Tarski's Semantic Theory of Truth

[@KaneB]

Correspondence theory: kzbin.info/www/bejne/eYmueaSbgK5jgZY Coherence theory: kzbin.info/www/bejne/oYHVkJhqbpiIp8U Pragmatist theories: kzbin.info/www/bejne/q3WWpoWcec-SpZY

[@RestIsPhilosophy]

I think you’ve done enough to justify a ‘philosophy of truth’ playlist at this point.

[@yourfutureself3392]

True

[@KaneB]

Done!

[@Chris.4345]

True?

[@veganphilosopher1975]

Philosophy had so many great minds behind it in the early-mid 1900s. I wonder if we'll ever see so many leading intellectuals engaged in philosophy again.

[@helagewurz-ketchup6124]

they exist - behind a DeGruyter paywall

[@aaronchipp-miller9608]

I've been getting enjoyment out of these videos for almost a decade. Thanks bro

[@KaneB]

Great to hear! Thanks!

[@claytongroth2348]

Hey Kane. I really enjoy and appreciate your content here. Literally the SEP of YT. General suggestion for you (maybe doesn’t apply to this video as much): I’d love if you would add “merits” sections to your videos with equal frequency to “objections” sections. Two reasons. One, it would help the educational value of your videos for people trying to locate their views with respect to various positions. Two, it can sometimes come off as if you do a lot of “dunking on” ideas which gives a slightly negative impression the more videos from your channel one watches. Outstanding work though overall. Bringing philosophy to the people!

[@KaneB]

The basic problem with this is that there just isn't as much to say with respect to the merits of positions as there is for the objections. In general, it seems to be harder to build a positive case for any given position than it is to object to it. Actually, there's probably a straightforward explanation for this in that for any given position, there will often be many more philosophers who reject the position than there will be philosophers who accept it; and even when two philosophers accept the same position, they will often disagree on the details.

[@KaneB]

For example, take physicalism. This is a relatively popular position as far as philosophical views go, with over 50% support on the 2020 PhilSurvey. Moreover, this is a view that has had wide support for a very long. We've had decades to build a strong case for it. But if you look at the SEP article on physicalism, the section "The Case for Physicalism" lists only two arguments, and both of them are pretty crummy.

[@claytongroth2348]

@@KaneB I see the point. Equal time/effort towards “pluses” seems wrong. Perhaps then a quite brief section on “hey here is the upshot of this position…”?

[@italogiardina8183]

There is an implicit comparative value in a semantic theory of truth by token of being semantically indexed to social prototypes such as 'I am worse off iff the close other is better off then me'. The comparison then has a complex interdependency semantically with related prototypes like 'my group is worse off iff the close other group is better off then mine'. This extends to intergroup comparison which allows for translation of paradox, which ought to be a linguistic universal implicit in language self referential complex interdependency that pits polarising extremes together as 'this sentence is false'. Early languages would then not qualify for a semantic theory of truth which suggests that the advent of complex social structures like the notion of 'nation' is possible iff an some kind of semantic theory of truth can be constructed due to obvious contradictions such as 'I live in an imagined nation within my nation state'. This fear of subversive though a political reality with the advent of the historical secret police who would verify authentic citizen ascription to national identity. Tarski's semantic theory of truth is a product of a political era where one would better hold an account of in-group to out-group truth conditionality in order to survive with dignity.

[@grivza]

And why should this be the original mechanism and not anything else, like to give a naive example spirituality/superstition, trying to express the sentiment of persistence of a person after his death, "Even if he is not here, he is here". There are myriads of sentiments that might have pushed towards a similar formulation. No doubt Tarski was a product of his time, everyone is. The owl of Minerva flies at dusk or what's the phrase.

[@italogiardina8183]

@@grivza Agreed that Negative existential’s pose a dilemma of authenticity of sentiment for those who have opinions that are non contemporary

[@whycantiremainanonymous8091]

With formal mathematical languages, one is free to define whatever one wishes. It is the attempt to cram natural languages into Tarski's mold (which takes off in the 1960s, most prominently with Davidson, and leads to formal semantics, truth-conditional semantics, and their progeny) that yields plenty of well-paid dogmatic lunacy.

[@KaneB]

Well paid? Could you please direct me to the magical paradise where analytic philosophers earn good money lol

[@whycantiremainanonymous8091]

@@KaneB A generation or two ago there were good university jobs to be had, and proponents of that nonsense had way too many of them. Now the likes of us (well, I wouldn't categorise myself as Analytic, but Continental pays even less...) have to seek a livelihood elsewhere. But, notably, that makes questioning old dogma and still getting a job that much harder.

[@rezamahan7109]

Thank you Kane, as always!🙏

[@onion4062]

So is the open sentence "x is y or not x is y" true, because it is satisfied by all sequence of objects?

[@grivza]

Not if you have more than the 2 traditional truth values.

[@ericm9495]

@@grivza What do you mean by traditional truth value? Aren't there only 2 traditional truth values?Don't you mean to say "not if you have the 2 traditional truth values and some non-traditional truth-value"? Also how would having an additional non-traditional truth value mean that "x is y or not x is y" does not have the traditional truth-value of "true"?

[@ericm9495]

I believe "all sequences of objects" means both finite and countably infinite sequences. So a sequence with 1 member wouldn't satisfy "x is y or not x is y" since there is no second element to plug into y. but a closed formula like "snow is Kane or not snow is Kane" would be satisfied by ,and also the empty sequence etc.

[@KaneB]

Good question. Unfortunately, I'm not sure. This definitely works if we bind the variables with quantifiers -- so: "for all x and for all y, x is y or not x is y." In that case, we have a logical tautology which is satisfied by all sequences of objects and is straightforwardly true. However, it doesn't seem like we actually need the quantifiers here for this sentence to come out as true, per Tarski's definition of truth. There might be some technical reason why that doesn't work, but I'm not so au fait on the formal machinery.

[@luszczi]

​@@KaneB Hold up. This isn't an open sentence, it's a disjunction of an open sentence and its negation, a simple tautology. Therefore satisfaction (or any deeper structure of the proposition "x is y") doesn't need to be analyzed here. And if it were to be analyzed, it should be analyzed piecewise (first as "x is y" and then the truth value of "it is not the case that x is y" is obtained by negating the previous one). It would then trivially be satisfied on one side or the other. Of course, identity must be a predicate in the language, or we wouldn't be able to say "x is y" in the first place. Unless y stands for "any predicate in the language" and not an object, but then the answer is analogous, if a bit more unwieldy. Now am I right or is there something I failed to notice here? Been a few years since I had to learn this.

[@onty-op5587]

What is the difference between satisfaction and truth? It seems like satisfaction is "truth under an assignment", while truth is "truth under every assignment". But this would mean you're defining truth in terms of truth, right?

[@warwolt]

Satisfaction is a relation holding between an object and a predicate. An object s satisfies a predicate P iff P(s). It's a technical term from predicate logic

[@onty-op5587]

@@warwolt Right, but in order to know that P(s) you must know that P(s) is true. It seems satisfaction relies on the notion of truth.

[@freddevault5584]

@@onty-op5587 Satisfaction seems to rely on truth, but it only seems so. Keep in mind that truth, for Tarski or Davidson, is primarily a predicate of sentences. Then keep in mind that the theory is compositional, and that predicates ("white", "green", "north of", etc.), when given an assignment, are only the simplest sentences. We want our theory of truth for a language to yield a value for all the possible sentences, including sentential connectives and quantifiers, etc. Finally, keep in mind that the project is to create a theory of truth for a language, not to say what is true about the world. Semantics NEQ Physics (nor Metaphysics). So, yes, n-ary Predicates are defined as being "Satisfied" by those ordered n-tuples drawn from the domain of discourse which hold true of the predicate under assignment, but the resulting theory of truth for a language can still be illuminating, notwithstanding the incoporation of existing knowledge. "The Morning Star is the Evening Star" expresses an interesting astronomical fact, even though the co-extensional sentence "Venus is Venus" only expresses a tautology.

[@onty-op5587]

@@warwolt I think I understand the issue now. Satisfaction does not rely on the notion of truth, but rather provability in the meta-language. So truth is reduced to provability in the meta-language.

[@我有发嘉然视频的瘾]

Thank you, I understand a lot

[@jonasjensen9305]

Doesn't this just kick the can down the road, though? It sounds like saying, “A statement is true if it translates to a statement that's true”, which amounts to little (a little, but not much) more than saying it's true if it's true.

[@grivza]

This is just used to resolve the self-referential paradoxes, differentiates between the level on which propositions are made and the mechanics of truth inference. But if you want an actual, "real life", empirical use of this conceptualization, consider that it allows you to be more precise, now being able to pinpoint in the point of discord between the two levels.

[@hss12661]

You should do a video on how Davidson inversed the order of explanation by assuming truth to be more primitive than satisfaction/denotation etc.

[@KaneB]

I kinda hate Davidson. I might cover his work at some point, but I think that would be a better fit for a series on meaning rather than truth.

[@hss12661]

@@KaneB Why do you hate Davidson?

[@onion4062]

I love these more technical videos!

[@tomholroyd7519]

14:00 exactly what I was saying. N-categories

[@cloudoftime]

I'm not sure what I missed; why is it that a sentence becomes "satisfied" by sequences that _begin_ with the "satisfying" object(s)? What is it about the _beginning_ position that secures the satisfaction?

[@СергейМакеев-ж2н]

Because every variable (x,y,...) is, from a technical standpoint, a number in the sequence: "x is white" is formally written as "object #1 is white" "x is higher than y" -> "object #1 is higher than object #2" You can have a sentence that says "object #137 is white", and it would only be satisfied by those sequences whose 137th element is white. But that's still a "beginning", because, to judge the truth or falsehood of this sentence, it is enough to take the first 137 objects and throw out the infinity of remaining objects. In general, as every sentence only mentions a finite number of these numbers, every sentence only depends on _some finitely-sized beginning_ of the sequence.

[@cloudoftime]

@@СергейМакеев-ж2н Did I miss where it was stated that there is some reference to "object #1" being the formalized position? I didn't hear nor see anything being stated about ordered positions being necessary or entailed within the formalization. Hence my question. Can you help guide me to where this was established or substantiated? Also, what assigns this ordered hierarchy, and is that not relevant?

[@СергейМакеев-ж2н]

@@cloudoftime He said "for technical reasons" to skip over it, because it's too long to explain. The order comes from the way that the concept of a "variable" is established in the first place. To know what a "variable" even is, we use a hypothetical "list of all possible variables". This list must be infinite, as there can be statements with an arbitrarily large amounts of variables: "x is less than y", "x is less than the sum of y and z", "x is less than the sum of y, z, v, w, a, b and c", etc. To simplify working with variables (and to not depend on how many letters you have in your alphabet), we can rename them all to x1, x2, x3, x4, and so on ad infinitem. Then, a variable name is nothing more than a number. That is much simpler that keeping track of all the different letters. When it comes time to substitute objects in place of variables, we use a simple procedure: take an infinite sequence objects, and associate x1 with the first element, x2 with the second element, and so on.

[@KaneB]

@@СергейМакеев-ж2нYep, that's my understanding of it. It didn't seem important for communicating the basic philosophical ideas of Tarski's theory, so I skipped it.

[@Danilaschannel]

isn't satisfaction defined through truth? how can we use it to define truth 🤨

[@СергейМакеев-ж2н]

No, satisfaction is not defined through truth. It is defined by a large-but-finite dictionary of predicate rules ( "x is white" is satisfied by all white things; "x is a prime number" is satisfied by all prime numbers; ... ), plus a small list of rules for "and", "or" and other connectives. No mention of truth there.

[@hss12661]

It's recursive.

[@EduardoRodriguez-du2vd]

I suppose that there are two types of correspondence that relate an existing entity and a concept that represents it. If I define "unity" and then define "double", the concept "double" will always have a true relation to the concept "unity", for practical purposes, derived from a deductive inference. The relationship is circumscribed by my definitions. There is no room for variations. Reality will not interfere in those relationships or in my definitions. If I define that a block of stone is a cube and that joining it to another similar block would be the "double", reality limits the absoluteness of my statement. That statement only has one chance of being true. And that probability will always be less than one hundred percent. One can rely on an abstract construction with relationships defined by someone. But one cannot trust the relationships of reality. It must always be verified and the verification will always be only provisional. There is no such thing as an absolute glance.

[@hss12661]

Shizopost.

[@EduardoRodriguez-du2vd]

@@hss12661 I suppose you find it easier to give that answer than to give some kind of argument. A shame. You condemn me to ignorance. :)

[@ZZwoolyZZ]

I just cant get one thing out of my mind. Why cant truth be a contradiction? People seem to assume it must not be.

[@flyingpenguin8901]

My problem with Tarski's semantic theory of truth is that, although we can accept that " is true iff grass is green", we must also accept the fact that the grass is always greener on the other side, which means that I'm not satisfied. :( Jokes aside, I've just discovered your channel and I love this video! Thanks for the explanation!

[@justiceiria869]

That sounds like a "you" problem rather than the grass's problem.

[@fabiogfranco]

Wouldn’t Gödel’s incompleteness theorems nullify Tarski’s attempt at defining truth?

[@petrusboniatus]

This is very nice ❤. I kind of knew these concepts from computer languages that allow you to do formal proofs like prolog, lean or Idris but I didn't know were they came from.

[@Tocinos]

It's true that truth is true because if truth weren't true then it wouldn't truly be true. True?

[@pecfexfextus]

found this very relevant and illuminating because i'm trying to learn more about logic (though from a mathematical perspective)

[@whycantiremainanonymous8091]

Watch out where the huskies go And don't you eat that yellow snow.

[@justus4684]

Wooooo🙀🙀🙀

[@InventiveHarvest]

Oh, the mental gymnastics people go through to avoid dialethism! It seems to me that Tarsky's theory of truth fails in a few regards. Although, I must admit that this may just reflect my failure to understand Tarsky's theory. First of all, it seems to fail at correspondence. We are comparing a sentence in a base language to a sentence in a meta language. No longer then are we comparing anything to reality. Second, it seems to fail at actually solving the liar paradox. It claims that the liar paradox is false because "this sentence is false" does not exist in the meta language. But this is the case for all semtences in the base language. Sentences in the base language do not exist in the meta-language, so they would all be false. Third, is the thing about sequences. This isnt making sense to me at all. How does the sequence, "Earth, Jupiter, Mars" tell anything about the sentence "snow is white" unless one already knows the truth value of snow being white? "Earth, Jupiter, Mars" trivially cannot be plugged into "snow is white" and also it cannot be plugged into "snow is not white". It does nothing for either case. I do like Aristotle's drfinition of truth. The way he states it seems to point to the problems of trying to define truth and just says, truth is problematic, take it or leave it.

[@grivza]

This sentence is false, is false because it doesn't appear in the base language. It references the sentence of the meta language, which isn't part of the base. So he does solve the liars paradox, in the cheapest way possible by basically saying "We don't allow self reference".

[@KaneB]

(1) We use a meta-language to compare an object-language sentence to some state of affairs (or, in technical contexts, to our models). That is, ""snow is white" is true iff snow is white" involves a comparison between the sentence "snow is white" and the fact that snow is white. We're not locked into our language; we use our language to refer to things that are outside the language. This is the sense in which the semantic conception is a kind of correspondence theory. Though as I noted in the video, this is controversial: many philosophers interpret the semantic conception as deflationist. (2) Object-language sentences don't exist in the meta-language, but they do exist in the object-language, and the meta-language contains names for those sentences. The Liar sentence exists in the meta-language, but it's false because, under Tarski's interpretation, it purports to pick out a sentence of the object-language and fails to do so. The problem is basically the same as if I said: (S) "Snow is white" is true-in-German. But of course, German does not contain the sentence "snow is white." Of course, we could be using "snow is white" as the name for the German sentence "Schnee ist weiss", in which case (S) will be true. But if we're obtaining the name in (S) by simply enclosing the sentence to which we wish to refer in quotation marks, then (S) will be false, since there is no such sentence in German. (3) Yeah, this strikes me as a problem if we want to use Tarski's theory to understand the ordinary concept of truth. It's fine for formal purposes to take truth as a special case of satisfaction and ordinary sentences as open sentences without free variables. But presumably, the only reason why we say that "snow is white" is satisfied by all sequences of objects is that we make the prior judgment that snow is white (and so, "snow is white" is true). Of course, this can be cashed out in terms of the fact that snow satisfies "x is white," but again, we might think that the only reason why we make this judgment is that we make the prior judgment that snow is white. Somebody who thinks that snow is black would say that snow fails to satisfy "x is white." We have to keep in mind that Tarski's aim was to define truth for formal languages. Whether his analysis can do much to illuminate our ordinary concept of truth is another matter.

[@hss12661]

You don't understand Tarski's truth theory at all. And if you think that dialetheism is a serious position, then please don't do philosophy. Please!

[@InventiveHarvest]

@@hss12661 I'm too busy doing your mom

[@bigol7169]

Is mathematics philosophy?

[@biblebot3947]

There’s some philosophy involved but overall, no.

[@AM-gx3dy]

Logic, the base of math, is philosophy. Math is more of a language (sort of) build upon it

[@bigol7169]

@@AM-gx3dy that makes sense to me. Maths definitely isn't a science though, given you don't experiment. But then, even logic is considered its own thing now.

[@RuthvenMurgatroyd]

Yes in the pure original sense of the term. Love of truth, the study of certain knowledge. The formal sciences are the purest forms of philosophy and logic is the most fundamental of all science as it establishes the laws of reason. Mathematics is logic.

[@biblebot3947]

@@RuthvenMurgatroyd logic isn’t really a science though.

[@bertrc2569]

I'm sorry but there is no issue of true or false in a sentence that does not describe a reality. 'this sentence is false' has no meaning. There has to be a statement about a reality! Same with maths. 1+1 = 3 is meaningless. We are playing with symbols, not reality. If I take 1 apple and a second apple and state that i have 3 apples we can ask properly if this is the truth. If something is not true we are on a long path. Possibly infinite. If its true the journey is over. What might be true in an imaginary, nonsensical statement or 'pure maths' can be argued to infinity, therefore indicating the false.

[@tomholroyd7519]

P is true iff P is true. This is why we need n-category theory, to separate the levels

[@K1ngsd1]

Completely uninformative and irrelevant. Im shocked that this is taken as some kind of deep discovery.

[@KaneB]

Uninformative? Perhaps. Irrelevant? Like it or lump it, pretty much all of the contemporary work on truth, plus philosophy of language and philosophy of logic more broadly, was heavily influenced by Tarski's work here.

[@luszczi]

Tarski's definition seemed deceptively obvious to me as well, until I gained an appreciation for what the problem was and how versatile this solution is.

[@tomholroyd7519]

Sort of odd that it is so hard to define truth. Perhaps validity is a better concept. #RM3 (both true and false is valid)

[@Hvantmiki]

you get a lot of absurdities if that is the only consideration. for example the conclusion " the moon is made of cheese" can be a valid conclusion to any number of arguments. for example "anything higher up than 10 meters is made of cheese, the moon is higher up than 10 meters" it is in the form of a syllogism, it is obviously formally valid then. and both premises are valid in all sorts of ways. it is grammatically valid, and if it were not then it would be trivial to put in in a grammatically valid form. it is valid as a premise, even in a old-fashioned form where a premise needs to be able to be either true or false. and especially in philosophical discussion where truth and falseness should be ignored and only validity considered. I don't know if you can have coherent philosophy without claiming things are true or false. can not use any sort of argument. even arguments for claiming something is valid or not

[@superanto8763]

Wooooo🙀🙀🙀