[hist-analytic] One Brief Addendum Discussion of Aune's ETK, Chapter Two: Modus Ponens/Tollens
Danny Frederick
danny.frederick at btinternet.com
Fri Oct 30 16:01:41 EDT 2009
Hi Steve,
This argument (if the first sentence is a conditional):
1 If he knows, he's not telling
2. He's telling
3. Therefore, he does not know.
is valid because its premises are inconsistent, just like the other
argument. I am assuming here that telling implies knowing. As in the other
case, we can 'prove' the inconsistency informally. But we can also show it
formally by using predicate logic. This would do it:
If Ka then ~Ta [Premise 1]
Ta [Premise 2]
If Ta then Ka [meaning postulate]
>From premise 2 and premise 1, we get ~Ka.
>From premise 2 and the meaning postulate, we get Ka.
Putting the two together, we get a contradiction.
If you don't like meaning postulates, you can use Quine's trick to get rid
of them. That is, 'he's telling' gets put into logical form as:
'Ta & (x)(if Tx then Kx)'; that is, the predicate 'y is telling' gets
transcribed as 'Ty and (x)(if Tx then Kx)'.
Then the argument becomes:
If Ka then ~( Ta and (x)(if Tx then Kx))
Ta and (x)(if Tx then Kx)
The inconsistency of these two premises can be 'proved' formally.
Best wishes,
Danny
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