/sci/ - Science & Math

[Anonymous No.11280330]

Can someone help me with these maths?
I'm trying to proof wrong the non-contradiction principle. Tell me if I'm wrong, and may you be blessed to figure out the contradiction of this principle when applied to itself.

[Anonymous No.11280333]

[Anonymous No.11280340]

>>11280333
that's not how perspective works...

[Anonymous No.11280347]

>>11280340
????

[Anonymous No.11280362]

>>11280333
based comfy trips

[Anonymous No.11280388]

>>11280347
>>11280333
both .gifs have buildings out of basic 2 points perspective.
All the .gifs you've been posting lately around /sci/ are only somewhat decent at estabilishing a mood, but the fundies are all fucked up 90% of the times.

[Anonymous No.11280392]

>>11280388

[Anonymous No.11280396]

>>11280392
subscribe

[Anonymous No.11280402]

>>11280392
>>11280396
ya gifs are hit and miss, i try to gather as many as i can and mix it up

[Anonymous No.11280409]

>>11280402
this one is cool

[Anonymous No.11280411]

>>11280409
ya i liek this 1 too, the color is nice

[Anonymous No.11280418]

and this 1. i liek the responsiveness of the birds and how they fly about when the train goes by, and then return to the powerline when it's gone

[Anonymous No.11280495]

>>11280330
[math] (P\land (P\to Q))\to Q [/math]
is proven by
[math] \lambda \langle p, f\rangle.\, f(p) [/math]
In words,
given a proof of [math] P\land (P\to Q) [/math], use modus ponens to conclude [math] Q [/math].

The principle of non-contradition is the special case of the above with Q a false proposition, i.e.
[math](P\land (P\to F))\to F [/math]
which you may write as
[math] \neg(P\land \neg P) [/math]

Which happens to be a classical equivalent of LEM,
[math] \neg P\or P [/math]
So going from here, and weaken it to
[math] \neg P\or \neg \neg P [/math]
and then use distributivity,
[math] (\neg R\lor \neg S) \to \neg (R\land S) [/math],
the you also get
[math] \neg(P\land \neg P) [/math]

[Anonymous No.11280499]

>>11280330

[math] (P\land (P\to Q))\to Q [/math]

is proven by

[math] \lambda \langle p, f\rangle.\, f(p) [/math]

In words, given a proof of [math] P\land (P\to Q) [/math], use modus ponens to conclude [math] Q [/math].

The principle of non-contradition is the special case of the above with Q a false proposition, i.e.

[math](P\land (P\to F))\to F [/math]

which you may write as

[math] \neg(P\land \neg P) [/math]

----

This in turn happens to be a classical equivalent of LEM,

[math] \neg P \lor P [/math]

So going from here, and weaken it to

[math] \neg P \lor \neg \neg P [/math]

and then use distributivity,

[math] (\neg R\lor \neg S) \to \neg (R\land S) [/math],

then you also get

[math] \neg(P\land \neg P) [/math]

[Anonymous No.11281539]

please use tex

[Anonymous No.11281620]

>>11280330
You can't disprove non contradiction, it's an axoim.
Logics without the law of non-contradiction are called "paraconsistent logics" and they are fucking stupid and don't do anything.
If you need to reject one of Aristotle's 3, reject excluded middle. You get constructive math which works but is strictly weaker than classical logic.

[Anonymous No.11281983]

>>11281620
>but is strictly weaker than classical logic
You may put it like that. However, it should be highlighted what "weaker" ought to mean here.
Namely, for every classically provable proposition, there is an intuitionistically provable statement, which is classically equivalent to it.

There are infinitely many propositions and some of them have a classical proof and not a constructive one.
But all classical statements have a proof of a statement that is constructive, until the very last step:
E.g. if P is any statement in propositional logic provable from a set of axioms A, then ¬¬P is intuitionistically provable from (an even weaker set of axioms than) A as well.
https://en.wikipedia.org/wiki/Double-negation_translation..

Similarly, ¬(P∧¬P) as in >>11280499 is constructively provable and, for any P, classically equivalent to ¬P∨P (LEM).

>Logics without the law of non-contradiction are called "paraconsistent logics" and they are fucking stupid and don't do anything.
This is not really accurate.
Paraconsistent logics tend to prove non-contradiction correct, with the same proof as in >>11280499. Moreover, many Paraconsistent logics are indeed also meta-logically non-contradiction (so the logic reflects correctly on itself).

What happens is that paraconsistent logics don't adopt the principle of explosion, so that from having proven a false proposition, one is allowed to draw any conclusion.

This isn't as bad as one may think, it mostly just renders disjunctions involving negations a dead end.
In particular, the disjunctive syllogism (seperate true from ruled out possibilities) relies on it:
((P ∨ Q) ∧ ¬P) implies Q
The proof of this requires you to have non-contradition, so that the case P ∧ ¬P enables you to prove Q.
If you don't have that, then there's use in ∨.

It's like a programming language where you have to know all your if-clauses at compile time.
Those logics still permit you to prove many implications.

[Anonymous No.11281993]

>>11281620
>but is strictly weaker than classical logic
You may put it like that. However, it should be highlighted what "weaker" ought to mean here.
Namely, for every classically provable proposition, there is an intuitionistically provable statement, which is classically equivalent to it.
E.g. non-contradiction ¬(P∧¬P) is constructively provable, as in >>11280499. And, for any P, classically equivalent to P∨¬P (LEM).
All classical statements have a proof of a statement that is constructive, until the very last step:
E.g. if P is any statement in propositional logic provable from a set of axioms A, then ¬¬P is intuitionistically provable from (an even weaker set of axioms than) A as well.

https://en.wikipedia.org/wiki/Double-negation_translation..


>Logics without the law of non-contradiction are called "paraconsistent logics" and they are fucking stupid and don't do anything.
This is not really accurate.
Paraconsistent logics tend to prove their non-contradiction, with the same proof as in >>11280499.
Moreover, many paraconsistent logics are indeed also meta-logically non-contradictory (so the logic reflects correctly on itself).
What happens is that paraconsistent logics don't adopt the principle of explosion, so that from having proven a false proposition, one is allowed to draw any conclusion.

This isn't as bad as one may think. It mostly just renders disjunctions involving negations a dead end.

In particular, the disjunctive syllogism (separate true propositions from ruled out possibilities) relies on it:
((P ∨ Q) ∧ ¬P) implies Q
The proof of this requires you to have explosion, so that the case (P ∧ ¬P) enables you to prove Q.
If you don't have that, then there's less use in "∨".

So that is a bit like a programming language where you have to know all your if-clauses at compile time.
Those logics still permit you to prove many implications. And the nice thing is that they have less axioms, so they are consistent with wilder semantics.

[Anonymous No.11282421]

Is this an cyberpunk thread?
Japan is scared, now more than ever.

[Anonymous No.11282425]

>>11282421

[Anonymous No.11282441]

>>11282425
https://youtu.be/sttm8Q9rOdQ

[Anonymous No.11282455]

>>11282441
LOL DROPPIN HISTORY BOMBS IN THIS BITCH HELL YA

[Anonymous No.11282834]

>>11281993
>disjunctive syllogism
or you drop disjunction introduction

[Anonymous No.11284309]

bump 4 future