/philosophy/ - Philosophy

This got me thinking and I no longer think implication is ok at all. It is too loose of an operator.

a->b

a

therefore b

Can be something like Noon then Sun is up

Noon

Therefore Sun is up

And yeah that is a valid, sound argument according to formal logic, but it isn't a valid deductive argument I think because it doesn't state the connection between the terms a and b, it assumes they are connected. Thus you can have arguments like

Noon then 1+1=2

Noon

therefore 1+1=2

Which is clearly valid in formal logic, even though its clearly invalid as a deductive argument because there is no connection between the two terms. Basically, even valid sound arguments using implication in formal logic are not necessarily valid deductive arguments. And yeah, if the antecedent is false then the conditional is true is pretty ridiculous a thing to maintain.

>>7291

What about p -> q = ~p v q? Do you agree with that?

>>7298

I agree they are equal, I just don't know if its a necessarily valid deduction, or a valid deduction according to the rules of formal logic. That is, even if they are equal, now I'm doubting whether a deduction from ~p v q is a good deduction or not. Please help me if you can. Maybe an example will help. Lets say we have an argument, and somewhere in that argument arrives as a premise a v b. I no longer know why we say this premise must be true. I know why we want it to be true, so we can do something else in the argument or end it there, but I don't know anymore why, when we find ~a, we must say b. I could understand it if b = ~a, that would be obvious, but if the content of the terms is not connected(like for example, man is a rational animal or man is not a rational animal vs man is a rational animal or man is bipedal), I just don't know if the necessity of the deduction holds, even though it necessarily follows from the rules of the logic.

Does any of this make sense?

>>7299

Perhaps it isn't possible to have an argument with unrelated disjuncts, because their relation is necessarily the argument.

>>7258

There's nothing wrong with the material conditional (where false antecedent = true conditional) because that's just a name we give to one of 16 possible truth functional dyadic operators. And to really see why we identify it with (one version of) the if/then in ordinary language, you'll have to learn about logical implication in argument forms, and then realize that argument forms can be translated into single sentential expressions (any valid form can be translated into a single-sentence theorem, that is, a tautologically-true sentence in logic, which is to say a sentence that is necessarily true no matter the input values of the constants/variables). In those translations, logical implication (the "therefore" of an argument form) literally becomes the material conditional (the horseshoe, arrow, or whatever symbol you want to use). You are right to suspect that the if/then of ordinary language doesn't always mean the same as that truth-functional material conditional operator though. It's just, philosophers have known this forever, sorry to say. Sometimes there's talk of it under the name 'indicative conditional'. There's also the 'causal conditional'. Worth also looking into is the 'counterfactual conditional'. Read about them on SEP or something if you're interested. The thing is, these conditionals are not truth-functional (sometimes one combination gives us one truth value, sometimes the same combination gives us another). All this stuff is known and taught the further you learn about logic in philosophy.

>>7446

What logic do you subscribe to anon?

>>7447

Modern classical logic I guess. I have a soft spot for dialetheism, but I don't really keep track of paraconsistent logics.

>>7450

How do you figure quantum logic works with anything? Do you think it can be consistent with AI? (Also wats ur degree? )

>>7451

I'm not well versed in the quantum logic debate, but many-valued logic is supposed to work better for quantum, since it looks like truth value indeterminacy (also relevant in the debate on vagueness) has a possible place in quantum. I know AI stuff less, sorry to say (just not my area of focus). I have a master's in philosophy, bachelor's was also in philosophy.

>>7453

Do you have a reading list for analytic philosophy or philosophy in general I can read?

>>7454

Not specifically for AI/quantum logic, but if you are interested in some logic stuff (like the earlier-mentioned indicative, causal, and counterfactual conditionals) you can find some stuff on SEP (Stanford Encyclopedia of Philosophy). When it comes to philosophy in general, it's not a bad idea to get some basic feel from a rough historical survey. At least know some basic Presocratics, Socrates/Plato/Aristotle, and the early moderns (Descartes to Kant). For analytic philosophy, area of interest will probably determine what things you'll want to prioritize reading, but a safe place to start analytic philosophy in general would be some of Frege's work ("Sense and Reference" would be ideal) and Russell's ("On Denoting" would be ideal) on descriptivism. I'd recommend reading those two articles at the very least.

>>7446

What is well-known isn't relevant, nor is the possibility that the material conditional makes sense in some other paradigm. You glossed over the point of the OP entirely, sorry to say: to rate my truth table. You shouldn't make assumptions about people's intentions that aren't implicit, then pretend like your commentary is relevant still.