I never thought about the connection between logic and probability before, though now it seems obvious. I’ve read a few introductory logic texts and deductive reasoning always seemed a bit pointless to me (in RL premises are usually inferred from something). -
To draw from a literary example, Sherlock Holmes use of the phrase “deduce” always seemed a bit deceptive. You can say “that color of dirt exists only in spot x in London. Therefore, that Londoner must have come in contact with spot x if I see that dirt on his trouser knee.” This is presented as a deduction, but really, the premises are induced and he assumes some things about how people travel.
It seems more likely that we make inferences, not deductions, but convince ourselves that the premises must be true, without bothering to put real information about likelihood into the reasoning. An induction is still a logical statement, but I like the idea of using probability to quantify it.
A different question about 1-8. I was able to figure out how he got A!B = !B (where ! is bar) but using the Boolean identities he provides, I couldn’t get to B!A = !A. Can anyone enlighten me on this?