[hist-analytic] Discussion of Aune's ETK, Chapter Two: Modus Ponens/Tollens
Baynesr at comcast.net
Baynesr at comcast.net
Fri Oct 30 09:09:43 EDT 2009
Sorry Danny, I just don't understand much of this. For example, you bring in Davidson, but I see no reason to: where are the event variables for example, if you are taking a Davidsonian approach?
It is obvious the argument is valid IF the first premise is a conditional. I argue against this. You ignore the argument. I don't mind that. But if, f as you say the premises are inconsistent, then of course anything follows and modus ponens needn't enter the picture at all.
Elsewhere, I've argued that Davidson is wrong on the treatment of adverbials, in particular across prepositional phrases where the verbs are causal. Can't digress into Davidson, now.
Of course Bruce likes what you say, but I don't think his argument (or yours) rules out seeing that the premise (first) is no conditional at all etc. In short, you've ignored my argument and substituted reasons for thinking the argument is invalid. I agree it is invalid but it is not a modus ponens, tollens, argument etc.
I think the question "What is modus ponens?" is somewhat rhetorical. It's a rule that says that if you have 'p implies q' and 'p' then you can derive 'q'. No mystery here, OR we are in for a revolution in logic, which I doubt.
----- Original Message -----
From: "Danny Frederick" <danny.frederick at btinternet.com>
To: "hist-analytic" <hist-analytic at simplelists.co.uk>
Sent: Thursday, October 29, 2009 4:42:01 PM GMT -05:00 US/Canada Eastern
Subject: RE: Discussion of Aune's ETK, Chapter Two: Modus Ponens/Tollens
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.
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