Frederik, lists,
I'm dissatisfied with my previous post in this thread, I feel like I've
missed the forest for the trees. While I'm not convinced that there's a
theorematic applied deduction in the Wegener example, still, the idea of
continental drift is not merely a simplifying explanation of the fit
between continental coastlines, it's also an idea that anybody would
call nontrivial. It involves a complex new idea, and, if true (as it
turned out to be), would foreseeably be a basis and foundation for much
further discovery. Its nontriviality doesn't give it intrinsic
abductive merit in the way that its plausibility does, but said
nontriviality still makes it something to be prized if it pans out (as
it did). But so far, that's the nontriviality of prospective
discoveries, what about a nontriviality of how one got to the abduction
of continental drift? I'm trying to think of some parallelism between
its abduction and theorematic deduction, so as to analogize the idea of
abductive nontriviality to deductive theorematicity. Roughly, something
involving nontrivial changes of standing beliefs about geology, changes
equivalent to the idea of continental drift. Well, when even I think I'm
talking too much, it's time I call it a day.
Best, Ben
On 4/20/2015 12:58 PM, Benjamin Udell wrote:
Frederik, lists,
You wrote,
My argument, which I may not have made sufficiently clear in the
chapter, is that the small step from having spatiotemporal cell
phone information represented in long lists of coordinates - and
to synthesize that same information in one geographical map, is a
corollarial step.
Yes, I agree that it's corollarial. I see that I didn't make my
agreement clear, sorry about that. I saw it as a case where
corollarial reasoning makes clear that which, as a practical matter,
was quite obscure. I took it as a case of mere complication, as
opposed to complexity in the sense of nontriviality.
You wrote,
I admit it is more difficult, in general, to precisely extend the
corollarial/theorematic distinction to applied cases - but as you
can see I did the attempt picking map examples. The central
problem for my pov seems to be that in applied cases you should
not only include what is given in axiomatics (topographical maps
largely respecting Euclidean geometry) but also in the more or
less implicit ontological assumptions in the area of application -
this is why i count Wegener's map experiment as theorematic. Taken
as pure geometry, it is a trivial translation to move South
America eastwards to compare its coastline with Africa's - but in
terms of geology, it requires the addition of a "new idea" -
namely that continents may move.
I think that the mathematical shifting of the South America map to
compare its coastline with the Africa map's coastline is required, or
at any rate helpful, in order to bring a surprising geological
phenomenon to light - the good match. One has ignored geological
assumptions in order to do this, and then, looking at it and bringing
geological assumptions back into account, one is surprised. Then the
idea of an actual geological movement of continents is considered and
abduced as a simplifying explanation because it sheds some light how
the good fit could have physically happened as a matter of course.
1. Here in the abduction, unlike in theorematic deduction, one has
_/concluded/_ in the new element, as opposed to introducing it in
order to conclude in something else.
2. Concluding abductively in the proposition of such geological
movement, amounts to assuming it as a basis for deducing conceivable
practical implications. Here in the predictive deduction, the new
element (the hypothetical assumption), unlike the new element that
makes a deduction theorematic, is asserted in the original conditions
of the deductive problem, not introduced in some construction along
the way.
3. The inductive tests of the deduced predictions will tend to support
or overturn the hypothetical assumption; now the new element, the
hypothetical assumption, is that which the reasoning would conclude by
supporting or overturning, the reasoning's thesis, unlike in a
theorematic deduction.
If we look at the above inquiry cycle as a whole, then the
hypothetical assumption, although it is a new element, is that which
one seeks to confirm or overturn, and that is not the role played by
the new element in a theorematic deduction.
Yet, - a theorematic deduction's introduction of a new or outside idea
(not part of the problem's explicit conditions or contemplated in the
thesis that is to be proved) reminds one of an abductive inference's
introduction of a new or outside idea to become the conclusion. And I
agree that that's a phenomenon worth explaining. All I can think of at
the moment is that it's as if the new element in the theorematic
deduction were introduced by a higher-level or methodological
abduction - 'if I introduce this idea, I might be able to deduce the
thesis as a matter of course'.
Best, Ben
On 4/20/2015 11:31 AM, Frederik Stjernfelt wrote:
Dear Ben, Franklin, lists,
Den 19/04/2015 kl. 20.05 skrev Benjamin Udell <[email protected]
<mailto:[email protected]>>:
Franklin, lists,
I agree with Jon, thanks for your excellent starting post.
You wrote,
[....] Why can't corollarial reasoning, which involves
observation and experimentation, reveal unnoticed and hidden
relations? After all, on p.285-6, Frederik mentions the work of
police detective Jorn "Old Man" Holm and his computer program,
which Frederik describes as a "practical example of corollarial
map reasoning" (p.285). In this example, Holm uses the
corollarial reasoning to reveal information about the
whereabouts of suspects. Doesn't the comparison of the map
reasoning with suspects' testimony end up revealing unnoticed
and hidden relations?
There's a distinction that some make between complexity and mere
complication. Corollarial reasonings may accumulate mere
complications until the result becomes hard to see, although it
involves little if any complexity in, more or less, the sense of
depth or nontriviality.
I don't know whether there's a theorematic approach to Jørn Holm's
diagrammatization that would show its result in a nontrivial aspect,
and anyway its diagrammatic, pictorial presentation already leaves
one in no doubt that a pattern is revealed.
Certainly the comparison between Holm's map and suspects' testimony
may give nontrivial results - but that comparison was not my point -
My argument, which I may not have made sufficiently clear in the
chapter, is that the small step from having spatiotemporal cell phone
information represented in long lists of coordinates - and to
synthesize that same information in one geographical map, is a
corollarial step. It does not contain any new information which was
not already there in the list, but it brings the information together
in one conclusive sign so as fo facilitate the charting of e.g. the
trajectory of single cell phones on the map.
I admit it is more difficult, in general, to precisely extend the
corollarial/theorematic distinction to applied cases - but as you can
see I did the attempt picking map examples. The central problem for
my pov seems to be that in applied cases you should not only include
what is given in axiomatics (topographical maps largely respecting
Euclidean geometry) but also in the more or less implicit ontological
assumptions in the area of application - this is why i count
Wegener's map experiment as theorematic. Taken as pure geometry, it
is a trivial translation to move South America eastwards to compare
its coastline with Africa's - but in terms of geology, it requires
the addition of a "new idea" - namely that continents may move.
Best,
Frederik
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