SUO: One Calculus At A Time
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| 14.6. Fuzzy Sets
|
| Fuzzy set theory is a more-or-less categorical idea that some claim has
| application to computer modeling. It appears to be closely related to
| topos theory. In fact, it appears to us that the interesting core of
| the subject is already implicit in topos theory. ...
|
| Barr & Wells, 'CT for CS', p. 325.
|
| Barr, M. & Wells, C.,
|'Category Theory for Computing Science',
| Prentice Hall, London, UK, 1990.
Incidental Musements:
http://www.spaceagepop.com/forefilm.htm
http://www.zrc-sazu.si/www/fi/vestniki/filve102.htm
P.S. It's called a "lodestone" because it swings into line
with the "lodestar", the "leading" star, or Polaris.
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Tom Johnston wrote:
>
> Some brief reflections on Whitehead's ontology (in Process and Reality,
> and also in Modes of Thought), FWIW:
>
> the twin problems of (a) permanence and change, and (b) universals and
> particulars, hve defined the field of ontology since Heraclitus, Parmenides,
> Plato and Aristotle.
>
> On permanence and change: for Heraclitus, the change/permanence problem
> was how to explain permanence, since everything was always changing.
> For Parmenides, that problem was how to explain change, since everything
> always (already) is. (Kirk & Raven is still the best source for the
> pre-Socratics.)
>
> On universals and particulars (later, realism and nominalism): for Plato,
> universals are the "really real", particulars have dependent derivative
> reality, and the universals/particulars problem is how to explain the
> relation between them (the problem well presented in his dialog Parmenides,
> and called the "third man argument"). For Aristotle, particulars are the
> "really real", and universals have dependent derivative reality as the
> essence, or essential form, of particulars.
>
> This is background for discussing Whitehead. For Whitehead, the universals
> are "eternal objects", and the particulars "actual occasions". Actual
> occasions are the ontological flip-side of the spatial-temporally enduring
> objects of the basically Aristotelian ontology which we all share. Instead of
> enduring objects changing spatial-temporal locations, and also other properties
> (their instantiation of universals like color, shape, and so on, for example),
> Whitehead built his ontology on contiguous events (the actual occasions).
>
> Spatial-temporal contiguity of a series of events was the foundation on which
> Whitehead's account of permanence and change is built. Each actual occasion
> instantiates any number of eternal objects (with the same "how do particulars
> and universals relate to one another" problem that Plato and Aristotle
> struggled with).
>
> Permanence, for Whitehead, was accounted for by a set of actual occasions
> which were contiguous in time, and overlapping in spatial location. For as
> long as a contiguous subset of those occasions, for example, instantiated
> the eternal object Red, then that particular object was red. At some point,
> let's say, the first of two contiguous occasions instantiated Red, but the
> next one instantiated Pink, and the third one White. That object, whatever
> it was, just changed from red to white. Change, for Whitehead, was accounted
> for thusly.
>
> What we call stable objects, in the world around us, are thus for Whitehead
> a series of occasions which are contiguous in time and overlapping, from one
> occasion to the next, in space. By and large, any pair of occasions participate
> in the identical set of eternal objects, and it is this "by and large" common
> participation which causes us to distinguish that series as a particular, as
> object extended in space and time. It is the grounds on which we chunk the
> world around us into different things.
>
> Thus, in Whitehead, we see quite clearly the convergence of ontology's
> two major themes -- universals and particulars, and permanence and change.
> He encourages us to look at "things" as a series of contiguous events sharing
> enough common and slowly changing properties to distinguish themselves as a
> "thing" from their surroundings. He provides this ontology as an alternative
> to an ontology of "stuff" which endures through time and slowly changes its
> properties.
>
> Which is why Whitehead's metaphysics is called "process philosophy".
>
> I find it a delightful mental exercise to think of the world around me in
> Whiteheadian terms. I think that just as biological evolution could have
> taken a very different turn a few hundreds of millions of years ago and
> ended up with equivalently intelligent creatures who would have looked
> much different from us, so too the history of everyman's ontological
> world view could have taken a Whiteheadian turn some long time ago,
> and if it had, then today we would all experience the world in
> those occasion-centered rather than "stuff"-centered terms.
>
> But I don't think Whitehead gets us any closer to solving basic problems
> of particulars and universals, of enduring objects (when does something
> cease being that thing, and some new things begin to be?), or of
> permanence and change.
>
> And I think that Wittgenstein had, if not the answer, at least a really creative
> suggestion. He suggested that we are held captive by the Aristotelian notion of
> a substance and its essential nature, and then with its accidental properties.
> When the essential nature changes, the thing becomes a new thing (of a different
> kind). When an accidental property changes, the thing is still the same thing, of
> the same kind. Repaint my car, and it's still a car, and it's the same car it was
> before I painted it.
>
> But suppose I take it to Monster Garage (a TV series), and they transform it
> into a three-wheeled vehicle. Is it still a car? How about a chopping it down
> further and making a two-wheeled vehicle with an engine and a place to sit.
> Hasn't my car become a motorcycle now? If so, when did that change happen?
>
> This is a diachronic version of Wittgenstein's famous example about games.
> Tennis, chess, bridge, video games, etc. What do they all have in common?
> Don't answer the question, Witt said, because it's a bad question. We call
> them all "games" because there are "family resemblances" among them, even
> though there is no core set of properties which are definitive of being a
> game (and in abandoning the idea of a definitive set of properties, Witt.
> suggests we abandon the Aristotelian framework of essential vs. accidental
> properties.)
>
> I am new to this discussion group, though I've been observing for a few months.
> I see a flexible mathematical framework for loosely coupling ontologies together.
> But what are you going to do about problems like these? Substituting Witt. for
> Aristotle, it seems to me, on the problem of particulars, enduring objects,
> identity, etc. is a good idea. But the best mathematics we have to model that,
> I think, is fuzzy logic. But I've seen no discussion of fuzzy logic in this forum.
>
> Quine's demolition of the analytic/synthetic dichotomy does for concepts what Witt's
> family resemblances does for things. It blurs the sharp distinctions. In particular,
> it blurs the dichotomy between a statement being true by definition (analytic a priori,
> in Kantian terms) and being true by empirical matter of fact (synthetic a posteriori,
> in Kantian terms).
>
> To illustrate (taken from an obscure article by A. J. Ayer): at one point in history,
> it was observed that loadstones attracted iron and steel. At that point, "Loadstones
> attract iron and steel" was an empirically true, synthetic, statement. Over time,
> that changed. Now, "Loadstones attract iron and steel" is true by definition;
> if something didn't attract iron and steel, we wouldn't call it a loadstone.
> So now, that is an analytic statement.
>
> When did the change happen? When did the statement change its status from true by observation to true by definition? There is no point at which this happened. We have here a continuum, from synthetic to analytic, not a dichotomy between the two. We have here the linguistic equivalent of replacing the Aristotelian distinction between essential and accidental properties with the notion of a continuum of family resemblances.
>
> So maybe my biggest question to this group is this: which side do you come down on, dichotomies or continuua? If the former, then I, in good philosophical company, think you will be forever struggling to make your SUO work, because you will have started from the wrong premise. But if the latter, where are the discussions of these issues?
>
> Tom Johnston
>
> -------Original Message-------
> From: "John F. Sowa" <sowa@bestweb.net>
> Sent: 07/08/03 08:15 AM
> To: Jon Awbrey <jawbrey@att.net>
> Subject: Re: SUO: Re: One Stone Makes a Beach
>
> >
> >
> Jon and Ted,
>
> You're both right:
>
> > JA: For information on space, time, spacetime, physical objects,
> > physical processes, and so on, read books by mathematicians
> > and physicicts.
> >
> > TD: "Spacetime," yes. "Space" and "time," no.
> > Taken separately these are not physical concepts.
>
> The qualifications for serious research in space, time, and
> spacetime must include research-level depth in physics, mathematics,
> metaphysics, and logic. Two of the very few people who have had
> that level of depth in those subjects are Charles Sanders Peirce
> and Alfred North Whitehead.
>
> Whitehead wrote a book on relativity, in which he developed an
> alternative to Einstein's theory of general relativity, but without
> assuming that gravity warps space. It agrees with Einstein's version
> in most respects, but there are some minor areas where it makes
> different predictions. Physicists have taken it seriously and
> carried out experiments to test the differences.
>
> The general conclusions seem to be:
>
> 1. On some of the areas of disagreement, Einstein's version seems
> to make better predictions.
>
> 2. It might be possible to revise Whitehead's version to give
> a better agreement with experiment, but there is no need
> to do so.
>
> 3. However, nobody has successfully brought gravity into the
> Grand Unified Theory (GUT) with the other basic forces,
> and having more than one alternative theory is useful for
> providing some perspective for future research.
>
> For Whitehead's metaphysics, see his _Process and Reality_,
> which many people regard as the most profound book on ontology
> written in the 20th century. And by the way, Whitehead did read
> Bergson's work and said that it had been a strong influence on
> his approach.
>
> I believe that Peirce's semeiotic and Whitehead's process philosophy
> are complementary and that a synthesis of both of them would make
> the best available foundation for ontology. I wrote an article
> that outlines my suggestions for following that recommendation:
>
> http://www.jfsowa.com/pubs/signproc.htm
>
> Following is a (still unfinished) paper, in which I develop the
> presentation of processes and causality (and related topics on
> space and time) in more detail:
>
> http://www.jfsowa.com/ontology/causal.htm
>
> John Sowa
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