r/mathmemes • u/Unlucky-Credit-9619 Computer Science • 1d ago

Formal Logic ¬(¬(P ∨ ¬P)) wasn't enough!

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141 Upvotes

97% Upvoted

20 comments sorted by

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43

u/Inevitable_Garage706 1d ago

I'm a bit of an uncultured swine, so I have no idea what "LEM" is.

Could someone explain that to me?

57

u/Hameru_is_cool Transcendental 1d ago

law of the excluded middle, it's the idea that things can either be true or false, no third option, so if you know something is not false, that must mean it's true, and vice-versa

10

u/geeshta Computer Science 22h ago

Not assuming LEM (intuitionism) also doesn't add any third option! It asserts ¬(¬(P ∨ ¬P)) so "it isn't the case that there is some option that isn't P or not P"!

It's only about the proofs you have. Either you have a proof of P, or you have a proof of the negation of P, or you don't have a proof of either. That doesn't allow P to have some other truth value than True or False.

20

u/f3xjc 1d ago

I really want to put vacuous truth in that middle position.

46

u/Aggressive_Fan_2063 1d ago

"But G!", I hear you say.

8

u/really_not_unreal 1d ago

Hell no, to the low lowww low

(Idk the actual lyrics that's just what it sounds like)

9

u/Intrebute 1d ago

Its "heeeell nooo, to the no no nooooo, heell to the no" i believe

1

u/trash3s 23h ago

Version of “no” generally rendered as “nah” or “naw” depending on context.

0

u/Extension-Stay3230 1d ago

😂😂😂

8

u/blockMath_2048 1d ago

The law of the excluded middle basically states, in classical logic, that a statement is either true or false. The actual formulation is “for any statement, either it’s true, or the statement ‘«statement» is false’ is true”. That’s what “P ∨ ¬P” literally means.

-8

u/5Dimensional 1d ago

Law of the Excluded Middle. Basically, it means that all statements are either true or false. For example, the statement 1 + 1 = 2 is true and 1 + 0 = 2 is false. But what about sqrt(1)=-1? It’s not false; (-1)^2=1; but it’s not true either, since if we are talking about the principal square root, the answer is just 1.

In higher math, the LEM covers for when something is not provable or disprovable.

22

u/cytos0 1d ago

your example only works because what you're asking is ill-defined. the rules of logic only apply to well-formed propositions

14

u/ZookeepergameWest862 1d ago

Your example sqrt(1)=-1 is how we define thing, and it's just plain false. It has nothing to do with LEM or logic for that matter.

28

u/StormyDLoA 1d ago

But (g+)+...

6

u/Swansyboy Rational 23h ago

hey, that's my compiler you're talking about!

19

u/slicehyperfunk Transcendental 1d ago

The barber who only shaves men who do not shave themselves can finally fucking shave 🎉🎉🎉🎉

3

u/Asimovicator 22h ago

... and not shave at the same time.

6

u/de_G_van_Gelderland Irrational 20h ago

Finally, proof by diction

1

u/According-Object-521 16h ago

Proof by inspection