You don't see the difference between what I wrote and what you wrote? Are you suggesting that what you said is the same as what I said? I see a difference.

If Fred's belief is false, and Fred's belief is that the tree is an English Oak, then "The tree is an English Oak" is false. To be false is to be not true. So Fred's belief is different to what is true.

Which was my point.

So I'm not seeing a problem.

Truth ranges over propositions and such. — Banno

Is hitting the target a property of the arrow? — Srap Tasmaner

By the way, if I was quoting someone, I didn't know it.

But can you fill it out? — Banno

I can tell you what I was thinking; it's not complicated. In order to tell you some part of how things stand in our shared world, I must be accurate. Big as the world is, it is possible to miss when aiming at it. If I tell you Donald Trump won the 2020 presidential election, my arrow has gone wide. It may make a bullseye on some other world, but not on this one.

Now we seem to agree that having struck the target is not merely the condition of the arrow, but involves the target as well. They are related in a certain way, and it is that relation that we call "having hit the target". Examine the arrow, and you will find it is no different from any other, no different from one that missed the target entirely, no different from one still in the quiver. On all this, I take it we agree.

Truth is when you hit the target.

Hence I avoided "Truth is a property of propositions and such". — Banno

Indeed.

But if you don't mean that truth is a property of propositions, I don't know what you mean when you say "Truth ranges over propositions and such." "Ranges over" how? What does that mean? Does the rest of the world play any part in this ranging that truth does?

Hmm. In order to miss the target, there must be a target to miss. In order to lie, or to be mistaken, there must be a truth.

I don't know what you mean when you say "Truth ranges over propositions and such." — Srap Tasmaner

Nor do I, apart from that it is propositions and such that are true, or not. In a way this is stipulating the sense of "true" we are using here; as might be opposed to a true friend or a true note.

If true claims can be unwarranted and unwarranted claims can be true, then defining truth in terms of warrant seems unwarranted. — Pie

Consider the accepted though controversial definition of knowledge as justified, true, belief (JTB theory of knowledge). A proposition p is knowledge IFF

There's a knower K

a) who has the belief p
b) p is true
c) p is justified

If all conditions a, b, c are fulfilled K knows p and that's knowledge. Clearly, since p is true is a separate condition (b) to justification (c), the conclusion is obvious viz. that whether p is true or not needs to be determined independently of its justification. For that the first port of call is a definition of truth that has nothing to do with justification i.e. we can't say that a proposition p is true IFF there's proof of p. What might this definition (of truth) be and how are we going to verify/falsify the truths of propositions in a way that skips proofs/justifications?

In order to miss the target, there must be a target to miss. — Banno

And I must be shooting at it. I do other things as well.

But yes, it stands to reason there's a target. Problem?

it is propositions and such that are true, or not — Banno

And the arrows that are stuck in the target are indeed there, can be counted and so on. But you would count them not because they are arrows, but because they are arrows that are stuck in the target. There are lots of arrows. Arrows are cheap. What makes an arrow interesting, given that I was aiming at the target, is that it hit.

We can move on to nails I hit right on the head, if you're tired of archery.

For that the first port of call is a definition of truth that has nothing to do with justification — Agent Smith

Indeed, if belief and truth were not different, then all we would need for knowledge would be justified belief.

@Sam26?

Problem? — Srap Tasmaner

Only that those who might suppose there to be no difference between truth and belief do not seem to have the benefits of a target for their arrows.

I don't see that we have a point of disagreement.

But this exchange reminds me of Kant's distinction between logic as such, and transcendental logic -- the primary difference being one abstracts from spatio-temporal relations, and the other does not. If you'll allow the indulgence, I believe it goes back to Aristotle's definition of non-contradiction which you are mirroring here, Janus --

link

“It is impossible for the same thing to belong and not to belong at the same time to the same thing and in the same respect” (with the appropriate qualifications) (Metaph IV 3 1005b19–20). — Aristotle in the SEP on Logic




Still, worth highlighting that the relationship between time and logic is thorny. In a sense logic should be timeless. Yet we live in time. What to do with that? — Moliere

Personally I think the attempt to separate logic from temporality and spatiality is doomed to fail, or to yield an insipid and uninteresting logic, that is merely formal, and suitable only for "bean-counter" types. I think you are right about the connection to Aristotle. My questioning of the role of time and place in such formulations as 'it is either raining or not raining, but not both' shows the ambiguity of the idea of place. Time is easier for us to delimit since we have clocks.

Other examples like 'an object cannot be both black and white all over' are much less ambiguous. We can visualize the impossibility of an object being two colours or tones all over very easily, just because such a thing is impossible to imagine.

So, I believe that what seems self-evident in logic is so because of what we perceive and what we can imagine perceiving, and what we can consequently imagine being the case. To my way of thinking this is the essence of modal logic; what is impossible in all worlds just is what we find impossible to imagine, and I think what we can imagine is constrained by the general characteristics we are able to identify in what we perceive. If we perceived very different images of the world with very different characteristics, then we would be able to imagine what for us, as we are, is unimaginable, and our logics would be correspondingly different.

Indeed, if belief and truth were not different, then all we would need for knowledge would be justified belief. — Banno

I believe in mathematics truth is defined as provable i.e. knowledge is justified true belief (truth is redundant i.e. subsumed under justification).

I believe in mathematics truth is defined as provable i.e. knowledge is justified true belief. — Agent Smith

Is your belief that Paris is the capital of France true or merely justified? If you want to say it's true and justified then it would count as knowledge according to JTB. But if you want to say it's true, does that mean that you know it's true or you merely believe its true?

If you can say you are certain that Paris is the capital of France and that therefore 'Paris is the capital of France' is true, then if you were correct then you could be said to know that your belief is true and justified.

It's odd that JTB says that in order to know something, what we take ourselves to know must be justified and true. But if we knew both of those conditions were satisfied, we must already know whatever it is we know to be true independently of its being justified, since they are separate criteria.

That's why I say that to know is to be certain, as distinct from merely feeling certain. But then how can we ever be certain that we are certain? It makes it look like JTB says we can have knowledge but never know (in the sense of not merely believe, or feel certain, but be certain) that we do, because that would involve an infinite regress.

A complex post; above my paygrade pal.

Anyhow, we're in Gettier problem territory as per my map. There seems to be an gap between truth and justification i.e. even if you have a proof for a proposition p, p can still be false. Go figure! From an induction perspective this makes complete sense of course but from a deduction point of view - the conclusion is necessarily true if the premises are and duely plugged into a valid argument form - it doesn't. You mentioned infinte regress, gold star for you!

A complex post; above my paygrade pal. — Agent Smith

I think it's just a post just going around in circles, making it seem complex, but it is the inevitable going around in circles when trying to claim not merely belief, but knowledge (except in the case of that which is presently perceived) that is the problem. Belief may consist in feeling certain, but we don't merely want to feel certain, since then it would be possible to be wrong, but aspire, futilely, to be certain; in other words to be able to claim knowledge that we, per impossibile, know that we know and know that it cannot be wrong.

Of course, for all practical, non-skeptical, purposes we have all kinds of "certain" knowledge.

So you agree that truth is a relation between a proposition and something else. There might be more that goes into that, but it's at least that.

Here's a variation on this theme. Consider the arrow again. You could say Hit(some-target, some-arrow), and that would be a two-place predicate. But you could also, given a target, produce a one-place predicate, Hit-this-target(some-arrow). You get the one-place predicate by partially applying the two-place predicate.

Now compare how we handle truth in possible worlds semantics. Is truth a one-place predicate? It can be, if you have fixed which world you're talking about, but the general form would be True(P, W), right? It's a start, but you'll often see more, adding a catchall "situation", ⟨P, W, S⟩, or time and location, ⟨P, W, L, T⟩. You could certainly add language, and deal directly with sentences. However complex this relation becomes, you could always curry it to get back to a one-place predicate "true".

But truth is only a one-place predicate by assumption or by choice.

It's at the very least a relation between a proposition and something else. Agreed?

I think it's just a post just going around in circles, making it seem complex, but it is the inevitable going around in circles when trying to claim not merely belief, but knowledge (except in the case of that which is presently perceived) that is the problem. Belief may consist in feeling certain, but we don't merely want to feel certain, since then it would be possible to be wrong, but aspire, futilely, to be certain; in other words to be able to claim knowledge that we, per impossibile, know that we know and know that it cannot be wrong.

Of course, for all practical, non-skeptical, purposes we have all kinds of "certain" knowledge. — Janus

Fallibilism springs to mind. Methinks we've set the bar so high that we can forget about 1^st, 2^nd, and 3^rd positions, there isn't even one who can make the jump.

I say we make do with what we got ... pray and hope for the best!

So you agree that truth is a relation between a proposition and something else. — Srap Tasmaner

Did I? Seems a step too far. I think I maintained that truth ranges over propositions, in order to contrast it with belief, which seems to involve both propositions and believers.

truth ranges over propositions — Banno

Maybe you should rephrase that for Srap Tasmaner's benefit.

So you agree that truth is a relation between a proposition and something else. There might be more that goes into that, but it's at least that. — Srap Tasmaner

Yes, if truth were not a relation between a proposition (or belief) claiming (or believing) whatever and something else that provides the conditions for thinking the proposition or belief to be true, then truth would be an empty wheel spinning in the void.

You seem a bit too preoccupied with where you believe my position is mistaken. That's several times now where you've charged my position with some sort of confusion or mistake that you imagine, I suppose, that you understand. It's almost as if you do not understand that your ontology for meaning, truth, and belief stops at meaningful marks whereas mine digs a bit deeper.

Well, hold on a second there. Suppose the case of seeing the sheet-as-sheet. — Moliere

What's the difference between seeing the sheet and seeing the sheet-as-sheet?

Fallibilism springs to mind. — Agent Smith

The idea of fallibilism in relation to belief makes sense, but not so much in relation to knowledge. To be fallible is to be possibly wrong and if knowledge is true, how could it be wrong? There seems to be a mighty hole in the AP submarine!

:up: Maybe life is precisely about there being a (mighty) hole in your sub and limping safely back to port. Sophia is elusive.

Seems a step too far. I think I maintained that truth ranges over propositions — Banno

No progress there, so let's revisit "ranging", then I'll give up:

I don't know what you mean when you say "Truth ranges over propositions and such."
— Srap Tasmaner

Nor do I, apart from that it is propositions and such that are true, or not. In a way this is stipulating the sense of "true" we are using here; as might be opposed to a true friend or a true note. — Banno

So your position is that "true" is a word that can be applied to various things -- statements, beliefs, friends, bicycle wheels, and so on -- and you've chosen some of those things that seem related and said you're using the word "true" in the sense that it applies to those things; and the sense in which the word "true" ranges over some of those things is, well, that you can apply the word "true" to them.

Anything to add?

What's the difference between seeing the sheet and seeing the sheet-as-sheet? — creativesoul

Sheet-as-sheet is stronger :strong:

statements, beliefs, friends, bicycle wheels, and so on — Srap Tasmaner

Not so much bicycle wheels. Statements, beliefs, sentences, utterances, yes. And yes, there is not much more to its analysis than is given in a T-sentence. I've been maintaining a deflationary account, with nothing more substantive like coherence or correspondence.

I like small truths. I've found them more... congenial. Other views suffer hubris.

Again, this is ill-formed, mixing predicate and propositional terms with abandon. — Banno

I asked a related question elsewhere and got this as the answer by someone more knowledgeable than me:

This way you can formalize the sentence "if the cat is on the mat then that cat exists" as

Q(a)→∃x(x=a)

where a is that cat, and Q(y) means that "y is on the mat".

But if you prefer, perhaps address the English language translation:

1. for all p, the proposition that p is true if and only if p
2. for all p, if the proposition that p is true then the proposition that p exists
3. for all p, if p then the proposition that p exists (from 1 and 2)
4. for all p, the proposition that p is false if and only if not p (from 1)
5. for all p, if the proposition that p is false then the proposition that p exists
6. for all p, if not p then the proposition that p exists (from 4 and 5)
7. for all p, the proposition that p exists (from 3 and 6)

Are you saying that 2 and 6 are false?

But you can't get to "q exists". That'd be an instance of the existential fallacy. That a set has a particular attribute does not imply that the set has members.

The more precise form of my argument takes as a premise ∀p: T(q) ↔ p and so concludes ∀p: ∃x(x=q). It doesn't conclude ∃p: ∃x(x=q), and so there is no existential fallacy.

Fred's belief is different to what is true. — Banno

What does this difference amount to? How is Fred's false belief different from someone's true belief, other than one propositional statement is true and the other is false, which amounts to a difference about the facts. Also, I do believe truth and falsity are properties of propositions.

For me, the content of a belief is expressed as statements/propositions. Moreover, I don't see how Searle can get away from the idea that there is a relationship between what Fred believes and his statement that he believes it. As if there is some mistake here to be avoided. The only mistake is adding in these extraneous notions. I don't see any of these theories adding anything important to the idea of truth. I think Wittgenstein had a point about these kinds of theories, which is why he tried avoiding them.

Such constant symbols cannot be quantified...

Just that. The argument is ill-formed.

What can we do?

Well, we might take "t" as a first-order predicate over a domain of propositions; I gather you want to do something like this. It's fraught, as should be clear by now. All it does is assume that propositions exist by putting them into the domain.

We might try a free logic, but then we'd have an expression something like "whatever is true exits", and fall foul of the inexpressibility of Existence Conditions

Can you demonstrate something on that basis?

Just that. The argument is ill-formed. — Banno

Did you bother even reading the rest of what was said?

This way you can formalize the sentence "if the cat is on the mat then that cat exists" as

Q(a)→∃x(x=a)

where a is that cat, and Q(y) means that "y is on the mat".

It's not ill-formed.

And, to use ordinary English language, are you saying that the below is false?

If the cat is on the mat then that cat exists

What does this difference amount to? How is Fred's false belief different from someone's true belief, other than one propositional statement is true and the other is false, which amounts to a difference about the facts. Also, I do believe truth and falsity are properties of propositions. — Sam26

Well, a difference as to the facts is exactly a difference as to which statements are true.

And it's held by someone other than Fred.

That's it.