Yes. It’s equivalent to iff B → A and D, E, F… from which we can derive if B → A.
Lol yes, but I’m trying to demonstrate something much more annoying.
Firstly, I think “X is an odd number” necessarily entails that “X is a real number”, since no odd numbers are anything but real numbers. They necessarily are since this is true by definition, and so I wouldn’t hesitate to say that an odd number is necessarily sufficient to entail a real number.
The annoyingness I’m bringing to the table is that of necessity encompassing sufficiency and more.
So you’re not interested in the notion that necessity and sufficiency don’t have to be mutually exclusive and incompatible?
Fair enough, though I maintain it’s a good point, which also happens to back up previous statements I’ve made on the thread. Sorry for inflicting “backing them up” on you.
I read the first two lines as the premises to which you referred, and the second two as supposed inferences from them. I now think you meant to include all 4 as your premises.
I’m not a master Bayesian, though I am familiar with Bayes Theorem.
I take it from your clarification that you weren’t meaning to say that all deductive logic rules are derived from the laws of probability, as though logic was fundamentally based on probability, but reading more into your use of the word “derivable” rather than “derived” I’m guessing you meant they’re simply included in one specific “natural consequence of basic probability theory” (and therefore probability as a whole?). That would make a lot more sense.
I agree with that completely. In fact, I believe the exact opposite of the statement ‘They are mutually exclusive and incompatible’. It’s more of a ‘two sides of the same coin’ type situation.
Lets say you had two statements, A and B, such that if you knew A was true, you also know (can prove) B is true.
A is sufficient for B, in this case, but not necessarily necessary.
B, on the other hand, is necessary for A (A can’t be true if B is not true, so B is required to be true for A to be true), but not sufficient.
My only point was that all of this talk of necessity and sufficiency, in my experience, almost always takes place in the context of deductive logic, as above. I’m disagreeing with this post of yours:
Suffiency and necessity, as concepts, seem most naturally expressible in deductive logic (A implies B expresses both concepts at once, as I demonstrated above), but because Deductive reasoning can be seen as a subset of inductive reasoning if you have a full understanding of probability theory (Bayes theorem helps), those concepts are also both fairly easily expressible in inductive reasoning as well.