Re: Tautologies and Empirical Truth

From: patty (pattyNO_at_SPAMicyberspace.net)
Date: 10/30/04 

Date: Sat, 30 Oct 2004 17:35:09 GMT

Lester Zick wrote:

> On Sat, 30 Oct 2004 10:55:34 GMT, "alan jones" <ob2@freeuk.com> in
> comp.ai.philosophy wrote:
>
>
>>>If a tautology is universally true, alternatives to the tautology
>>>cannot be true and must be universally false. And, further, this
>>>must be true of all tautologies.
>>
>>'Alternatives to the tautology?' Do you care to explain what
>>is meant by alternatives? This extract would seem to suggest
>>a situation of either / or. Yet I would say its possible to have
>>alternative language to describe the same truth, even a truth
>>which encompasses the first without contradicting it.
>
>
> Well, well. Someone has finally raised a pertinent issue, one which I
> find somewhat perplexing. If a tautology excludes no possibility, the
> only alternative to a tautology would have to be the one thing it
> excludes, which is the "no possibility". Which I take to mean self
> contradiction.
>

Ok ... another way of saying that might be to say that there are no
alternatives to a tautology except to change our web of belief. To
contemplate that there is an alternative and not change our web of
belief is perhaps fun ... but nerve wracking.

Incidentally i think we have been playing rather free and loose with
this word "tautology". We need to distinguish things like tautologies
from things like axioms. Both of which are true in all cases inside of
a web of belief. A tautology says nothing about the world outside of our
web (or about how to change our web). But an axiom can be falsified by
looking outside.

For example consider our web to be:
  Axiom [1]: "p or (not p)"
  Tautology [2]: "Parallel lines either meet or they don't meet"

Now [2] is certainly true in all cases in our web - especially since i
put that axiom in there - yet it does not excludes any possibilities -
it is a tautology. On the other hand [1] excludes the possibility that
"p and (not p)", yet is taken as true for all p in our web - it is an
axiom.

Incidentally in my personal web i occasionally peer outside and find a
"p" and it's "not" both sitting there, both apparently true, staring me
in the face. Hence i dont always hold axiom [1] to be true. Hence my
logic is intensional.

patty

Relevant Pages

  • Re: Unfalsifiable Tautology = Evolution
    ... definitional statements have interesting and surprising implications ... This is an axiom, not a tautology. ... An axiom is a statement you assume to be true. ... previously understand the implications. ...
    (talk.origins)
  • Re: "Theorem" in Mendelson ?
    ... An inference rule applied to a tautology results in a ... Either B_i is an axiom, ... B_1 cannot be a direct consequence of some preceding wfs in the ... sequence, because there are no preceding wfs. ...
    (sci.logic)
  • Re: OT: Solipsism
    ... >> one even define a tautology other than by appealing to the rules ... The axiom that for each line, and a point not on this ... >to the first line describes euclidean geometry. ... >if one doesn't look at space alone, but at spacetime (and always includes ...
    (rec.arts.books.tolkien)
  • Re: Null-Axiom Set Theory
    ... The logical axioms resolve to tautology, ... The notion of the use of the excluded middle in the null axiom theory ... Thus there is no need for an axiom of infinity because upon the ... My notion is that they're theorems of the null axiom theory. ...
    (sci.logic)
  • Re: mathematical language
    ... Your example corresponds to what I think is a tautology. ... >statement which excludes no logical possibility" took me a while to parse, ... >level of negation and still maintain, ... useless and anything which is useless is a tautology and circular ...
    (comp.theory)