Necessary and (False or Vacuous) [corrected]
May 11th, 2008, search relatedRelated posts :: Necessary and (False or Vacuous) [corrected] :: Necessary and (False or Vacuous) [corrected] :: Necessary and (False or Vacuous) [corrected] :: Necessary and (False or Vacuous)
Anthony Crifasi wrote:
>On 5/5/08, *Joseph Polanik* wrote:
>>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
>>recently, you’ve argued that you’ve been misunderstood.
>>>>your argument for [1] seems to be that Q is undeniable.
>>>I have never said that Q is undeniable. I have only argued that it
>>>is a necessary implication of self-existence.
>>yes; but, you also say that Q is false; and, you haven’t yet come to
>>grips with the oddity of having a primary premise, [1] above, that is
>>a conditional statement whose consequent is false.
>>if the consequent of a condition is false; then, the truth value of
>>the conditional as a whole depends on the truth value of the
>>antecedent — in this case ‘I exist’.
>The truth value of a conditional as a whole is simply the implication
>of consequent by the antecedent, regardless of the truth of the
>consequent. If the consequent is false, the dependence of the
>consequent is not thereby false, but only the antecedent itself.
not so!
the truth value of the condition itself is dependent on the truth values
of the antecedent and consequent — not the other way around.
furthermore, the truth value of the condition can be caluclated
according to the following table:
Truth Table Values for a Conditional
P -> Q
[1] T T T
[2] T F F
[3] F T T
[4] F T F
in the above table (which may not be aligned if you don’t get plain
ASCII email), there are three columns of T’s and F’s. the first and
third of these give the truth values of the individual propositions;
and, the middle column of T’s and F’s gives the truth value of the
implication itself.
with only two propositions, there are exactly 4 combinations of truth
values for the two propositions. of these, the only one that results in
a value of ‘false’ for the implication is condition 2 where a true
premise implies a false conclusion.
your premise 2 asserts -Q; meaning, that Q is false. hence, the relevant
rows in the above table are [2] and [4]. hence the three points made
previously:
>if the antecedent ‘I exist’ is True then the conditonal is False
>if the antecedent ‘I exist’ is False then the conditonal is Vacuously
>True
>thus, Professor, your defense of Heidegger is based a premise that can
>only be false or vacuous.
you may want to check out Peter Suber’s website on logic at http://www.earlham.edu/~peters/courses/l… where there is a
more extended discussion of truth tables. also good is http://www.abstractmath.org/MM/MMConditi….
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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