# [hist-analytic] Discussion of Aune's ETK, Chapter Two: Modus Ponens/Tollens

Danny Frederick danny.frederick at btinternet.com
Thu Oct 29 16:42:01 EDT 2009

```Hi Steve,

It seems to me that your discussion of the following example is
unnecessarily complicated:

If it rained yesterday, it did not rain hard (yesterday)
It did rain hard (yesterday)
Therefore, it did not rain yesterday.

The argument is plainly valid (on standard logical principles) because the
premises are inconsistent. The second premise entails 'it rained yesterday.'
The second premise in conjunction with the first entails (by modus tollens)
'it is not the case that it rained yesterday.' Thus the two premises
together entail a proposition of the form 'p and not-p.'

I think the example may be confusing because, if we restrict ourselves to
propositional logic, the inconsistency of the premises cannot be seen: they
come out as simply 'if p, then not-q' and 'q.' But if we use predicate
logic, along with Davidson's analysis of the logical form of statements
about events, the inconsistency of the premises becomes evident, thus:

If (Ex)(Rx & Yx) then ~ (Ex)(Rx & Hx & Yx)

(Ex)(Rx & Hx & Yx).

>From the second premise we get: (Ex)(Rx & Yx). From the conjunction of the
first and second we get: ~(Ex)(Rx & Yx). The premises are formally
inconsistent.

The argument is not a counter-instance to modus tollens at all. Its
conclusion contradicts one of its premises because the premises contradict
themselves.

Cheers.

Danny

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