Joe, upon reflection, one more detail that I'd like to add to my last post (which I assume you read).
There are, of course, degrees of belief - belief is not just an either-or matter. Thus, I may strongly believe something, and more weakly not-believe that same thing, without self-contradiction. and this is true not only 'in practice' (irrespective of logic) but also 'in principle' (following logic).
Thus, beliefs based on inductive logic, with reference to probabilities of truth, will have degrees. If something has a probability of only 70%, then my belief in it should have a 70% degree (strong), and my non-belief in it should have a 30% degree (weak).
Something about you (optional) logician-philosopher
Hi Avi, sorry about the late response. I've just moved house and have been without internet for a couple of weeks.
Regarding your last post, I think you're referring to so-called 'epistemic' probability, i.e. the interpretation of probability as a degree of belief, as opposed to other interpretations such as probability as an objective frequency. There has been a lot of heat generated over the years about which interpretation is the 'correct' one, but it seems to me that the differences have been exaggerated. To my mind, a degree of belief (say 70%) in a proposition must take into account the frequencies involved if it's to have a firm rational basis. Nor do I think there is any basis for a hard dividing line between probability and deductive logic.
For example, take the classic deductive syllogism :
All men are mortal
Socrates is a man
So, Socrates is mortal
This is valid and so it is impossible for the premises to be true and the conclusion false. An example of a 'statistical syllogism' is :
99.9% of men are mortal
Socrates is a man
So,Socrates is mortal
In this case, while it's possible for the premises to be true and the conclusion false, it's not likely. But what is so special about 99.9%, as opposed to 100%, which makes the first argument part of logic but the second not?
