Re: Epistemology 201: The Science of Science

From: Paul Bramscher (brams006_nospam_at_tc.umn.edu)
Date: 01/27/05 

Date: Thu, 27 Jan 2005 12:41:08 -0600

The Sophist wrote:
> Paul Bramscher wrote:
>
>> (1) All apples are red.
>> (2) This Cortland is a variety of apple.
>>
>> Necessary conclusion #1: This Cortland is red.
>>
>> That's a necessary truth.
>
>
> Sure, it is a necessary truth that this conclusion follows from those
> premisses.
>
>> Let's add a couple more axioms:
>>
>> (3) Decayed apples turn brown.
>> (4) This Cortland is decayed.
>>
>> New (necessary) conclusion #2: This Cortland is brown.
>
>
> Well, of course this follows, but now the axiom set is inconsistent, so
> anything at all follows from it. The original conclusion also still
> follows, for instance.

I mean that #3 and #4 are added to #1 and #2 (not floating out there on
their own):

This:

(1) All apples are red.
(2) This Cortland is a variety of apple.

Color = red

Versus this:

(1) All apples are red.
(2) This Cortland is a variety of apple.
(3) Decayed apples turn brown.
(4) This Cortland is decayed.

Color = brown

So the addition of more axiomatic statements (to a previously existing
system) clearly changes what must be (necessarily) true. This game, I'm
sure could produce an infinite flip-flop between colors of the apple.

(1) All apples are red.
(2) This Cortland is a variety of apple.
(3) Decayed apples turn brown.
(4) This Cortland is decayed.
(5) Red paint will make things red.
(6) This apple is painted with red paint.

Color = red

And so on -- new information changes what the truth table (necessarily)
concludes. Truths are scoped situations, only in relation to their
axioms. So I humbly submit that since even a mere machine can perform
truth table logic flawlessly (probably better than humans), that the
real problem facing logic is in the assembly of relevant axioms. I see
this as largely the domain of science, human sensibilities and biases
(experimental, procedural, social, financial limitation, etc.)

Unfortunately, that's where things get icky.

Relevant Pages

  • Re: Epistemology 201: The Science of Science
    ... > necessary truth simpliciter. ... > otherwise (say if not all apples are red). ... I think that a cortland is red. ... possibility that it is no longer fresh -- but still allow that fresh ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... > necessary truth simpliciter. ... > otherwise (say if not all apples are red). ... I think that a cortland is red. ... possibility that it is no longer fresh -- but still allow that fresh ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... > necessary truth simpliciter. ... > otherwise (say if not all apples are red). ... I think that a cortland is red. ... possibility that it is no longer fresh -- but still allow that fresh ...
    (sci.physics)
  • Re: Epistemology 201: The Science of Science
    ... it is a necessary truth that this conclusion follows from those ... >All apples are red. ... >This Cortland is a variety of apple. ... >Decayed apples turn brown. ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... it is a necessary truth that this conclusion follows from those ... >All apples are red. ... >This Cortland is a variety of apple. ... >Decayed apples turn brown. ...
    (sci.cognitive)
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