Sure, something might be (as yet) unjustified and yet could be justified. In which case, since it could be justified, there is something which counts as it's justification. — Banno

What does it mean that something counts as its justification? Are you just repeating the claim "p can be justified"? What is the difference between (1) and (3)?

It woudl help considerably if you explained what you think a justification might be. I've already pointed out that mere logical entailment will not do. — Banno

It's whatever distinguishes knowledge from a mere true belief.

As a specific example, if "the cat is in the box" is true then perhaps the strongest justification is looking in the box and seeing the cat. That's an ordinary reason that we can be said to know that the cat is in the box.

Given that looking in the box and seeing the cat is always possible in principle, every case of "the cat is in the box" being true is justifiable, even if it hasn't yet been justified (i.e. we haven't yet looked in the box) – and even if it never is justified (i.e. we never look in the box).

So, at the very least, we should be antirealists about cats in boxes.

You want (1) not to entail (3). — Banno

I don't even know what (3) is. You won't explain it.

Again, I suspect you are equivocating. First you treat (2) and (3) as meaning different things, allowing you to say that (3) follows from (1) without saying that (2) follows from (1), and then you treat (2) and (3) as meaning the same thing, allowing you to say that if (2) is false then (3) is false.

So spell it out for me. What does (3) mean? How does it differ from (1) and (2)?

As it stands, anti-realism simply says that (1) is always true and (2) is sometimes false. And that's it. There is no additional proposition (3).

(1) entails (3). (2) entails (3). — Banno

So you have:

P1. If (1) then (3)
P2. If (2) then (3)

And then you seem to go:

C1. If not (2) then not (3).

That's denying the antecedent.

It would still really help if you explain what (3) means, and how it differs from (1) and (2).

This is your game. you get to decide, I supose. — Banno

You're the one who has introduced new grammar, so you need to explain it.

1. p can be justified
2. p is justified
3. p has a justification

I can't help but think that you're equivocating. You say that (1) entails (3), say that (2) is false, somehow use that to conclude that (3) is false, and so use that to conclude that (1) is false.

Sure. But "can be justified" entails "has a justification". — Banno

What is the difference between "is justified" and "has a justification"?

Only if you do not wish to allow for justifications in other possible worlds. — Banno

What? It doesn't follow because it doesn't follow, just as the spouse example doesn't follow.

Your other analogs do not work. — Banno

They work perfectly. They show that your re-phrasing of the claim has changed the meaning of the claim.

Do you really want to say that if a proposition is true than in some possible world there is a justification? Fine, then for you every truth has a justification. — Banno

That simply does not follow.

If some entity is a person then in some possible world it has a spouse. Therefore, every person has a spouse?

No, obviously not.

If every truth is justifiable, then for every truth there is some justification. — Banno

Just no.
"can be justified" does not entail "is justified".
"can be killed" does not entail "is killed".
"can be broken" does not entail "is broken".

It's honestly crazy that I have to explain this to you.

The point of that was to show that there is a meaningful difference between these two propositions:

1. If A is B then it can C
2. A can be B only if it has C

Banno is repeatedly misinterpreting/misrepresenting (1) as (2).

Sure you do. If you want to deny A→B then you must give an example of A^~B. — Leontiskos

Firstly, I don't. One approach is to show that A→B is a contradiction or is in some other sense incoherent. Antirealists often do this by addressing the meaning of the word "true" and explain that this meaning is inconsistent with unknowability.

Secondly, it is the realist who denies p → ◇Kp, and so if you follow your own reasoning you must provide an example of an unknowable truth.

Were Michael to disagree with this, he would have to show us a justifiable truth with no justifcation. — Leontiskos

No I don't. Just as the realist doesn't have to show us an unknowable truth.

Another example:

1. If the vase is fragile then it can break
2. The vase can be fragile only if it has a break

These do not mean the same thing. (1) is true and (2) is false.

If, for antirealists, as you say, all truths are believable and justifiable, you can drop the modality. p→Jp — Banno

No we can't. Dropping modality changes meaning.

These mean different things:

1. All truths are believed and justified
2. All truths are believable and justifiable

↪Michael It says that if something is mortal, then there is an something which is the death of that thing. Pretty plain. — Banno

This still doesn't explain what that means.

In ordinary English we say that if something is mortal then it can die; we don't say that if something is mortal then something it its death. I understand the former, not the latter.

No. I'm saying that somethign can be mortal only if it has a death — Banno

What does that mean? It doesn't even appear to be grammatically correct.

The set of true propositions is on your account a proper subset of the set of propositions with a justification. — Banno

No it's not. That would be:

1. p → Jp

That's not what is argued. What is argued is:

2. p → ◊Jp

Do you understand the difference?

To better explain it, I am saying:

1. If something is mortal then it can die

You are misinterpreting/misrepresenting this as:

2. Something can only be mortal if it’s dead

If, for antirealists, as you say, all truths are believable and justifiable, then for any given truth there is some justification. On your account, a proposition can only be true if it has a justification. — Banno

You’re making the same mistake. I explained it clearly above:

Note that these mean different things:

1. If a proposition is true then it can be justified
2. A proposition can only be true if justified

In propositional logic:

3. p → ◊Jp
4. ◊p → Jp

At least, (4) is my best attempt at formulating (2). The position of the "can" is a little confusing. — Michael

Do you understand what (1) and (3) mean?

This should not be so hard. — Leontiskos

You’re right, it shouldn’t. Which is why I don’t understand why you are taking issue with what I am saying.

It is simply an a priori fact that from “p and not p” one can derive any conclusion, and so any argument with “p” and “not p” as premises is valid.

I don’t know what you mean by “appealing” to the principle of explosion.

It’s like saying that we “appeal” to modus ponens.

We use modus ponens to derive some conclusion and we use the principle of explosion to derive some conclusion.

This is all a priori reasoning based on logical axioms, not some a posteriori proposition that is possibly false.

I don’t know what you mean by “presupposing” the principle of explosion.

See the “⊢ Q” at the end? That means that Q follows from the bit before.

We’ve already established that “(P ∨ Q) ∧ ¬P” is true, so therefore “Q” is true.

Yes

Why? — Leontiskos

Because of the reasoning explained here.

And again, if that is no more than that it can be made the consequent of a material implication, that is trivially right. So again, what is it to be "justified"? — Banno

Yes. And if B then A→B, for any A or B. So if we take justification as being the consequent of a material implication then that any truth is justified is trivial.

But is that what you mean? — Banno

I don't really understand what you're asking.

We have realists claiming that some truths are unknowable and antirealists claiming that all truths are knowable.

Assuming that knowledge is justified true belief, this reduces to the realist claiming that some truths are either unbelievable or unjustifiable and antirealists claiming that all truths are believable and justifiable.

What counts as justification is certainly an issue worth considering at some point, but I don't think it's particularly relevant to the current issue being discussed.

We can tentatively just say that it’s whatever distinguishes knowledge from a mere true belief.

(do I need to add that if it is justified, then it is by that very fact justifiable?) — Banno

Sure, justified entails justifiable. But justifiable does not entail justified. Antirealists are only claiming that if a proposition is true then it is knowable (justifiable), not that if a proposition is true then it is known (justified).

Returning back to a previous comment of yours:

Just to be clear, my target here is the idea that a proposition can only be true if justified. — Banno

Note that these mean different things:

1. If a proposition is true then it can be justified
2. A proposition can only be true if justified

In propositional logic:

3. p → ◊Jp
4. ◊p → Jp

At least, (4) is my best attempt at formulating (2). The position of the "can" is a little confusing.

It's valid. I don't even know what you mean by "not presupposing the principle of explosion".

As I said, there aren't two arguments; there is one argument:

P1. P ∧ ¬P
P2. P ∧ ¬P ⊢ P (conjunction elimination)
P3. P ⊢ P ∨ Q (disjunction introduction)
P4. P ∧ ¬P ⊢ ¬P (conjunction elimination)
P5. (P ∨ Q) ∧ ¬P ⊢ Q (disjunctive syllogism)
C1. Q

But we don't have to write out P2 - P5 because they are all necessarily true; they are some of the rules of inference. We can leave it as:

P1. P ∧ ¬P
C1. Q

I haven't said that this has something to do with every kind of valid argument. It has nothing (necessarily) to do with modus tollens or modus ponens, for example.

Michael is adamant that any such claim which does not explicitly rely on explosion is implicitly relying on explosion. — Leontiskos

No I'm not.

No, the issue is that if (2) is true then no one can presuppose (1), because the proposition in question is justifiable. — Leontiskos

Anyone can suppose anything.

1. Suppose that I am a woman.
2. I am not a woman.
3. Therefore, supposition (1) is false.

If you don't believe that (2) is true then you might assert (1), perhaps because someone has tricked you into believing that I am a woman.

The issue is that if (2) is true then "We are brains in vats" is not representative of global skepticism at all. (2) does not invalidate global skepticism, it invalidates the idea that "We are brains in vats" is representative of global skepticism. — Leontiskos

I don't understand what you're saying here at all. All I can do to correct is you is to re-quote the IEP article on the brains in a vat argument:

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)

1. Suppose, "We are brains in vats" can be true even if it is not possible to justify such a proposition
2. "We are brains in vats" is (justifiably) false
3. Therefore, supposition (1) is false — Leontiskos

That's basically what I said.

The issue is that if realism is true then supposition (1) is true. Given that supposition (1) is false, realism is false. That's Putnam's reasoning.

Michael thinks your construal of validity is true in virtue of the principle of explosion. — Leontiskos

No I don't. I'm saying that P ∧ ¬P ⊢ Q is valid and that P ∧ ¬P ⊢ Q is called "the principle of explosion".

Much like P → Q, P ⊢ Q is valid and that P → Q, P ⊢ Q is called "modus ponens".

Specifically, you want to say that realism entails that <"We are brains in vats" can be true even if it is not possible to justify such a proposition>. You then go on to attempt to justify the proposition, <"We are brains in vats" is false>. Even supposing you succeed, your success would show that the putatively unjustifiable proposition is in fact justifiable, which moots the criterion of realism (per your strange/exaggerated definition). — Leontiskos

It's a simple modus tollens:

1. If realism is true then it is possible that we are (unknowably) brains in a vat
2. It is (knowably) not possible that we are brains in a vat
3. Therefore, realism is false

I don't see that you can substitute □(p → ◊Kp) for ∀p(p → ◊Kp). — Banno

Yeah, going over it again I think I misunderstood what the article was saying about the relationship between the two.

The "principle" of explosion directly infringes the law of non-contradiction. It's silly to even call it a principle. — NotAristotle

The principle of explosion is simply the acknowledgement that if we apply the rules of inference to a contradiction then we can derive any conclusion we like. That is simply an a priori fact about propositional logic.

Obviously almost nobody will accept that a contradiction can be true.

Although there are dialetheists like Graham Priest who argue that they can.

Just to be clear, my target here is the idea that a proposition can only be true if justified. — Banno

But that's not what has been said. What has been said is that if a proposition is true then it is justifiable.

So, what? — Banno

So it entail global skepticism, which might be seen as undesirable. And if Putnam's argument is a sound refutation of global skepticism then it's a sound argument against realism.

And if the reasoning here is correct then it entails that nothing is known; my counterpart to Fitch's paradox.

Every unjustifiable truth is unjustified but not every unjustified truth is unjustifiable. Realism allows for unjustifiable truths, and that is a problem.

The wikipedia article you cited literally says the principle of explosion is "disastrous" and "trivializes truth and falsity." — NotAristotle

It says "the existence of a contradiction (inconsistency) in a formal axiomatic system is disastrous", which it is.

Given that P ∧ ¬P entails Q, we must be sure that we never allow for P ∧ ¬P to be true.

This has already been explained to you. — Leontiskos

He's talking about something else. I'm taking about this:

P1. P ∧ ¬P
C1. Q

This is literally the principle of explosion:

In symbolic logic, the principle of explosion can be expressed schematically in the following way:

P ∧ ¬P ⊢ Q For any statements P and Q, if P and not-P are both true, then it logically follows that Q is true.

---

Your contention that argument 2 cannot ever exist without argument 1 is magical, ad hoc thinking. There is nothing serious about it. — Leontiskos

See the section titled "Proof" which includes all my additional steps P2 - P5. They don't need to be made explicit because they are inherent rules of inference.

There's also Banno.

It's in that post above. There's Hart, McGinn, Mackie, and Routley. And of course Fitch himself.

You ask me for an example and then complain that it's just one example?

And you accuse me of sophistry and not being serious... :roll:

This is evidence of your sophistry. — Leontiskos

How is it sophistry? I have provided the source. It's right there, explicitly saying "the realist believes that it is possible for truth to be unknowable in principle."

All I've asked is for you to give me an example of a realist who holds to your strange version of realism. — Leontiskos

Again, read the article:

Rediscovered in Hart and McGinn (1976) and Hart (1979), the result was taken to be a refutation of verificationism, the view that all meaningful statements (and so all truths) are verifiable.

...

Mackie (1980) and Routley (1981), among others at the time, ... ultimately agree that Fitch’s result is a refutation of the claim that all truths are knowable, and that various forms of verificationism are imperiled for related reasons.

I am going to limit myself to serious interlocutors. — Leontiskos

I am being serious. Read up on the principle of explosion.