/sci/ - Science & Math

>>12337176
You can make up your own truth tables if you want to. It all works anyway as long as you stay consistent.

these bools or somethin?

>>12337182
why call it "implies" instead of some nonsense word that clearly doesn't connote something entirely different?

>>12337176
If p is true it implies q is true delete this thread dumb fuck.

>>12337176
q can have other causes than p, but p always implies q

>>12337182
>>12337261
But it is the correct table for implication. What makes you think otherwise?

>>12337176
Iff can be rewritten as two implication arrows. I don't think truth preservation holds if it's anything else

>>12337176
Imagine p and q as English statements

the absolute state of /sci/.....

>>12337176
False premises lead to arbitrary conclusions. Happens on this board a lot.

>>12337176
Because that's what it means? Literally all p -> q really means when you get right down to it is that truth table. Thats all it is. Just like how p v q is that truth table, or p v q is another. You can assign names like AND, XOR, or whatever you want, but all the equation means is... What it means. It's a way of showing that truth table.

But if you want an explanation without that, basically, it's a statement. p implies q. So if you have q, you better also have q. If you don't have p, then q can be whatever.

>>12337825
>If you have q, you better have q
Sorry I meant if you have p, you better also have q

If it rains, you get wet.
You're wet. That doesn't mean it rained, though.

But if it rains, you will get wet.

>>12337825
I think it can be understood formally like this but if you assert iff irl it conforms to two implications and is objectively derivable off the ontology of eqr.

>>12337176
It's a bad candidate for "implies", but it suffices for most math - in particular because there a theories like set theories which gives you the legos to express other notions.

If you want to go beyond the math (as in, what's math as taught in math departments, which usually don't care about logic and foundations), check out frameworks such as

https://en.wikipedia.org/wiki/Relevance_logic

>>12337843
And if it doesn't rain, but you are wet, you can still be wet regardless of whether it rains or not. It's not simply the relationship by itself but the relationship must conform to how truth and falsity works.

https://www.logicmatters.net/resources/pdfs/IFL2_LM.pdf
spends two whole chapters on this topic, so you can read that if you're interested. But basically "if" has a lot of meanings in English, while "" has one meaning which only depends on the truth or falsity of the statements it connects.

Lets explain it in simple terms. There is the following theory: If Stacy goes to the club, Chad always goes too.

Now, lets assume that Stacy doesn't go to the club; in that case it doesn't matter what chad does, he can go to the club or not, the theory remains correct. The only time the theory is actualy wrong is if stacy goes to the club and chad doesn't.

S: true C: true = true
S: true C: false = false (the theory is wrong)
S: false C: false = true
S: false C: true = true

The reason why the last two options are true is because the theory has not been disproven. It doesn't matter what Chad does if Stacy doesn't go to the club.

>>12337176
p = it rains
q = the earth is wet

p=0,q=0: it didn't rain, the earth isn't wet

p=0,q=1: it didn't rain, but the earth is wet

p=1,q=0: it did rain, but the earth isn't wet

p=1, q=1: it did rain, the earth is wet

All but the third are logically valid.

>>12337176
blame Russell, he changed it from "conditional" to "implication"