There's a bunch of stuff that needs to be separated out here.

There is a relevance argument against BIV. You take Realism ⊨ ◇BIV, which i thinks is overreach. I say Realism → (BIV v ~BIV), and for independent reasons ~BIV.

Separately, if one rejects p↔︎◇Kp and accepts accepts p → ◇Kp and accepts p → ◇Kp then presumably one rejects ◇Kp→p. If it is possible to know something, then it must be true - one cannot know things that are false. ◇Kp does entail p.

Another, again separate, point is that if p ⊭ (q ∧ ¬Kq) then p ⊨ (p→(q→Kq)). If p doesn't entail that there is something we don't know, then it entails that we know everything. And so again antirealism entails omniscience. This result contradicts denying Fitch.

If something exists then it is possible to know that it exists, and if it is doing something then it is possible to know that it is doing that thing, and if it is not doing something then it is possible to know that it is not doing that thing, and if it doesn't exist then it is possible to know that it doesn't exist – with the same reasoning applied to the past, the future, and counterfactuals. — Michael

What you describe here is as compatible with realism as antirealism.

Generic Realism:
a, b, and c and so on exist, and the fact that they exist and have properties such as F-ness, G-ness, and H-ness is (apart from mundane empirical dependencies of the sort sometimes encountered in everyday life) independent of anyone’s beliefs, linguistic practices, conceptual schemes, and so on. — SEP Realism

This raises the further issue of the suitability of the sort of second-order formalisation we have been using. We've been focused on Kp, that p is known. We could have focused instead on that p is believed, or agreed, or doubted. These again are propositional attitudes, relations between us and the proposition p. Truth is generally not one of those relations. That is the basis of what I have been arguing here. Hence my first point in this thread:

...realism holds that ...stuff... is independent of what we say about it; anti-realism, that it isn't. — Banno

I meant that truth or falsity is a property of judgements.

Oh, ok. My mistake.

Being a theist he could say that the cat is on the mat is true because God is there to judge it to be so. I guess we can say that truth is a property of judgements, if a judgement would qualify as a a kind of proposition, although that question would open up some other issues I suppose. — Janus

So a theist might attempt to adopt a modified Tarski, such that "p" is true IFF p is willed by god. It might be more honourable if @Leontiskos came out with this openly.

There is a relevance argument against BIV. You take Realism ⊨ ◇BIV, which i thinks is overreach. I say Realism → (BIV v ~BIV), and for independent reasons ~BIV. — Banno

Assuming the law of excluded middle, BIV ∨ ¬BIV is a truism, and is true even if ¬◇BIV. Realism entails more than this, as explained in the IEP article:

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. [See Fallibilism.] 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)

So, again, R → ◇BIV, ¬◇BIV ⊢ ¬R.

◇Kp does entail p. — Banno

No it doesn't, just as ◇p does not entail p. You appear to have confused ¬p ∧ ◇Kp with ◇(¬p ∧ Kp), despite my suggestion not to.

Another, again separate, point is that if p ⊭ (q ∧ ¬Kq) then p ⊨ (p→(q→Kq)). If p doesn't entail that there is something we don't know, then it entails that we know everything. — Banno

I don't understand what your logic is here.

I am saying nothing more than that if a sentence like "it is raining" is true then it is possible to know that the sentence "it is raining" is true, but that the same reasoning does not apply to a sentence like "it is raining and nobody knows that it is raining". It very explicitly does not allow the substitution that is central to Fitch's paradox.

What you describe here is as compatible with realism as antirealism. — Banno

I addressed this in an earlier post:

But then maybe we need to distinguish between two types of realism; one that denies phenomenalism/idealism and one that denies the (restricted) knowability principle. Labels notwithstanding, Devitt's "realism" might be consistent with Dummett's "anti-realism". — Michael

Semantic realism claims that every meaningful declarative sentence is either true or false, which entails that either the counterfactual sentence "if Hitler hadn't killed himself then he would have been assassinated" is true or it is false. This is not compatible with the claim that if such a counterfactual is true then it is possible to know that it is true, because it is impossible to know whether or not such a counterfactual is true.

I've brought up counterfactuals several times now, but I don't recall you ever addressing them, so perhaps you can now. Are counterfactual propositions like the above truth-apt?

...realism holds that ...stuff... is independent of what we say about it; anti-realism, that it isn't. — Banno

There is a difference between p → ◇Kp (if something is true then it is possible for someone to know that it's true) and Bp → p (if someone believes that something is true then it's true). If you are suggesting that anti-realism is arguing the latter then you misunderstand anti-realism.

Right, the theist might say that God's will and God's judgement are all of a piece. For us, on the other hand what we will to be the case and what we judge to be the case are two different matters. The "direction of fit" you often mention.

Assuming the law of excluded middle, BIV ∨ ¬BIV is a truism, and is true even if ¬◇BIV. Realism entails more than this, as explained in the IEP article: — Michael

Yep. You repeat stuff I've already addressed. Only a certain interpretation of realism implies that BIV is possible. That interpretation is not the only one. This is set out in the first half of the paragraph you cite.

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...

Or to phrase this differently, it is possible, logically speaking, that your are indeed a vat brain - Putnam's argument fails to show otherwise. The idea is to be rejected not on logical grounds as Putnam supposes, but on more pragmatic grounds as set out by Davidson and Wittgenstein.

And you will not agree with that, as is your right. So the point is moot. Few things are as tedious as discussions of The Matrix.

No it doesn't, just as ◇p does not entail p. Despite me literally telling you not to, you appear to have confused ¬p ∧ ◇Kp with ◇(¬p ∧ Kp). — Michael

Not at all. ~p→~◇Kp ↔︎ ◇Kp → p. If something is not true then it is not possible to know it is true; hence if it is possible to know something then it is true.

Semantic realism... — Michael

Again, I'm suggesting that the choice between applying realist and antirealist logics is context-dependent. So I do not agree that "every meaningful declarative sentence is either true or false" and hence I do not agree that counterfactuals must be either true or false. (Edit: however, I am happy to take "if Hitler hadn't killed himself then he would have been assassinated" as false. He might have been hit by some random artillery fire.)

If you are suggesting that anti-realism is arguing the latter... — Michael

No. Realism is applicable when "a, b, and c and so on exist, and the fact that they exist and have properties such as F-ness, G-ness, and H-ness is independent of anyone’s beliefs, linguistic practices, conceptual schemes, and so on", and to this list we can add knowledge. In cases where truth is dependent on anyone’s beliefs, linguistic practices, conceptual schemes, or knowledge, then antirealism might be applicable.

Yep. God explains everything, and hence is useless for any sort of clarification.

:up:

Or to phrase this differently, it is possible, logically speaking, that your are indeed a vat brain - Putnam's argument fails to show otherwise. — Banno

It certainly does attempt to, arguing that the correct theory of meaning entails that it is not logically possible that we are brains in a vat. But I'm not trying to argue about the merits of Putnam's argument against the possibility of brains in a vat; I'm simply explaining why the case is made that "it counts against realism that it might permit global skepticism".

If something is not true then it is not possible to know it is true; hence if it is possible to know something then it is true. — Banno

This is not how modal possibility works. Again, you confuse ¬p ∧ ◇Kp with ◇(¬p ∧ Kp).

◇Kp means ◇(p ∧ JBp), where JBp means that p is justifiably believed. ◇(p ∧ JBp) does not entail p and so ◇Kp does not entail p.

Again, I'm suggesting that the choice between applying realist and antirealist logics is context-dependent. So I do not agree that "every meaningful declarative sentence is either true or false" and hence I do not agree that counterfactuals must be either true or false. — Banno

So you're an anti-realist about counterfactuals?

No. Realism is applicable when "a, b, and c and so on exist, and the fact that they exist and have properties such as F-ness, G-ness, and H-ness is independent of anyone’s beliefs, linguistic practices, conceptual schemes, and so on", and to this list we can add knowledge. In cases where truth is dependent on anyone’s beliefs, linguistic practices, conceptual schemes, or knowledge, then antirealism might be applicable. — Banno

And now you're back to failing to distinguish between Kp and ◇Kp.

The antirealist allows for p ∧ ¬Kp, regardless of what Fitch might think. The anti-realist very explicitly says that there are things we don't know.

The relevant concern is whether or not something exists that is impossible to know exists. The anti-realist says that nothing like this exists. If something exists then it is possible to know that it exists (even if we don't in fact know). As Dummett says, there are no verification-transcendent truth conditions (which is not the same as saying that there are no unverified truths).

Would this mean (this question is out of the blue. I have no thoughts on it) that an anti-realist is in some sense committed to foregoing any truly divine cosmological concepts?

This is not how modal possibility works. — Michael

Are you saying this is invalid? I don't think so.

~p→~◇Kp ↔︎ ◇Kp → p. — Banno

◇Kp means ◇(p ∧ JBp), where JBp means that p is justifiably believed. ◇(p ∧ JBp) does not entail p and so ◇Kp does not entail p. — Michael

Substituting (p ∧ JBp) for Kp we get. ~p→~◇(p ∧ JBp) ↔︎ ◇(p ∧ JBp) → p, which is valid. You keep repeating "you confuse ¬p ∧ ◇Kp with ◇(¬p ∧ Kp)" without showing where.

So you're an anti-realist about counterfactuals? — Michael

No. Context.

The antirealist allows for p ∧ ¬Kp, regardless of what Fitch might think. — Michael

This somewhat begs the question, since of course the antirealist wants the commonplace, that there are things we don't know, to be true. The issue here is how to formulate antirealism so that it is constant with there being things we don't know.


Is the difference in our views now that while I think one can choose realist or antirealist approaches in different situations, you think realism inconsistent in all cases? If not, what do you think the difference between our positions is?

Are you saying this is invalid? — Banno

No, I'm saying that ◇Kp ⊬ p, just as ◇p ⊬ p, and so ¬p ∧ ◇Kp is consistent, just as ¬p ∧ ◇p is consistent.

So both the antecedent and the consequent of your biconditional are false. This should be apparent after you performed the substitution:

¬p → ¬◇(p ∧ JBp) ↔︎ ◇(p ∧ JBp) → p

This is unsound because:

◇(p ∧ JBp) ⊬ p
¬p ⊬ □¬(p ∧ JBp)

The issue here is how to formulate antirealism so that it is constant with there being things we don't know. — Banno

That's been done. As the article says:

The intuitionistic anti-realist takes solace in the fact that she is not committed to the blatantly absurd claim that all truths are known.

...

Notice that T-knowability is free of the paradoxes that we have discussed. It is free of Fitch’s paradox and the related undecidedness paradox.

...

Dummett’s knowability principle or DKP, like Tennant’s, is not threatened by the knowability paradoxes, and for the same reason.

The antirealist claims that there are unknown truths but that all unknown truths of the appropriate kind¹ are knowable. With respect to ontology, there are unverified truths but there are no verification-transcendent truth conditions.

_{1 e.g. p exists and has property q}

you think realism inconsistent in all cases? — Banno

I'm not arguing against realism. I am explaining that you are misrepresenting anti-realism. It isn't what you think it is; it neither claims nor entails that all truths are known, it isn't idealism, and it isn't phenomenalism. That there are things we don't know and that things exist even when we don't see them doesn't refute anti-realism.

¬p ⊬ □¬(p ∧ JBp) — Michael

Well, yes, that's kinda the point.

That's been done. — Michael

Yep. With the consequences set out in the SEP article:

The debates surrounding the proper characterization of semantic anti-realism go far beyond the scope of this entry. As for the knowability proof itself, there continues to be no consensus on whether and where it goes wrong.

The antirealist claims that there are unknown truths but that all unknown truths of the appropriate kind1 are knowable. With respect to ontology, there are unverified truths but there are no verification-transcendent truth conditions. — Michael

Some do. Good for them. The question of whether they are right remains open.

it neither claims nor entails that all truths are known — Michael

That, Michael, remains an open question. You misrepresent my position. Again, I am suggesting that different logics might have application in different contexts; that we can adopt a realist approach in some circumstances and an antirealist approach in other circumstances; that it is not all-or-nothing.

Well, yes, that's kinda the point. — Banno

What do you mean? You're the one who brought up ¬p → ¬◇Kp, not me. I am simply explaining that this is not true a priori because ¬p ⊬ □¬(p ∧ JBp).

- You and @Banno are simply contradicting yourselves. You think truth is and is not dependent on minds. I'm not sure what else there is to say here.

It's coherent to say 'it is true that the planet will still exist when humanity has become extinct'. — Janus

Then you're saying that there will be a truth without minds, if you think there are no non-human minds.

They are not saying the same thing; one says it is true now and the other says it will br true then. — Janus

You still haven't given any explanation of how one can make true statements about the future without claiming that something will be true in the future. These are the same unaddressed issues we faced at the very beginning of the conversation.

Right, the theist might say that God's will and God's judgement are all of a piece. — Janus

The theist need only say that God is or has a mind. Not hard.

I'm not sure what else there is to say here. — Leontiskos

Then don't say anything.

There is a difference between something's being the case and something being said to be the case. Pretty simple, but apparently not for you.

It's coherent to say 'it is true that the planet will still exist when humanity has become extinct'.
— Janus

Then you're saying that there will be a truth without minds, if you think there are no non-human minds. — Leontiskos

No I'm not. I'll try one last time. We can say it is true now or we can now say it is true that the planet will still exist when humanity is gone. There will be nobody to speak the truth when humanity is gone. There will be no truth or falsity then if truth is a property of propositions or judgements and there is then no mind to propose or judge.

Existence on the other hand does not depend on minds, propositions or judgements.

You still haven't given any explanation of how one can make true statements about the future without claiming that something will be true in the future. These are the same unaddressed issues we faced at the very beginning of the conversation. — Leontiskos

I have given an explanation, so the issues have been addressed. You. apparently don't want to hear the explanation and continue to conflate existence with truth.

:up: