Truth and Meaning — Banno

Thanks, I have downloaded it. I understand more this week about Tarski's STT than last week, and hopefully more next week than this week, but I think that there is coherent light at the end of the tunnel, unless I'm mistaken.

Anyway, I suggest not saying: 'snow' is denoted as snow
But instead: snow is denoted by 'snow' or 'snow' denotes snow — TonesInDeepFreeze

Tarski used "denote", but I don't think this term is strictly grammatically correct, but that is the word he used. I think snow is named "snow" would be better, rather than "snow" denotes snow. Denotes infers points to, and "snow" is doing more than pointing to snow.

I agree with "snow" denotes snow and snow is denoted by "snow", but I still believe that "snow" is denoted as snow is grammatically correct.

Within a sentence, "as" points forwards, and "by" points backwards. The Cambridge Dictionary supports this, giving the examples of i) Fetal heart rate is denoted as the percentage of time in fetal tachycardia per 12-hour period ii) a marking is graphically denoted by a distribution of tokens on the places of the net.
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liar paradox problem — TonesInDeepFreeze

In L, "this proposition is false" is a paradox.
In the world there are no paradoxes. An apple is an apple, if an apple is to the right of an orange then the orange is to the left of the apple, an apple can never be a non-apple.
To avoid paradox in language we need to ensure that language corresponds with the world, because the world is logical.
Tarski is aiming at the same goal.
From the IEP - The Semantic Theory of Truth - "To be satisfactory SDT must conform to so-called conditions of adequacy. More specifically, this definition must be (a) formally correct, and (b) materially correct Condition (a) means that the definition does not lead to paradoxes and it is not circular."

IE, paradoxes in language may be avoided by ensuring that language corresponds with a world that is logical.

(As an aside, correspondence works not when a concept in the mind corresponds with an object in the world, but rather when a concept in the mind corresponds with a public word that has been established during an Institutional Performative Act. The word can be concrete as in "apple" or abstract as in "beauty". Conversation then becomes about the public word, which in its turn corresponds with concepts in the minds of all those taking part in the conversation.)
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Tarski doesn't even say that 'snow is white' is true — TonesInDeepFreeze

You wrote - the denotation of 'snow' is: precipitation in the form of small white ice crystals formed directly from the water vapor of the air at a temperature of less than 32°F (0°C)
The denotation of 'white' is: has the achromatic object color of greatest lightness characteristically perceived to belong to objects that reflect diffusely nearly all incident energy throughout the visible spectrum

It is true that Tarski does not say that white is a necessary condition for snow.
However, this is part of the problem that Tarski uses the analytic proposition "snow is white" rather than a synthetic proposition such as "snow is always welcome" .

You wrote - "snow" is precipitation ..............white...............
You didn't write "snow" is precipitation.........which may or may not be white.........

This infers that white is an intension of "snow", meaning that white is a necessary condition for "snow".

Ask anyone in the street whether snow is white or purple, and I am sure nearly all would say white. People know "snow" is white, in an analytic sense.
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Tarski says, "Let us suppose we have a fixed language L whose sentences are fully interpreted." — TonesInDeepFreeze

As an example of interpretation, "snow" is frosty stuff and "white" is the colour of St Patrick's Day T-shirt are external

From the IEP - The Semantic Theory of Truth
"A standard objection against STT points out that it stratified the concept of truth. It is because we have the entire hierarchy of languages Lo (the object language), L1 ( = MLo), L2 (= ML1), L3 (M L2), …. Denote this hierarchy by the symbol HL. It is infinite and, moreover, there is no universal metalanguage allowing a truth-definition for the entire HL."

IE, for each MML there is a language L, and for each language L there is a ML.
Where L = "snow is white"
MML = "snow" is snow and "white" is white
ML = "snow is white" is true IFF snow is white
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The truth or falsehood of 'snow is white' is not dependent on 'snow' naming snow (precipitation...) and 'white' naming white (the chromaticity...). — TonesInDeepFreeze

Given snow is white

If in MML One, "snow" denotes snow - and "white" denotes green
Then in the ML "snow is white" is false

If in MML Two, "snow" denotes snow - "white" denotes white
Then in the ML "snow is white" is true

IE, the truth or falsehood of "snow is white" is dependent on naming in the MML.
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should we take it that Raatikainen's summary of Putnam is correct? — TonesInDeepFreeze

Raatikainen argues against Putnam's objections to Tarski's theory.
However, for me, Raatikainen doesn't make his case, and Putnam's objections to Tarski's theory of truth make sense to me.

Panu Raatikainen, More on Putnam and Tarski
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but maybe Tarski is conceding that we can't have a truth definition that covers all interpretations, but only, for each interpretation, its own truth definition? — TonesInDeepFreeze

You wrote: "Let M interpret 'snow' as the frosty stuff, and 'white' as the color of a St. Patrick's day T-shirt"

Yes, within a particular MML, there is only one interpretation. Between different MML's there are different interpretations.
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If 'white' denotes green, then 'snow is white' is true iff snow is white is not true. But it is still true. Made explicit — TonesInDeepFreeze

Yes, but each new denotation requires a new MML.

In MML One, "snow" denotes snow and "white" denotes green.
Therefore the T-sentence "snow is white" is true IFF snow is white is valid

In MML Two, "snow" denotes snow and "white" denotes white
Therefore the T-sentence "snow is white" is true IFF snow is white is valid
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Tarski's schema is a definition not a claim of a logical truth — TonesInDeepFreeze

IEP - The Semantic Theory of Truth
"To be satisfactory SDT must conform to so-called conditions of adequacy. More specifically, this definition must be (a) formally correct, and (b) materially correct Condition (a) means that the definition does not lead to paradoxes and it is not circular."

Yes, but is founded on logic in order to avoid paradox and circularity.
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Given a language L, and an interpretation M of L, and a sentence P of L: A sentence 'P' is true per M iff P. That's just like any textbook in mathematical logic. No meta-metalanguage. — TonesInDeepFreeze

From Wikipedia - Mathematical Logic - Concerns that mathematics had not been built on a proper foundation led to the development of axiomatic systems for fundamental areas of mathematics such as arithmetic, analysis, and geometry.

In a language L there could be "1 + 1 = 2", "1 + 1 = 5", "1 + 1 = 3"
These may be true or false
The axiom 1 + 1 = 2 exists within a Metametalanguage (MML)
This allows in the Metalanguage (ML) the T-sentence: "1 + 1 = 2" is true IFF 1 + 1 = 2
Note that the axioms are not in the ML, and the ML cannot question the axioms that it has been given.

Tarski used "denote", but I don't think this term is strictly grammatically correct, — RussellA

It doesn't have to conform to ordinary linguistic usage in this narrower technical one. And this technical one itself isn't universally agreed. Or rather, @TonesInDeepFreeze will be in the know as to how far Tarski's usage (as clarified above) is agreed, in modern logic and maths related discourse. I'm only vaguely aware that many people diverge from this usage, and follow such examples as Russell's classic (On Denoting) which appears to imply singular reference.

The reason I'm aware of that divergence is that I'm a fan of Goodman's (and others') deliberate indulgence of the multiple (along with singular) interpretation. According to which, denotation is any pointing of a word (or in Goodman's case even a picture) at one or more things. And thus not necessarily singular (as for Russell). Specifically, naming or definite description when singular (e.g. "snow" of snow), or description when general (e.g. "white" of white things). But generally, any pointing (of a word), or labelling (with or by a word).

I think snow is named "snow" would be better, rather than "snow" denotes snow. — RussellA

@TonesInDeepFreeze - is it right to say it's both, for Tarski (as for Goodman and Quine)? Naming is a species of denotation?

Denotes infers points to, and "snow" is doing more than pointing to snow. — RussellA

Yes! (Passing over infers for implies.) And no! It's all pointing!... just how is "snow" doing more than pointing to snow??

Would you please tell me what textbook(s) in mathematical logic is the source of your understanding of the basics of this subject? Then, if I have the book, I can see better how we can at least agree on the basics.

I don't think this term is strictly grammatically correct — RussellA

'x' denotes y.

That is grammatically correct.

That usage is well established in everyday language and in logic.

Denotes infers points to — RussellA

That is not correct.

The word 'denotes' doesn't infer. People infer; words don't infer.

I still believe that "snow" is denoted as snow is grammatically correct. — RussellA

I'd like to see somewhere an example of

'x' is denoted as y.

If I saw someone write that, then I wouldn't know what it is supposed to mean:

(1) 'x' is denoted by y.

Which is backwards.

or

(2) y is denoted by 'x'.

Which is correct.

Your Cambridge examples are about relations between things: fetal heart rate and percentage of time. We're talking about the relation between a word and a thing.

In the world there are no paradoxes. — RussellA

Two separate things:

(1) An inconsistent theory has theorems that are contradictions. That is syntactical.

(2) There are no true contradictions. That is semantical.

To avoid paradox in language we need to ensure that language corresponds with the world, because the world is logical.
Tarski is aiming at the same goal. — RussellA

In the kind of formal theories most pertinent to this subject, contradictions are stated in a language, but the concern is whether they occur in theories. Tarski is not worried about whether languages are consistent, since 'consistent language' doesn't even make sense. What are consistent or not are theories.

I don't know where Tarski is supposed to have couched anything he said in a way similar to what you wrote. I don't know where Tarski is supposed to have said anything fairly paraphrased as "the world is logical". What are logical or not are inferences and arguments.

the definition does not lead to paradoxes and it is not circular. — RussellA

Right. And the way that is achieved is by adhering to certain definitional forms with certain restrictions.

IE, paradoxes in language may be avoided by ensuring that language corresponds with a world that is logical. — RussellA

No, you are adding that, from your own notions. Unless you show me exactly what Tarski wrote that can be reasonably paraphrased as "ensuring that the language corresponds with a world that is logical". Again, where does Tarski say "the world is logical"? What would he mean by it when what is logical or not is not a world but rather an inference or argument? And where does Tarski say a language corresponds with the world. What corresponds or not with a world is a sentence or theory.

It is true that Tarski does not say that white is a necessary condition for snow. — RussellA

Does Tarski even say that snow is white? In the "standard interpretation" of 'white' and 'snow', we get that 'snow is white' is true. But it is not precluded that the words can be interpreted otherwise. I went into detail about that in my previous post.

Tarski uses the analytic proposition "snow is white" — RussellA

Please say where Tarski says 'snow is white' is analytic.

I really do not want to get bogged down into an endless debate about analytic/synthetic, but you are taking a leap with it here regarding Tarski, unless you show us where he said that 'snow is white' is analytic.

rather than a synthetic proposition such as "snow is always welcome" . — RussellA

He could have used that also.

We say for any statement P,

'P' is true iff P.

Whether P is synthetic, analytic, or supercalifragilistic:

'P' is true iff P.

'Bob's car is white' is true iff Bob's car is white.

That's another instance of the schema.

The schema does not at all require that its instances be analytic sentences.

You wrote - "snow" is precipitation ..............white...............
You didn't write "snow" is precipitation.........which may or may not be white........ — RussellA

That's a good point. I overlooked that I chose a definition that happened to include 'white' in the definiens of 'snow'. That was a mistake. I don't know whether Tarski even had a scientific definition of 'snow' in mind, and especially one that has 'white' in the definiens. So, I don't know whether Tarski thought of a particular definition so that he regarded 'snow is white' as analytic. I highly doubt that he did.

I should have chosen one such as this:

"precipitation in the form of ice crystals, mainly of intricately branched, hexagonal form and often agglomerated into snowflakes, formed directly from the freezing of the water vapor in the air"

The point of the Tarski schema is not to define 'is true' for just analytic sentences.

"grass: vegetation consisting of typically short plants with long, narrow leaves, growing wild or cultivated on lawns and pasture, and as a fodder crop"

So 'grass is green' is not analytic.

'grass is green' iff grass is green.

"snow" is frosty stuff and "white" is the colour of St Patrick's Day T-shirt are external — RussellA

The interpretation of the words takes place in the metalanguage.

What is your definition of 'external'?

From the IEP - The Semantic Theory of Truth
"A standard objection against STT points out that it stratified the concept of truth. It is because we have the entire hierarchy of languages — RussellA

Correct. To define 'is true' for sentences in a metatheory, requires a meta-metatheory, ad infinitum.

But that doesn't entail that for the object language we can't both interpret it and state the definition of 'is true' in the metatheory. In ordinary mathematical logic we do give interpretations of an object language and also state the definition of 'is true' per each interpretation - all in one metatheory. (Or is there something I'm overlooking?)

Yes, within a particular MML, there is only one interpretation. Between different MML's there are different interpretations. — RussellA

Let L be the object language.

Let x(y) be the metalanguage for y.

m(L) interprets L

mm(L) interprets m(L)

ad infinitum

There are not clashes of interpretation.

The axiom 1 + 1 = 2 exists within a Metametalanguage (MML) — RussellA

An axiom is written in a language but occurs in a theory.

For example, the axiom

Ax(x+0 = x)

is written in the language of first order PA and it occurs in first order PA.

The language of a theory and the theory itself are different things.

TonesInDeepFreeze will be in the know as to how far Tarski's usage (as clarified above) is agreed, in modern logic and maths related discourse. — bongo fury

I know some of the basics of mathematical logic pretty well, but I'm not even within a telescope's distance of being an expert on it or anything other than jazz, and even on that subject I'm outclassed by a number of greater experts.

It doesn't have to conform to ordinary linguistic usage in this narrower technical one. — bongo fury

I am using 'denote' in the everyday sense:

"stand as a name or symbol for"

'denotes', 'names', 'stands for', 'symbolizes'. All good.

'Chicago' denotes Chicago.

Chicago is denoted by 'Chicago'.

The denotation of 'Chicago' is Chicago.

In the most ordinary context of mathematical logic:

An interpretation (model) is a certain kind of function from the set of symbols. The function maps a symbol to an element of the domain, an n-ary total function on the set of n-tuples of the domain or an n-ary relation on the domain, depending on the kind of symbol.

'denotes', 'names', 'stands for', 'symbolizes'. All good. — TonesInDeepFreeze

What about 'describes'? If that's too different, then probably I jumped to conclusions, and 'denotes' is singular for Tarski, as for Russell and many others?

For an n-place (n>0) relation symbol, the denotation is an n-place relation on the domain. — TonesInDeepFreeze

And in the case of an adjective or one-place relation symbol, perhaps the denotation is, for Tarski, singular, even though a set?

The T schema doesn't dictate

1) The type of truth object (sentences vs propositions)
2) The nature of the equivalence relation (analytic necessity vs material necessity vs modal necessity)
3) Whether the schema is used prescriptively to exhaustively define the meaning of "truth" e.g as in deflationary truth, or whether the schema is used to non-exhaustively describe truth but not explain the truth predicate, as in inflationary truth.

I don't have answers to those questions.

The T schema doesn't dictate

1) The type of truth object (sentences vs propositions)
2) The nature of the equivalence relation (analytic necessity vs material necessity vs modal necessity)
3) Whether the schema is used prescriptively to exhaustively define the meaning of "truth" e.g as in deflationary truth, or whether the schema is used to non-exhaustively describe truth but not explain the truth predicate, as in inflationary truth. — sime

1) Tarski was dealing with sentences.

2) The biconditional is for material equivalence.

2) It's a definition.

And no! It's all pointing!... just how is "snow" doing more than pointing to snow?? — bongo fury

The meaning of denote
The exact meaning of "denote" is debated, whether in linguistics or mathematics, and books have been written about the topic, e.g., Umberto Eco Meaning and Denotation, John Lyons Language and Linguistics, Bertrand Russell On Denoting.

"Snow" does more than point to snow
Starting with @Tones whereby the denotation of 'snow' is: precipitation in the form of small white ice crystals formed directly from the water vapor of the air at a temperature of less than 32°F (0°C). Remove the expression "formed directly from the water vapor of the air at a temperature of less than 32°F (0°C)", as this describes how "snow" formed rather than what "snow" is. As "snow" is precipitation, can remove the expression precipitation. Therefore, can simplify the denotation of "snow" as small white ice crystals.

In the world we observe small, white, ice crystals, which we name "snow". The unstated and reasonable assumption is that small, white, ice crystals is snow. Therefore, we have named snow as "snow", ie, "snow" is the name for snow and "snow" refers to snow.

Note that the intension of "snow" is white, such that white is necessary but not sufficient for snow.

But note also that snow does not exist independently of its properties. Snow is small, white ice crystals in the sense that A is A. If the properties small, white and ice crystals were removed, there would be nothing left. IE, it is not the case that first we observe small, white ice crystals and then we observe snow, rather, we observe them contemporaneously as they are the same thing.

When I hear the word "snow", there are two aspects. On the one hand, "snow" denotes snow, in that "snow" is actively pointing out something in the world, namely snow. On the other hand, "snow" is passively being denoted by small, white ice crystals.

Similarly, when I hear the word "unicorn", the word "unicorn" is doing more than pointing to a unicorn. When I hear the word "beauty", the word "beauty" is doing more than pointing to beauty.

IE, words have meaning even when there are no unicorns or beauty in the world for them to point to.

Tarski's usage of denote
Tarski in The Semantic Conception of Truth and the Foundations of Semantics uses denote for one or more items.

For example, he wrote:
1) The expression "the father of his country" designates (denotes) George Washington.
2) We have seen that this conception essentially consists in regarding the sentence "X is true" as equivalent to the sentence denoted by 'X' (where 'X' stands for a name of a sentence of the object language).
3) While the words "designates," "satisfies," and "defines" express relations (between certain expressions and the objects "referred to" by these expressions)
4) We should reconcile ourselves with the fact that we are confronted, not with one concept, but with several different concepts which are denoted by one word

In summary, the meaning of "denote" is much debated, and words do more than pointing to snow and unicorns in the world.

@TonesInDeepFreeze

You are quibbling over details and things I never said.

In summary, the meaning of "denote" is much debated, — RussellA

Not really. In maths and logic it covers at least "designate", "name", "refer to", "map to", "point to", "apply to", "be satisfied by", and "be true of"; and for Goodman and others also "describe" and "depict".

It goes from word to thing, not from thing to word, or from word to word.*

and words do more than pointing to snow and unicorns in the world. — RussellA

Maybe. It gets interesting. But hopeless if you misunderstand "denote".

3) While the words "designates," "satisfies," and "defines" express relations (between certain expressions and the objects "referred to" by these expressions)
4) We should reconcile ourselves with the fact that we are confronted, not with one concept, but with several different concepts which are denoted by one word — RussellA

Don't edit when quoting.

* Except where the object denoted is itself a word. But not from word to co-referring word.

The exact meaning of "denote" is debated, — RussellA

It's just the ordinary sense here.

And that is supported by the fact that it was Tarski himself who specified how symbols of the object language map with an interpretation mapping.

Look it up. Read up on Tarksi and model theory.

Starting with Tones whereby the denotation of 'snow' is: precipitation in the form of small white ice crystals formed directly from the water vapor of the air at a temperature of less than 32°F (0°C). Remove the expression "formed directly from the water vapor of the air at a temperature of less than 32°F (0°C)", as this describes how "snow" formed rather than what "snow" is. As "snow" is precipitation, can remove the expression precipitation. Therefore, can simplify the denotation of "snow" as small white ice crystals. — RussellA

When you just completely skip what I wrote about that, you are in bad faith as a discussant. Here it is:

You wrote - "snow" is precipitation ..............white...............
You didn't write "snow" is precipitation.........which may or may not be white........
— RussellA

That's a good point. I overlooked that I chose a definition that happened to include 'white' in the definiens of 'snow'. That was a mistake. I don't know whether Tarski even had a scientific definition of 'snow' in mind, and especially one that has 'white' in the definiens. So, I don't know whether Tarski thought of a particular definition so that he regarded 'snow is white' as analytic. I highly doubt that he did.

I should have chosen one such as this:

"precipitation in the form of ice crystals, mainly of intricately branched, hexagonal form and often agglomerated into snowflakes, formed directly from the freezing of the water vapor in the air"

The point of the Tarski schema is not to define 'is true' for just analytic sentences.

"grass: vegetation consisting of typically short plants with long, narrow leaves, growing wild or cultivated on lawns and pasture, and as a fodder crop"

So 'grass is green' is not analytic.

'grass is green' iff grass is green. — TonesInDeepFreeze

You are quibbling over details and things I never said. — RussellA

They are critical details. And I also posted about matters that are not mere details. And you went right past the very critical substantive reply to you, as instead you restated your own contention again, ignoring that I had just clearly rebutted it. That is bad faith posting and bad faith to put the onus on your interlocuter in that instance.

And if you think I've misrepresented what you've said, or strawmamned you, then you can say specifically where.

I'll say it again (as this is certainly not a mere "detail"):

The schema says that for any sentence P, we have:

'P' is true iff P.

He does not say that 'P' has to be analytic.

Look it up. Anywhere.

I'll say it again (as this is certainly not a mere "detail"): The schema says that for any sentence P, we have: 'P' is true iff P. He does not say that 'P' has to be analytic. Look it up. Anywhere. — TonesInDeepFreeze

My goal is to understand Tarksi's Semantic Theory of Truth, not get bogged down in unimportant detail and misunderstandings.

I wrote "Denotes infers points to, and "snow" is doing more than pointing to snow."
You wrote "That is not correct. The word 'denotes' doesn't infer. People infer; words don't infer."
Of course I am not suggesting that the word "denote" is doing the inferring.

Of course the T-sentence "P" is true IFF P is not a detail. It is extremely important. I never said it was a detail.
I said that in my opinion "snow is white" is an analytic proposition.
I never said that in my opinion "P" is an analytic proposition.
I never said that Tarski said that "P" has to be analytic.

Not really — bongo fury

I had written: "the meaning of "denote" is much debated".

I agree that the word "denote" can mean from a word to thing or things. Yet there is more to it than this. For example, people agree that beauty is a combination of qualities, such as shape, colour, or form, that pleases the aesthetic senses, yet millions of words have been written about the meaning of beauty.

For example, Umberto Eco in Meaning and Denotation 1987 wrote: "Today denotation (along with its counterpart, connotation ) is alternatively considered as a Property or function of (i) single terms,(ii) declarative sentences (iii) noun phrases and definite descriptions. In each case one has to decide whether this term has to be taken intensionally or extensionally: is denotation tied to meaning or to referents? Does one mean by denotation what is meant by the term or the named thing and, in the case of sentences, what is the case ?"
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But hopeless if you misunderstand "denote". — bongo fury

I had written: "when I hear the word "unicorn", the word "unicorn" is doing more than pointing to a unicorn".

The sentence is about "pointing", not "denoting".
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Don't edit when quoting. — bongo fury

When an article is edited, the article is changed. My three quotes were neither edited nor paraphrased, they were verbatim and in context.

When an article is edited, the article is changed. — RussellA

Are you suggesting you quoted from a different edition of this article? https://www.google.com/url?sa=t&source=web&rct=j&url=https://sites.ualberta.ca/~francisp/Phil426/TarskiTruth1944.pdf&ved=2ahUKEwjWm9HtsZ76AhX8S0EAHZ8tANMQFnoECA8QAQ&usg=AOvVaw2wFEunA8J8bXe0NoxT516Z

If so, grateful for a link. Otherwise, how on earth are your four (three??) quotes

neither edited nor paraphrased, they were verbatim and in context. — RussellA

They are presented as a single quote; they come from 3 different pages; and your number 3 is a half sentence seemingly about "denote" and completed by number 4 that turns out to be about "true".

They are presented as a single quote; they come from 3 different pages — bongo fury

They are quite clearly not presented as a single quote, because the four quotations are individually numbered 1), 2), 3) and 4).

You have the document so obviously know they aren't a single quote.

The important knowledge to be gained from these quotations is that Tarski can use one expression to denote one or more objects, concepts or expressions.

They are quite clearly not presented as a single quote, because the four quotations are individually numbered 1), 2), 3) and 4). — RussellA

Not as separate quotations, no they aren't. I had to go to the article to discover the editing.

You have the document so obviously know they aren't a single quote. — RussellA

Oh that's ok then? No, it isn't. Don't edit when quoting.

The important knowledge to be gained from these quotations is that Tarski can use one expression to denote one or more objects, concepts or expressions. — RussellA

Trying to make Tarski look confused isn't helping you.

Trying to make Tarski look confused isn't helping you. — bongo fury

At no time have I ever suggested that Tarski was confused.

Are you making this up? Bye.

My goal is to understand Tarksi's Semantic Theory of Truth — RussellA

That's good. You started out in this thread pretty confused. Hopefully some of the comments from posters have helped you.

not get bogged down in unimportant detail and misunderstandings — RussellA

.

The details I have mentioned are not unimportant.

What misunderstandings? Your own? Or posters misunderstanding one another? In either case, misunderstandings deserve to be remedied. I have misunderstood things in this thread. I corrected myself.

I wrote "Denotes infers points to, and "snow" is doing more than pointing to snow."
You wrote "That is not correct. The word 'denotes' doesn't infer. People infer; words don't infer."
Of course I am not suggesting that the word "denote" is doing the inferring. — RussellA

You seem not to know what you've written, even immediately upon quoting yourself: "Denotes infers [...]". That which infers is doing the inferring.

Of course the T-sentence "P" is true IFF P is not a detail. It is extremely important. I never said it was a detail. — RussellA

No, you just protested that you don't like all the detail. I don't know what you mean is included in that. I didn't claim what you think is the unneeded detail. But an important point that you kept not responding to is that the schema is not concerned with only analytic sentences. So I reiterated that point, stressing it's not a mere detail, whether you think it is or not.

I said that in my opinion "snow is white" is an analytic proposition. — RussellA

And now have skipped twice the very exact response I gave about that.

I never said that Tarski said that "P" has to be analytic. — RussellA

Granted. And to be exact, I did not say you had. Rather, you kept saying that you think 'snow is white is analytic' (while skipping my replies about that). I wouldn't know why you think it being analytic is important, unless perhaps you think that Tarski chose it for the reason that it is analytic. So, without claiming that you had said that the schema disallows synthetic instances, I stressed that indeed it does not.

To recap:

'Snow is white' is analytic or not depending on the definition of 'snow'. With a definition of 'snow' that includes 'white' then I'd say 'snow is white' is analytic. But I showed you another definition in which 'white' is not included.

If the analyticity of 'snow is white' does not imply that Tarski chose it because it is analytic and thus that the schema is meant to convey that its only instances should be analytic, then what is the point of going on about the purported analyticity of 'snow is white'?

But now I see that you finally state your agreement that the instances of the schema don't have to be analytic.

So what's next? Most importantly, what's for lunch?

Tarski in The Semantic Conception of Truth and the Foundations of Semantics uses denote for one or more items.

For example, he wrote:
1) The expression "the father of his country" designates (denotes) George Washington.
2) We have seen that this conception essentially consists in regarding the sentence "X is true" as equivalent to the sentence denoted by 'X' (where 'X' stands for a name of a sentence of the object language).
3) While the words "designates," "satisfies," and "defines" express relations (between certain expressions and the objects "referred to" by these expressions)
4) We should reconcile ourselves with the fact that we are confronted, not with one concept, but with several different concepts which are denoted by one word — RussellA

And that is misleading.

First, at least it is misleading formatting. The items are from very different parts of the paper, and not a list he made, as it looks from your formatting, of considerations about 'denote'.

Second, (4) is not about the meaning of the word 'denote' but rather it's about the meaning of 'true'. That 'true' has different conceptions.

(Thanks to bongo fury for catching all that and causing me to notice it too.)

However, Tarski does mention elsewhere that there are different senses of 'denote', but it's a highly technical matter he's addressing. Usually, he uses 'denotes' or 'names' in the very ordinary sense of the words.

It's ludicrous that you bring Umberto Eco into this. Tarski in 1931 and 1944 is concerned with mathematical logic, not literary criticism. He uses 'denotes' in a very ordinary sense, not anticipating what Umberto Eco might say decades later.

And to drive the point home about what Tarski means by 'denote', he gives the formulation of the method of models in which symbols are mapped to individuals, functions and relations. That is a formalization of the idea of symbols denoting those individuals, functions, relations.

It's the very simple idea:

'Chicago' maps to Chicago.

'Carl Sagan' maps to Carl Sagan.

'Cats' map to cats.

'maps to in an interpretation', 'denotes', 'names', 'refers to'. Different words doing the same job here.

If you want to understand Tarski and not be bogged down in misunderstandings, then you'd do well to start there, and to refrain from dripping goop all over by ridiculously dragging Umberto Eco into it.

Second, (4) is not about the meaning of the word 'denote' but rather it's about the meaning of 'true'. That 'true' has different conceptions. — TonesInDeepFreeze

The complete paragraph containing item 4) is:
It seems to me obvious that the only rational approach to such problems would be the
following: We should reconcile ourselves with the fact that we are confronted, not with one
concept, but with several different concepts which are denoted by one word; we should try to make these concepts as clear as possible (by means of definition, or of an axiomatic procedure, or in some other way); to avoid further confusions, we should agree to use different terms for different concepts; and then we may proceed to a quiet and systematic study of all concepts involved, which will exhibit their main properties and mutual relations.

How is this paragraph about the meaning of true. The word "true" isn't mentioned. ?

Tarski wrote that we are confronted with several concepts denoted by one word, ie, one word may denote several concepts.

How is this not about the meaning of the word "denote" ?
===============================================================================

Tarski in 1931 and 1944 is concerned with mathematical logic, not literary criticism. — TonesInDeepFreeze

I have never said that Tarski was concerned with literary criticism.

Tarski's article The Semantic Conception of Truth and the Foundations of Semantics was published in 1944.

Within the article he wrote:
Semantics is a discipline which, speaking loosely, deals with certain relations between
expressions of a language and the objects (or "states of affairs") "referred to" by those expressions. As typical examples of semantic concepts we may mention the concepts of
designation, satisfaction, and definition as these occur in the following examples:
the expression "the father of his country" designates (denotes) George Washington; snow satisfies the sentential function (the condition) "2 is white"; the equation "2 . x = 1" defines (uniquely determines) the number 1/2.

The Cambridge Dictionary defines semantics as the study of meanings in a language.

I haven't said that Tarski was not concerned with mathematical logic. I pointed out that Tarski had a concern with the semantic conception of truth, and the semantic conception of truth is not the same as the mathematical conception of truth.

You write that Tarski is using "denote" in the ordinary sense of the word.

@TonesInDeepFreeze: "However, Tarski does mention elsewhere that there are different senses of 'denote', but it's a highly technical matter he's addressing. Usually, he uses 'denotes' or 'names' in the very ordinary sense of the words."

Are you saying that the ordinary sense of the word "denote" is the mathematical sense of the word "denote" ?
===============================================================================

It's the very simple idea: 'Chicago' maps to Chicago. 'Carl Sagan' maps to Carl Sagan. 'Cats' map to cats. — TonesInDeepFreeze

It is a simple idea until one considers how "a unicorn" maps to a unicorn, or "beauty" maps to beauty.

How exactly does "beauty" map to beauty. ?
===============================================================================

If you want to understand Tarski and not be bogged down in misunderstandings, then you'd do well to start there, and to refrain from dripping goop all over by ridiculously dragging Umberto Eco into it. — TonesInDeepFreeze

We are specifically discussing the meaning of the word "denote".

You wrote that "He uses "denotes" in a very ordinary sense"

I am pointing out, as Umberto Eco pointed out, that the meaning of "denote" is far more complex than as used in the ordinary sense of "a cat" denotes a cat.

If you reject Umberto's Eco's later contribution, then perhaps consider earlier contributions by Frege and his theory of sense and denotation 1892, Russell's On Denoting 1905 or Saussure's Course in General Linguistics based on notes of lectures 1906 to 1911.

How exactly does "snow" denote snow ?

In the ordinary sense, "snow" denotes snow because "snow" denotes snow.

If the answer to that was agreed, then many of the problems in the philosophy of language would be well on the way to a solution.

The complete paragraph containing item 4) is:
It seems to me obvious that the only rational approach to such problems would be the
following: We should reconcile ourselves with the fact that we are confronted, not with one
concept, but with several different concepts which are denoted by one word; we should try to make these concepts as clear as possible (by means of definition, or of an axiomatic procedure, or in some other way); to avoid further confusions, we should agree to use different terms for different concepts; and then we may proceed to a quiet and systematic study of all concepts involved, which will exhibit their main properties and mutual relations.

How is this paragraph about the meaning of true. The word "true" isn't mentioned. ? — RussellA

It is remarkable that you say that. It is quite an example of willfully ignoring a mass of context. 'truth' or 'true' are mentioned 15 times in the section in which that paragraph is in the middle.

[begin quote; bold and italics added]

14. IS THE SEMANTIC CONCEPTION OF TRUTH THE "RIGHT" ONE?

***The subject of this section is whether the semantic conception of truth is the only right one.

I should like to begin the polemical part of the paper with some general remarks.

I hope nothing which is said here will be interpreted as a claim that the semantic conception of truth is the "right" or indeed the "only possible" one. I do not have the slightest intention to contribute in any way to those endless, often violent discussions on the subject: "What is the right conception of truth?" I must confess I do not understand what is at stake in such disputes; for the problem itself is so vague that no definite solution is possible. In fact, it seems to me that the sense in which the phrase "the right conception" is used has never been made clear. In most cases one gets the impression that the phrase is used in an almost mystical sense based upon the belief that every word has only one "real" meaning (a kind of Platonic or Aristotelian idea), and that all the competing conceptions really attempt to catch hold of this one meaning; since, however, they contradict each other, only one attempt can be successful, and hence only one conception is the "right" one.

*** We're not getting in arguments premised on the view that there is only one right concept of truth.

Disputes of this type are by no means restricted to the notion of truth. They occur in all domains where - instead of an exact, scientific terminology - common language with its vagueness and ambiguity is used; and they are always meaningless, and therefore in vain.

*** The concept of truth is not the only subject over which there are such arguments. When the subject matter is not exact enough, there are such arguments.

It seems to me obvious that the only rational approach to such problems would be the following: We should reconcile ourselves with the fact that we are confronted, not with one concept, but with several different concepts which are denoted by one word; we should try to make these concepts as clear as possible (by means of definition, or of an axiomatic procedure, or in some other way); to avoid further confusions, we should agree to use different terms for different concepts; and then we may proceed to a quiet and systematic study of all concepts involved, which will exhibit their main properties and mutual relations.

*** In situations where a word is used to denote more than one concept, we should agree to use different words.

Referring specifically to the notion of truth, it is undoubtedly the case that in philosophical discussions - and perhaps also in everyday usage - some incipient conceptions of this notion can be found that differ essentially from the classical one (of which the semantic conception is but a modernized form). In fact, various conceptions of this sort have been discussed in the literature, for instance, the pragmatic conception, the coherence theory, etc.

*** There have been a lot of different concepts of truth.

It seems to me that none of these conceptions have been put so far in an intelligible and unequivocal form. This may change, however; a time may come when we find ourselves confronted with several incompatible, but equally clear and precise, conceptions of truth. It will then become necessary to abandon the ambiguous usage of the word "true," and to introduce several terms instead, each to denote a different notion. Personally, I should not feel hurt if a future world congress of the "theoreticians of truth" should decide - by a majority of votes - to reserve the word "true" for one of the non-classical conceptions, and should suggest another word, say, "frue," for the conception considered here. But I cannot imagine that anybody could present cogent arguments to the effect that the semantic conception is "wrong" and should be entirely abandoned.

*** There could be competing concepts of truth that are all just as rigorous. In that case, we would oblige by using a word other than 'truth'.

[end quote]

Yes, the concept of denote itself is one of those that has differing views. But that's not Tarski's point. Rather his point is that, among concepts having differing views, the concept of truth is in particular one of them. The section is not about what we mean by 'denote' but about the concept of truth and the word 'truth' and the fact that the word 'truth' denotes different things for different people. Especially, Tarski is not at all saying he uses the word 'denote' in different ways.

/

I have never said that Tarski was concerned with literary criticism. — RussellA

Yes, and I didn't say that you did. It's my point that he wasn't discussing literary criticism; and dragging Umberto Eco into this is quite aside understanding Tarski.

Within the article he wrote:
Semantics is a discipline which, speaking loosely, deals with certain relations between
expressions of a language and the objects (or "states of affairs") "referred to" by those expressions. As typical examples of semantic concepts we may mention the concepts of
designation, satisfaction, and definition as these occur in the following examples:
the expression "the father of his country" designates (denotes) George Washington; snow satisfies the sentential function (the condition) "2 is white"; the equation "2 . x = 1" defines (uniquely determines) the number 1/2. — RussellA

Yes, and 'denotes' there is in the sense you've been told about in this thread.

I haven't said that Tarski was not concerned with mathematical logic. I pointed out that Tarski had a concern with the semantic conception of truth, and the semantic conception of truth is not the same as the mathematical conception of truth. — RussellA

Wow. You miss the very central point of his articles. Tarski is concerned with providing a rigorous mathematical formulation of the adjective 'is true'. Read the articles.

Are you saying that the ordinary sense of the word "denote" is the mathematical sense of the word "denote" ? — RussellA

When Tarski is using everyday examples, he uses the everyday sense of 'denote'. Then he goes on to make it even more rigorous mathematically.

It is a simple idea until one considers how "a unicorn" maps to a unicorn, or "beauty" maps to beauty. — RussellA

Tarski talks about the fact that in everyday situations we don't have precision. He says that he does not claim to provide an explication of the concept of truth that can withstand all the vagaries of natural language. Nor does he claim to explicate the notion of 'denote' that can withstand whatever disagreements there may be among different settings.

I am pointing out, as Umberto Eco pointed out, that the meaning of "denote" is far more complex than as used in the ordinary sense of "a cat" denotes a cat. — RussellA

Of course it can be as complex as one wants it to be. But Tarski starts with an ordinary intuitive sense and then goes on to pin it down for more rigorous contexts. Read his articles.

/

In sum:

(1) Tarski's overriding concern is with defining 'is true' in context of formal languages for mathematics and the sciences.

(2) He uses an ordinary sense of 'denote' (or cognates of 'denote), but then moves on to instead specify the method of formal modals, where 'denote' is subsumed by certain kinds of functions from linguistic objects to model theoretic objects. This is the movement from informal semantics to formal semantics that Tarski provides.

(3) Whether 'snow is white' is analytic or not is not part of Tarski's concern in the two articles. Moreover, as pointed out: Whether 'snow is white' is analytic depends on which definition of 'snow' we're looking at. There are common enough definitions in with 'white' is not in the differentia.

The definition:

The statement P is true IFF P.

An example:

"Snow is white" is true IFF Snow is white.


Argument A

1. Snow is white $\to$ "Snow is white" is true.
2. Snow is white.
Ergo
3. "Snow is white" is true. [1, 2 MP]

Argument B

1. "Snow is white" is true $\to$ Snow is white.
2. "Snow is white" is true.
Ergo
3. Snow is white. [1, 2 MP]

---

Doesn't this lead to a chicken-and-egg situation?

We can't know "Snow is white" is true unless we know Snow is white and/but we can't know Snow is white unless we know "Snow is white" is true.

Tarski's overriding concern is with defining 'is true' in context of formal languages for mathematics and the sciences. — TonesInDeepFreeze

Tarski's approach is certainly rigorous. I would say logical rather than mathematical or scientific.

He wrote in The Semantic Conception of Truth and the Foundations of Semantic: "The predicate "true" is sometimes used to refer to psychological phenomena such as judgments or beliefs, sometimes to certain physical objects, namely, linguistic expressions and specifically sentences, and sometimes to certain ideal entities called "propositions." By "sentence" we understand here what is usually meant in grammar by "declarative sentence"; as regards the term "proposition," its meaning is notoriously a subject of lengthy disputations by various philosophers and logicians, and it seems never to have been made quite clear and unambiguous. For several reasons it appears most convenient to apply the term "true" to sentences, and we shall follow this course".

As formal languages include logic, mathematics, the sciences and linguistics, it is clear from his article that his definition of "true" is more relevant to the formal language of linguistics than either mathematics or science.

He uses an ordinary sense of 'denote' (or cognates of 'denote), but then moves on to instead specify the method of formal modals, where 'denote' is subsumed by certain kinds of functions from linguistic objects to model theoretic objects. This is the movement from informal semantics to formal semantics that Tarski provides. — TonesInDeepFreeze

I agree that Tarski was concerned with formal rather than informal language.

As he wrote in The Semantic Conception of Truth and the Foundations of Semantic: "While the words "designates," "satisfies," and "defines" express relations (between certain expressions and the objects "referred to" by these expressions)." IE, "designates" ("denotes") is about relations.

The word "denote" may be used in different ways, but as there is no substantial difference in meaning between the "ordinary" sense of the word "denote" and a formal sense of the word "denote", he cannot have moved from an "ordinary" sense to a formal sense.

Whether 'snow is white' is analytic depends on which definition of 'snow' we're looking at. — TonesInDeepFreeze

I doubt there are many definitions of "snow" whereby being white isn't included as a property.

I would say logical rather than mathematical or scientific. — RussellA

First, my point stands that you said the word 'true' is not in the paragraph you quoted, but you intentionally ignored that the words 'truth' or 'true' are mentioned 15 times in the surrounding paragraphs. My point stands: He was talking about 'truth' having different meanings to different people, not about 'denotation' having different meanings. One might think that, for purpose of clear communication, you would admit this now. Instead, where I gave you the actual quoted context, with 15 mentions of 'truth' or 'true', you just go on to post as if it doesn't exist.

About formal languages, mathematics, and the sciences, read the papers! And read the IEP and SEP articles about them. It is a plain fact that Tarski's overriding concern is with languages for mathematics and the sciences. It's throughout the papers.

it is clear from his article that his definition of "true" is more relevant to the formal language of linguistics than either mathematics or science. — RussellA

No, it is overwhelmingly clear that his primary concern is formal languages for mathematics and the sciences. Tarski takes pains to point out that we can't expect to nail the definition of 'true' for informal contexts and that his proposal is directed at mathematics and the sciences. Moreover, a great amount of the paper goes on to actual mathematical formulations of the definition of 'true'. The papers are steeped in it. The primary area of concern is model theory, which is a subject of mathematical logic. Man, you need to read the papers, and for even more much needed background, get a textbook in mathematical logic so that you can appreciate the fruit of Tarski's work.

The word "denote" may be used in different ways, but as there is no substantial difference in meaning between the "ordinary" sense of the word "denote" and a formal sense of the word "denote", he cannot have moved from an "ordinary" sense to a formal sense. — RussellA

But he did! He showed the method of models, mathematically. Read the papers!

My points stand: (1) Tarski's overriding concern is with formal languages for mathematics and the sciences. (2) In the passage you quoted, Tarski is not about the fact that 'denotation' has different senses but about the fact that 'truth' ('true' also) has different senses. Either merely blithely or dishonestly, you misrepresented Tarski with your original 1-4 decoction, and then again by choosing just one paragraph from the middle of the other paragraphs. (3) Whether or sentence is analytic or not is not part of Tarski's concern in the particular regard of his schema.

But you will keep replying with your confused, uninformed and dogmatic misinterpretations. I'm running out of time to keep correcting you.

How exactly does "snow" denote snow ?

In the ordinary sense, "snow" denotes snow because "snow" denotes snow. — RussellA

What does this have to do with Tarski?

The statement P is true IFF P. — Agent Smith

Where did Tarski write that?

The quote marks are crucial.

'P' is true iff P.

Doesn't this lead to a chicken-and-egg situation? — Agent Smith

It's a biconditional. Formal definitions are biconditionals. He's not saying how we know that 'snow is white' is true. He's only giving a definition of 'is true'.

Moreover, if you want to know that 'snow is white' is true, then you can look at snow to find out.

The mere fact that a formulation is a biconditional doesn't entail that we can't move from right to left (or from left to right) to make our inferences.

You really really need to read a book on the subject of formal logic. Otherwise, you will continue to incessantly spin out in your own confusions.