It seems that that argument would be valid, but only if one accepts that an argument is valid iff there is no interpretation s.t. all premises are true and the conclusion is false per Tones' definition.

If it turned out that validity required more than what that definition suggests (I think it does), then the argument you stated may well turn out to not be valid, as I think is the case. — NotAristotle

You seem to be putting the cart before the horse.

It's not the case that the word "valid" means something and then we try to give a proper description of this meaning, and that we disagree on the proposed definition.

Rather, a bunch of logicians got in a room together and decided that if an argument's conclusion follows from its premises using the rules of inference then they will name this type of argument "valid". And that if the premises are also in fact true then they will name this type of argument "sound".

I don't know what you're talking about.

This recent argument started as a discussion on Fitch's paradox, which examines the anti-realist's knowability principle: ∀p(p → ◊Kp).

Realists reject this knowability principle, claiming that ∃p(p ∧ ¬◊Kp).

Assuming that knowledge is justified true belief, the realist's claim is that there is at least one proposition that is true but that either cannot be believed or cannot be justified (e.g. by seeing evidence that it is the case).

Given that the realist has no a priori reason to suggest that no use of "the cat is in the box" can be one such proposition, the realist accepts that it's possible that some use of "the cat is in the box" can be true but that either it cannot be believed or cannot be justified (e.g. by looking in the box and seeing the cat).

There's also the IEP article I quoted here. Although in that specific case they consider the proposition "I am a brain in a vat" rather than the proposition "the cat is in the box".

That ((P→Q)∧Q), therefore P is not valid, whereas ((A∧¬A)∧(P→Q)∧Q), therefore P is valid, does seem strange to me. Inconsistent premises don't seem to have anything to do with whether the argument "follows." Although I have a feeling that Tones will have something to say about that. — NotAristotle

I am a man and I am not a man. Therefore I am rich.

The argument is valid; the conclusion follows from the premise. We can show this in four parts:

1. If "I am a man and I am not a man" is true then "I am a man" is true.
2. If "I am a man" is true then "I am a man or I am rich" is true.
3. If "I am a man and I am not a man" is true then "I am not a man" is true.
4. If "I am a man or I am rich" is true and if "I am not a man" is true then "I am rich" is true.

But I don't think you're quite acknowledging the nuances of realism in that post. See here where I offer an example involving cats in boxes.

For your specific example, realism entails that even if we examine the entirety of the Solar System with the most sophisticated scientific instruments possible, and even if we fail to see a cup, it might still be the case that there is a cup orbiting the Sun.

Or on the other hand, even if we do (seem to) see a cup, it might still be the case that there isn't a cup (e.g. we're being deceived by someone or something casting an illusion).

These possibilities make justification of anything rather problematic.

I agree with your substitution. So what's the problem?

"to an adequate degree"?

This proposition is true:

1. We do not have evidence that we are brains in a vat

If realism is correct then this proposition is true:

2. It is possible that we are brains in a vat and that we cannot have evidence that we are brains in a vat

My suggestion is that if we cannot have evidence that we are brains in a vat then (1) does not sufficiently justify the claim that we are not brains in a vat.

I gave reasons above. — Leontiskos

But your reasoning is not directed at what I was claiming. You said "you are trying to claim that it follows from your premises that there are truths which are both known and unjustifiable".

I'm not trying to claim that, because that claim would be a contradiction.

You are conflating the possibility of skepticism with skepticism. — Leontiskos

I'm not sure what you think I'm arguing, or what you mean by the possibility of skepticism.

The skeptic doesn't say "we are brains in a vat"; the skeptic says "we might be brains in a vat". Something like "it is possible that we might be brains in a vat" is redundant, as, at least using S5 modal logic, ◇◇P↔◇P.

You are trying to claim that it follows from your premises that there are truths which are both known and unjustifiable — Leontiskos

I'm not.

I'm trying to explain this:

One proposal is to construe metaphysical realism as the position that there are no a priori epistemically derived constraints on reality (Gaifman, 1993). By stating the thesis negatively, the realist sidesteps the thorny problems concerning correspondence or a “ready made” world, and shifts the burden of proof on the challenger to refute the thesis. One virtue of this construal is that it defines metaphysical realism at a sufficient level of generality to apply to all philosophers who currently espouse metaphysical realism. For Putnam’s metaphysical realist will also agree that truth and reality cannot be subject to “epistemically derived constraints.” This general characterization of metaphysical realism is enough to provide a target for the Brains in a Vat argument. For there is a good argument to the effect that if metaphysical realism is true, then global skepticism is also true, that is, it is possible that all of our referential beliefs about the world are false. As Thomas Nagel puts it, “realism makes skepticism intelligible,” (1986, 73) because once we open the gap between truth and epistemology, we must countenance the possibility that all of our beliefs, no matter how well justified, nevertheless fail to accurately depict the world as it really is. Donald Davidson also emphasizes this aspect of metaphysical realism: “metaphysical realism is skepticism in one of its traditional garbs. It asks: why couldn’t all my beliefs hang together and yet be comprehensively false about the actual world?” (1986, 309)

I try to prove an even stronger version of this using propositional logic here.

So you think you need antirealism to avoid being a vatted brain. Right. — Banno

These mean different things:

1. We are brains in a vat
2. It is possible that we are brains in a vat

In propositional logic:

1. P
2. ◊P

If realism is correct then (2) is true. Putnam argues that (2) is false and so that therefore realism is incorrect.

Repeatedly you either fail to understand or intentionally ignore the distinction between what is said to be true (or known, or proved) and what is said to be possibly true (or knowable, or provable).

Sure. And they do this by rejecting classical logic. — Banno

Well, yes. That’s how Dummett defined the distinction between realism and antirealism; realists commit to the classical logic of bivalence and antirealists reject it.

Realism does not commit to vat brains. — Banno

It entails their possibility. Antirealism provides an opportunity to dismiss the notion as nonsense.

and from which follows that that all truths are known. — Mww

Well, no.

The antirealist argues that if "the cat is in the box" is true then it's possible for someone to know that it's true, e.g. by looking in the box and seeing the cat. The fact that it's possible for someone to look in the box and see the cat does not entail that someone already knows that the cat is in the box: perhaps nobody knows because nobody’s looked.

The realist argues that "the cat is in the box" can be true even if it's not possible for someone to look in the box and see the cat.

Which is more reasonable? I say the former. The latter arguably doesn't even make sense. What does it mean for it to be not possible for someone to look in the box and see the cat (despite the cat being in the box)? Looking in the box and seeing the cat is certainly not a contradiction, so it can't be that.

Some musings.

Let's take the knowability principle from Fitch's paradox: ∀p(p → ◊Kp).

According to this, "a marker of necessity functions as a universal quantifier: it indicates that the basic proposition is true in all possible states of affairs. A marker of possibility functions as an existential quantifier: it indicates that there is at least one state of affairs in which the basic proposition is true."

So the knowability principle can be rephrased as:

□(p → ◊Kp)

The realist rejects this knowability principle.

But under S5 ¬□(p → ◇Kp) → □¬Kp.

So if the knowability principle is false and if S5 is correct then nothing is knowable (and so nothing is known)?

What is it about antirealism that you have to say? — Banno

The first thing is that it isn't any of your strawmen. Antirealism doesn't claim, and nor do antirealists acknowledge that it entails, that all truths are known.

The second thing is that it is consistent with a deflationary account of truth.

The third thing is that it avoids certain absurdities that realism allows for, e.g. that it is possible that we are unknowably brains in a vat.

The fourth thing, albeit directed at Janus, is that it is not obviously wrong.

It seems to me that you ignore most of what I've writ, preferring to nit pick a few near-irrelevancies. — Banno

I’m sorry but this is quite the ironic thing to say given the rest of your response to my post. Pot, meet kettle.

And I don’t think I’ve ignored anything?

I think a better example is: “Banno has stopped beating his wife”.

Assuming, I hope, that you have never beaten your wife.

The choice is between saying that there are unknown mathematical truths and saying that there are unknown physical truths. I'd entertain Kripke's approach to truth for maths but not for physics. So we can usefully say that Goldbach's conjecture so far has no truth value but that there is water on Miranda is either true or it is false. — Banno

How do you get from “there are unknown mathematical truths” to “Goldbach's conjecture so far has no truth value”? And who has denied that that there is water on Miranda is either true of false?

Again, you don’t seem to fully acknowledge the distinction between being knowable and being known.

If Goldbach’s conjecture is provable then even if it hasn’t yet been proven it is true.

If water on Miranda is provable then even if it hasn’t yet been proven there is water on Miranda.

Perhaps the best way to understand antirealism is to rephrase Putnam’s argument against metaphysical realism: if there are unknowable truths then it is possible that “we are brains in a vat” is an unknowable truth. It is not possible that we are brains in a vat. Therefore, there are no unknowable truths.

The problem with realism is that it entails this kind of global skepticism. If there are unknowable truths then there are unjustifiable truths, and if there are unjustifiable truths then a proposition not being justified is not a good reason to reject it.

In fact, for all the realist knows, perhaps almost all truths are unknowable and so unjustifiable, which arguably gives them even less reason to reject an unjustified proposition.

"P" is true IFF P. — Banno

The above sentence is true because the sentence fragment on the left hand side (“‘P’ is true”) means the same thing as the sentence fragment on the right hand side (“P”).

You appear to be trying to conflate deflationism and disquotationalism. They are not the same thing. One can be a non-deflationary disquotationalist (in fact I seem to recall Tarski as thinking of his theory as a type of correspondence theory).

Well, no. That's far too vague. One is about the weather, the other is about a sentence. But (1) and (2) are arguably truth- functionally equivalent. — Banno

I’m confused. Are you a truth deflationist or not? A truth deflationist will accept that (1) and (2) mean the same thing. But now you say that they don’t mean the same thing and are only “truth-functionally” equivalent. That strikes me as being decidedly non-deflationary.

Ok, so are you agreeing with Dummett? — Banno

I’m just offering an example of what I think is a deflationary anti-realism.

Yeah, they can reject it all they like. It doesn't follow that they are right. ∀p(p→◊Kp)⊢∀p(p→Kp — Banno

As the SEP article says, “Fitch’s proof is not a refutation of anti-realism, but rather a reason for the anti-realist to accept intuitionistic logic. … without double negation elimination one cannot derive Fitch’s conclusion ‘all truths are known’”.

If you think this is wrong, tell me why. — Banno

I don’t think it’s wrong. I just don’t understand why you think that antirealism about mathematics doesn’t entail that all mathematical truths are known/attitudes but that antirealism about the weather entails that all truths about the weather are known/attitudes.

We are sometimes surprised by things that are unexpected. How is this possible if all that is true is already known to be true? — Banno

The claim isn’t that all truths are known. The claim is that all truths are knowable. Remember, anti-realists reject Fitch’s conclusion.

Overwhelmingly, you and I agree as to what is true. How is that explainable if all there is to being true is attitudes? How to explain why we share the same attitude? — Banno

The claim isn’t that all truths are attitudes. The claim is that all truths are knowable.

We sometimes are wrong about how things are. How can this be possible if all that there is to a statement's being true is our attitude towards it? — Banno

The claim isn’t that all truths are attitudes. The claim is that all truths are knowable.

I honestly don’t understand what you think antirealism is.

Remember, you claim to be a mathematical antirealist. Presumably you accept that mathematical truths aren’t attitudes and that there are unknown mathematical truths. So simply extend your understanding of propositions about numbers to propositions about medium sized dry goods.

it remains unclear how this helps the topic, or relates to it any more than bringing in intension. — Banno

So we have this:

Sentences (1) and (2) mean the same thing.

Dummett then argues that (2) is only meaningful if it is verifiable. This is his Language Acquisition Argument.

If (1) and (2) mean the same thing and if (2) is only meaningful if it is verifiable then (1) is only meaningful if it is verifiable.

If (1) is only meaningful if it is verifiable then unknowable truths make no sense.

One of us is clearly misunderstanding the other. I’ll try to rephrase what I was saying more clearly:

1. “It is raining” is true
2. It is raining
3. “It is not raining” is true
4. It is not raining

Sentences (1) and (2) mean the same thing.
Sentences (3) and (4) mean the same thing.

This is precisely the deflationary account that you claimed to support above.

The problem is that no conjecture can be proven to be true or false, so on the antirealist view, assuming you have correctly outlined it, no conjecture could be either true or false. — Janus

I’m not sure what you mean.

The conjecture “alien life exists on Pluto” can be proven true or false by going to Pluto, looking everywhere for life, and then either finding it or not finding it.

But "'it is raining' is true" means that it is raining, not "it is raining". — Banno

Take these two sentences:

1. “It is raining” is true
2. “It is not raining” is true

According to your reasoning, (1) means that it is raining and (2) means that it is not raining.

It’s not clear what you mean by “means” here. Do you mean “entails”? If so then there are two issues:

The first issue is that when I say “means” I don’t mean “entails”; I mean “is semantically equivalent to”. So, (1) is semantically equivalent to “it is raining” and (2) is semantically equivalent to “it is not raining”.

The second issue is that (1) doesn’t entail that it is raining; rather, (1) being true entails that it is raining. You appear to be mixing up your use and mention.

And it’s important to remember that, at least if we accept the premises of Fitch’s paradox, we’re dealing with modal possibility, i.e that if it is not possible to know something then it is necessarily unknown, e.g that in no possible world does anybody know it.

If the antirealist says we can know whether or not there is a god or a multiverse then they should be able to give an account of how that would be possible. — Janus

That’s not exactly what they’re saying. They’re saying that:

1. If “God exists” is true then it is possible to prove that it is true
2. If “God exists” is false then it is possible to prove that it is false
3. If it is not possible to prove that “God exists” is true and not possible to prove that “God exists” is false then “God exists” is neither true nor false

Dummett’s argument is that the disagreement between the realist and the antirealist concerns the logic of truth. For the realist, every proposition is either true or false. For the anti-realist, some propositions are neither true nor false.

And yet we obviously cannot know either of those. — Janus

It's not obvious to the anti-realist.

If your only "argument" against anti-realism is that it's "obviously" wrong then it's not an argument, just a denial.

A simple account would be to first argue that "'it is raining' is true" means "it is raining", and then to argue that "it is raining" is meaningful only if it describes a verifiable event. It would then seem to follow that "'it is raining' is true but unverifiable" makes no sense.

At least I believe that's the general gist of Dummett's antirealism.

The antirealists must be wrong though because they cannot rule out the possibility that unbeknownst to us there might be unknowable truths. Just stipulating that truths are only truths if they are known seems obviously wrong as it does not accord with the general notion of truth.

What if the question is changed to whether there are unknowable actualities instead? What about, for example, the question regarding the existence of God? We know we cannot know the answer to that, no matter how plausible or implausible the existence of God might seem. Would you say there cannot be a truth about whether or not God exists, despite that fact that it is obviously impossible to know? — Janus

You're just asserting that antirealism is "obviously" wrong. It's not obvious to the antirealist. The antirealist will argue that it is your "common sense intuition" that it wrong.

According to the antirealist, if God exists then we can know that God exists, and if God doesn't exist then we can know that God doesn't exist.

We know it is impossible to answer the question as to whether there is more than one unknowable truth. — Janus

This is the very thing that the anti-realist disagrees with. The ant-realist claims that we can know that there are no unknowable truths. In fact, the anti-realist claims that we do know that there are no unknowable truths. To many anti-realists, the very concept of an unknowable truth is incoherent. To many anti-realists, "X is true" means "X is verifiable".

But that has been shown to be false — Janus

No it hasn't.

What do you think the truth or falsity of "there are unknowable truths" is knowable means?

It means that one of these is true:

a) "there are unknowable truths" is true and we can know that it's true
b) "there are unknowable truths" is false and we can know that it's false

You haven't shown that (b) is false.

As an example to explain this, the truth or falsity of "there is a cat in the box" is knowable means that one of these is true:

c) "there is a cat in the box" is true and we can know that it's true
d) "there is a cat in the box" is false and we can know that it's false

so 1. must be true. — Janus

Yes.

The truth or falsity of "there are unknowable truths" is knowable.

The realist will say that it is knowable that "there are unknowable truths" is true.
The anti-realist will say that it is knowable that "there are unknowable truths" is false.

These are my (1) and (3) respectively.

I provisionally assume that "there are unknowable truths" is unknowable and then show that this leads to a contradiction, which shows it must be false. — Janus

Remember that there are four options, not two:

1. "there are unknowable truths" is knowably true
2. "there are unknowable truths" is unknowably true
3. "there are unknowable truths" is knowably false
4. "there are unknowable truths" is unknowably false

(4) is a contradiction so we can rule that out.

If (2) leads to a contradiction, as you say, then we can rule that out.

But that still leaves both (1) and (3). Your suggestion that if (2) is false then (1) is true is a non sequitur.

However if the starting assumption is that the truth or falsity regarding the existence of unknowable truths is unknowable then we know that there is at least one unknowable truth. — Janus

You assume "there are unknowable truths" is unknowable and then conclude "there are unknowable truths" is knowable.

This is still a contradiction.

You must pick one of these:

1. "there are unknowable truths" is unknowable
2. "there are unknowable truths" is knowable

If you pick (1) then you cannot conclude (2).
If you pick (2) then you cannot use (1) to justify it.

What about all the truths regarding what happened in the pre-human past? Are they unknowable? You might say they are not unknowable in principle. — Janus

They will likely say that propositions about the past are neither true nor false because they (and their negations) are unverifiable.

Fair, so I suppose I should "if P then Q" means "not-P or Q or both".

However if it is right that the truth or falsity regarding the existence of unknowable truths is unknowable then we know that there is at least one unknowable truth. There is no contradiction — Janus

That is literally a contradiction.

The first part in bold is saying that "there are unknowable truths" is unknowable and the second part in bold is saying that "there are unknowable truths" is knowable.

If there is a truth as to whether there are unknowable truths, then that truth is an unknowable truth. So we know there is at least one unknowable truth. If you think there is something wrong with the reasoning, then say what it is. — Janus

I explained it in that previous post.

You go from a) "there are unknowable truths" is unknowably true to b) "there are unknowable truths" is knowably true. This is a contradiction. If (a) is true then (b) is false and if (b) is true then (a) is false.

A ⊻ ¬A ↔ A ∨ ¬A

I have shown that we know there is at least one unknowable truth. — Janus

No you haven't. You've just asserted it, hence why you are begging the question.