Michael

But that's the non-omniscience principle? Without it we must accept that every true proposition is known to be true – which is what Fitch's paradox sh...

The formal definition is ?p(p ? ¬Kp): there exists some proposition p that is true and not known to be true. For example, either "the Riemann hypothes...

I've done so a couple of times: here and here.

Fitch's paradox shows that if all truths are knowable then all truths are known. Some truths aren't known, therefore some truths aren't knowable.

That's not how the rules of inference work.

There exists a being x and a time t such that x knows at t that proposition p is true: ?x?t(Kxtp) 1. p ? ??x?t(Kxtp) 2. p ? ¬?x?t(Kxtp) 3. ??x?t(Kxt(p...

See here for an explanation in ordinary language.

Where's the language game here? 1. p ? ?Kp (knowability principle) 2. q ? the Riemann hypothesis is correct 3. r ? the Riemann hypothesis is not corre...

By someone at some time. In fact the opposite: Kp ? ?Kp. No, because if you address the formal logic of the argument you will see that it entails a co...

In reality, yes. However, Fitch's paradox shows that the knowability principle entails that there are no unknown truths. That's why Fitch's paradox sh...

OK. But it's still the case that the argument shows that, given the knowability principle, all truths are known. However, it's a fact that some truths...

If there are no unknown truths then all truths are known.

OK. This has nothing to do with Fitch's paradox.

The argument shows that if we assume p ? ?Kp then p ? Kp follows. Kp ? Kp is a truism that doesn't need Fitch's paradox to prove. No, I need to show t...

By "known truth" I mean "a proposition that someone knows to be true" and by "unknown truth" I mean "a proposition that no-one knows to be true."

A known truth. Yes, either "the Riemann hypothesis is correct" is an unknown truth or "the Riemann hypothesis is not correct" is an unknown truth. Whi...

Which is a false interpretation. I've explained the logic several times.

And yet we don't know which of "the Riemann hypothesis is correct" and "the Riemann hypothesis is not correct" is true, but one of them must be. There...

The non-omniscience principle is the principle that there is some proposition p that is true and that we don't know to be true. Either "the Riemann hy...

This has no bearing on Fitch's paradox.

Us, now.

p is "the Riemann hypothesis is true". q is "the Riemann hypothesis is false". Either p or q is true and neither p nor q is known to be true. Therefor...

As I said to Luke, this isn't what Fitch's paradox is (necessarily) saying. It's saying that there is some proposition that is not known to be true. T...

Does it? On the opposite view, what is needed to hold all material things together for them to have regularities?

The fuzzy term "common logic" but not the term "fuzzy logic"? Sorry, couldn't help myself. :wink:

However, this seems a well reasoned reassurance: Why Other Fundamental Rights Are Safe (At Least for Now)

The problem with that is that it's relatively easy to overturn a law. Even if the Democrats are able to pass a federal law to protect these rights, wh...

Yes, his solution is probably the one I'm most partial to. See here.

Yes, I was considering the same sort of thing. I think this kind of self-referential knowledge is victim to the same problems as other self-referentia...

I think you're the only one guilty of equivocation here. In the context of the argument, Kp means "it is known that the statement p is true". It does ...

Then that's a denial of the knowability principle. The problem is that if you insist on the knowability principle then the only other way to avoid a c...

Maybe if I make it clearer you can see: 1. p??Kp (knowability principle) 2. q ? p?¬Kp (define q as something that is true but not known to be true) 3....

1. p??Kp 2. ¬Kp 3. p?¬Kp??K(p?¬Kp) The logic is straightforward and results in a contradiction.

The knowability principle is the principle that a statement is true if and only if it is possible to know that the statement is true. If it is not pos...

Then I will offer a specific example of p: 1. if the Riemann hypothesis is true then it is possible to know that the Riemann hypothesis is true 2. we ...

We don't know that p is true in this case.

No, it shows that every true statement is known to be true. I explained this here. I'll try to be even clearer now: 1. if p is true then it is possibl...

Yes, and as the knowability principle is the principle that p is true if it is possible to know that p is true it then follows from what you say here ...

No it isn't. The non-omniscience premise of the argument is that there is some statement p that is not known to be true. We might very well know of th...

On the grounds that we can't know both that p is true and that we don't know that p is true. That's a contradiction.

But we don't know which of the statements is true, which means that we must reject the knowability principle. The argument is that if it is possible t...

I don't see how that addresses the paradox. Assuming the law of non-contradiction and the law of excluded middle, either "the box is empty" is true or...

I don't understand what this is saying at all.

Actually, thinking on it more, even this might not be correct. Consider the statement "there exists more than one mind" (or even the more specific "th...

I think it more accurate to say that if idealism is true then all true statements of the form "p exists" are apparent to a conscious mind, which doesn...

Yes

I’m saying that the truth of “if X had happened then Y would have happened” does not depend on the existence of a parallel world where X and then Y ha...

Yes.

That a statement is about a mind isn’t that it’s truth depends on someone knowing it to be true. This is where there appears to be some equivocation. ...

I don’t think that truth depends on the existence of some corresponding entity. Claims about the future can be true even if the future doesn’t exist. ...