🚀 go-pugleaf

I have been reading the last few postings on logic and meaning, and it seems
to me that there are two uses of the word logic that are being used 
interchangibly. One one hand there is formal logic, where sentences are 
mapped to precise symbolic formula. There are a set of inference rules and,
depending on the system, a few axioms, from which all well formed formuli
can be derived. The odd thing is that this sort of logic alows the derivation
of all sorts of formuli that are, in my opinion, at least, nonintuitive.
One example would be that if we know that it is not the case that a 
proposition P implies a proposition Q, it is possible to derive P 
(ie. P is true) and not-Q (Q is false). An English translation of that would
amount to something like "It is not the case that if it is raining then 
the moon is made of green cheese," which implies that "it is raining" and
"it is not the case that the moon is made of green cheese," neither of
which follow intuitively from the original statement. Essentially, logic of 
this sort fails to capture a number of intuitive notions like causality.
	On the other hand there is also the less formal logic of "if I
step in front of a speeding bus, I will get hurt." (I think someone said
something like that recently) This makes sense, and seems logical, but it 
cannot be demonstrated formally without the addition of a number of 
premises having to do with the implications of stepping in front of,
speeding, and so on. We do not think of that sort of everyday statement
as logical in the formal sense, if for no other reason than we do not tend
to think of things in the language of P and Q's and strict implication and so
on. 
	On a slightly related topic, when people are given the following
scenario :Linda has been very active in social concerns for most
of her life. During college she was involved in a number of organizations
whose aim was to bolster the rights of the underrepresented. 
People are then asked "which of the following is more likely:
1) Linda is a bank teller.
2) Linda is a bank teller and active in the feminist movement."
People almost always choose 2) even though the likelyhood of a conjunction
is always less than the likelyhood of one of the conjuncts.

I am not quite sure what that means, but it is true...


Loren Frank
frankl@carleton.edu