were created & redefined in a new system that will always preserve truths, and in this new system we allowed both A & ~A to happen at the same time and we used the term X for whatever A & ~A is, then your system of logic becomes inferior to this new system so long as it is grounded. The problem here is that there’s so many systems and some can’t make heads or tails about which they’re using. In other words, we assume the leading principles of our reasoning is absolute.
According to Pierce, the reasoner should choose a method which he holds would always lead to the truth or would be generally conducive to the ascertainment of truth, if such a thing is possible.
If you are referring to the argument presented in the beginning I hope you realize I am arguing against it, not promoting it. Also, all this can be solved simply using Kleen's three-valued logic system and simply adding in indefiniteness. That is a much simplier explanation than attempting to do away with the law of non-contradiction which is not necessary by any stretch of the imagination.
InspiringPhilosophy I’m referring to 4:57 “Any attack on the laws of logic is self refuting”
To be clear, I’m not saying we should do away with the law of contradiction. I’m simply pointing out that some seem to neglect that if the laws of thought governs your entire system of reasoning, you’ll reject any other system that violates its principles and call it (in this case) “self refuting” even though the conflicting system is a distinct set of axioms or postulates capable of producing truth. So if we consciously or unconsciously hold one system of logic over another, this sets up blocks when it’s assumed as the sufficient laws of all thought or of all reasoning, which is unnecessary since we have conscious free will and don’t have to restrict ourselves to the principles that spark a particular thought in the first place.
So to say that “using logic to attack logic is self refuting” is biased in favor of the laws of the system that produced that claim because a distinct set of laws can be made to say other logic systems are refutable provided it’s own principles leads to truth or a higher degree of truth. Obviously this would be “self refuting” or contradictory when you’re using a system where its own rules says so.
I say this not to attack the laws of logic because they work remarkably well in certain areas. My last comment was meant to convey that the reasoner should be conscious of their general method in the ascertainment of truth. Ex: If contradictions are not allowed in one system because it doesn’t work and if contradictions are allowed in another system because it does work, the reasoner should apply these methods accordingly. This is where conscious free will & pragmatism comes
Hi IP! I really enjoy your apologetics, your historical scholarship and some of your philosophy. You are doing great things for Christ and hope things get better and better. On that note, I do take issue with the way you presented Godel's Theorem. I think you misrepresented and severely simplified the goal and the conclusion of that very very significant proof. For clarification for everyone:
Godel posited that you could talk about any well-defined logical system using the system itself (or another well-defined system) to prove it. He proved that for any logical statement you could do operations using numbers as a heuristics completely separate from syntax and from the system you are trying to prove as true.
The problem: He proved that any logical system proposed would have either one of two issues necessarily (using that word in the strong sense). Either the system would be incomplete (meaning that you can't prove all possible truth statements using the logic) or would be incoherent (meaning that logic would prove something contradictory). The implication here is not simply that "no one can know everything" which is trivial as you say. The point is that it seems as though no one can effectively claim that one logical system is superior over another. That's hefty stuff! And definitely hefty stuff when dealing with an epistemic skeptic.
So the questions become: Which logical system should we use? How do we know if the system that we chose is either consistent or complete? With missing logical truths how can we ever be sure that any conclusion is correct?
And there's much more to it beyond that. There's a lot to debate and unpack that the skeptic has ground to stand on that you haven't really defended against adequately. Just as long as they are not a total skeptic and accept that some form of logic exists (because as you said to say otherwise is self-defeating).
I also took issue with you example in Mathematics but that's a different issue.
Pax!
Right, but my point is you still cannot prove any logical system is entirely consistent. So absolute truth is beyond our reach. I don't see what you take issue with. I only brought up Gödel to refute the intail argument though.
I guess what I'm trying to get at (which just became clear to me as the problem I'm really trying to point out) is that anyone who is using Godel's theorem as a tool for skepticism is gonna be more sophisticated than the average person who goes "derp derp logic isn't real," or "derp you can't trust logic derp." I think you make efficient work of the simple skeptic who is totalitarian in their skepticism of logic. The sophisticated skeptic (i.e. the one using Godel's theorem as an argument) recognizes that there must be *some* type of logic but is (with good reason) skeptical that that logic can be known. Sorta like what deism is to theism... ish. And so their distrust of logical proofs could be valid with the proper explanations and discourse about what they specifically believe about logic in light of Godel's theorem. Your video doesn't refute the sophisticated skeptic. Which I suppose isn't the point of the video entirely. Especially because you didn't advocate for one logical system or set of logical operators, etc. But it still feels as though you are being a bit too light given the heaviness of the theorems and philosophies (some having very complex and grand in implication) and how they could possibly work in the skeptic's favor. Your refutation of the premises and conclusion of the proof as listed in your video are accurate-- especially pointing out its self-defeating nature-- so you did what you set out to do. Let me know what you think about my sentiments as I may be being too specific for the intended audience tbh.
God bless!
Laws of logic are built in with or soul when God blew his life into us.
The problem is interchanging truth with fact. Truths and facts aren’t interchangeable.
1:20 I don't think this is correct. The dictionary is not giving a technical definition. Here's a better definition, "A proposition is a composite expression (that is, speech) that signifies what is true or false" (from Oesterle, Logic: The Art of Defining and Reasoning, Second Edition, p. 81)
I think the problem with "Easter is the best holiday" is more because the sentence is ambiguous. If it's understood to mean "Easter is so-and-so's favorite holiday" then it can in fact be assigned a truth value (it's true if Easter really is his favorite holiday, and false if it isn't). If this sentence is taken to be an objective fact, then we need to determine just what makes a holiday to be "good" (or "the best"). If such objective criteria exist then we can actually check to see if Easter is the best holiday and we can assign an appropriate truth value. If objective criteria do not exist then the notion of a "best holiday" is incoherent and this expression isn't a proposition at all.
I think the problem is actually premise #3. "This statement is false" is NOT a proposition. A proposition by definition signifies something that is true or false, but "This statement is false" does not signify anything that's either true or false, therefore "This statement is false" is not actually a proposition, therefore premise #3 is false.
3:15 That's interesting. Thanks for sharing :)
Are there any skeptics who claim that we need absolute certainty before we can accept anything as true? How many skeptics are denying the laws of logic altogether? This feels like a straw man, but I'm willing to hear this out.
Look up the ancient greek schools of skepticism.
+InspiringPhilosophy
Ah. Thanks for the response. That's interesting. I'll have to look into that more, but I still think you may have mischaracterized skepticism when you said skeptics require absolute certainty before they will believe something. I think the opposite is true. Skeptics don't believe absolute certainty exists, so they hold beliefs without absolute certainty, but accept that those beliefs could be false. Absolute certainty seems to be important to theists, but I've never quite understood why.
I would consider myself a skeptic, and I try proportion my degree of confidence in each claim with the evidence, never asserting absolute certainty of any of them. I also accept (or assume) that the laws of logic as evidently true (while still accepting the possibility that the laws of logic are a description of how humans necessarily think rather than an infallible description of how all possible universes must work). Am I mis-labeling myself in your opinion, or is this video directed at a different kind of skeptic?
@@BrooklynRagtag babble
@@g--br1el985 Is that an accusation? Not everything you personally don't understand is "babble." I'm just saying properly skeptical belief doesn't require absolute certainty. Does that clarify it?
the statement/argument : 'absolute-certainty will always be beyond our reach' is a contradiction, because by saying that, one is ironically actually proving that absolute-certainty does indeed exist!
True, but it is based on probabilities. It is most probable absolute-certainty will always be beyond our reach.
Came here after watching Alex O'Connor's video about Epistemological nihilism.
Atheist: "Therefore the laws of logic are not true".
Theist: "How do you know that?"
Atheist: I proved it with logic.
Geez...did all you folks read the same bad resources? VICIOUS CIRCLE FALLACY. i even did a video about it. You are failing miserably.
Can i use logic to show logic is illogical? Indeed i can, and it is done all the time. There is nothing 'self-refuting'. This is a breath taking non-sequitur.
If i say "That statement is false." OR "That inference is invalid." OR "That logical system is inconsistent."; i am using logical statements to evaluate other logical statements, inferences (or arguments), and logical systems. There is nothing self-referential or 'self-refuting' about it. Different levels of logical inquiry require different levels of logical evaluation, and assertions. In all of these statements i can say generally "I am using logic to show logic is illogical." With no 'self-refutation', no 'self-contradiction' and no fallacy committed. Get informed.
manager One,
I understand what you're trying to say, but if logic is illogical, then you're using illogical logic to make a judgement that logic is illogical... I hope you can follow what I'm trying to say. It is self-refuting.
If logic does not transcend the human mind, and does not exist beyond the human conception, then it doesn't exist. That would mean all logic all together would be a logical, including the logic you're using to judge other logic by. As a matter of fact, if logic does not transcend us, then your statement is not true which relies on logic to validate itself. It's neither true or false, neither my statement is true or false.
But we know that there are logical absolutes that transcend the human mind, because there are certain non contradictory laws that apply in the physical universe. For example, something cannot both exist and not exist at the same time and in the same sense, regardless of our opinion on logic. That means it's an objective truth that remains consistent beyond our opinions. That would mean we do not invent logic, we assume it.
That is why we say this is illogical, or that is not illogical, appealing to an absolute. If logic comes from the mind, and there are transcendent laws that go beyond the human mind, that would imply a Transcendent mind beyond the universe, meaning God exists.
This could also further imply, that if one says logic only comes from the human mind, it implies there is no Transcendent mind (God) that exists. It could therefore become a claim that God does not exist, which would require evidence...
@@Bi0Dr01d Well, i have 4 videos on the nature of logic, and they show exceptions to the 'absolute laws of logic.' I also show how we use logic to show logic is illogical all the time without fear of self-refutation. . I also explain how you are employing the viscous circle fallacy. Logic is an extracted model of some subset of existence or reality. Logic is a tool, and like all tools, it has design limitations and design flaws. Logic tells us what follows (necessarily or not necessarily) from a given set of premises. If the results are true, this is incidental to logic. You could say: "If A it is a sniggledump, then A is a turtlewink. A is a sniggle dump. Therefore, A is a turtlewink. And logic wouldn't care. If A, then B, A . Therefore, B. Logic doesn't care what A and B are. Logic cares about successful manipulation of the model and nothing else. I am a Christian man and let me be perfectly clear. There is no 'logic of God' any more than there is a 'fork of God' or 'salt of God'.
Simple logic says that causing pain to someone for an eternity of time after giving him to exist a finite imperfect life, cannot be just nor loving nor merciful. Therefore we are reading the Scriptures in a wrong way.
I don't understand your claim concerning "propositions." By logical definition, a proposition is a statement that is either true or false--at least in principle. Statements may be neither true nor false, such as, "Ice cream is the best dessert." All propositions are statements, but not all statements are propositions. Value statements, for example, are not logical propositions at all. But there is a confusion here. Premise two is simply fine. It is Premise three that presents the problem: "The proposition 'This proposition is false' is neither true nor false." There is a proposition referenced here that is simply missing. We don't what this proposition assets. It is not clear that this is a paradox.
For example, if I say, "Plato was a Roman emperor. This proposition is false." No one should have a problem. But the statement offered "The proposition 'This proposition is false' is neither true nor false" is quite acceptable. It is misidentified as a proposition. It is simply a confused statement; moreover, it IS neither true nor false. Why? Because in the misidentified statement, I have no idea what the second occurrence of the word "proposition" refers to, and it must refer to something. Until I know what this proposition asserts, I cannot call the entire statement a proposition and then evaluate it logically. Its truth value remains uncertain until what is hidden is made clear.
Suppose I say, "There is intelligent life in the star system of Alpha Centauri ." Is that statement True or False? I have no idea. We await empirical evidence. It remains neither true nor false until we get it. That creates no paradox. Similarly, until we know what the hidden proposition actually assets in the above example, we cannot even begin a logical analysis. If it this: "The proposition, 'This proposition (Plato was a Roman Emperor) is false,'" then we have no logical problem. If it is this: "The proposition, 'this proposition (Plato was not a Roman Emperor) is true,'" that offers no problem, either. Confusion creates this problem, not a logical paradox.
I agree that Gödel's proof points to the limits of knowledge, not the refutation of logic. I don't see how confusing the definitions of "propositions" and "statements" helps here. Propositions must have a truth value, at least in principle. Statements do not carry that requirement.
I think you're making some false assumptions. Bona fide propositions can be neither true nor false, just ask an Intuitionist about the Law of the Excluded Middle. As they don't believe said law is a tautology, it fails to come out as true in all models in Intuitionistic Logic. Meaning that in said logic, there are propositions which are neither the case nor not the case. So arguing from a definition seems question begging in this case.
Of course we know what the proposition is. And to demonstrate this, one can even use your approach to eliminating the paradox in order to restate it. "This proposition is neither true nor false." If the standard Liar sentece is neither true nor false, so too must this one be neither. But the propositions says, of itself, that it is neither true nor false. Which means it's true. But that means it's both true and neither true nor false. This is known as a Revenge Paradox and attempts to diffuse the paradox the way you have don't work for this exact reason. A demonstrative is a perfectly valid part of language and self-reference is not an incoherent notion. "This sentence is an English sentence" is clearly true, yet self-referential and the proposition is definitely not missing.
Gödel's proof is not a limit on knowledge at all, it's not even a limit on logic. Gödel's Incompleteness Theorems show a limit on provability in formal systems capable of expressing arithmetic truths. I think IP completely misunderstood this, as he mistakenly said it was about "all truths", when it's not about truths of any sort, just provability in mathematics.
Thank you for the video, It´s a great help !
The absolute skeptic is skeptical of everything except his own skepticism.
This topic has a lot to do with the book Godel, Escher, Bach
Hooray for self reference.
Sounds like GK Chesterton.
This is nitpicking because I am not a nihilist but isn't it wrong to say that you have to have an alternative to something in order to show that something is invalid? Yes paradoxes are annoying but they remain paradoxes nonetheless. If the laws of logic disprove the laws of logic than that's simply the case. For example I don't see why one couldn't conclude that we are forced by our nature to use logic even if it isn't valid. Demonstrating the internal inconsistency of something by pointing to our inability to use the opposite doesn't change the internal inconsistency of something. The way I see it as long as logic remains useful it's ultimate status doesn't change how it's been useful so far.
in Premise 3 the proposition alluded to as "This" is not clearly defined. It is more of a trick than anything else. Can't we think of a better example of a proposition that is readily understandable that can be shown to be neither true nor false?
I agree. There is no real benefit in radical skepticism and it is self defeating. I cannot see how you could actually live by this type of philosophy since it has no relation to the real world where I live. I have to use all the tools I have and the community share with me. I have both a heart and mind and seek a balance with these. I have made leaps of faith that some people are nice and trustworthy and some are not; but, this is normally by evidence of past behaviors. I have hoped that the future would be okay. I have loved and cared and put myself out on the limb. These 'soft' skills are big; faith, hope. and charity are BIG. I use them on a daily basis and they are 'particle' ways of getting by.
We can epistemically understand the meaning of i when you make it equal x. All you've done is change the label of the variable, but it is still assigned the same function, and as such, the conclusion i=i is false.
i = -1/i
Multiply both sides by i
i^2 = -1
i = sqrt(-1)
Just like x,
because i has been made equal to x and applies to the same functions.
You don't know it is false because we don't know i.
i is x. It's x we don't know.
In your argument, you conclude that i=i, but i also equals x, and x = sqrt(-1), as shown on the same slide. As such, i must suffer the same paradox x suffers.
There's part of your argument missing how you derive that changing the function to refer to i therefore results in i=i instead of i = sqrt(-1)
What is it that happened here?
Are we to take this to mean sqrt (-1) = 1/(sqrt(-1))?
In which case, we know i. is is a second truth value.
So, for the proposition, are you proposing it is always i, or it is -1,1, or i?
Which takes you outside classical logic and fails to defend the axiom of the excluded middle.
What? Where did I say I was defending the law of excluded middle? Where did I say I was specifically defending classical logic?
Ahhhh. I see. Well, that ambiguity is kind of important. It makes more sense if you weren't, of course. I acknowledge my error.
I still can't replicate how you got i=i though. What's missing?
To be fair, the argument I presented, in the beginning, was ambiguous and that is what I was trying to address. Several people presented it to me at different times to show me logic cannot be trusted or can have an objective bearing on reality so I did a video on it. So that was all I was trying to do.
i is the square root of -1. So do -1/ the square root of -1.
-1/i = i
Its self refuting.
Godel's Completeness and incompleteness theorems prove two things about the nature of logic. One, any sufficiently large logical system (certainly a logical system that asserts 'logical absolutes' qualifies), will yield an explicit contradiction as a true statement (which is the definition of logical inconsistency). And of course, once you allow one contradiction to be true, all other contradictions are also concluded to be true. The other side of Godel, is that for a logical system to be complete, and consistent, IT MUST BE LIMITED AND FINITE. This video ignores these proofs, and has no answers for them.
I was going in-depth into that.
@@InspiringPhilosophy This is how i account for logic: Logic is not laws imposed upon existence or reality. Logic and mathematics are extracted models FROM some subset of existence or reality. When we discovery more about the world around us, we change the model. That is why there are many different logical systems, and why they are in contradiction with each other. This is to say, what is a contradiction in one logical system, is not a contradiction in another logical system (the same goes for identity). I will await your critique:
Good video IP! It´s refressing that you have started to do philosophy videos again.
More coming next month
InspiringPhilosophy
I think the videos suffer from a few weaknesses. Here's a couple.
-The issue is the definition of proposition I define differently. I could define them as primary truth bearers.
-I think the issue is simply they could be arguing for another system of logic . One that allows for contradictions.
-Gödel's theorem is directed towards mathematical logic.
My definition of proposition comes from Groothuis who states that a proposition is a truth claim.
Too bad he doesn't understand the topic he is dealing with.
Is this you responding to some of Carneades.org points? I think he's a brilliant thinker, a good friend and one of the best philosophy channels on YT, but this is where I seriously disagree with him on since he is a Pyrrhonian sceptic and thus doubts the laws of logic. I find it pretty much impossible to doubt the laws of logic while using them. Also, it's hard to doubt that my mind exists haha since of course as Descartes made the point; who's doing the doubting?
I am not sure if he presented it first. In the past, I received this argument through comments, so I copied and saved it for a later response video.
InspiringPhilosophy I think he did on YT many years ago. It's in the beginning of his video "Arguments for Indirect Skepticism."
Another person I saw a while back use this argument from Carneades.org was someone called "Christian Existentialist."
I actually used the point that premise two is false and it's right that there are some propositions which are neither true or false.
InspiringPhilosophy Also, in my spare time, I'm making a video series called: "The Materialist Delusion."
I will send you it when it's uploaded.
Ellis Farrow Oh... going to put it on your channel?
please do.
I have a fun problem for you that this video made me think of. solve this paradox using logic.
1 ÷ 3= .333... (one third)
but
.333 × 3 = .999....
so 3/3rds is less than 1?
curtis sanders Might be an infinite set of 3's seeing how 3 is not rounded up.
0.333×3.01=1.00233 - somethings being list somewhere. o.0
.999999.... = 1
I believe you can write 1/3 in another base just fine.
0.9999999... is the same thing as 1. So there is no paradox in the first place
There is so much wrong with this video that should be obvious to anyone who's studied logic or mathematics at the college level.
Where are people getting the idea that Atheists don't except logic?
I see it over and over yet I see no reason as to so many making this argument.
Explain this to me.
By the way I'm both a proponent of Logic and an Atheist as are most Atheists I know.
Heck it was Logic that played a big part it me being Atheist.
They get it from us. They see us criticize their logic and they want us to look like hypocrites so they say we have bad logic. When they can't discriminate against gays they say we are persecuting them. When we point out the racism of religious leaders of the past (and of the present) they say evolutionists support social darwinism and eugenics. IMO they are projecting.
This video misses the point entirely. Lets assume there are logical absolutes. Now we appeal to factual information; there are many logical systems; these many different logical systems define contradiction differently. These many different definitions of contradiction contradict each other. In light of these facts, explain how the law of non-contradiction is absolute or universal in light of these facts. The same goes for logical identity.
We are not talking about different logical systems, simply that logic, in general, has to be objective. Working systems that contradict are different specific theories of logic, but they are built on premise that there is underlying objective truth and we are trying to find the best system to understand that.
You said this: " but they are built on premise that there is underlying objective truth and we are trying to find the best system to understand that." Objective truth? Let's assume for a moment there is "Objective truth X." out there somewhere. The question arises; do we ever know X AS objective truth? Or is our knowing of X always corrupted by genetics, culture, upbringing, etc etc? I contend even assuming there is X out there, we are never certain we know it AS objective truth X. We can utilize logic in trivial matters with certainty (Either A is a tree, or A is not a tree.) But when we get into more complex matters is where all this discussion disappears into obscurity and uncertainty (Heisenberg). When you throw in Christian theological notions like the Fall, we see the NECESSITY of corruption of our knowing of 'objective truth X.' And to assert that we CAN know X AS objective truth, is a violation of that essential doctrine.
Is it objectively true we are never certain we know it AS objective truth X?
Is it objectively true we only utilize logic in trivial matters with certainty (Either A is a tree, or A is not a tree)?
I don't think Spencer-Brown is correct when the says that the equation x^2 + 1 = 0 is paradoxical and self-referential.
There is nothing paradoxical about an equation that has no solutions. He starts out assuming real numbers, and there is no real solution to the equation. Big deal. That's not a paradox. There are no positive solutions to x + 1 = 0. Again, no paradox, just a lack of solutions.
There is also nothing self-referential about it, just because x appears as a square. Just because a variable appears twice in an equation does not mean it refers to itself. For one thing, to be self-referential, a thing has to refer to itself. I don't know how an equation can refer to an equation, but just having a variable appear twice does not do the job.
What this mean that the skeptic is the one with a burden of proof to prove logic is not true, rather than someone else proving it is true?
I don't have to 'prove logic is not true.' All i have to do is show that logical values vary (definitions of 'contradiction' vary and definitions 'identity' also vary). And the notion of some 'logical laws' being absolute and always true, is destroyed. And so is your entire apologetic enterprise.
manager One
so you're talking about semantics, because of varying definitions, is this correct?
For example, without logic, one could say that there can be a such thing as a square circle.
On the other hand, without logic, No One would be able to Define what a circle is and what a square is, therefore this contradiction would not apply?
Concerning the post you made in the other thread,
You Said "Logic is a tool, and like all tools, it has design limitations and design flaws."
Okay, so you're saying logic is "designed", created by the human mind, and used as a tool, as I stated above. Which means, you're making a claim that logic does not transcend the human mind, implying no Transcendent mind Beyond the human mind that uses logic. So on one hand, your saying you're a Christian, on the other hand, you're implying God doesn't exist, or God is not logical. As you said, there is no "logic of God". Do you absolutely know God does not use logic, or are you assuming that? Do you have evidence for your claim concerning what goes on in the mind of God?
If logic has limitations and flaws, how can it be trusted? Aren't you using potentially flawed logic to determine whether logic is flawed or not? How would you know that the logic you are using now to make a judgement of other logic, isn't flawed, without simply assuming it? Isn't that self-refuting? What will you reply with? Logic?
How can you state whether logic is flawed or not without assuming an absolute? If logic is a tool, and you're using logic to judge the tool itself, then you are appealing to something beyond the tool, otherwise that is a "vicious circle".
@@Bi0Dr01d First of all, 'square circle' assumes a bivalent logic. That is 2 value, true and false. There are many logical systems that are 'many-valued'. which means, there are many value gradations between 'true and 'false' Second of all, we could indeed define 'circle' by simply observing the world around us, and extracting a model based upon those observations, and assert a definition of 'circle' that comports to that observation and model. Indeed, that is how logic and mathematics works, we observe something about the world around us, extract a model representing that observations, and develop systems to manipulate the model.
manager One so you are just talking about definitions and semantics...
Can you respond to my other message?
Also, logic is from reasoning and pertaining to the science of distinction between what is true and what is false. There are many things which happen outside of logic. One’s own logic is the beholders own understanding through what they may have experienced, sure at some point there will be a logical explanation to something that before was beyond comprehension. Many things happen beyond our own logic that we can’t explain or reason, this is the case where things can be true and false, such as the never ending staircase. Still haven’t drawn that yet. Hmmm... I’ll have to try that next. I know this is and old video but figured I’d share my thoughts. Other than that it is a good video and brings to question many things such as logic itself and what all we really don’t know. Hopefully you’ve been keeping up with your videos on here. Philosophy is a very interesting subject. I think, therefore I am.
Hi! @InspiringPhilosophy could you make a video on proving a priori knowledge (non-empirical evidence)? I can't fully articulate the arguments I find online and it is a well-needed groundwork on convincing reductionists. Thank you and God bless!
I don't think you can prove such things, as I explain in this video. We argue it is intuitive and not proven false.
Attacking logic?.... illogical
I really wanted to like this channel, but you guys do not simply provide the information, and let people come to their own conclusions. You actively advocate for certain positions, and then act like it's the only reasonable position, and therefore, anyone who disagrees with your position is inherently wrong.
You did this same thing with "Moral Realism", but in actuality there are many valid options, with each having intelligent adherents. You do not "steel man" your opponent's arguments, you simply advocate for yours, and pretend that everyone else is wrong.
"He who knows only his side of the case knows little of that." - John Stuart Mill
I present arguments of what I think is the most coherent worldview. I never said I was not expressing my views.
I have a problem with this, your premise (the laws of logic are a human construct) doesnt follow your conclusion (that logic doesn't exist). Just because the human construct (logic) which codifieds, defines, and aids us in understanding the predictable ways in which our universe works (reality) was made by humans, does not mean that the human construct is an invalid tool to use. Evidence supports logic as being a valid tool when used within the set of reality that it was organized to describe. That does not mean reality conforms logic, it means logic conforms reality.
It's similar to mathematics, they are useful tools that describe the universe, but both are created by man and not objective.
Why could it be trusted universally if it was constructed? The English language is a human construct but it cannot be used to predict the motion of planets, yet logic and mathematics can.
InspiringPhilosophy ..Good point. If I find a counter to what you're saying, I will present it. Thank you.
@InspiringPhilosophy
Would you make a video about Presuppositional Apologetics?
I think this video is somehow related to it.
And also, what are your thoughts about this approach in apologetics?
Thanks for your videos. They are really helpful :)
I reject it, as I do not think it works.
HTRA 21 I prefer the classical/evidentialist approach. It'd be nice to see one day an IP vid on this in-house debate among Christians: apologetics methodology.
Presuppositional Apologetics is in fact, the weakest form of Christian Apologetics. Van Til was a moron. Bahnsen was very well informed about recent developments in logical inquiry and language analysis. But sadly, Bahsen's loyalty to van Til caused him to abandon the tools he learned in that training, and he dwindled into dishonesty and intellectual suicide (in my opinion).
@@TCSpartan7 All rational apologetics (logical or evidential) collapse and fail.
@@manager0175 Personaly, I think that the mere existence of pressupositional apologetics and similar things says something sad about humanity.
It means that humans are so tied to certain ideas that they would never let them go.
Using the laws of logic in a form of a syllogism to disprove logic.
yeah we escape logic every night in our dreams. Art wouldn't exist if it couldn't escape the bounds of logic
IP - WHAT HAPPENED TO YOUR "quantum physics debunks materialism" video!?
Still here: ruclips.net/video/4C5pq7W5yRM/видео.html
Its been blocked. I receive this message:
This video contains content from Discovery Communications, who has blocked it in your country on copyright grounds."
:(
It depends on what country you are in. In the US it is still fine because it is non-profit work.
His last point is actually pretty good 👍🏻
Excellent video and argument. You are very right, and I have tried to defend this argument many times against skeptics with variable success. But now there is a video to refer to too. I appreciate that :)
Wait whY aren't we able to be 100% certain??
When proposition is now superposition
And now he argues he rejects classical logic 😂
At 3:20, how do you say that "This statement is false" is equivalent to "x = -1/x"? I see no way to map one to the other.
Why? I explain it oscillates in an analogous way and we are just plugging in variables.
@@InspiringPhilosophy I don't see anything analogous about them. If you plug in the wrong number into any equation with a variable, you'll get a contradiction; substitute 5 for x in x = 4, for instance. So what?
After I made the above post, I dug out my copy of Spencer-Brown, which I admit I haven't looked at in decades, and don't remember anything about it. After a brief look, it seems he introduces this equation to motivate the introduction of "imaginary" values to logic. I could be wrong, though.
Could someone please provide me with some clarification: Premise 2 sounds like it's supposed to represent "The law of Excluded Middle", am I wrong in saying that or does that mean the law of Excluded Middle is false?
Also, I agree that you would need to assume a separate set of axioms in order to try and refute the laws of logic, otherwise you are using logic to refute logic. However, I would not call those separate axioms "logic" as that seems like an equivocation fallacy. It sounds like you want to say, "You need to assume new axioms to refute the current human understanding of logic" as opposed to what you actually said, "You need logic to refute logic".
Also, I am 99.9999% sure that the laws of logic are true, but that doesn't mean I'm 100% sure because I believe that no amount of evidence can objectively prove anything, it either refutes a statement, or it supports it. I have not seen anything refuting the laws of logic yet so I still believe they are true, but I won't go as far as to say they are objectively true, I don't think anything can be proven to be objectively true unless I am misinterpreting the word objectively.
Other than those 3 things, it's a nice video. I would not be able to find those 3 mistakes without logic.
Well, there are different theories of logic. Most just simply want to update the classical laws of logic. So in that sense, you are correct.
Skye Chen
*Could someone please provide me with some clarification: Premise 2 sounds like it's supposed to represent "The law of Excluded Middle", am I wrong in saying that or does that mean the law of Excluded Middle is false?*
Premise two is not the law of excluded middle, it is the principle of bivalence. Excluded middle means that for every proposition (p), either (p) is true or it's negation (-p) is true. It's very important to get the verbiage correct which is why logicians use so many precise terms.
en.wikipedia.org/wiki/Principle_of_bivalence
en.wikipedia.org/wiki/Law_of_excluded_middle
@skyechen2673 if you are not able to to definitely that a state is true or false it means that it is not bounded properly. If we arrived at a point where two things are true then what we are using to define it is in adequate.
Ie an ac light bulb seems to be on but if we reduce the time span enough we will get to a point where it's either on or off.
I would say anytime you find something that is disobeying excluded middle it means we don't understand enough about it.
Can you cite one place this argument was actually used? I'm a 40 year old atheist and I've literally never heard an atheist argue this.
Well, never once did I say atheists use this argument. Did you actually watch the video or just the lying response video?
As for where the argument came from, it came from an epistemic skeptic, who the video was really addressing: ruclips.net/video/pBlDGTZUOek/видео.html
Of course, we can't expect Martymer81 to do actual research, can we?
inspiringphilosophy.wordpress.com/2019/02/12/illogical-propaganda-of-martymer81/
This channel is a chrsitian defending foundation. The question is why is this video relevant to theism?
Yeah but what counts as logic?
I've never heard anyone say that you can have propositions that are neither true or false. Even the example you gave doesn't seem to prove your point. "Easter is the best holiday" is a true statement with respect to the person who said it. For example, if I said "Easter is the best holiday" and you said "Easter is the best holiday", those would actually be two different propositions--even though they're the same sentence. Because when I say it, it has the meaning "Easter is Chris's favorite holiday", but when you say it, it has the meaning Easter is your favorite holiday.
chrisctlr it's relative at that point
It's subjective in one sense (i.e. I like Easter, because of personal reasons), but it would still be a true proposition. A proposition is not merely a sentence, but the meaning behind that sentence. So if I said "Easter is the best holiday", it would have the meaning of "Chris thinks Easter is the best holiday", which would be objectively true. Things can't be "true for me, but not true for you." If it's "true for me" that Easter is the best holiday, then it's true for you that I think Easter is the best holiday.
Such a flawed, flawed argument.
A three year old could tear it apart.
Can someone please explain to me the law of identity? Even after researching for a while I still don't understand what it is.
The law of identity states “B is B” for example I am me and you are you. Kyle is Kyle and Bob is Bob.
Bob is not Kyle
Kyle is not Bob
I am an atheist who is currently trying to figure out how to approach Van Til style presuppositional apologetics and it's quite odd I seem to be arm in arm with IP in this debate.
Van til was a moron, greg bahnsen is a better representative of presup...but he blows too
Any response to Alex Malpass from you?
The laws of logic are derived from the billions of neurons communicating with each other in our brain to form a thought. Each neuron in our brain is therefore independent from each other and have it's own unique information. The brain is an organ that learns and adapts for itself. The biggest mistery here is, where does this intelligence of each neuron come from? Could our soul be a combination of many other souls? and could our souls also combine to form a soul of a higher being? Whatever the answer might be, intelligence cannot exist without knowledge, and for knowledge to exist, there must be a unified mind of a higher being ( God )
The proposition "this proposition is false" can neither be true or false unless the word "proposition" actually refers to something. "AH! But it refers to the proposition that this proposition is false"--a response like that misses the problem that you cannot assess "this proposition" until it's defined. Which proposition? The one that it's false? What does that even mean?
To say "this proposition is false" like saying saying "bladndkcsjxn is false"--the word is undefined without a referrent to something other than itself, else it's meaningless tautology.
It's an issue of self reference. Self reference sets up paradox. The "Liar's paradox" is just a formal proof that self-reference is indeterminable. Which is why it is that minded beings capable of self reflection (i.e. humans) are most certainly not deterministic in any classic sense. Read "Godel, Escher, Bach: An eternal golden braid" by Hofstadter. It's tough to slog through but extremely rewarding.
This is good man...
The argument is using the laws of logic to refute laws of logic...
Why would anyone deny Logic? Human Beings were created to understand Logic and Math, Even though there Brains are limited but still have knowledge.
Pastor Bell
Are you familiar with The Cartesian Demon concept? How do you know you're not being deceived by an all powerful evil God, therefore making knowledge impossible?
Robbie Desiato the answer is that knowledge would still be possible in such a scenario. Just much harder to obtain reliably
It is not a matter of 'denying logic'. it is a matter of showing the limits of logic. Logic is a tool, and like all tools, it has design limits and design flaws.
@1:23 - You read the colloquial definition of "Proposition". The specific _logical_ definition is depicted below that on the same screen shot (1.1). Thus, "Easter is the best Holiday" is not a valid proposition, logically. The original (P2) is purely definitional.
@1:52 - "Let's consider also this statement..." ... "This statement is either true or false. However, we cannot be sure if it is true due to lack of information."
Sure, we may not have the means to determine whether a given proposition is true or false, but that doesn't stop it from _actually_ being true or false.
@2:52 - "Many things will always just be 99% probably true, but absolute certainty will always be beyond our reach. So, because of that, we can also deny premise 3..."
No - you're conflating logical truth with epistemology. Again, our certainty of the truth (or falsehood) of a given proposition is utterly irrelevant as to whether that proposition is _actually_ true (or false). The mathematical example you follow up with is exclusive to the non-dichotomous nature of the system of mathematics, and can't be analogously applied to the dichotomous nature of truth propositions. If you disagree, please _directly_ address the proposition offered in (P3).
I have some slight issues with some aspects of the rest of the video, but they're mostly inconsequential to the overall matter.
BTW - I'm not trying to affirm the argument to which you're offering this rebuttal; I'm just identifying some immediate problems that I see.
First, you are in agreement certain propositions are not true or false. There is a wide variety of meanings, so that really doesn't address my point. I said that it can be defined as a statement or assertion that expresses a judgement or opinion, that it was only this necessarily.
Epistemology and understanding truth are related, since how we know things is required before we know if we can know truth. Plus, you says, "our certainty of the truth (or falsehood) of a given proposition is utterly irrelevant as to whether that proposition is actually true (or false). Well I never said the opposite. I merely pointed out we cannot know the answer but mathematically it is solvable. Mathematics is not completely separate from logic so I don't see your point.
_"First, you are in agreement certain propositions are not true or false. There is a wide variety of meanings, so that really doesn't address my point. I said that it can be defined as a statement or assertion that expresses a judgement or opinion, that it was only this necessarily."_
Well, no, not really. Given the formal, _logical_ definition of a proposition (which is apt since that's what's being discussed), the property of expressing a concept that can be true of false is precisely what qualifies a statement as a "proposition". It's equivocation to use informal definitions in situations in which a formal definition is apt. It'd be like arguing against a scientific theory using the colloquial use of "theory" in order to call it "just a guess".
_"Epistemology and understanding truth are related, since how we know things is required before we know if we can know truth. Plus, you says, "our certainty of the truth (or falsehood) of a given proposition is utterly irrelevant as to whether that proposition is actually true (or false). Well I never said the opposite. I merely pointed out we cannot know the answer but mathematically it is solvable. Mathematics is not completely separate from logic so I don't see your point."_
Yes, they're related, but my point is that the _objective_ truth of a given proposition is either true or false regardless of the awareness of minds to assign such labels. For example, I issue the proposition, "aliens exist" - even if no one knows, the proposition is still either true or false in actuality. As such, the epistemic barrier has absolutely no bearing on the objective truth of any proposition.
Regarding the mathematical example - no, you didn't assert the opposite. I wasn't saying that. And yes, mathematics and logic are not completely separate, but they're not equivalent either. Just because something _very similar_ to the original problem is demonstrably solvable in a _very similar_ but different system doesn't mean that the original problem is solvable in the original system.
And i'm speaking generally, as not all premises or propositions need to be known as true or false. Some are beyond our epistemic grasp. Also, you are assuming the formal definition must apply. Not always, unless we are in formal logic. With informal logic, that doesn't always apply.
I would disagree, since I argue all reduces to mathematics in some way. All problems can be represented with variables and solved in similar ways.
_And i'm speaking generally, as not all premises or propositions need to be known as true or false. Some are beyond our epistemic grasp. Also, you are assuming the formal definition must apply. Not always, unless we are in formal logic. With informal logic, that doesn't always apply. "_
Epistemology is completely irrelevant to whether a given proposition *is capable of being considered true or false* in regard to it's form, to which the argument pertains. This exclusively addresses whether the statement's form is *capable* of being considered true or false, NOT whether it's actually *known* to be true or false. I'm now beginning to repeat myself, so I fear we may be talking past each other...
The argument presented quite explicitly and directly addresses logic. That plus the Principle of Charity are my reasons why I think the formal definition is not only warranted, but demanded. Do you have the source available from which that argument originated? If so, perhaps they elaborated their intentions more.
_"I would disagree, since I argue all reduces to mathematics in some way. All problems can be represented with variables and solved in similar ways."_
I shall express my objection more explicitly, then. You represent the paradoxical proposition in mathematical form by simulating the dichotomy (1 or -1) and then solve the dilemma by breaking that dichotomy. In mathematics, that's quite acceptable since it's not dichotomous. *However,* the logical truth of propositions _is_ dichotomous (true or false) and there exists no third option in the logical system to solve it like you did in the mathematical system. This is why I asked that you _directly_ address and solve the paradoxical statement within the system of logic since that, and _not_ the system of mathematics, is what's being addressed.
I never said epistemology was relevant to whether a given proposition is capable of being considered true or false. i said our epistemic limits mean we cannot know whether it is true or false. So I am repeating my self as well.
Again, this in informal logic propositions are not always true or false but can be expressions or opinions. If we were in a system of formal logic, like modal logic you would have a point.
Again, the logical truth of propositions is not dichotomous (true or false). We can simply appeal to the same reasoning behind i. You can't just create a false dichotomy.
Could you stop butchering math please ? Godel's theorem doesn't say that AT ALL. Godel says "under some weak conditions, there EXISTS a sentence which cannot be PROVEN true or false".
Note the word EXISTS. Note the word PROVEN.
Did you even watch the video? My point was exactly that, some sentences cannot be proven true or false. I guess you just got your info from propaganda responses and didn't pay attention.
@@InspiringPhilosophy I did. 2:42
Read your sentence. If you don't understand the difference between
1) Some sentence cannot be PROVEN true or false.
2) We cannot prove something is true.
Later "but absolute certainty is beyond our reach". I am absolutely sure that in a consistent set of axioms, for all x x=x.
@@InspiringPhilosophy also, stop throwing strawmen. Dude, this theorem is my favourite math theorem, I was triggered by hearing another propagandist misusing it. The theorem is limited to math and just says "if you can do basic arithmetics and limit your set of axioms to allow a procedural verification, there will always be a setence neither true or false in your set of axioms".
But something can be true and impossible to prove (in the axioms of arithmetics), like the Goodstein sequences. True provable.
Again, did you even watch the video? Nowhere did I claim otherwise.
That is just wrong on so many levels and a quick google search would have revealed that: S. Choi outlines: “one of the Priest’s main motivations for Dialetheism is Gödel’s theorem. He applies Gödel sentence to a naive notion of proof in natural language and attempts to make an argument for Dialetheism.”
philpapers.org/archive/CHOCGI.pdf
Stephen Barr has an entire appendix on the philosophical implications of Gödel’s theorem in his book, "Modren physics and Ancient Faith."
The fact that you were triggered only shows how little you know yet think you know a lot.
@@InspiringPhilosophy so you are applying a MATHEMATICAL result outside of math and expect to be taken seriously ?
Godel's theorem needs
1) A first order "meta" logic (modus ponens, excluded middle, etc).
2) A restriction on your set of axioms (take the axioms "true arithmetics" and everything true is provable by definition)
3) Be able to do arithmetics.
If you don't meet the conditions, you cannot use the result. DUH. Dude, don't talk about math if you don't have a clue about math. And stop lying "I didn't say ortherwise", I quoted you.
I will note waste more time, spam another clueless answer, I won't come back. This is basically "oh he caught me lying, let's divert to something else".
Who else came after IP debated Matt Dillahunty a few days ago?
Dillahunty is also ignorant of logic and the nature of logic.
Is this video in defence of the statement "Classical logic is the right logic" or a critique to the statement "there is no right logic"?
I'm asking, because I simply have never seen anyone claiming that there's no right logic.
No. No where do I bring up the different views of logic. This is a rebuttal to epistemic skeptics (people who say logic cannot be trusted), not a defense of classical logic against other forms.
But I see two different possible form here. Either epistemic skeptics are saying "Classical logic cannot be trusted" or they are saying "Any form of logic cannot be trusted". I have seen some arguing for the first case, but I have never seen anyone arguing for the second.
Have you read Thomas Nagel's book "The Last word"? And I have dealt with some who have commented on my videos claiming we cannot trust logic, and they do not have beliefs, etc. Again, I am not defending classical logic and no where do I ever make that claim. It would be straw man to accuse me of that.
I'm not saying that you do, I'm trying to understand your point, because you do not clearly define your terms in the video. Also, I'm trying to make a review of Alex Malpass critique of your video:
useofreason.wordpress.com/2017/11/08/inspiring-philosophy-and-the-laws-of-logic/
Yeah, that guy accused me of things I never said. He read way too much into my video. For example, he writes, "He doesn’t seem to realise that if “Easter is the best holiday” is neither true nor false, then he is effectively conceding exactly the thing that the argument was supposed to be showing, i.e. that there are exceptions to classical logic."
Why on earth does he think I ever claimed there are no exceptions to classical logic? That was never my claim or the point of the video, which is why I never it brought up or even mentioned classical logic versus other forms...
It really surprises me that anyone tries to argue against logic. You can't do that without using logic. This the argument refutes itself as you said. But however my experience in college algebra points out to me that the number "i" is an imaginary number. What would you say to a skeptic who objects with that?
An imaginary number is nothing but a complex number, it isn't "imaginary" in any way and very real. That's why stuff like:
e^(ix) = cos(x) + isin(x) works just fine.
Very good, yet another example of the vicious circle fallacy. It is not self-refuting. Get informed.
manager One incorrect. Its equivocation. Nice try though
Too bad you aren't familiar with the vicious circle fallacy. You just committed it. www.viciouscircleprinciple.com has the section from Princpia Mathmatica (vol 1) that explains it. It is not self-refuting to use logic against itself. I also have a video showing how the fallacy works, and why it fails.
It is convenient that they introduce imaginary numbers to solve Russell's Paradox..since their solution is also imaginary :-)