Fwd: Re: Tautologies and other forms of circular reasoning.

[glen ropella]

Whoops!  Nick's client apparently constructs headers so that the list is
in the CC: header, which means my "Reply" was inadequate.  I should have
hit "Reply-All".


-------- Original Message --------
Subject: Re: [FRIAM] Tautologies and other forms of circular reasoning.
Date: Fri, 12 Apr 2013 15:01:28 -0700
From: glen <[hidden email]>
To: Nicholas Thompson <[hidden email]>

Nicholas Thompson wrote at 04/12/2013 02:18 PM:
> See how much of the following you both can agree with:
>
> (1)   We are talking here about a broad class of reasoning called circular,
> wherein the conclusion is at least partly determined, not by any facts about
> the world, but by information stated in the question.

I agree completely with this.

> (2) A tautology is the most narrowly defined example of such reasoning.  In
> tautology, we already know the answer when the question has been asked.   No
> doubts can be raised.  This meaning can be further limited to certain kinds
> of mathematical expressions.

I agree mostly with this.  The only exception is complicated deduction,
where many premises tortuously, mechanically, crank through to
"theorems" that aren't obvious in how they map back to the premises.
There are some people who believe this kind of "computational" deduction
is more than mere tautology.  There are some who reduce it to mere
tautology.

> (3) In circular reasoning, (a) the conclusion can  be -- at least partly --
> worked out from the question because the conclusion contains the question
> embedded in it but (b) it is not entirely circular, because it also contains
> other material that is not contained in the question.  So, for instance, if
> the question, "What selection pressure made polar bears white?" the answer
> "a selection pressure that made polar bears white"  is entirely circular.
> It is a simple repetition of the question as an assertion.  But notice that
> the answer , "A selection for white fur", while highly circular, is not
> entirely so because it rules out the possibility that the selection was for
> some correlated trait -- conservation of melanin, say.  That information is
> not entailed in the question.

I don't disagree or agree, here.  I think this equivocates on
"information" or "material not contained in the question".  The only way
to avoid this is to formalize the definition so that everything within
the circular part and the non-circular part can be unambiguously identified.

> (4) Without trying to settle the question of how many forms of semi-circular
> reasoning there might be, Lipton and Thompson described a class of
> semi-circular reasoning called "recursive".  (The idea in the name was that
> the conclusion of the reasoning "runs back" to the question for some of its
> information.  Thus, this part of the explanation is uninformative.)  In
> recursive reasoning, the uninformative part of the explanation is held
> within a frame that is itself informative.  If the question is, "Why is the
> oil in my car clean?", then the answer, "Because it went through a clean oil
> filter" is not completely circular but recursive, because the frame, "went
> through _____ filter" it rules out the possibility that the oil is clean
> simply because it has not yet been through the engine. The polar bear
> explanation above is another example of a recursive explanation.  "His AIDS
> symptoms are caused by the AIDS virus" is another.  We thought that these
> recursive explanations play an important role in the development of
> scientific explanations, because they guided scientists as they collected
> data that served to revise the frame while keeping the goal of the
> explanation clearly in view.  

I agree that there are some of these filter explanations that are
recursive.  But some of them are not.  And the more useful filter
explanations are not actually recursive, but merely iterative.

> 4.  Now where I am confused is about the relationship between completely
> circular reasoning and tautological reasoning.  The example given at the
> dictionary of philosophy of a tautology is "Both Paul and Mary were at the
> meeting; therefore Paul was at the meeting."  If this is the type-case of a
> tautological explanation, then I cannot see why "A selection pressure that
> made polar bears white" is not another example, given the question, "What
> selection pressure made polar bears white?"

I disagree with your dictionary. I think of a tautology as "saying the
exact same thing with different words", not saying a partly similar
thing with different words.  It's an if-and-only-if, not merely an if.

"P ^ M -> P" leaves out information.  So, saying "P" is not the same as
saying "P^M".

But, as I said above, there are some people who claim that all deduction
is tautology.  They would probably identify different types of tautology
(e.g. simple or minimal) versus a complicated (perhaps irreversible)
deduction.

> I think at least two of you can help me see where I am going wrong. I think
> you are going to tell me that I have mixed apples and oranges above, by
> talking indiscriminately about questions and answers and arguments and
> conclusions.  Can you straighten me out on that?   Can you specify the usage
> community for which your proposed usage is current?  Given the FRIAM group,
> can you suggest a usage convention you would recommend for our further
> conversation about plurality in scientific explanation?

I can't straighten anyone out. ;-)  But my suggestion would be that
tautology be used for the most direct, reversible, synonymous
statements: "polar bears are white because polar bears are white".  And
anything more sophisticated should be given another name.

--
=><= glen e. p. ropella
Oh man this egg is way too hot




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