ONT Critical Reflection On Method
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CROM. Discussion Note 1
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Jay,
Let me make a try at explaining some of this in plainer terms.
The topic of second intentional logic was raised most recently by Bernard Morand,
replying to a note that I cross-posted to the "Semiotics and Communication List":
http://yaka.univ-perp.fr/wws/arc/gdsemiocom
I thought that his comment was extremely helpful with respect to the entangled
questions of abstract objects, the processes of abstraction, the relationships
of abstractions to abstractees, and so on, that we were engaged in at the time.
But I have since come to realize that in making the conventional translation from
"higher intentional logic of relatives" (HILOR) to "higher order logic" (HOL) that
some very serious distortions are almost inevitably introduced into the discussion.
I am still trying to work out what might account for these losses in translation,
but the main fact seems to be that the traditions that have severally used these
terminologies have very different purposes attached to their use, whatever form
of "logically in principle" (LIP) conversion might be enunciated betweeen them.
I am adducing to the HAPA account a few canonical remarks from Peirce that
I hope will help to explain some of the things that the older traditions
regarded as belonging under the head of second and higher intentions:
So far:
http://suo.ieee.org/email/msg11271.html
http://suo.ieee.org/email/msg11277.html
If I had to give a midflight capsule summary, I would probably say that
the HOL concern is primarily levelled at issues of global coverage while
the HIL concern starts out primarily from local operations, especially the
formal logical processes that support "critical reflection on method" (CROM).
In a way that is yet to be made as clear as I would like, HILOR demands slightly
more "elbow room" than FOL can ever seem to afford -- but here it may not be the
cramp of FOL per se so much as the habits of 2-adic reductive thinking that have
been its accidents in history so far -- at any rate, HILOR doesn't really care
all that much right at first "how high is the sky" the way that it sounds if
you transduce higher intentional talk into higher order talk. That's the
best I can explain it right now.
Jon Awbrey
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> | I must lie down where all the ladders start
> | In the foul rag and bone shop of the heart.
> |
> | William Butler Yeats, "The Circus Animals' Desertion"
> |
> | http://www.web-books.com/Classics/Poetry/Anthology/Yeats/Circus.htm
>
> JA = Jon Awbrey
> JH = Jay Halcomb
>
> JH: Jon, I know not what this antick term, 'weenie logic' signifieth.
>
> JA: Sorry, that shudda been "over-weenie logic".
>
> JH: By the Rood! I am indeed mightily glad to hear of such doctrines as
> you've conveyed, scholiastickly, as they may yet be the saving of me.
>
> JH: For all along I've been in a great swivet and stew about whether
> 'tis better to marry or to burn, as a Saint has vouchsafed that
> one state was better than t'other. But it now has fallen out
> that learned men say that if we be but pleased in good sense
> to take the having and the not-having of a wife, we shall
> indeed find no repugnancy nor contradiction in the
> terms at all, betimes.
>
> JH: For example:
>
> http://etext.library.adelaide.edu.au/r/r11g/part135.html
>
> JH: Shall we not conclude that in like wise all nuptials may fare as
> well, both in good Holy order and with much attendant merriment?
>
> JH: Or, in simpler words, what formalized logic do you endorse,
> if any, and of which do you disapprove, Jon? And why?
> I freely confess it's awfully hard to tell.
>
> Jay, thanks for the chance to play the deadpun, as I really need the practice.
> But here, I think that I do e-spy a question to which I can e-spouse a re:ply.
>
> I got into this booming buzziness out of a desire to solve some problems.
> To make a long story short, that has led me by a winding stairway not to
> heaven, not just yet, but to that "foul rag and bone shop of the heart"
> that one finds at the _|_ of the recursed heap, and by this _|_ line to
> say that I am mostly concerned with what the grubby pragmatician might
> call "applicable computable logic" (ACL), and what all this monicker
> would likely suggest to the common sense problem solver. And here,
> from the _|_ of my heart, at the _|_ of this persistently recursed
> heap of problems that go about orphaned and unaddressed by high
> and mighty logicists of every persuasion, I don't really care
> a Fig 1 or Fig 2 what flag they fly over the rubble, so long
> as they get down from their high-rise vacant LOT's and help
> clean up the mess.
>
> JH: It might be, e.g., weak (finitary) 2nd order logic, monadic 2nd order logic,
> 2nd order logic itself, 3rd order logic, the theory of types, or something else.
>
> JH: Which do you think Peirce might have preferred?
>
> JH: Can you cite me some Holy Writ thereupon from the Canon to clear up the matter?
>
> See above, or read the writing on the wall (of the city of philosophy).
>
> Jon Awbrey
>
> JH: Nor discern I where be the 'coops of Principia',
> nor what strange fowl roost therein. Might this
> bespeak the fabled land of 'type theory', of which
> I have sometime heard strange ramifications?
>
> JA: Close, but no cigar. True, there's a mockingbird in this coop,
> but what I really had in my mental aviary was a bird like this:
>
> JH: Etc.
>
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