Philosophy Lexicon of Arguments

Law of the Excluded Middle: an assertion is either true or false. "There is no third possibility."See also bivalence, anti-realism, multivalued logic.

Author Item Excerpt Meta data
Bigelow, John

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Excluded Middle I 117
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:
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I 118
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).
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I 119
According to this "would have been" and "could have been" would be equivalent and we do not want that.

Big I
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990

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Ed. Martin Schulz, access date 2017-04-27