That's not the case. It's only the case that both KP and a&b can't obtain. a&b would be fine on its own. — Terrapin Station

Which is exactly what I said... You can't know the conjunction of a&b.

At any rate, this is easily solvable under my epistemology. There are no propositions that someone doesn't know. The idea of that is nonsensical. Propositions only obtain, and truth-value only obtains, when someone has the proposition or the truth-value judgment in mind. — Terrapin Station

This is not a solution because you change the subject. The paradox is directed at someone who believes that both a) there are unknown truths and b) all truths are knowable in principle, and the challenge is to show how both can be true at the same time.

Which is exactly what I said... You can't know the conjunction of a&b. — Fafner

You wrote: " so it follows that the conjunction of a. and b. cannot obtain." That's false. The conjunction of a and b can obtain. The conjunction of KP and a&b is what can't obtain.

This is not a solution because you change the subject. — Fafner

It's not changing the subject, it's just saying that "there are unknown truths" is false. That's the same subject. It's just disagreeing with the premise. Otherwise you'd have to say that any response (to anything) that rejects a premise is "changing the subject."

You wrote: " so it follows that the conjunction of a. and b. cannot obtain." That's false. The conjunction of a and b can obtain. The conjunction of KP and a&b is what can't obtain. — Terrapin Station

Oh I see what you mean, yes I made a mistake in my formulation, I'll fix it.

It's not changing the subject, it's just saying that "there are unknown truths" is false. That's the same subject. It's just disagreeing with the premise. — Terrapin Station

As they say in the Stanford article, the paradox is interesting because (a) and (b) don't seem to be mutually inconsistent (and thus it is surprising if they are), and this is something that people who don't accept one of the premises can agree about.

As they say in the Stanford article, the paradox is interesting because (a) and (b) don't seem to be mutually inconsistent (and thus it is surprising if they are) — Fafner

Yeah, I agree with that. It's not obvious that buying both (a) and (b) would be a problem, and the paradox, especially in light of buying (a) and (b) doesn't seem to have any obvious problem either.

The real problem is supposed to come a few steps later, because you can show that all true propositions are actually known. That result is quite congenial for you, but not for everyone.

Excellent formulation, dear departed member. I shall use it as a starting point to expose my refutation of the Fitch's paradox, for what it's worth.

( @Banno tells me in another thread that it's material for a doctoral thesis; those interested, I just ask that you quote TPF as your source of inspiration :smile: )

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. Maybe that's what Fitch tried to prove?

Note - this is a four year old thread. It would be helpful if you would point that out when you post. That being said, here is my response:

Lamest paradox ever.

Points well taken. I agree it's pretty lame.

Yes, I made pretty much the same objections to it in the other thread.

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). — Olivier5

I agree it makes no sense to say that a proposition about something unknown is true; the most that can be said is that it could be true.

Yes, I would think this is non controversial. I was just trying to write it down somewhere, not restart the debate.

1. F = p is true & p is unknown (true/false?) = there are unknown truths

2. All truths are knowable

3. Possible to know F [from 2]

4. We know F = Known that (p is true & p is unknown (true/false?)) [assume for reductio ad absurdum]

5. Known that p is true & Known that p is unknown [knowing a conjunction is to know each conjunct]

6. Known that p is true [5 Sim] = p is known

7. Known that p is unknown [5 Simp]

8. p is unknown [7, knowing the earth is round implies the earth is round i.e. knowing q implies q]

9. p is known & p is unknown [6, 8 Conj]

10. We can't know F [4 - 9 reductio ad absurdum]

11. p is true & p is unknown [assume for reductio ad absurdum]

12. Knowable that p is true & p is unknown [from 2]

13. Knowable that F (from 1, 2)

14. We can know F (from 13)

15. We can know F & We can't know F [10, 14 Conj]

16. ~(p is true & p is unknown) [11 - 15 reductio ad absurdum]

17. ~p v p is known [16 DeM]

18. p implies p is known [17 Imp]

19. All truths are known! [from 18]

A truth is not necessarily a proposition. If truth exists out there in the wild (if truth is out there), it may not be phrased in the form of neat English sentences yet, until someone does so.

A truth is not necessarily a proposition — Olivier5

An example!

A picture could carry some truth for instance.

Final Version Of Fitch's Paradox, From Wikipedia

1. All truths are knowable

2. p & ~Kp = F = there's an unknown truth

3. F is knowable [from 1]

4. K(p & ~Kp) [assume for reductio ad absurdum, from 3]

5. Kp & K~Kp [knowing a conjunction implies knowing the conjuncts]

6. Kp [from 5 Simp]

7. K~Kp [from 5 Simp]

8. ~Kp [Kq implies q]

9. Kp & ~Kp [6, 8 Conj]

10. ~K(p & ~Kp) [4 - 9 reductio ad absurdum]

11. ~LK(p & ~Kp) [from 10, ~Kq implies ~LKp]

12. p & ~Kp [assume "there's an unknown truth" for reductio ad absurdum]

13. LK(p & ~Kp) [from 12, 1]

14. LK(p & ~Kp) & ~LK(p & ~Kp) [11, 13 Conj]

15. ~(p & ~Kp) ["there's no unknown truth" 12 - 14 reductio ad absurdum]

16. ~p v ~~Kp [15 DeM]

17. ~p v Kp [16 DN]

18. p -> Kp [17 Imp]

19. If a proposition (p) then p is known

Legend:

L = possible
K = know
Kp = known p

A picture could carry some truth for instance. — Olivier5

How?

By showing it.

By showing it. — Olivier5

Do it then. Post a picture and show me a truth.

1. All truths are knowable. — TheMadFool

Incorrect assumption. Some truths are beyond the knowability by humans, by way of complexity or escaping detection.

simplification of 7 is unallowable (Incorrect, wrong)

Incorrect assumption. Some truths are beyond the knowability by humans, by way of complexity or escaping detection. — god must be atheist

Prove it!

simplification of 7 is unallowable (Incorrect, wrong) — god must be atheist

Why?

Here's an exercise for you: Erase every object in the picture that has a word for it. What are you left with?

Would that make any sense though?

If truth must be in the form of a proposition, then there is no unknown truth because there's no such thing as a realm of already formed English sentences waiting to be discovered. A proposition must be proposed by someone before it can exist.

Would that make any sense though? — Olivier5

It has to if you're right.

If truth must be in the form of a proposition, then there is no unknown truth because there's no such thing as a realm of already formed English sentences waiting to be discovered. A proposition must be proposed by someone before it can exist. — Olivier5

1. All truths are propositions [you disagree but haven't been able to make your case]
2. All propositions are known [Fitch's argument]
Ergo,
3. All truths are known. [from 1, 2]

It has to if you're right. — TheMadFool

Nope. The procedure only makes sense if truth can only be expressed in words. It's begging the question.

All truths are propositions [you disagree but haven't been able to make your case] — TheMadFool

You haven't been able to make yours either.

All truths are known. — TheMadFool

Only because there's no such thing as an "unknown proposition".

Nope. The procedure only makes sense if truth can only be expressed in words. It's begging the question. — Olivier5

You denied that truth has to be propositional. I asked you to prove it. You said a picture would do the trick. I pointed out that every object in the picture you posted has a word assigned to it - demonstrating my position on the issue or, as it matters to you, disproving your assertion that truth can be non-propositional.

In short, I refuted your argument because I assumed your position not mine. So, if there's any petitio principii, it's not me.

You haven't been able to make yours either. — Olivier5

Name a truth that's not propositional. We're going round in circles.

Truth is the property of being in accord with fact or reality.[1] In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, propositions, and declarative sentences. — Wikipedia

Name a truth that's not propositional. We're going round in circles. — TheMadFool

If I name it, I make it propositional. But okay, maybe you are right. Truths are descriptions of some state of affairs, therefore there is not such thing as an unknown truth.