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: