Modus Tollens vs Reductio Ad Absurdum
May 18th, 2008, search relatedRelated posts :: The Denial System :: The Denial System :: Assumptions About Predicating Nothingness :: Assumptions About Predicating Nothingness
Remedial Logic 101: Modus Tollens vs Reductio Ad Absurdum
Professor Crifasi,
one of your crucial claims seems to be that the proposition ‘I remain
self-identical throughout all my perceptions’ is a necessary condition
of existence.
this proposition may be symbolized, as follows:
[1]: P -> Q
where
P = ‘I exist’ [where ‘I exist’ = ‘I am not nothing’]
Q = ‘I remain self-identical throughout all my perceptions’
you also claim that Q is false; so:
[2]: -Q
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I. Modus Tollens
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given your two premises, [1] and [2], it is legitimate to deduce -P.
that’s modus tollens.
you seem to have confused modus tollens with reductio ad absurdum; for,
you say (complaining about me):
“How many times have I had to point out to you that a modus tollens
hypothetically presupposes what will be contradicted in the end?”
in the above example, you conclude -P; but, you don’t hypothetically
presuppose P. you just assume your two premises and draw your conclusion
via modus tollens.
not only do you not presuppose P; but, a good case can be made that you
actually presuppose -P, the very proposition you purport to conclude.
your premise [1] is a conditional; and, every conditional is implied by
the *negation* of its antecedent. this is one of the paradoxes of
material implication.
check the truth table. you’ll see that the following [theorem 51 in EJ
Lemmon’s _Beginning Logic_ p 59] is a logical truth of the propositional
calculus:
-P -> (P -> Q)
thus, one could replace your premises [1] and [2] with -P and -Q and
there would be no effect on the outcome. you could still prove exactly
what you can now.
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II. Reductio Ad Absurdum
============================
in any event, once we combine your argument and mine a contradiction is
created; and, thus, we have the opportunity/obligation to deny an
assumption upon which the contradiction rests.
your argument:
Let P = ‘I exist’ [where ‘I exist’ = ‘I am not nothing’]
Let Q = ‘I remain self-identical throughout all my perceptions’
[1] P -> Q [Assumption]
[2] -Q [Assumption]
[3] -P [MT 1,2] {Assumptions: 1,2}
your conclusion reached by modus tollens operation on lines 1 and 2;
resting on assumptions 1 and 2.
my argument:
Let T = ‘I am experiencing’
Let A = ‘I am attributing a predicate to I’
Let IPN = ‘it is Impossible to attribute Predicates to Nothing(ness)’
[4] IPN [Assumption]
[5] P [Conclusion] {Assumptions: 4}
‘P’ is introduced as the conclusion of the following:
I notice that I am experiencing and assert, T, ‘I am experiencing’.
[Experiential Fact (and report of same)]
I note that asserting T implies that ‘I am attributing a predicate to
I’; hence, A.
if ‘I am attributing a predicate to I’; then, by IPN, ‘I am not nothing’
which is already symbolized as ‘P’.
the contradiction:
[6]: P & -P [Conjunction 3,5] {Assumptions: 1,2,4}
by combining our arguments we can generate a contradiction.
the rules of Reductio Ad Absurdum, RAA, now require us to negate an
assumption upon which the contradiction rests.
“Now suppose that from an assumption A, together perhaps with other
assumptions, we can derive a contradiction as a conclusion; then RAA
permits us to derive -A as a conclusion from those other assumptions (if
any)”. [Lemmon, op.cit. p. 26]
here, the contradiction is derived from a set of assumptions; and,
therefore, we have a *choice* as to which one is to be negated.
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III. The Choice and its Consequence
======================================
obviously, I choose to negate [1]. you choose to negate [4].
I have no doubt that each of us believes he has made the right choice
for legitimate reasons; and, no doubt we will discuss those reasons;
but, the question at the moment is whether you understand the
logical consequences of your choice.
negating [4], IPN, ‘it is Impossible to attribute Predicates to
Nothing(ness)’, is equivalent to proving PPN, ‘it is Possible to
attribute Predicates to Nothing(ness)’
would you not agree?
* * *
that’s it, Professor.
I’m not *at this moment* contesting your assumptions, your conclusions,
your claims as to the evidence for your assumptions, or your reasons for
choosing which assumption to negate following the derivation of a
contradition.
at the moment, I’m just asking you whether you admit that negating the
impossibility of attributing predicates to nothing(ness) is equivalent
to proving that it is possible to attribute predicates to nothing(ness).
Joe
–
Philosophy is, after all, done ultimately in the first person for the
first person. — H-N Castaneda
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http://what-am-i.net
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