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
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
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
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.Not sure where that leads you. — Olivier5
Sure. But they're highly unlikely to do so. By contrast, the program that I wrote is certain to produce true propositions.Monkeys hitting randomly at a typewriter could produce English sentences too. — Olivier5
. 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
By contrast, the program that I wrote is certain to produce true propositions — InPitzotl
Sure; I'm fine with that too, so long as we don't suppose proposers understand things.Well then, that thing is the proposer. — Olivier5
Of course. I programmed it to generate true propositions.That's only because you limit it to very simple arbitrary statements — Olivier5
Computers can do lots of things.So computers can sort letters alphabetically. — Olivier5
The point is to correct you, not to impress you.Big deal. — 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.Try and have your Inspiron 3847 answer questions about real states of affairs, like elephants and castles for a change. — Olivier5
Sure; I'm fine with that too, so long as we don't suppose proposers understand things. — InPitzotl
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
You have two 3's here... could I request a renumber? (Be careful; you reference things by number a lot). — InPitzotl
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. — Olivier5
A proposition can be false or undecidable. — Olivier5
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
18. If there is a proposition then, that proposition is known
QED
Where does Fitch commit an error, make a boo boo? — TheMadFool
Fitch's paradox is about true propositions. — TheMadFool
It makes no difference whatsoever to my argument that there is no such thing as an unknown proposition — Olivier5
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.If there was a proposition that was not known, what would make it a proposition? — Mww
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