Same topic as https://thephilosophyforum.com/discussion/15304/mathematical-truth-is-not-orderly-but-highly-chaotic/

Is it ok if we just copy-and-paste the replies? Or should we link to them?

Yes, which is why I keep trying to find some better, more perspicuous ways to carve up "force." I was leaning toward believing that "force" itself should be strictly separated from both assertion and illocution... — J

If not assertion or illocution or denotation, then what is force? There is still no clear account of what this thread is about.

I believe that in order for a sentence to be about something, it has to be used. — frank

So could you not understand what a sentence is about unless it is clear it was being used to make, say, an assertion rather than ask a question? Isn't it a bit more complex than that?

Seems to me that "The cat is on the mat" is about a cat and a mat. And we at least have some idea of what that piece of paper scribed with "Berlin" might be about.

Isn't being about something just a part of the use?

So can't we understand what a statement is about without asserting it to be true or false?

Perhaps we might agree that one might understand what an utterance is about, but not if it were a question or a command... we might partially understand it... or understand part of it.

I don't think anyone has made that claim. — frank

Well, perhaps you haven't. Then we agree that there is a difference between what a sentence is about and what is done with it?

So it'd be neat to set up a system where we seperate out the judgement about our expressions from what they are about, so we could work through any inconsistencies in their content apart from their force.

Enter, Frege.

: Ok, but

Folk seem too keen on claiming that one cannot understand what a statement is about without deciding if it is true or false. That's not right.

I'd just note that the whole apparatus of first-order logic works for fiction. Frodo walked into Mordor, therefor by existential generalisation something walked into Mordor.

An utterance is just sounds or marks. Literally, nothing else. A sentence is a grammatically correct sequence of words, but a sentence has no specific meaning.

A proposition is expressed by an uttered sentence. A proposition is along the lines of content. — frank

Yep. It might be helpful to add "statement" between "sentence" and "proposition". A statement is the concatenation of a noun phrase and a verb phrase. "The cloud is thoughtful". They differ in syntax from questions and commands, although these distinctions blur at the edges. "Is the cloud thoughtful?" "Make the cloud think!".

I find it useful to think of propositions as that subset of statements that take a truth value - so maybe not "The cloud is thoughtful" and maybe not "The present King of France is Bald".

What's perhaps salient here is that we can understand what a statement is about, and indeed, what it would take to make it true or false, while not knowing if it is true or if it is false, and certainly without having to make a judgement as to it's truth. There have been plenty of examples hereabouts - "the grass is green", "the cat is on the mat".

And again we have the important difference between the content of the statement and what is done with the statement.

A proposition is expressed by an uttered sentence. — frank

Sure. But one can utter a sentence without expressing a proposition. And without making a judgement as to the sentence's truth.

Yep.

In order to judge that the definition is true, one already must have a grasp of what it is to be true and what it isn't. So the definition is superfluous.

That's my understanding, and how I read Frege's comment. To judge that a given definition of truth is true, one already must have a grasp of the nature of truth.

Hence Convention T, the minimum that must be the case. "p" is true if and only if p.

Parmenides' questions — J

It's just that so many of the reviews take this as central. It seems these folk would scrap modality. We do think things like "what if I hadn't answered your post?". So perhaps they are wrong and there is no mystery here. That would help explain why no one has been able to set out Kimhi's argument coherently.

I've been one who is inclined to think that ChatGPT and such are not at all mirroring how human minds work, since they are in the end only picking one word after another based on preferential probabilities. I'm now entertaining the reverse view, that many human minds are indeed also only picking one word after another based on the reaction they get. :worry: Hence Trump and Trolling. And many of the replies here. And perhaps Parmenides?

Good. I’m only vaguely aware of how Frege’s concavity differs from our modern universal quantifier, but I think I can still ask these next questions. The Fregean universal quantifier ranges over objects as well as formulae/functions, right? So maybe my question about “Frege on the Beach” (sounds like a hit song) could be phrased as: "When you comprehend the term ‛Berlin’ (as I’m going to assume you do, Herr Frege), does your comprehension depend on the universal-quantification symbol? And then, should you choose to use the term to fulfill a function, does the existence commitment change to ∃x?” So the idea is that ∀ can range over names or terms that are not (yet) part of functions. Clearly, I’m trying to find a way to make a name (and its sense) a “thinkable thought” without violating Frege’s understanding of what logic can do. Does this sound at all sensible to you? — J

I haven't been able to follow this. But at the beginning of this thread I had an intuition that there was some blurring of the notion of force in Frege that has been set out in subsequent work, which is why I went to the trouble of explicating the nature of illocutionary force. "Force" here is used to talk about intentionality, about what we are doing with the words at hand. So we speak of a difference in force between "Grass is green" used as an assertion, command or question. That's illocutionary force, operating at the level of sentences. There's also a difference in using "Berlin" for a city, a person or a rock band, and this might also be called a difference in "force". My understanding is that in choosing the judgement stroke to range over the whole expression Frege removed the illocutionary force. But the "force" that denotes remained. Hence we are able to use the same letter for the same item in the expression, giving us extensionality.

Frege may well have thought that proper names relied on quantification. Russell, arguable, did just that with his Definite Descriptions. But it's no longer so popular.

Yes, that’s how I understand it too. — J

Good. Names are given meaning by being given an interpretation. For propositional logic that interpretation is just "⊤" or "⊥", something that is quite explicit in Frege. But of course there followed Russell's paradox, the controversy about Basic Law Five, the theory of Definite Descriptions, possible world semantics, rigid designation and so on. IT all became quite complicated, and very fruitful.

Yep. "Berlin" names Berlin. "Berlin is the weirdest city" names the true (!). But that's not an end to it, since we can also take "Berlin is the weirdest city" and treat of its parts, concluding that if Berlin is the weirdest city, then something is a city. And here we move from propositions to predicates, from the 0th level to the first level.

Again, it is important to note that the very same sentence may have more than one logical treatment. seems to miss this.

In a way, the OP is asking about the extent to which meaning is use. In what circumstances can we drop use and still have meaning? This is assertoric force: — frank

Sure. What I was at pains to set out in the first few posts here is the difference between asserting a statement and understanding its content. Both involve intentionality, with the "t"; but we can understand the content of a sentence separately from it's illocutionary force. And here I am using a language unavailable to Frege, but which owes much to his work. Frege showed us that if we treat the intentionality (with a "t") of the content extensionally (without a "t") we get some very interesting results.

I gave the quote where Frege himself says that the judgement stroke applies to the whole:

...assertion, which is expressed by means of the vertical stroke at the left end of the horizontal, relates to this whole. — Quoted in SEP 1879a: §2

Ok. Not sure what that has to do with Davidson and Tarski.

"The cat is on the mat" is a string of letters. It's also a well-formed sentence in English, making it a locution. It can be used, amongst other things, to talk about the spacial relation between the cat and the mat. But it might also be used by a secret agent to give the order "Attack at dawn!". The step from a locution to an illocution requires some sort of interpretation, in which perhaps the parts are given a reference, perhaps some other sense. It might be used to say that it is tru that the cat is indeed on the mat, to assert that the state of affairs presented is indeed the case. It might also be used to ask if the cat is on the mat: "The cat is on the mat?". That it has the grammatical form of a statement does not imply that all that can be done with it is to make assertions. If it is used as something that can be either tru or false, then we have some grounds for calling it a proposition. We can consider the content of the sentence, the cat and the mat, and understand which cat and which mat, and yet not know if it is being used as a statement or a question or for something else entirely - perhaps to say that the dog, who sleeps on the mat whenever it is inside, is outside - The cat is on the mat" means that the dog is outside. And then there are perlocutions.

And so on.

All this is not definitive, nor complete, but just a list of some of the aspects that might be considered from even such a simple string of letters. It gets complicated, quickly.

Now one way of dealing with statements is to seperate out the things that are at least prima facie referred to, and to examine the structure of those references. As it turns out Frege showed how we might do this by placing the judgement stoke at the beginning of the expression, thereby separating out the extension from it's locutionary force - although he would not have described what he did in this way. Doing this allowed the development of a quite sophisticated area of investigation, that ultimately helped with developments in truth theory, Model theory, undecidability, modal logic, set theory and so on, and which is central to the workings of device on which you are reading this.

That looks to me to be quite tho opposite of "When a logician separates assertion from proposition, meaning becomes unstable".

So I don't understand your thinking here.

Forgive my extemporising.

Ok. I haven't used any of Davidson's ideas here. So I can't see how that impacts this thread.

Property is the result of the luck of inheritance or the gains of conquest. — Paine

Property is a legal convention, as pointed out. You don't inherit unless there are conventions of inheritance. Conquest is theft until ratified. Something is "mine" only if relevant others agree.

It's arsehole.

Sure, it's a piece of mathematical logic. That doesn't render it meaningless. So are you taking on Tarski, the relevance of which to a discussion of Frege and mathematical logic is obvious, or perhaps Davidson, for daring to suggest that first-order logic might tell us something about language? Which?

What? Can you clarify?

Ok. Whatever else you might think about truth, it's pretty hard to disagree with Tarski. Is that what you want to do?

Ownership is public. You own something only if the rest of us agree that you own it.

That was Marx's argument — Paine

I don't think so. It's about language. the contention is:

Basically ownership is about control. — Benj96

If this were so, then a thief, who gains control over what they steal, would correctly be said to own the the thing stolen.

But that ain't so.

Instead a thief is considered to illegitimately deprive the owner of control.

So ownership cannot be about control.

But pretending it is suits the needs of the authoritarians amongst us.

Sure.

And every other attempt to define truth collapses too. For in a definition certain characteristics would have to be stated. And in application to any particular case the question would always arise whether it were true that the characteristics
were present. So one goes round in a circle. Consequently, it is probable that the content of the word " true " is unique and indefinable — The Thought: A Logical Enquiry

A bit later we get Tarski's definition of truth in terms of satisfaction, getting around the recursion by using metalanguages. I'm contending that what Tarski does is a working through of the implications of Frege's system; that satisfaction is to a large extent implicit in Frege.

Edit: Satisfaction is a pretty straight forward notion. "The cat is on the mat" is true if the cat is one of those things that satisfies "...on the mat" just means that "the cat is on the mat" is true if the cat is one of the items in the group of things "...on the mat".

, As I understand it, 0th level terms - a,b,x - name individuals. Included amongst those individuals are propositions, which in turn name a truth value. So (2+2=4)=(5-3=2)= ⊤. These all name the same individual. So "Berlin" might name the city, and "2+2=5" might name the false.

Deciding what these terms refer to is done when one gives an interpretation to the letters.

Propositions have truth values in virtue of being names for the true or the false.

"Berlin" is not usually interpreted as a name for either true or false, so it doesn't have a truth value.

“What would Frege say about comprehending a singular term?” — J

On this account, both "Berlin" and "2+2=4" are names. Indeed, if a proposition is considered to be a statement with a truth value, then any proposition is just the name of either the true or the false. Assuming bivalency, of course.

Frege sets up existence in terms of satisfaction - though he doesn't use that term. He uses the concavity as a version of the universal quantifier. So far as existence is defined, it is defined in terms of universal quantification. It was working through this that led to Model Theory. So there is much to be said here.

I don't think he defines truth. Rather, he points out that, say, 2+2=4 and 3+3=6 have the same truth value - they are expressions that refer to the same thing. He goes on to point out that

We do not need a specific sign to declare a truth-value to be the False, provided we have a sign by means of which every truth-value is transformed into its opposite, which in any case is indispensable. — SEP

Hence he presumes two truth values without giving any account beyond reference. 2+2=4 names the true; 2+2=5 names the false.

I'm happy to be shown otherwise.

To put it simply, I do not see Parmenides problem. We do think about things that are not the case.

If you have the Tractatus at hand, do a search for "logical space" – the space containing all possible propositions. Have a flick through the results. The way this appears to work is that some subsets of all the possible propositions can be put together consistently, providing a picture of reality, giving us then the task of choosing one picture of the world.

We can think that the cat is on the mat, or that the cat is not on the mat. We choose which to say is true. That judgement is distinct from the coherence of the picture in logical space.

So I am afraid it seems I, and I think others, do not see the problem.

That there is disagreement as to how to read Frege's most basic expressions does not bode well for anything more than bickering in this thread. Here's something very basic and quite important, something I pointed out pages ago...

Notice also that for Frege there is a structure literally hanging from the ⊢. So we have

read from bottom to top, for what we might now write as
∀A∀B(A→(B→A)).
In the modern version all the assertive paraphernalia on the left is removed. Along with it goes much of the implication of commitment. (again, stolen from SEP) — Banno

The judgment stoke occurs once in the expression, at the beginning. It affirms the whole expression, not each individual line separately.

To this I will add:

The horizontal stroke, from which the symbol judgement is formed, binds the symbols that follow it into a whole, and assertion, which is expressed by means of the vertical stroke at the left end of the horizontal, relates to this whole. — Quoted in SEP 1879a: §2

My bolding.

Again, Frege moves the intensional judgement to the left, so that it has within its scope the remainder of the expression, and so sets the judgement aside, allowing the expression to be understood extensionally - that is, allowing the to instances of "a" to be identical.

The overwhelmingly vast majority of true statements about the natural numbers cannot be expressed in language — Tarskian

How’s that?
So they are not well-formed? Something is amiss.

Yep.

That could still be either one. — schopenhauer1

Well, no. "General public" might do.

But your confusion in regard to Kimhi's thesis is warranted.

Speaking roughly, there are folk who think logic is about working out what is true and what is not. Perhaps there is some historical justification for that. On this view there is a requirement that logic be the connection between thoughts and words. This might be the sort of thing McDowell and Kimhi are looking for.

But logic is more about which of the various things we can say are consistent with each other, and what that consistency might be. Science, rather than logic, is more about what is the case and what isn't, .

More a group sharing a way of life and language.

This put me in mind of the thread on Nice Derangement..., where I found the following:

Understanding an utterance in a language you know is not a voluntary action. You don't get the meaning through a conscious and laborious process something like decoding an encrypted message. If there's good reason to think you are doing something like this, you do it out of habit and a facility developed through countless hours of practice, quickly and without attention. You have to pay attention to the speaker, but not to the process of decoding. Or you're not doing anything like that. I would hope this is an empirical question. Either way, understanding is not something you usually should be described as "doing". It's more like something that happens to you.

There is something similar with speaking. Not just with respect to phonetics, not even just with all the mechanical bits of language production, but even in what you say. Think back over the last few days of verbal exchanges you had at work or in a social setting: in how many of those did you have to, or choose to, consciously and with effort decide what to say? Most of the time we effortlessly select the words to use, assemble them into a sentence and utter that sentence, but more than that, very often we don't even have to think about what to say; it just comes to us, which is to say, it just comes out.

Again, there are questions about how to describe what's going on here, but candid speech is, at least very often, habitual, requiring no more conscious effort than understanding the speech of others. — Srap Tasmaner

At some stage seeking explanations stops, and we act.

And to your unanswered question,

Do we agree up to here? — Srap Tasmaner

I think so. I baulk a bit at 'understanding is not something you usually should be described as "doing"', since we do say that he did or didn't understand... We treat it as something we do.

And you are only a couple of thousand behind in total posts. You seem to be catching up.

1.05.

Yep.

Now my response is that we as a community choose to use "the sky is blue" to set out something about the way things are (or are not, when it is overcast). But you don't seem to like this answer. I suspect you want a theory that sets out, for any given sentence, if it is true or no. That's not what logic does. Rather it is about the consistency of what we say.

From the next paragraph: "...the extension is a relation between a and a fact in the world that must obtain". That's not quite right. Extensionality is a consequence of identity. So sets are extensionaly the same when every element of A is also an element of B, and vice versa. Definitions of extensionality in subsequent logics follow this form. That is, the relation is pretty clear. The text asks:

In virtue of what is the forceless combination Pa associated with the truth-making
relation that a falls under the extension of P, and thus with the claim Pa, rather than
with the truth-making relation that a does not fall under P (or falls under the extension
of ~P), and this with the opposite claim ~Pa?

The answer, by example: if P={a,b,c} then Pa is true; if P={b,c,d} then Pa is false.

Of course this doesn't tell us if a is an element of P. That's something you will have to do, an act you might choose to perform. And something quite different to logic.

SO on to the next paragraph, where we find the bit quoted:

Frege’s system of logical notation, depending as it does on a distinction between the intensional force and extensional force of predicates, cannot account for the inference: “p”→ “A judges p”→ “A rightly judges p.” Within the context of “A judges,” “p” takes on a different intensional force (its sense) from when it stands alone, even though its extension (its reference) remains the same; it is intension, rather than extension, that permits inference. — Boynton

This seems pretty much on the money. "⊢p" does not follow from "p". But that's kinda the point Frege makes, and solves with his nomenclature. In setting out Modus Ponens for example, Frege doesn't write
⊢p⊃q
⊢p
⊢q
such that each is within it's own intensional bracket; he writes
⊢(
p⊃q
p
q)
The first is invalid; the second, brilliant. Again, Frege is setting aside the intensional aspect in order to display the extensional. Frege's system 'cannot account for the inference: “p”→ “A judges p”→ “A rightly judges p."' because it is invalid. It simply does not follow from p, that A judges p, nor that A rightly judges p.


Indeed, calling it an "inference" is extremely problematic.

Ok, so we can consider the review in a bit more detail.

The first paragraph makes it clear that the intellectual predecessor here is McDowell. SO the idea is some thing like that declarative sentences are true in that they are identical to a thinkable (an odd nominalisation), securing a connection between mind and truth. Apparently for McDowell, a true thinkable just is identical to a fact. I'm not overly familiar with McDowell, but it seems to me worth noting that what a "true thinkable" is, is far less clear than is the notion of satisfaction that it appears Kimhi wants it to replace.

But again, what is going on here remains unclear. The foremost puzzle is what sort of "identity" might hold between things as divergent as thinkables and facts. So the puzzle that the identity theory of truth wants to solve is the puzzle fo what is going on on the right hand side of a T-sentence: 'p' is true iff p; and it attempts to solve this by an additional identity, between the thinkable'p' and the fact p. Now the identity that holds between 2+3 and 5 is reasonably clear; there are numbers on both sides of the "=". For an identity to hold between a thinkable and a fact, they must be the same sort of thing. I can't see how what McDowell is proposing is an improvement on the T-sentence.

Seems to me that these considerations sit with the Wittgenstein of the Tractatus. And I have noted that the quotes from Wittgenstein used here indicate more dependence on the early rather than later Wittgenstein. My "solution" to the T-sentence issue – so far as there is one – is that on the left, 'p' is being mentioned, and on the right, it is being used (cue and ).
And this might be why I'm not seeing much of worth in what has been said about Frege. It's answering a question already answered, and in a better way.