#
I studied philosophy in university and I recall that one of my tutors for symbolic logic was trying to walk me through a problem by saying that if you have a large enough set of premises, two of them will inevitably contradict one another. I've always had trouble understanding (and consequently, accepting) this proposition because: if one conceives of reality as a set of claims (e.g., I am right-handed, electron X is in position Y, 2 + 2 = 4, etc.) there are an infinite number of "premises" to the "argument" that is reality and consequently reality is self-contradictory. Am I missing something here? Can you explain which of us is right about this and in which sense? I should mention that I don't necessarily have a problem with reality being self-contradictory, but that really throws symbolic logic out the window (and doesn't throw it out the window at the same time)! Thanks to all respondents for their time.
-JAK

Maybe the tutor was thinking something like this (I seem to recall it from Popper). Let's consider only atomic (simple) contingent propositions (A, B, C, ... , Z) that are logically independent of each other. The probability that an atomic contingent proposition is true is less than 1 and greater than 0 (an atomic contingent proposition is true in at least one possible world and false in at least one possible world). Suppose P(A) is X (where 0 < X < 1). And suppose P(B) is Y (where 0 < Y < 1). Sure, the set {A, B} is consistent (or satisfiable), and the conjunction A&B will be true in at least one possible world. But there's a hitch: P(A&B) is the product of X and Y, which means that P(A&B) is less than P(A) and less than P(B). Let's increase the number of atomic propositions in our set to get {A1, A2, A3, ... , An}. Again, the set will be consistent, but the probability that the set (or long conjunction) is true is the product of the individual probabilities of each proposition; the more propositions...

- Log in to post comments