What is the Postmodern Philosophy of Truth? (Tarski and Lyotard)
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- Опубликовано: 25 июл 2024
- An explanation of Jean-François Lyotard's theories of postmodern truth, and how they interact with things like Godel's incompleteness theorems and Tarski's proof of the indefinability of Truth.
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Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy, The Oxford Companion to Philosophy, The Routledge Encyclopedia of Philosophy, The Collier-MacMillan Encyclopedia of Philosophy, the Dictionary of Continental Philosophy, and more! (#Postmodernism #Truth)
The point about "softening" the "modernist" position connects to something I've been saying a lot since your start of this series helped me frame where postmodernism fits into my own spectrum of philosophical approaches: the "modernism" that "postmodernism" attacks is not just the literal negation of postmodernism, but rather, an opposite extreme in some ways further from postmodernism than that literal negation, which opposite extreme cannot help but collapse into postmodernism upon sufficient examination; but that does no harm to the actual negation of postmodernism.
I called my own philosophy "commensurablism" before I even realized what postmodernism really was. It has two core principles that I call "universalism" and "criticism", and your first video in this series made me realize that postmodernism is basically just the negation of both of those. However, those two principles of mine also entail another two principles that I call "liberalism" and "phenomenalism", and postmodernism *does* seem to generally agree with those.
The thing that postmodernism calls "modernism" appears to consist of the negation of those latter two principles. Those negations in turn do entail my first two principles, but that's not a bi-entailment: anti-phenomenalism does entail universalism, but universalism doesn't have to be anti-phenomenal; and anti-liberalism does entail criticism, but criticism doesn't have to be anti-liberal.
And since universalism entails liberalism and criticism entails phenomenalism, if you start with that position postmodernists call "modernism", you end up contradicting yourself, as its two core principles end up entailing each other's negations. So you would reasonably end up agreeing with the postmodernist on the negation of those two principles, settling on what I called liberalism and phenomenalism. But that leaves the question of universalism and criticism completely unanswered, and the collapse of anti-liberal anti-phenomenal "modernism" gives no grounds on which to reject those -- the postmodernist just throws that most precious baby out with the dirty bathwater of their own accord, without any rational need to do so.
My point here is that the "softened" "modernism" is actual, sensible modernism, and the "modernism" that "postmodernism" objects to is a straw man. Saying that there are universal truths and we can gradually narrow in on them by weeding out falsehoods -- basically, that we can make progress -- is *not* the same thing as saying there is something transcendent of all experience that we can build an absolutely certain complete picture of from the ground up. But postmodernism objects to the former as though it were the latter, and in doing so attacks a straw man that has no bearing on the former, which is the actual negation of postmodernism.
I am unable to follow your argument completely (something about not being able to see the Pfhorrest for the trees 😒), but I do like your final paragraph, as I’d be perfectly satisfied if postmodernism were attacking a strawman of its own invention.
You state a common misconception of Gödel that connects closely with Tarski's theorem: that every (sufficiently powerful) language contains "unprovable truths". The theorem actually concludes that every such language must either be capable of expressing statements to which it *cannot assign* a truth value (making them unprovable, and the model incomplete), or else it will have to assign some of its statements *both* truth values (making the model inconsistent). Assuming consistency and thus incompleteness, *within the object language* those statements that are not assigned truth-values *are not considered true* . It's only in the meta-language that some of those statements the object language cannot prove can be called "true" -- but then, the meta-language is also capable of *proving* them true.
In short, within a given language, there are no "true but unprovable" statements. You have to mix talk of meta and object languages to make a claim like that: a statement of the object language is true (and provably so) in the meta-language, but unprovable (and so not considered either true or false) in the object language.
Wow, I've heard this misconception like 50 times already. Thanks
I just thought of an analogy with a different philosophical issue, Moore's Paradox.
From the outside, in the third person, we can look at someone and say "they have no way of knowing whether P or not-P, but nevertheless, P is true."
But from the inside, in the first person, we cannot coherently say "I have no way of knowing whether P or not-P, but nevertheless, P is true", because in saying "P is true" we imply that we think we know that P is true.
Likewise, Godel's theorem says that sufficiently powerful languages can be capable of formulating statements that they are then unable to prove either way, and looking at those languages in the third person, talking about them in a meta-language, we can say "look, here's a true statement that this language isn't able to prove", and we can prove (in the meta-language) both that that statement is true, and that the object language is incapable of proving it.
But when talking about a language *in that language itself* we cannot coherently prove "here is a statement that is unprovable but true".
By the meta-language being capable of proving them true, do you mean appealing to intuition? I don't really see what other argument could there be made.
@@werrkowalski2985 No, like, to do a Godel proof, we have to use one language (the meta-language) to talk about another language (the object language), and using the meta-language we can prove that there are expressions that the object language can make, that are true, but that the object language can't prove are true. In order to prove that, we have to be able to prove that said statements are true -- in the meta-language we're using to talk about all of this -- as well as that the object language can formulate such statements but can't prove them. So, in the meta-language, there are provably true statements that some other language is provably unable to prove. But, in that other language itself, we couldn't prove "this statement is true but unprovable", because obviously that would involve proving it true.
So in the meta-language, the given statement is provably true, and the object language is provably unable to prove it. But in the object language, the statement is just unprovable, and so can't be provably called true or false at all. The object language assigns no truth-value to such statements, because it can't prove them. The meta-language assigns a truth value to them, but then it can also prove them.
@@Pfhorrest Right, I'm not a mathematician, but I'm wondering what could be an example of such a statement, in mathematics or in some other language, that would be at the same time shown to be unprovable in the language in question, but would be proven to be true on the meta level, in some other way than appealing to intuition. Let's take for example a fundamental axiom of mathematics, say that the number 2 is after number 1, such an axiom is unprovable in the language of mathematics without assuming the truth of that axiom, but on the meta level when we talk about mathematics it does _seem_ to us that the number 2 is after number 1, and the number 3 is after number 2, and so on ad infinitum. So we would appeal to intuition here. Would there be some other way to know that an axiom like that is true?
your videos are really good! have been watching for so many years and I'm glad to see you're still posting. Keep up the good work!
love the leotard for lyotard haha
It's that thing conservatives of all stripes try to make me very afraid of while using its actual methodology.
Regarding the self refutation claim, I think it commits the straw man fallacy by ascribing the modernist position that there is an objective truth to the post modernist and then refuting their argument.
The claim that "if all metanarratives are not true, then so is this metanarrative" is only problematic if the intention was to state an objective truth. Lyotard and most poststructuralists discard the notion of a singular truth. In one sense, truth may be an intra-narrative phenomenon. Consequently, each metanarrative has its own truths. The truth of Lyotard's metanarrative is that there is no narrative-independent truth, including his own statement that there is no narrative-independent truth as it is only meaningful in the context of his metanarrative or given the rules of his language-game.
I disagree with you, because if it is as you say and his claim about meta-narratives is not supposed to be objectively true, then it is irrelevant. He must at least assume that it is true within the meta-narrative of those to whome he is communicating ascribe. Otherwise he is not saying anything.
What does it mean to say that truths are only true within a meta-narrative, but that very statement not being objectively true? What is the meta-narrative within which he makes the claim. Saying that something is not objectively the case is a statement within the modernist meta-narrative itself. If it is not tell me what meta-narrative this claim is embedded in.
So tell us the rules of the language game., otherwise we cannot even understand the meaning of the claim.
No - even the talk about language games happens within the modernist meta-narrative in my estimation. If he is using private language his statement is meaningles to us.
We wouldn't object to his claims if he wasn't using the very instruments he is rejecting.
I think there are subjective truths and objective truths. Subjective truths seem to be easier to acknowledge, like I have a religious experience that confirms my belief or something like that but objective truths seem to be the harder to work with. Language plays a roll in defining our world but I think that's why experimentation is so important. We can argue all day that I had Cheerios for breakfast, the milky bowl, the box ect. But I can prove I had Cheerios if I throw up.
If you believe you are telling the truth in this video, why would anyone think that truth is subjective? "Truth is undefinable", congratulations, you have just done the exact opposite of what you are trying to do: you have just defined something which you consider true. Disclaimer: I know very little about philosophy.
Eh! A little off here.
This has always been my interpretation : the idea of Tarski’s Undefinability theorem is that if we have our vocabulary for talking about the world, and we want to know if the notion of “truth” is definable in that vocabulary (Tarski has something called “the convention T” that’s meant to give a criteria for what a truth predicate should look like for classical logic), then we know that either “truth” can’t be expressible/definable in terms of the vocabulary or the notion of “truth” that we defined won’t actually line up with all the uses we have for evaluating truth about descriptions of the world (that is, there might be things that are actually true that our defined notion of “truth” considers false, or there might be false statments that this notion of “truth” calls true. The actual idea of the proof is essentially just showing that you can show if “truth” is definable, then you can form the sentence “There is a true sentence that asserts its own falsehood.” and show such a sentence exists (assuming you have a notion if negating statements, a logical property called “diagonalization”, and that contradictions aren’t allowed to exist in your logic).
I hope that makes sense.
Does P=NP?
The truth is what the facts are.
Just one remark: your audio sounds like someone is turning it up and down very rapidly so one sentence is quite loud and the next one is inaudible and then the next one is loud again and so on.
💟
Frugality with example leaves people philosophically hungry 😏
To get the take on Godel promoted here (maths cannot prove all truths) you have to have a Platonist take. That is, you have to assume there are only eternal truths and falsehoods, nothing in-between. This seems decidedly un-postmodern! Let me explain.
Godel did not incontrovertibly show that some truths transcend provability. That's an interpretation. Godel just showed that we have to choose between completeness and consistency. In other words, he showed that if mathematics is complete, it necessarily contradicts itself; and if it doesn't contradict itself, it's necessarily incomplete. The proof is agnostic about which axiom we drop.
In the spirit of postmodernism, let's ask why philosophers and mathematicians pick the "non-contradiction" metanarrative. I'm not being facetious: non-contradiction is a metanarrative because it is just one consistent interpretation of Godel's proof.
Many mathematicians choose an ontology that drops completeness because their field relies on proof by contradiction: if consistency isn't axiomatic proofs by contradiction are suspect because the law of excluded middle (the proper name for the Platonist assumption in the first paragraph) that they rely on won't hold in all cases (even it does in most). Prominent mathematicians don't like the whole history of their field being called into question, so there is a cultural bias towards Platonist interpretations of Godel's theorem and lots of inertia. Similarly, philosophers like to drop completeness because it validates their work: if the math guys can't prove all truths with their formal systems, that gives us more of a niche to talk about other truths!
Here's the problem: there's no reason to assume consistency! The possibility of inconsistency in math is no more shocking than the possibility of flip-flop gates. After all, one can imagine a circuit that implements the same rules as a formal system, thereby actualizing mathematics, that has a branch ending in a flip-flop gate for one of its paths (i.e. proofs). There's nothing shocking about this. It does not imply that formal systems (mathematics) are impotent to describe reality, it's just that actual reality admits more possibilities than Platonists assumed (eternal 1s and 0s are the only possibilities). Internalize this, drop the philosophical bias toward Platonism and the problems go away. Many theoretical computer scientists have. Many mathematicians (constructivists) have too, despite the historical Platonistic bias of their field. Heck, even non-constructivist mathematicians often accept constructivist arguments these days and only use nonconstructive proofs for pragmatic reasons (nonconstructive proofs are often much easier and usually turn out to have constructive versions at a later date as a point of historical fact, implying truth is likely even if not rigorously established).
Philosophy needs to start updating its takes on Godel so as to avoid naive arguments. "Mathematics has to be consistent" is just one metanarrative for the data! Heck, that might be generous since you could argue the alternative interpretation is actually an objectively better narrative for the data (i.e. it fits the data better because the Platonist interpretation of Godel seems to fail to explain our construction of flip-flop gates as a point of fact).
Whoever says that there is no truth wants you to not believe him; so don’t! (Sir Roger Scruton)
Truth cannot be defined does not mean that we can't know what truth is. Also not all true statements being provable isn't equivalent to them not being knowable. Proof isn't the only way to gain knowledge and defining is not the only way of identifying.
Tarskis theorem is only concerned with language not being able to express what truth is. However it is petfectly possible to know what truth means without being able to put it into language.
The problems adressed are concerning language not knowledge itself. The reason is that language is not the thing in itself but points to something else. Truth can therefore only be pointed to. That in no way means it's unknowable, maybe only unsayable. This is explored in deth in Buddhism. One story is that Buddha held up a flower and noone understood the meaning except for one student who gained knowledge and liberation. Understanding is said to have been directly transmitted mind to mind without concepts.
So dear Carneades, the skeptic, we can say that postmodern philosophy of truth and postmodern philosophy in general has succeeded and manage to stay in the current thought, at least partially?
And, regarding if truth is something we can define, notice that when we say that not all truths are provable, we are indirectly saying that a proof is a subset of the set of truths. A proof is a type of truth, so that is a path where we can define the whole set.
What I got from the first 4 minutes: We can prove truths subjectively, but won't know if we can prove truths objectively