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- Jan 26, 2012
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Use truth table to determine the validity of the argument:
. . [tex]\begin{array}{c}q \to p \\ p \vee q \\ \hline \therefore\;p \end{array}[/tex]
Going towards death ia a completely different thing from ,i am already deadgrowing old leads to death.
i am either growing old, or i am dead.
therefore, i am dead.
(strictly tongue-in-cheek, i assure you).
Wrong.in math, "p implies q" means: if p is true (now!), q is true (now!).
Again wrong. The implication is the same as that in mathsin english "p implies q" means: if p is true (now, or at some point in the future)), q either is, or will be true (we use the same word for an act of deductive and inductive reasoning)
I never said that : "p and q" is the same as "if p then q"no, "if p and q" is not the same as "if p then q".
Is logical implication ,for you , the same as implication?implication in english carries with it a "time-sense", often one will say:
"if (this happens) then (that *will* happen)". note the change of tense.
logical implication has no such "time-sense" bound up within it (in general), logical priority is not temporal. we do not say: 2 is even implies 2 will not be odd, someday.
natural language does NOT express the same ideas as in math: natural language is inherently ambiguous, the whole purpose of logic is to remove (insofar as possible) that ambiguity. the semantics of natural language is much subtler than mathematics, if i say:
"see what i did there?"
there are two obvious meanings:
1) did you perceive the event that occurred
2) did you understand the intent of my action
because the word "see" has a literal and figurative meaning. math (and especially logic) strives to eliminate the figurative meaning (although some of it creeps in in the names we gives to mathematical objects). i can't call a number "prime" just because it fetches a high price in the marketplace, at least not in a proof of number theory.