Atla wrote: ↑Sat Jan 26, 2019 5:55 pm

Guess so, I don't know much about this, so I may be writing bollocks. I avoid Western philosophers.

I would be interested in whatever could provide empirical evidence of our logical intuitions, say e.g. Modus ponens, A ⊢ (A ∨ B), or (A ∧ B) ⊢ (A ∨ B). Most people with a training in formal logic will be inevitably biased but a non-Western tradition may be very interesting in this respect.

Atla wrote: ↑Sat Jan 26, 2019 5:55 pm

Although I studied computer sciences for a few years, and learned mathematical logic, I for example have no idea what the hell this is supposed to mean:

The truth table associated with the material conditional p->q is identical to that of ¬p∨q.

p q p->q

T T T

T F F

F T T

F F T

I vaguely remember having to memorize this truth table line by line because half of it makes no sense to me.

Laugh! I had my first introduction to formal logic when I was 19 years old, at university. And I just experienced something very similar. I was listening to the guy explaining truth tables. Everything was going smoothly with the conjunction, the disjunction, the exclusive disjunction, the negation, the equivalence... And then we got to the truth table of the implication. I was just looking at the truth table he had written on the blackboard and my brain just puked. OK, I thought, that's seriously wrong. It's only much later that I realised most people felt the same (excluding the biased "trained" brain-washed). One author I read also admitted many students protested at the material implication.

Still, we can take the material implication as an approximation of the real logical implication. I'm sure you will accept that the first two lines of its truth table seem to say something true about it.

I also think that, at the time, mathematicians didn't have the resources to produce a better definition. The "tragedy", though, is that since then, generations of students, and therefore mathematicians, have been taught the dogma of the material implication and probably look down on Aristotle as "wishy-washy philosophy". Modern mathematical logic should have been called "theory of material formal logic", rather than the misleadingly dishonest "classical logic".

Still, it's funny to see people with a higher-education in maths systematically opt for a definition of validity in line with the material implication and thereby flunk simple tests like my Joe the Squid argument, whereas the untrained are more likely to get it right, at least those who are not insane.

EB