Re: What isn't a tautology?
- From: "George Dance" <georgedance04@xxxxxxxx>
- Date: 16 Jul 2005 09:32:31 -0700
Chris Menzel wrote:
> On Fri, 15 Jul 2005 18:36:05 -0600, Douglas Theobald
> <dtheobald@xxxxxxxxxxx> said:
> > P1. A tautology is a statement whose column in a truth-table contains
> > nothing but Ts.
> > P2. Stipulative definitions are true by definition.
>
> But not in virtue of their propositional logical form, which is what is
> tested in a truth table.
That looks right; a logic using definitions needs a Def rule as well
(either that the terms are equivalent, or that they can be substituted
for each other).
> Consider, e.g., "A prime number is a positive
> integer > 1 whose only positive integer divisors are itself and 1",
> i.e.: (x)(Prime(x) <-> Integer(x) & x > 1 & (y)(Integer(y) & y > 1 &
> Divides(y,x) -> (y = 1 v y = x))). This definition has a complex
> logical form in predicate logic, but its propositional form is simply
> that of an atomic sentence P; it's not a negation, conjunction,
> disjunction, conditional, or biconditional.
Sorry, but it looks like a biconditional to me:
A<->B (A="a is prime"; B="a's only positive integer divisors are a and
1")
> So stick it on a truth
> table and you get:
>
> P | P
> -----
> T | T
> F | F
>
> So it's not a tautology.
True. (A<->B isn't a tautology either, so your point still stands.)
.
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