Re: An argument against modus ponens

On 3 Sep, 21:54, John Jones <jonescard...@xxxxxxx> wrote:

Modus Ponens:
If P, then Q.
P. Therefore, Q.

The "If" announces a truth value. So "if P" requires the consideration
of another element or object through which a truth value may be
ascertained. If we eliminate the ontological and existential status with
which the term "if" baptises its objects, then modus ponens reduces to

The "if... then..." is not substancial. One could give examples of
(logically) *necessary* statements made by those words (e.g. "if x is
father, then x is male"), or even made with other words. Conversely,
one could give examples where "if... then..." are used to state
*contingent* states of affair (e.g. "if it rains, I will take my
umbrella"), or even made with other words.

You are rather conflating informal and formal, where the formal
statement 'P -> Q', and actually, *any* formal statement, has simply
*no meaning at all* unless one gives (or has been given) the specific
*rules* of the system at hand.

That said, such informal statements of the form "if... then.." are
really second-order statements in case you state a logical necessity
(this is not the case for contingencies, where the statement is first
order):

'A entails B' =def 'A and not-B is incongruent (inconsistent)'

Or, equivalently:

'A entails B' =def 'A -> B is a logical necessity'

The first order symbol '->' is simply of *no use* without second order
expressions like "it is analytic" or, equivalently, "it is a (logical)
necessity", despite those words are usually left implied; but, they
can be left implied *after* the concepts and notations (the rules) for
the system have been specified: it is -- to put it simply -- a
shortening of the notation, but the second-order qualification is
still there, although unuttered.

Now, you can have Modus Ponens formalized as (using brackets for
clarity):

( P -> Q, P ) |- Q

But that rather reads:

'P -> Q and P' entails 'Q'

Otherwise equivalent to:

'(P -> Q and P) -> Q' is necessary.

Until you study that little bit of logic you are straight trying to
argue with, you'll just be telling nonsense, mostly, as I think, by
conflating -- arbitrarily and with no criteria -- informal and formal
notions, natural language and formal languages.

BTW, have you read that book from Strawson? Again: IMHO, that is
*exactly* what you are after. I mean, unless it is nonsense what you
are after.

-LV
.