Were'd it go? — Banno

:chin:

No problem, @Banno. I know you mean well.

I have never studied Philosopy. I only had a course in College, based on the philosophy of Epictetus. On the other hand I have read really a lot of philosophical books (i.e. books with a philosophical content), but not on Philosophy itself, as a discipline or field of knowledge. Yet, I know about a few common terms, but I use them scarcely, only as a "garnish" or a common reference (e.g. materialism, dualism. etc.). But I can do very well without them! :smile:

I stick to simple logic/critical thinking/reasoning. Sometimes I use the (fuzzy) term "common logic", which is not a logic "common" to all, but the priviledge of only a few! By "common", I mean "simple". My mottos: Simple is beautiful. Simple is efficient.

Sometimes I use the (fuzzy) term "common logic" — Alkis Piskas

The fuzzy term "common logic" but not the term "fuzzy logic"?

Sorry, couldn't help myself. :wink:

The seeming paradox is due to adopting a point of view that lays outside of the world of human experience, outside of time and space, the POV of God. If you take time and the human condition into consideration, the Fitch's paradox simply disappears.

Within the boundaries of human experience, a proposition is some statement that someone proposes, at some point in time. A proposition is a proposal made by a proposer (?). Before it was proposed, the proposition simply did not exist.

Or if you prefer, it could only exist in the mind of God. Or maybe some superpowerful alien... Not in a human mind.

Likewise, a statement does not exist before it is stated by some author or another. A phrase does not exist before being phrased.

So, within human experience, it makes no sense to say that a proposition no one knows about is true. The proposition needs to exist first. Once it is proposed, then and only then can the question of its truth be asked, and thus be put into existence, and only then, can the question be answered (or not).

Now, in some sense "truth is out there", the world is what it is and not otherwise. But this "truth out there" is not yet phrased in the form of propositions.

No, you did well. You proved my point that one of the bad things about naming or categorizing "logic" is that it may lead to confusion! :grin:

it makes no sense to say that a proposition no one knows about is true — Olivier5

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. That's not the same thing. For example, the Riemann hypothesis is not known to be true. The paradox can be applied to this single proposition (see my next comment).

What if the Riemann hypothesis is false? Then we do not reject 1. It is not enough that we don't know whether p is true; it must also be true. "p" means/entails "p is true". This is where the equivocation lies. — Luke

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. Therefore, either p∧¬Kp or q∧¬Kq. Then applying the knowability principle, either ◊K(p∧¬Kp) or ◊K(q∧¬Kq). Both are contradictions.

So either every true proposition is known to be true (abandon non-omniscience) or for some true propositions it is not possible to know that they are true (abandon knowability principle).

¬Kp could mean that we don't know the content/meaning of p and/or that we don't know the truth of p; that we don't know the Riemann hypothesis and/or that we don't know that it is true. — Luke

In the context of Fitch's paradox it means that we don't know the truth of p.

It's saying that there is some proposition that is not known to be true. — Michael

Known by whom, and when? To know is an action done by people, and not a passive state of affairs. Some people know, some people don't. To be known is NOT a quality intrinsic to things.

If I state: "Back in antiquity, people didn't know that the earth orbited around the sun" it means something like: "it was true back then that the earth orbited the sun, and folks weren't aware of it at the time, but now we modern folks are aware of it." So it would be like a truth unknown to antiquity folks, but known to us modern folks.

And indeed it is perfectly possible to know that "In antiquity, people didn't know that the earth orbited around the sun". But of course, the folks back in antiquity didn't know that they didn't know that.

Known by whom, and when? — Olivier5

Us, now.

Known by whom, and when?
— Olivier5

Us, now. — Michael

And someone else at another time would have a different knowledge. So there's no such thing as 'a truth known', or 'a truth unknown', in the absolute. It all depends on who does the knowing and when.

And someone else at another time would have a different knowledge. So there's no such thing as 'a truth known', or 'a truth unknown', in the absolute. It all depends on who does the knowing and when. — Olivier5

This has no bearing on Fitch's paradox.

So either every true proposition is known to be true (abandon non-omniscience) or for some true propositions it is not possible to know that they are true (abandon knowability principle). — Michael

What I'm trying to say is that we can abandon the principle of non-omniscience (as given) without implying that all (known and unknown) truths must be known. I believe that all the argument implies is that only known truths must be known; or, more to the point, that no unknown truths can be known.

The principle of non-omniscience implies that there are unknown truths which are or can be known. This is simply a contradiction in terms. If a truth is known then it cannot be unknown, and if a truth is unknown then it cannot be known (per modal principle D in the SEP article). If a truth becomes known then it is no longer unknown. To repeat: no unknown truths can be known and only known truths must be known.

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 hypothesis is correct" or "the Riemann hypothesis is not correct" is one such proposition (as per the law of excluded middle, and given that the Riemann hypothesis has neither been proven nor disproven). Fitch's paradox shows that if a proposition p is true iff it is possible to know that p is true then it follows that either we know that "the Riemann hypothesis is correct" is true or we know that "the Riemann hypothesis is not correct" is true; that there is no proposition p that is true and that we don't know to be true.

Yes, my mistake. It is the substitution of NonO into KP which is the problem. These principles combine to imply that an unknown truth is knowable. However, the independent argument shows that it is impossible to know an unknown truth. Therefore, NonO is rejected and hence all truths must be known.

According to logic, known truths and unknown truths forever stay that way. Otherwise, we could allow for an unknown truth to become known, but then it would no longer be an unknown truth.

In other words, @unenlightened was right.

The implication for the argument remains what I said earlier: no unknown truths can be known and only known truths must be known. That still doesn't seem very omniscient to me, given what we know.

Therefore, NonO is rejected and hence all truths must be known. — Luke

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. Therefore not all truths are known.

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. Therefore not all truths are known. — Michael

Well, I'm saying that the argument implies only that known truths are known, which excludes knowing unknown truths. The independent argument given in the SEP article shows that it is impossible to know unknown truths.

Well, I'm saying that the argument implies only that known truths are known — Luke

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

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

I don't believe that you have.

Is "either the Riemann hypothesis is correct or the Riemann hypothesis is not correct" a known truth or an unknown truth? You've said that that's a known truth, but you've also used this to argue that not all truths are known.

On the other hand, it is unknown which one is true, so you cannot claim that one of them is a known truth.

Is "either the Riemann hypothesis is correct or the Riemann hypothesis is not correct" a known truth or an unknown truth? — Luke

A known truth.

You've said that that's a known truth, but you've also used this to argue that not all truths are known. — Luke

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

On the other hand, it is unknown which one is true — Luke

Which is precisely the point. Fitch's paradox entails that we do know which one is true. Given that we don't know which one is true me must reject the knowability principle.

This has no bearing on Fitch's paradox. — Michael

I think it does. To be known is NOT a quality intrinsic to things, therefore 'an unknown truth' or a 'known truth' have no clear meaning. They are not concepts, just noises made with mouths. One would need to state precisely to whom the truth is known or unknown for these phrases to have a meaning.

Yes, either "the Riemann hypothesis is correct" is an unknown truth or "the Riemann hypothesis is not correct" is an unknown truth. — Michael

You disagreed with my claim that the argument implies only that known truths are known. However, in order to show otherwise, you would need to demonstrate that some unknown truth can be known. Since you do not know which one of the above statements is true, then you have not demonstrated knowledge of an unknown truth.

To be known is NOT a quality intrinsic to things, therefore 'an unknown truth' or a 'known truth' have no clear meaning. — Olivier5

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."

You disagreed with my claim that the argument implies only that known truths are known. — Luke

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.

However, in order to show otherwise, you would need to demonstrate that some unknown truth can be known. — Luke

No, I need to show that there are no unknown truths, which is what Fitch's paradox does; see above.

Someone, somewhere, at some point in time has some knowledge.

If one treats knowledge as a tick-the-box thing, as a feature or commodity, as a mathematical variable that is either present or absent or equal to 12, and existing independently from any particular human knower, then one may indeed end up in a mental glitch.

Just because one can write down K(p) doesn't imply that this scribbling means anything precise.

However, in order to show otherwise, you would need to demonstrate that some unknown truth can be known.
— Luke

No, I need to show that there are no unknown truths, which is what Fitch's paradox does; see above. — Michael

In order to disprove my claim, which is that the argument demonstrates that only known truths are known, then you would need to show that there are no unknown truths? Doesn't that just support my claim? If there are no unknown truths then only known truths are known.

You seem to want to draw from Fitch's conclusion that not only are known truths known, but also that unknown truths are known, such as that (e.g.) "the Riemann hypothesis is correct". I don't draw this absurd conclusion from the argument.

Someone, somewhere, at some point in time has some knowledge. — Olivier5

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

If there are no unknown truths then only known truths are known. — Luke

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

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

Also, if there are no unknown truths, then only known truths are known.

Also, if there are no unknown truths, then only known truths are known. — Luke

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 aren't known. Either "the Riemann hypothesis is correct" or "the Riemann hypothesis is not correct" is one such truth that isn't known.

Therefore, the knowability principle fails.

However, it's a fact that some truths aren't know. Either "the Riemann hypothesis is correct" or "the Riemann hypothesis is not correct" is one such truth that isn't know. — Michael

So there are unknown truths? Are they knowable?

This is what I am denying, since if an unknown truth becomes known, then it is not an unknown truth.

Therefore, the knowability principle fails. — Michael

Not according to Fitch's argument.