Sunday, May 10, 2009

85 Alfred Tarski

I am not a mathematician. Tarski was and a very good one too. So he is way out of my league. Therefor I wont discussus here his contributions to fundamental logic and mathematics. It wouldn't make you happy either, way too technical and as such not a philosophical issue for us.

But Tarski was one of those philosophers that brought semantics within the scope of linguistic analysis. Since Frege we are focussed on the relation between sentences and the extra-luiguistic objects, which they refer to.

Most important in this discussion is the question, when do we say that a sentence, a proposition is true. We can even go a step further: when is say of a sentence, that it is true, do I say something meaningful at all?

Gottlob Frege was probably the first philosophical logician to express something very close to the idea that the predicate "is true" does not express anything above and beyond the statement to which it is attributed.

"It is worthy of notice that the sentence "I smell the scent of violets" has the same content as the sentence "it is true that I smell the scent of violets". So it seems, then, that nothing is added to the thought by my ascribing to it the property of truth. (Frege, 1918).

When the verification principle is your tool to establish the truth, you can express yourself even stronger, like Alfred Ayer did by declaring that the redundancy of the truth predicate implies that there is no such property as truth:

There are sentences, according to Ayer, in which the word "truth" seems to stand for something real; and this leads the speculative philosopher to enquire what this "something" is. Naturally he fails to obtain a satisfactory answer, since his question is illegitimate. For our analysis has shown that the word "truth" does not stand for anything, in the way which such a question requires.

So, that is one position: just proof that the word "truth" doesnt mean anynything at all in the sense that it adds something to a statement, which isnt in the statement itself.

Tarski took another position with his semantic theory of truth: Roughly, it states that the concept of "truth" for the sentences of a given language cannot consistently be defined within that language.

Let me give you an example: This sentence is not true. Here we have a problem: whne we take this sentence for true, that sentence is not true.
Tarski suggested, that we have to read this sentence in an other way. We need a language, a meta-language, to say something about that sentence (object-language) that states a fact.

So we should read it as "This sentence is not true" is true, if this sentence is true. Or to give you less abstract example. "Snow is white" is true if and only if snow is white. "Schnee ist weisz" is true in German if and only if snow is white.

In other words, when the sentence "Snow is white" really refers to a state of affairs then the sentence is true. In semantics we need a language to talk about how the object language works, how it relates to extralinguistic objects.

In the early 1930s Tarski formulated the semantic method, which is his most important achievement in logic. The essence of the method, as you may understand now, consists in discussion of the relations between expressions and the objects they denote.

Almost from the beginning the methods of semantics exerted a profound influence on philosophers engaged in the construction and study of exact scientific languages.

Semanties opened new possibilities in these studies, which formerly were limited to purely syntactic problems and thus were unable to express relations between languages and extralinguistic objects.

Semantics offered a natural tool for the discussion of such relations. The price one had to pay was the use of a much stronger metalanguage than the one sufficient for syntax.

At any rate, semantic methods became an accepted tool in the study of scientific languages. Contemporary studies in the methodology of science are primarily concerned with the syntax and semantics of the language of science.

The Discussion

[13:22] Alarice Beaumont smiling
[13:23] Herman Bergson: The concept of truths is a huge issue....this is only the tip of an iceberg
[13:23] Qwark Allen: oh yes
[13:23] Herman Bergson: So much on tarski
[13:24] Alarice Beaumont: wow... much :-)
[13:24] Mickorod Renard: would it be true to say that was heavy?
[13:24] Alarice Beaumont: yes.. heavy is better!
[13:25] Herman Bergson: I think the most interesting point here is, that some philosophers claim that the predicate "true" doesnt mean anything at all
[13:25] AristotleVon Doobie: It would seem to me that truth is not in the delivery of a statement but in the acceptance of it
[13:25] hope63 Shepherd: true: lol
[13:25] arabella Ella: i shall follow wittgenstein in saying ... whereof i cannot speak, thereof i shall be silent ... tarski is i find the most difficult philosopher to understand ;)
[13:25] Herman Bergson: Yes..This subject is tough
[13:25] Gemma Cleanslate: he was so mathematical too and geometry also entered in
[13:26] Herman Bergson: Yes Arabella, when you read about his work on logic an mathematics....I rest my case too..:-)
[13:26] Gemma Cleanslate: so it is a mixture of math and linguistics
[13:26] arabella Ella smiles
[13:26] Samuel Okelly: i am struggling to comprehend what was meant by a mathematican to say there was no "true" (and consequently no "false" too?)
[13:26] Herman Bergson: but what we can learn from his ideas is how he solves the paradox of the liar
[13:27] Mickorod Renard: yes?
[13:27] Herman Bergson: I think to see the meaning of Tarski, you should focus on semantics
[13:27] Alarice Beaumont: how?
[13:27] hope63 Shepherd: well.. we would have trouble trying to follow our who was that -the xeno question?
[13:27] Bubblesort Triskaidekaphobia: that would be to say that "false" has no value either?
[13:27] Herman Bergson: in fact Tarski himself didnt investigate natuaral language at all.
[13:28] arabella Ella: if i may break my silence ... i think it was a tautology for him to say "Snow is white" if and only if snow is white ... therefore he trivialised truth
[13:28] Herman Bergson: The main issue related with the concept of truth is the semantical notion of reference
[13:29] Herman Bergson: No arabella, that wasnt meant
[13:29] AristotleVon Doobie: this lack of value is in relation to spoken langues I presume?
[13:29] arabella Ella: but what do you get from such a statement about snow ... absolutely nothing emerges from it in my view
[13:29] Herman Bergson: it means The reference of the sentence "Snow is white" is a fact if snow is white
[13:30] AristotleVon Doobie: surely true and false have absolute value on a personal level
[13:30] Alarice Beaumont: snow can b dirty.. so it is not always white
[13:30] Herman Bergson: In science we have theories, collections of statements...
[13:30] Qwark Allen: something like "clear as water" if water it`s not poluted
[13:31] hope63 Shepherd: personal and absolute are in contradiction ari..
[13:31] Bubblesort Triskaidekaphobia: so... what Tarski is saying is that truth refers to nothing in the real world?
[13:32] arabella Ella: ok herman so if we translate the snow sentence to this ... A is true if and only if A ... what meaning or sense can you draw out of such a statement?
[13:32] Herman Bergson: Ayer and many empiricists, Tarski supported a kind of correpondence theory between the statement and extraluiguistic state of affairs
[13:32] arabella Ella: I mean what does it add to the simple sentence A is true?
[13:32] Gemma Cleanslate: i understood him to mean that if it is true of something then it is true!
[13:32] AristotleVon Doobie: we make our decisons on which path to take based on our understaniding of true and false
[13:32] Herman Bergson: but truth doesnt say anything about the real world, but about the condition of the has reference or it hasnt
[13:33] arabella Ella: ok i see
[13:33] Mickorod Renard: yea, I think I follow
[13:33] arabella Ella: so he takes truth to be something related to the sentence and not to the reference or referent of the sentence?
[13:33] Herman Bergson: YEs indeed
[13:34] Bubblesort Triskaidekaphobia: so... Tarski would not say that his writings are true then... but how would he describe his writings then... if they are not false they must be true... and I think we can assume that at least he beleived they had an element of truth to them, right?
[13:34] Herman Bergson: Truth is a property of a statement , not of the world or a state of affairs, he says
[13:34] Gemma Cleanslate: yes
[13:34] Samuel Okelly: what is the implication of this herman? (a statment having reference or not)
[13:35] Herman Bergson: the implication of this......
[13:35] arabella Ella: it is a claim which goes against what most of us intuitively feel, such as I believe snow is white because I perceive snow to be white
[13:35] arabella Ella: therefore it is true that snow is white
[13:35] hope63 Shepherd: i don't think tarski regarded true -false as contrary-dualistic....
[13:36] arabella Ella: how did he solve the cretan barber paradox then herman?
[13:36] Herman Bergson: Well we must not forget that Tarski mainly developed his ideas for fromal languages
[13:36] arabella Ella: such as logic and mathematics?
[13:36] Herman Bergson: YEs in a way Russell did too,
[13:37] Herman Bergson: by saying that a sentence cant refer to itself
[13:37] arabella Ella: ok ty
[13:38] arabella Ella: although it is actually not the sentence refering to itself but the words of which the sentence is composed and their meanings which refer to themselves in the case of the cretan barber
[13:38] hope63 Shepherd: mathematics-back to the roots of philosophy- eureka:)
[13:38] Herman Bergson: Within formal languages his theory of object language - metalanguage works, but he was in doubt whether it would apply to natural languege as well.
[13:39] Gemma Cleanslate: are there those applying these concepts to follow up on his ideas??
[13:39] Herman Bergson: So he hadnt high hopes of finding a adequate definition of truth for natural languages
[13:40] arabella Ella: and we must remember that the cretan barber paradox is formulated in natural language not in a formal language
[13:40] Herman Bergson: I think a lot of people who study semantics are yet looking for this definition
[13:41] Herman Bergson: I only can advise you to have a look at the entry Truth in IEP and Stanford and Wiki
[13:41] Herman Bergson: and you'll see what a broad debate it still is
[13:41] AristotleVon Doobie: it is my mind that is the sole identifier of what it true and what is false based on my existing empirical data or researched data to he validity of a statement
[13:41] hope63 Shepherd: lol-- i think this will be an eternal debate:)
[13:42] Herman Bergson: but this present day debate has its roots in the philosophical developments
[13:42] Herman Bergson: from Wittgenstein on
[13:42] Herman Bergson: I must admit it is somewhat too much for me too to digest in such a short time
[13:42] hope63 Shepherd: for me it is another approach of the debate of universals in the past....
[13:43] Mickorod Renard: can you give an example where in life tarski's idea would impact on our usual methods
[13:43] Herman Bergson: You could say that Hope
[13:43] Herman Bergson: Difficult question, Mickorod
[13:43] Mickorod Renard: ahhh,got u there herman
[13:44] Herman Bergson: But I think that talking about the truth of scientific theories is the place to look
[13:44] hope63 Shepherd: mick-- herman doesn't know your personal usual methods lol
[13:44] Mickorod Renard: ok ty
[13:44] Herman Bergson: and investigating the semantic justification of such a theory
[13:44] Mickorod Renard: I am not surea bout my personal methods myself
[13:45] Gemma Cleanslate: well then his impact on present philosophers is all about the truth issue then
[13:45] hope63 Shepherd: introduce me to your girl-- and i'll tell you:)grin
[13:45] Mickorod Renard: grin
[13:45] Herman Bergson: Keep in mind that a category of philosophers say, like Ayer, that the word Truth has no scientific meaning, Just remember the words of Frege too
[13:46] Herman Bergson: There you have a serious problem
[13:46] Mickorod Renard: what word would the scientific world transpose instead of truth?
[13:47] hope63 Shepherd: proven...
[13:47] Herman Bergson: Snow is white is just the same as it is true that snow is white
[13:47] hope63 Shepherd: verified..
[13:47] Mickorod Renard: ok,,cool
[13:47] hope63 Shepherd: agreed on-...
[13:47] Herman Bergson: this it is true doesnt add something special to the statement
[13:47] AristotleVon Doobie: maybe 'this snow is whte'
[13:47] Bubblesort Triskaidekaphobia: would lies exist if truth does not exist then?
[13:48] hope63 Shepherd: first agree on snow.. than on white.. :)
[13:48] Herman Bergson: problem
[13:48] AristotleVon Doobie: but all snow is not white, only 'this snow' is white
[13:48] hope63 Shepherd: in non -scientif language bub:9
[13:48] Herman Bergson: just take the verification principle
[13:48] Mickorod Renard: in scientific terms maybe lie doesnt exist but unproven
[13:48] Herman Bergson: Yes Mickorod..that would be an answer
[13:49] hope63 Shepherd: hey-- doesn't anyone read what i typed? lol
[13:49] AristotleVon Doobie: no
[13:49] Herman Bergson: Maybe you now have some idea of how to approach the problem of the concept of truth at least
[13:49] AristotleVon Doobie: :))
[13:50] AristotleVon Doobie: kidding hope
[13:50] hope63 Shepherd: herman-- it's only one of the approaches possible.)
[13:50] Alarice Beaumont: well.. not easy in rl ;-)
[13:50] Mickorod Renard: sorry, I have to go urgent
[13:50] Herman Bergson: very true Hope, that is why I instructed you to dig into th e concept of truth as stated in the IEP, Stanford and Wiki..:-)
[13:51] arabella Ella: well herman i think you need the concept of truth to build good arguments but when you move on to the axioms it gets to be more and more difficult to provide evidence for truth of any sort
[13:51] arabella Ella: bye mick
[13:51] hope63 Shepherd: so long mick
[13:51] Herman Bergson: I am not sure arabella
[13:52] Gemma Cleanslate: bye midk!!
[13:52] Gemma Cleanslate: Mick
[13:52] hope63 Shepherd: well- i think arabella is saying the more answers we find the more questions we get:)
[13:52] Herman Bergson: In stead of truth you can have concepts like reference or consistency
[13:52] Gemma Cleanslate: see you Tuesday maybe
[13:52] arabella Ella: i think basic axioms even in maths are created by humans and as building blocks they cannot be proved to be true or false
[13:52] Gemma Cleanslate: wow
[13:53] Gemma Cleanslate: i have to say i disagree with that arabella
[13:53] arabella Ella: like the Peano axioms
[13:53] Herman Bergson: I agree....and we'll come to that station again when we meet people like Kuhn and Feyerabend
[13:53] AristotleVon Doobie: I think one must get as close to the turth as is possible with the facts available
[13:53] arabella Ella: or the basic building blocks of matter ... molecules, etc
[13:53] hope63 Shepherd: like bush before the iraki invasion ari?
[13:54] Herman Bergson: maybe there isnt truth but only consistency, non contradiction, within our theories
[13:54] AristotleVon Doobie: yes, hope ...a brilliant man obviously
[13:54] AristotleVon Doobie: not
[13:54] arabella Ella: i would agree with that statement herman
[13:54] hope63 Shepherd: a philosopher lol
[13:54] Herman Bergson: I would suggest NOT to read what Hope types
[13:54] hope63 Shepherd: ty herman:)
[13:55] AristotleVon Doobie: LOL
[13:55] Alarice Beaumont: lol
[13:55] arabella Ella: hey herman philosophy should stand for freedom of speech and expression right?
[13:55] Samuel Okelly: :)
[13:55] Herman Bergson: sorry Hope, this is about epistemological matters, not political statements
[13:55] hope63 Shepherd: ty ara:
[13:55] Alarice Beaumont: i think somehow it does Arabella :-)
[13:56] Herman Bergson: I agree Alarice, but that doesnt deny me the wish to stay within context here
[13:56] hope63 Shepherd: herman-- be honest-- philosophers have influenced politics in the past...
[13:56] AristotleVon Doobie: yes, herman is right of course
[13:56] hope63 Shepherd: heureusement:)
[13:56] Herman Bergson: That is not our discussion today Hope
[13:56] hope63 Shepherd: ( keeping my head down)
[13:57] Alarice Beaumont: that's what we have Herman for.. Hope.. to keep us on track :-)
[13:57] Herman Bergson: today the discussion is how the concept of truth relates to statements, and even the question whether the word true means something or not
[13:58] arabella Ella: i think what Hope really meant was that the concept of truth is often abused by people in power
[13:58] Herman Bergson: And I hope, that At least I succeeded in explaining to you where to look for the debate and what the debate is about
[13:59] Herman Bergson: I think arabella, that that is a much broader discussion about the meaning of words as used in science and in ordinary language
[13:59] Gemma Cleanslate: see you tuesday all i hope!! leaving now
[13:59] AristotleVon Doobie: and I think that politicians do use language to propagandize
[14:00] Qwark Allen: and me to
[14:00] Qwark Allen: i hope
[14:00] arabella Ella: yes of course herman but as a person who is not a mathematician i think it is so difficult to relate to non formal languages
[14:00] Herman Bergson: Sometimes, and I would refer to Strawson here, the word truth isnt used as a word with reference, but as a linguistic act
[14:00] Qwark Allen: ty herman
[14:00] arabella Ella: bye gemma bye qwark
[14:00] Qwark Allen: cya all later
[14:00] AristotleVon Doobie: bye Qwark
[14:00] Herman Bergson: Bye Qwark
[14:00] Alarice Beaumont: ooopss... bye qwark!
[14:00] hope63 Shepherd: herman-- we could get into a large discussion what truth and science had to do in historical views of values which affected everyone..:)
[14:00] AristotleVon Doobie: he was having a struggle
[14:00] arabella Ella: yes herman i love the idea of linguistic acts ... will we cover those too?
[14:01] Herman Bergson: Yes, for our next philosopher is Austin
[14:01] hope63 Shepherd: ask galilei
[14:01] arabella Ella: ok Austin and spilt ink then
[14:02] Herman Bergson: spilt ink?
[14:02] arabella Ella: he has an essay with something like that in the title but i too need to refresh my memory on austin
[14:03] Herman Bergson: Well one title is: How to do things with words!
[14:03] arabella Ella: yes
[14:03] hope63 Shepherd: read goethe's faust- the scholar scene:)
[14:03] Herman Bergson: So I'll see you next Tuesday then, and we'll do something with words again ^_^
[14:04] arabella Ella: thank you herman
[14:04] arabella Ella: bye everyone
[14:04] AristotleVon Doobie: Thanks you Herman
[14:04] SALDOG Brezoianu: Thank you so much for everything, Professor. :)
[14:04] hope63 Shepherd: sorry i can't be with you on tuesday.. ( that's why i spilled more ink as usual) lol
[14:04] Herman Bergson: Thank you for this discussion, not an easy subject but I think we managed quite well :-)
[14:04] Samuel Okelly: thanks again herman :) once again we have lots to think about :)
[14:04] SALDOG Brezoianu: Bye everyone...and take care. :)
[14:04] Herman Bergson: Definitely on this issue Samuel, yes
[14:04] AristotleVon Doobie: bye Saldog
[14:04] Alarice Beaumont: my head is spinning!
[14:04] Alarice Beaumont: bye

Posted by herman_bergson on 2008-09-22 14:42:56

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