Yes, it can be encoded in symbols, in bits, whatever; — Art48

Indeed. Aka a "text".

but what is it irrespective of any encoding? — Art48

Nothing. Don't be greedy.

John: The book is in my room — Michael

Our upcoming discourse on this topic will be safely and perpetually interpretable as pointing all appropriate paraphrases of "the book" and of "is in my room" at the same region of space-time.

Jane: What you say is wrong because the book is not in your room — Michael

I predict that our discourse will either reject that basis for interpretation or become far less agreeable.

his assertion being true or false has nothing to do with what he believes (or what Jane believes), and everything to do with whether or not the book is in his room. — Michael

But it has everything to do with agreement about the reference of words in the discourse, as well as the things thereby referred to. No truth without language.

1. Tq <-> p ... premise — TonesInDeepFreeze

Realists would argue that there is no connection; that there is some possible world where it is raining but where nothing is uttered. — Michael

Do you mean where p without Tq?

Or where not even p, because that's an utterance?

But if uttering p is ok to describe (from outside it) the state of some utterance-free world, why not also Tq?

what logic am I using when I say that if John is bald then John exists?
— Michael

"John exists" is not expressed in mere predicate logic. You need modal logic for it. — TonesInDeepFreeze

Why not (with "J" for "is John" and "B" for "is Bald"),

∃x (J(x) ∧ B(x)) => ∃x (J(x))

?

Now to say that the rock exists is not to say something about the rock. Existence is not a predicate in the way being granite is. — Banno

Only insofar as our favourite logic treats it with a special predicate (ish) called a quantifier.

∃x T(x) ∧ R(x)

But in other words,

An x exists such that x is this and x rocks.

Hmm, how about a rockifier?

Яx T(x) ∧ E(x)

An x rocks such that x is this and x exists.

Obviously this would be silly. But the utility of the canonical expression is in requiring an upfront commitment as to the perfectly sensible question whether or not such an x exists.

Things in the past existed, things in the present exist, and things in the future will exist. — Michael

Or, e.g. for physics, some existing things are spatio-temporal regions wholly earlier than your present point of view, some temporally overlap that point of view, and some are wholly later.

On the other hand if "yesterday's rock", "today's rock", and "tomorrow's rock" refer to the same object [or region of space-time], and if that object [or region not only] exists [but also temporally overlaps your p.o.v.], then yesterday's rock [not only] exists [but also overlaps] and tomorrow's rock [not only] exists [but also overlaps]. — Michael

Yes, but any temporal slice of the region wholly earlier than today exists, and so does any temporal slice wholly later.

Perhaps a more relevant question would be "does the [temporally overlapping part of the] rock exist with the properties [that existing but temporally non-overlapping parts of] it [have] had in the past and/or will have in the future"? — Michael

where Fx means "x is a fairy". — Michael

I.e. the existing space-time region is a fairy.

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.

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".

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.

Applied literally, a magic ceremony.

Applied more widely, to habits more readily than instincts, I'd have thought, anything it's amusing to compare with a magic ceremony.

'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?

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??

I think we could say that the extension of a predicate or function symbol is the relation or function the symbol maps to. (?) — TonesInDeepFreeze

That is semantical. — TonesInDeepFreeze

The extension of a property is the set of all things that have the property.

That is philosophical. — TonesInDeepFreeze

Why/how? Is it that you aren't sure whether by "property" you (or others) mean

• a one-place relation symbol
• the subset of the domain the symbol maps to, or
• something more exotic?

?

The first is suggested by the notion of its having an extension.
The second is what I referred to by the ungainly "unary relation".
The third is suggested by the notion of things 'having' it.

Is the best course just to drop the term, then, as the nominalist recommends? Was my point originally.

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

Typo?

We didn't really get started here, did we? Never mind, I may try again tomorrow, with your forbearance.

monadic — TonesInDeepFreeze

Don't want more!

let's stick to n = 1? — bongo fury

Presumably he is talking about interpreting FOL sentences in general, though.

He doesn't say models. I said models. That's what I'm asking about.

Absolutely. And Goodman goes on in the next paragraph (and the link in the first quote will take you there via page 49) to explain how he would eliminate talk of corresponding relations for n > 1. But let's stick to n = 1?

Exactly.

I mean one-place? (Sure I've seen "unary" quite a lot but I doubtless have it wrong.)

Whatever is meant by 'predicate' and 'property' there, you asked about model theory. — TonesInDeepFreeze

I assumed that by 'predicate' was meant primarily linguistic predicate or adjective, but that this corresponds roughly to a unary predicate in FOL? And properties are the corresponding unary relations?

But you wouldn't need to mention those? I mean, you did mention them, as is usual, and my proposed revision was clearly eccentric, in context. So I was pleased when you didn't immediately reject it. I'm ready to hear that model theory would require reference to corresponding properties, contra Goodman.

So I was interested (and still am) in what you have to say.

I can't find a pdf, but here's the paragraph.

A second thread of Hochberg's article comes to something like this: a common predicate applies to several different things in virtue of a common property they possess. Now I doubt very much that Hochberg intends to deny that any two or more things have some property in common; thus for him as for the nominalist there are no two or more things such that application of a common predicate is precluded. Advocates of properties usually hold that sometimes more than one property may be common to exactly the same things; but Hochberg does not seem to be arging this point either. Rather, he seems to hold that a predicate applies initially to a property as its name, and then only derivatively to the things that have that property. The nominalist cancels out the property and treats the predicate as bearing a one-many relation directly to the several things it applies to or denotes. I cannot see that anything Hochberg says in any way discredits such a treatment or shows the need for positing properties as intervening entities.

E.g.

The nominalist cancels out the property and treats the predicate as bearing a one-many relation directly to the several things it applies to or denotes. — Goodman, p49

But no problem, either? Talk of properties when glossing use of a logical predicate is eliminable?

Even in model theory?

'Snow is white' is true iff what 'snow' stands for has the property that 'white' stands for. — TonesInDeepFreeze

Would you (or Tarskian model theory) accept

'Snow is white' is true iff what 'snow' stands for has the property that 'white' stands for [it, among other things]. — TonesInDeepFreeze

?

I am talking about how the spectrum — apokrisis

I know, but as usual you don't see where I'm coming from.

that allows your 50 shades of grey — apokrisis

Yours not mine.

This is confusing for sure. — apokrisis

With that attitude...

But after the separation of the potential, you get the new thing of the possibility of a mixing. — apokrisis

...and with those abstract nouns.

So we start with a logical vagueness - an everythingness that is a nothingness. — apokrisis

Do you mean, an indiscriminate application of colour words to the domain of things (or patches)?

We have a “greyness” in that sense. Something that is neither the one nor the other. Not bright, not dark. Not anymore blackish than it is whitish. You define what It “is” by the failure of the PNC to apply. You are in a state of radical uncertainty about what to call it, other than a vague and uncertain potential to be a contextless “anything”. It is not even a mid-tone grey as there are no other greys to allow that discriminating claim.

But then you discover a crack in this symmetry. You notice that maybe it fluctuates in some minimal way. It is at times a little brighter or darker, a little whiter or blacker. Now you can start to separate. — apokrisis

Do you mean, you are able to apply the words in a manner that begins to distinguish two different though still overlapping colours?

You can extrapolate this slight initial difference towards two contrasting extremes. You can drag the two sides apart towards their two limiting poles that would be the purest white - as the least degree of contaminating black - and vice versa. — apokrisis

But you're anticipating the later refinement (the bipolar continuum) and assuming it's intrinsic to the earlier distinction. I was pointing out that it isn't.

Once reality is dichotomised in this fashion, then you can go back in and mix. You can create actual shades of grey by Goodman’s approach. — apokrisis

Goodman's approach is concrete and clear. Yours is abstract and poetic.

A discrete classification in no way has to imply a continuous one.

How do we recognise the discrete except to the degree it lacks continuity. — apokrisis

If it's not a rhetorical question (and apologies to the OP if this is off topic)...

The final requirement for a notational system is semantic finite differentiation; that is, for every two characters K and K' such that their compliance-classes are not identical, and every object h that does not comply with both, determination either that h does not comply with K or that h does not comply with K' must be theoretically possible. — Goodman, Languages of Art

So not necessarily a matter of degree. Arguably a matter of discrimination. Which can be all or nothing. Witness digital reproduction. Where black and white are kept safely apart by grey, and there is no need for any collapse (or refinement) into 50 or more shades.

(Easy with those abstract nouns please, Apo...)

A kettle is not a word. — Michael

Agree.

A kettle being black is not a sentence. — Michael

Agree, but want to know if "a kettle being black" refers to any combination of these

• the particular kettle indicated by context
• the particular black thing
• kettles in general
• black things in general
• black kettles in general

... which might elaborate picture 2. Or whether you allege, rather, an entity corresponding to the whole sentence "the kettle is black", as per picture 1.

Which would be helpful if using were anywhere near as clear as mentioning. — Srap Tasmaner

Yes, good point, for whole sentences. Not, though, for nouns or adjectives, where the distinction is perfectly clear: use a word or phrase to mention a thing, and use a name of the word or phrase to mention the word or phrase. Mention means refer to. Albeit with a hint of 'in passing'.

For whole sentences, the distinction is clear enough if clarity is desired. Either

Use a sentence to mention an alleged entity corresponding to the whole sentence. And whether or not you commit to the existence of the entity thus alleged, try not to equivocate between that and the sentence itself (mentioned by use of its name). (Picture 1.)

Or

Use a sentence to use one or more of its component parts to mention actual things or classes. (Picture 2.) Or to perform your preferred speech act to which the picture does no justice.

Either way, drop "fact" and "proposition" and "state", if clarity is your aim. Choose "sentence" or "abstract truth-maker" or "situation" or "thing". For as long as these remain somewhat less easily confused.

Some non-linguistic feature of the world has to be a certain way. — Michael

Yes, a certain linguistic way.

The object referred to by the phrase “the kettle” has to have the colour property [be] referred to by the word “black”. — Michael

Or explain 'property'.

Deflation, or inflation?

and we have a more substantial account of truth. — Michael

How isn't it just a more substantial account of p?

Declarative sentences work by pointing a word or word-string at one or more objects. — bongo fury

Why is this at all un-obvious?

I suppose, because why would we need a sentence to point "white" at snow and not need another sentence to point "snow" at snow?

And, because perhaps we don't need a sentence to point "white" at snow. "White" already applies to what it applies to, and that happens to include snow. Otherwise the sentence wouldn't be true.

But we need a sentence to point out, highlight, the pointing or application of "white" to snow in particular, out of all the other things it applies to.

Is there something mysterious about correspondence? — Michael

For whole sentences, yes, a bit.

We have a sentence "the cat is on the mat", we have the cat on the mat, and we say that the former is about or describes the latter. Is that mysterious? — Michael

Yes, a bit, as soon as we notice that parts of the sentence taken separately are about or describe the cat on the mat.

"the cat" is about or describes the cat.

"the mat" is about or describes the mat.

"is on" is about or describes the notorious pair of objects.

Does it, or perhaps the whole sentence, be about or describe a relation? That could be mysterious and controversial. My objection to it, and to any supposed truth-making correlate of a whole sentence, even e.g. of (non-relational) "snow is white", is that it misunderstands how declarative sentences work, and further obscures the matter.

Declarative sentences work by pointing a component word or word-string at one or more objects. (Picture 2.) Thinking that the whole device points at a fact or state of affairs obscures the matter by suggesting that the fact has a similar structure to a sentence, or even a similar function. Perhaps we think the sentence is pointing at a pointing. Who knows what half-baked notions fly around, infecting believers and skeptics of correspondence alike.

A propositional attitude is a mental state held by an agent toward a proposition. — Wikipedia

What would have been wrong with calling such an attitude a sentential attitude? And making it a mental state held by an agent toward a sentence?

A proposition would be no less such an attitude than belief, fear, assertion, doubt etc. The proposition that snow is white would be (e.g.) the proposal that "snow is white" be accepted, or that "snow is white" correspond to reality, or that "snow is white" be true etc.

Not solving much, of course, as such attitudes generally don't.

But folks might be less prone to confuse sentence with reality.

True is what we call sentences which prevail: those whose tokens replicate successfully as free-standing (e.g. un-negated) assertions within the language.

What do you mean? — Bartricks

"True" is what we call sentence tokens that bear repeating on their own terms, which is to say, without contextualising in the manner of "... is untrue because..." or "... would be the case if not for..." etc.

Such contexts are potential predators, and must be fought off and dominated.

I was confusing contextualized meaning and referent. — hypericin

And so was I, but deliberately. As per Goodman: https://fdocuments.in/document/goodman-likeness.html

Not necessarily as per Putnam, but I think it's arguable he is problematising non-extensional meanings.

Unlike redundancy theories, however, the prosentential theory does not take the truth predicate to be always eliminable without loss. What would be lost in (11′) is Mary’s acknowledgment that Bill had said something. — IEP

And that Mary agrees. And you have at least two speakers to deal with if you don't.

So

truth a property of sentences (which are linguistic entities in some language or other), — Pie

reduces further to a property of utterances. E.g.



Language (and even logic) as opinion polling. Which gets my vote, although it can sound daft. As can coherence theory in general, after all.