Re: What isn't a tautology?

Douglas Theobald wrote:
> So I guess I'm the "pro-tautology" dude.
>
> For clarity, here is my reasoning, summarized from a thread
> elsewhere:
>
> Surely a definition is just another type of statement, a
> declarative sentence making an assertion. Isn't a definition a
> proposition that can be used as a premise in an argument? A
> definition is just a statement (like Fa or Gb), and so it should
> have a truth value. And in the case of stipulative definitions
> (the type of definition I am concerned with), the truth value is
> always T, by definition.

A definition is not a tautology and does not behave as a tautology.
Suppose you have a set of consistent premises, which contain no mention
of skirnobs. The following are two possible stipulative definitions of
"skirnob":

Definition 1: For all x, x is a skirnob if and only if x is shiny.
Definition 2: For all x, x is a skirnob if and only if x is not shiny.

The statements in definition 1 and 2 are mutually contradictory.
Nevertheless, you can add _either_ definition 1 _or_ definition 2 to
your premises without introducing any contradiction. Had, say,
definition 1 been a tautology, then definition 2 would have been a
logical contradiction and you couldn't add definition 2 to your
premises without making them inconsistent.

Erik

> "Stipulative definition: The arbitrary assignment of meaning to
> a term not previously in use. Although it may be relatively
> inconvenient or useless, such a definition can never be mistaken
> or incorrect."
> http://www.philosophypages.com/dy/s9.htm#stip
>
> Now, if you accept the following definition of tautology:
>
> "A statement form whose column in a truth-table contains nothing
> but Ts ..."
> http://www.philosophypages.com/lg/e10c.htm#taut
>
> then it follows that a stipulative definition is trivially
> tautologous.
>
> Futhermore, the statement (1=1) is an instance of (x=x), for
> which the truth-table contains nothing but Ts. And thus it is
> also tautologous.
>
> Douglas

.

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