Not sure where that leads you. It makes no difference whatsoever to my argument that there is no such thing as an unknown proposition... If computers can make propositions, what problem does that create?

Monkeys hitting randomly at a typewriter could produce English sentences too. So fucking what?

6. Know p is true & Know p is unknown [possible if 3/5]

...

9. p is an unknown truth & p is not an unknown truth [2, 8 Conj]

Ergo,

10. F is false = There are no unknown truths = All truths are known. [from 2 - 9 reductio ad absurdum] — TheMadFool

This is what I meant. You drop an assumption that can't be dropped. If you don't drop the same assumption, then you can't arrive at 9 and at 10. Hence, your drop is invalid.

Let me give you an example which is not your ill-put together attempt at proof.

George is 6 feet tall, and George is a boy.
Know that George is 6 feet tall, and know that George is a boy.
Know that George is 6 feet tall. (By simplification.)
Therefore George is not a boy.

This what I wrote about George follows the same structure that you employed. Find the logical mistake in it, and you found the logical mistake in your argument.

So you have complaints about the natural deduction rule simplification. Care to expand on that a bit.

1. The sun is hot & Grass is green.

Ergo,

2. The sun is hot. [1 Simplification]

Now,

3. Know p is true & Known p is unknown

Ergo,

4. Know p is true [3 Simplification] — TheMadFool

... but you claim in your parallel structure of the original argument, that the Grass is NOT green. That you can only claim because you drop the assumption that the grass is green.

6. Know p is true & Know p is unknown [possible if 3/5]

7. Know p is true [from 6 Simplification]

8. p is not an unknown truth [from 7]

9. p is an unknown truth & p is not an unknown truth [2, 8 Conj]

Ergo,

10. F is false = There are no unknown truths = All truths are known. [from 2 - 9 reductio ad absurdum] — TheMadFool

In this parallel example of the original argument, you drop the bold faced assumption in order to arrive at the bold-faced italics result. But you contradict your own assumption in this move, so the logic is ill, it is faulty. The fault with the logic is that in the simplification process you drop something that may not be dropped -- not allowed to be dropped.

If a proposition has an element that is essential to the proposition, you can't drop it. Yet you do that precisely.

Sorry, Mad Fool, this is the extent of my capability to explain your error. If you still don't understand my argument, that's fatal, because I can't provide a better one. So please don't ask for a better one.

Not sure where that leads you. — Olivier5

It doesn't lead me anywhere. I already knew all of this stuff. But it implies that a proposition does not need a "proposer". It also implies that a proposition does not need a "proposer" to be a true proposition. All a proposition needs to be created is to be some string that something creates.

Monkeys hitting randomly at a typewriter could produce English sentences too. — Olivier5

Sure. But they're highly unlikely to do so. By contrast, the program that I wrote is certain to produce true propositions.

. But it implies that a proposition does not need a "proposer". It also implies that a proposition does not need a "proposer" to be a true proposition. All a proposition needs to be created is to be some string that something creates. — InPitzotl

Well then, that thing is the proposer. If your computer is proposing a proposition, it is the proposer of this proposition.

By contrast, the program that I wrote is certain to produce true propositions — InPitzotl

That's only because you limit it to very simple arbitrary statements mechanically derivable from arithmetic. So computers can sort letters alphabetically. Big deal. Try and have your Inspiron 3847 answer questions about real states of affairs, like elephants and castles for a change.

Siri? How many castles can fit in an elephant?

Well then, that thing is the proposer. — Olivier5

Sure; I'm fine with that too, so long as we don't suppose proposers understand things.

That's only because you limit it to very simple arbitrary statements — Olivier5

Of course. I programmed it to generate true propositions.

So computers can sort letters alphabetically. — Olivier5

Computers can do lots of things.

Big deal. — Olivier5

The point is to correct you, not to impress you.

Try and have your Inspiron 3847 answer questions about real states of affairs, like elephants and castles for a change. — Olivier5

Not to be rude, but my voluntary role in this forum isn't to do tricks for your amusement; especially if you're going to ask for something so banally trivial it's pointless like a coding of a math equation or something complex like a 3d packing problem solver using irregular shapes.

Sure; I'm fine with that too, so long as we don't suppose proposers understand things. — InPitzotl

This is your take. Mine is that we have to suppose understanding for there being a proposer. But irrespective of which perspective you take, whether machines can be 'proposers' or not, it makes no difference to the argument that a proposition must be proposed by a proposer in order to exist.

This is your take. Mine is that they have. — Olivier5

I'm confused. You're now saying my program understands things?

I think we're done. Clarify your position, then get back to me if you want to engage me.

George is 6 feet tall, and George is a boy.
Know that George is 6 feet tall, and know that George is a boy.
Know that George is 6 feet tall. (By simplification.)
Therefore George is not a boy. — god must be atheist

K = known

L = possible

LK = knowable

1. (p & p is unknown) = p is an unknown truth = p & ~Kp (this is a truth)

2. All truths are knowable

3. K(p & ~Kp) = p is an unknown truth is known [from 2, assume]

4. Kp & K~Kp [from 2, knowing a conjunction is to know the conjuncts]

5. Kp [4 Simp]

6. K~Kp [4 Simp]

7. ~Kp [from 6, $Kq \rightarrow q$]

8. Kp & ~Kp [5, 7 Conj]

9. ~K(p & ~Kp) [3 - 8 reductio as absurdum]

10. p & ~Kp [assume]

11. LK(p & ~Kp) [2, 10, if true, knowable that true]

12. ~LK(p & ~Kp) [9, if not knowable, not possible that knowable]

13. LK( p & ~Kp) & ~LK(p & ~Kp) [11, 12 Conj]

14. ~(p & ~Kp) [10 - 13 reductio ad absurdum] {there are no unknown truths}

15. ~p v ~~Kp [14, DeM]

16. ~p v Kp [15 DN]

17. $p \rightarrow Kp$ [16 Imp]

18. If there is a proposition then, that proposition is known

QED

Where does Fitch commit an error, make a boo boo?

I have edited the post for clarity. I do agree that we're done with this tangent, in that whether machines can be 'proposers' or not makes no difference to the argument that a proposition must be proposed by a proposer in order to exist.

(edited: obsolete comment)

You have two 3's here... could I request a renumber? (Be careful; you reference things by number a lot). — InPitzotl

F**k!

17. If true, a proposition, then that proposition is known

Where does Fitch commit an error, make a boo boo? — TheMadFool

In assuming that this applies only to true propositions. In fact it applies to any proposition, true or not. An unknown proposition is an unproposed proposition. It's like an unthought thought: a contradiction in terms.

The propositions that are known are those that exist. They exist because they are known. There is no reservoir of unknown propositions out there, waiting for us to discover them and propose them. We make them propositions, or our computer surrogates.

In assuming that this applies only to true propositions. In fact it applies to any proposition, true or not. An unknown proposition is an unproposed proposition. It's like an unthought thought: a contradiction in terms. — Olivier5

When one makes a proposition or knows a proposition, truth is implied.

p (a propisition) = p (is true)

A proposition can be false or undecidable.

A proposition can be false or undecidable. — Olivier5

A proposition can be false, yes but when you state it, it means you're claiming it to be true.

(edited: obsolete comment)
Thanks @TheMadFool!

And you could claim that it's true but it could still be false. Makes no difference anyway. There is no such a thing as an unknown proposition, whether true, false or anything in between!

It'd be like unknown knowledge....

You could claim that it's true but it may still be false. Makes no difference anyway. There is no such a thing as an unknown proposition, whether true, false or anything in between! — Olivier5

Yes, but Fitch's paradox is about true propositions. Restrict the domain of discourse to true propositions and you'll get it, hopefully.

18. If there is a proposition then, that proposition is known

QED

Where does Fitch commit an error, make a boo boo? — TheMadFool

I explained it three times, I think. One gets tired of pointing out the same mistake. If you don't get my reasoning, and stick to your guns, it does not make Fitch's proof valid.

This is the point in reasoning when one would want an independent judge who is reasonable. Without that, it seems there is no way of convincing you of Fitch's error. And even the judgment of an independent thinker (who is not biased for you or for me) would not make a difference in your conviction. So why are we doing this? If someone makes an error in reasoning, and showing him his error makes no difference to anything in the world, then the debate is fucked. I tried to convince myself of that, and I stayed away for a while, but I get sucked in by incorrect reasoning and feel compelled to point out the mistake in it. Unfortunately nobody on this site is receptive to criticism, and if they can't fight it with logic, then they start to hate those who nailed them.

In this sense I am proud to be one of the most hated persons on this site.

That's another reason to quit here. No emotional support... yes, it is needed, if one encounters one failure after another of logically convincing others of the truth. It gets to you after a while, you feel like you are running in a ferret's wheel.

Enough if this already. It is really impossible to make you see your mistake, mad fool. And you are not the only one... all people who make propositions on this site are like you.

Enough of charging windmills. Enough of wasted brain cells. Enough of fanatic thinkers.

Fitch's paradox is about true propositions. — TheMadFool

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

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

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

$p \rightarrow Kp$

To what end, may I ask?

To get a more complete view of the problem.

To get a more complete view of the problem. — Olivier5

You cannot.

Watch me.

¬p→K¬p

¬p→K¬p — Olivier5

Let q=¬p. Then ¬p→K¬p is simply q→Kq, which is the same as p→Kp (under a change in labels).

Exactly.


.

It makes no difference whatsoever to my argument that there is no such thing as an unknown proposition — Olivier5

I must agree. If there was a proposition that was not known, what would make it a proposition? The idea of propositions in general, not created, hence not known, is fine, but the idea cannot be its own object.

Furthermore, it is true all propositions are known, iff the negation....
1.) is a contradiction, in the form all propositions are not known. “All propositions are known” is itself a known proposition, therefore the contradiction holds, or,
2.) is an impossibility, in the form not all propositions are known. In which case, some proposition not known must be proved, and the proof of it necessarily manifests as that proposition, which is then known, therefore the impossible unknown holds.

Another way to look at it is, the truth of P as such, relates a conception to itself. Any proposition in which the subject and predicate are subsumed under the principle of identity, cannot be falsified. If there is P, or when there is P, it is analytically true P is. Here too, the negation is also true, insofar as if or when there is no P, then P isn’t. It follows that to suppose it cannot be known whether or not P is or isn’t, is patently irrational, bordering on the pathologically stupid.

Mike drop, exit stage right.......

(Or maybe.....enter giant hook, yank speaker by the neck stage right)

If there was a proposition that was not known, what would make it a proposition? — Mww

We just finished this. Proposition 6 was a proposition on October 1, 2021, at 10:03:44pm. At that time, nobody knew what proposition 6 was. But at that time, I knew that it was a proposition. To know S is a proposition, it is not necessary to know S.

Why is this so difficult? And what is with this obsession to demand that propositions cannot be propositions if you don't know them?