In any case, it is NOT a realist point of view IMNSHO to imagine that ideas can exist independently of actual people having them, in some platonic realm.

In any case, — Olivier5

Wrong battle. I already know your position; you're now proselytizing.

Bis repetitas placent. And I cannot let it be said that it is antirealist to point out that propositions have to be proposed...

Let me proselytize a little more.

To think of knowledge as a commodity, like salt or copper, a thing that can exist irrespective of whether human beings pay attention to it or not, is the wrong way to think about it. Knowledge is not a commodity, it is an activity.

As a consequence, the unknown is NOT a commodity either. And it does not come already prepackaged in neat little English sentences called 'propositions'.

And I cannot let it be said — Olivier5

You have no choice.

that it is antirealist to point out that propositions have to be proposed... — Olivier5

Have to be proposed in order to... what?

in order to be propositions.

The topic is about propositions, but more formally about sentences. Yet it doesn't matter toward the point that 'Kq' does not stand for 'We know of the existence of q' but rather it stands for 'We know that q is true'.

"We don't know that the earth is round"

and

"We believe that the earth is flat" [...]

The differences are so easy to point out that I don't see the sense in asking about it. — TonesInDeepFreeze

There is no mistake in that.

Why is
q -> Kq
being stated?
— TonesInDeepFreeze
Because p -> Kp was stated. — InPitzotl

Who stated it? To be clear, Fitch does not hold that p -> Kp.

No one believes that as a generalization for all q.
— TonesInDeepFreeze
Apparently some people do. It's an antirealist position; the p doesn't exist until it's proposed, and it isn't true until you say it is, or some such thing. — InPitzotl

What specific quotation or reference is given by anyone (other than a flagrantly errant poster) that p -> Kp? The supposed antirealist notion is p -> LKp.

I am not sure that all discussants here understand:

(1) 'Kq' stands for "q is known to be true" and it does not stand for "q is known to be a sentence (or proposition)".

(2) Fitch is not arguing that for all p, we have p -> Kp. Fitch is arguing that if for all p, we have p -> LKp, then for all p, we have p -> Kp, but since it is not acceptable that for all p, we have p -> Kp, it is not acceptable that for all p, we have p -> LKp.

The topic is about propositions, but more formally about sentences. — TonesInDeepFreeze

It's about propositions. Let's not change the goal post.

As I said, the general topic regards propostions, but the formal portion of the argument uses sentences. One should read the expositions. And, again, it doesn't matter whether propositions or sentences, the critical point stands that the intended interpretation of 'Kp' is not "We know that p exists" but rather "We know that p is true".

Not all sentences have a clear meaning, not all sentences are about some state of affairs, and not all sentences are proposed as true. So the Fitch is about propositions, not sentences.

The distinction between propositions and sentences is an involved subject in philosophy and logic. [See, for example, Chuch's 'An Introduction To Logic' for one widely referenced treatment.] But no matter, it is not the case that the intended interpretation of the 'K' operator is that of knowing the existence of a propostion or sentence, but rather it is that the proposition or sentence is known to be true. Ignoring that point leads to incoherence.

One needs to read the expositions such as at SEP.

the intended interpretation of the 'K' operator is that of knowing the existence of a propostion or sentence, but rather it is that the proposition or sentence is known to be true. Ignoring that point leads to incoherence. — TonesInDeepFreeze

That's probably a fair point. The SEP is not very clear on this but I trust you.

Let me start by noting a residual ambiguity here. I can see two very different ideas of an "unknown truth":

1. An hypothesis or proposition that has been actually proposed as true by someone, which is in fact true but unbeknown of most, and on which truth value there is no consensus whatsoever yet. For instance: the CIA killed the Kenedy's (if it's in fact true).

2. An hypothesis or proposition that has not yet been proposed by anyone, that is in fact true. For instance: Charlie Chaplin killed the Kenedy's (if it were in fact true that he did but my money is on #1, and if I had not just now proposed it of course...).

While the first meaning is not problematic, I have explained at length why #2 is for me a logical impossibility. Sentences not yet said are not yet said. They don't sit out there in Plato's realm or some similar otherwordly place, waiting for us to say them.

What specific quotation or reference is given by anyone (other than a flagrantly errant poster) that p -> Kp? — TonesInDeepFreeze

Probably none; this was stated by TMF, and the view appears to be held by Olivier5 (haven't caught up here; you've likely already met).

SEP is clear that 'Kp' means "We know that p is true" and that the proof uses sentences. And Wikipedia is even more explicit (I don't automatically trust Wikipedia, but it is lucid on these points). There is no need to trust me; one can read for oneself.

this was stated by TMF — InPitzotl

Which is exactly why I am asking why it is being stated.

One my choose to hold that a proposition does not exist until it is has been expressed. But even if we restrict to the set of propositions that have been expressed, we have not vitiated Fitch's argument.

It is not the case that for all propositions p that have been expressed we have p -> Kp. Therefore, as Fitch shows in the proof, it is not the case that for all propositions p that have been expressed we have p -> LKp.

Understood, but the best I can do is link to context. @TheMadFool mentioned it, but there was something silly there with Fitch only applying to true propositions (follow it to see why I'm saying it's silly).

The furthest I can take you is there; I cannot go inside TMF!

Indeed.

One my choose to hold that a proposition does not exist until it is has been expressed. But even if we restrict to the set of propositions that have been expressed, we have not vitiated Fitch's argument.

It is not the case that for all propositions p that have been expressed we have p -> Kp. Therefore, as Fitch shows in the proof, it is not the case that for all propositions p that have been expressed we have p -> LKp. — TonesInDeepFreeze

That is indeed correct and I understand it is at least one of the 'traditional' readings. Not all propositions are necessarily decidable and we have good reason to think some are indeed not decidable.

In short: we have more questions than answers.

My beef was more with the other idea. The illogical one, which treats knowledge as a commodity.

Fitch's paradox is about true propositions.
— TheMadFool

I know. I'm extending it to false propositions as well. Sue me. — Olivier5

Apophatic Theology

Apophatic theology (via negativans): To deny of God all posssible predicates. So,

God is material. No! God is a male. No! God is x (any predicate). No!

In other words, where Q stands for any predicate and g is God, Qg is always false or ~Qg is always true.

Knowing something, say apples, is nearly always in terms of positive predicates i.e. I know an apple in terms of what it is and not in terms of what it is not.

In apophatic theology, we're asked to know God from what God is not i.e. all we know about God is what is false about God.

Apophatic anything: Knowing not by knowing what is true about that thing but by "knowing" what is false about that thing.

Update

The Justified True Belief Theory Of knowledge asserts that,

S (a person) KNOWS P (a proposition) IFF

1. P is true
2. P is justified
3. S believes P

This looks like a perfectly good definition of knowledge.

Consider now the following 4 paragraphs:

Paragraph 1: Apples are a fruit. Apples are sweet when ripe and they come in different varieties. Apples grow in temperate regions of the world and are widely consumed. Apples are rich in vitamins and antioxidants.

Paragraph 2: Apples are dogs. Apples grow in the desert and apples are found on Venus. Too, apples are cars and they eat meat.

Paragraph 3: Apples are not dogs. Apples don't grow in the desert and apples are not found on Venus. Too, apples are not cars and they do not eat meat.

Paragraph 4: Apples are dogs is false. Apples grow in the desert is false and apples are found on Venus is false. Too, apples are cars is false and they eat meat is false

Paragraphs 1, 3 and 4 contain all true propositions but paragraph 2 consists of all false propositions.

A) If S believes all true propositions in paragraph 1, it can be said that S knows these propositions and also that S has knowledge of apples.

B) If S believes all propositions in paragraph 2, we can say for sure that S doesn't know anything about apples.

C) If S believes all propositions in paragraphs 3 and 4, S knows these propositions BUT it feels odd to say that S has knowledge of apples.

D) Paragraph 3 and 4 are identical as NOT = is false.

Issues:

(i) The JTB theory of knowledge needs reviewing (see C).

(ii) If a proposition p is false, we can't know p (see B) but we can know that p is false, this is a different proposition, ~p (see C)

How does all this matter to Fitch's paradox?

Some have claimed that it's possible to know false propositions.

To clarify that assertion, consider apophatic theology: We can know God via negativans (by way of denying).

The basic idea behind apophatic theology is that we can know by not knowing which can be translated as knowing falsehoods (about God). All I know of God is what is false about God which is a very clever, roundabout, elliptical, way of saying I don't know anything about God.