|Law of the Excluded Middle: an assertion is either true or false. "There is no third possibility."See also bivalence, anti-realism, multivalued logic.|
Books on Amazon
Conditional of the excluded middle/conditionally excluded middle/Lewis/Bigelow/Pargetter: could be considered as an axiom:
(A would be > would be b) v (a would be > would be ~ b)
Lewis: Thesis: this is not always true.
StalnakerVsLewis: (1968, 1981) defends the conditional sentence from the excluded middle against Lewis:
We must consider cases of the following kind: there is a temptation to say that it can be wrong to assert:
"If I had gone to the movies yesterday, I would have watched The Fly."
And it can also be wrong to say:
"If I had gone to the movies yesterday, I would not have watched The Fly."
((s) Do not omit the front link for the second time!)
Bigelow/Pargetter: we might rather say:
"If I had gone to the movies yesterday, I could have watched The Fly (or not)."
Logical form: (a would be > could be b) u (a would be > could be ~ b).
That is, we deny something of the form
(a would be > would be b)
And we also deny something of the form
(A would be > would be ~ b).
So we deny both sides. Therefore, it seems that we must deny the conditionally excluded middle.
Conditionally excluded middle/Pargetter: these were intuitive reasons for his rejection. Now we must also consider some of its formal consequences:
Problem: would it be accepted, the difference between "would" and "could" would collapse.
Would/could/Bigelow/Pargetter: normally it is clear that
(a would be > would be b) entails a would be > could b)
((s) "would" implies "could").
Problem/Bigelow/Pargetter: if we accept the conditional sentence of the excluded middle (conditionally excluded middle), the inverse implication is also valid!
For (a would be > could be b) is by definition ~ (a would be > would be ~ b) and this is the negation of one of the two disjuncts in the conditionally excluded middle. Then we must assert the other disjoint, thus the assumption of (a would be > could be b) implies that (a would be > would be b).
According to this "would have been" and "could have been" would be equivalent and we do not want that.
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990