Fwd: Modern interpretations of Aristotle's logic

[James Thompson]

  I clicked on "Modern Interpretations of Aristotle's logic; there were about ten different messages included; all very good and interesting. 

Aristotle could not have done all that he did, had he not been very methodical.  Charles Darwin stated that he learned more from Aristotle, than from all his other predecessors.  Aristotle stated that mankind had always existed. For this to be true; for moderns it means that meteorites containing bacteria in salt crystals must have spread throughout the universe, bacteria garanteed to evolve into humans, man, when ever a meteorite landed on a favorable planet.  In Organic Chemistry, the molecules for both Chlorophyl and Hemoglobin, are very similar, benzene rings with long attachments, chlorophyl centered around a copper Ion, and hemoglobin centered around a ferric (iron) ion.  Of course, horseshoe crabs have bright blue blood, because of cobalt.  This indicates that plants and animals had a common origin.  When Plato died, Aristotle left Athens because he was dissappointed Plato left the Academy to somewhat inferior thinker, Nephew Spucipus.  The Greatest Mathematician of the day, Eudoxus, left with Aristotle for the same reason.  I have read that it was a society of professional mathematicians. the Pythaoreans, who invented the place system or using a zero, and a one; and invented the abacus also.  Prior to the electronic digital computer., skilled metrics using the abacus could keep up with the most modern electro-mechanical computer.   Eudoxus wanted to turn people away from astrology. so he constructed the geo-centric eartth  model for that reason, knowing better, and considering it had no practical consequences.  Eudoxus attribute part of his work to Thales, to make it seem the continuation of an ancient tradition; also, did the original work attributed to Euclid, etc.  Eudoxus seems to have considered himself on the same level as Aristotle, and also by others.   Euclid's formal system seems organized on criteria put down in the Metaphysics. A bust believed to be of Aristotle, with a Hook Nose, justifying Aristotle's nickname, Hook Nosed Aristotle, likely descended from a Levite on his father's side. Aristotle's Levite Ancestor, may have wanted to own property; Levites were Ancient Israel's gobernment bureaucrats, and could not own property, and had to retire after age 50;; this was to keep them honest; so the Levites were historie's first honorable and honest government bureaucrats. Aristotle held that Honor, was the ruling virtue, the one that must rule all other virtues, to protect them from being used  for evil.  Honor is to Honor the  Holy Spirit of The Truth above all else.  This is also the  Virtue that makes the sciences possible.


---------- Forwarded message ----------
From: pyrrho <c.brillow...@googlemail.com>
Date: Oct 17 2007, 1:27 am
Subject: Modern interpretations of Aristotle's logic
To: aristotle-logic


Hi Ron:

Thanks for your answer! So, you found a mistake in my considerations?

>This ^ is the mistake, a serious one, but it's
> an easy one to make. ...
>From your framework of sets and classes, variables etc. you are

completly right! But what I can see now is that I try to explain a
complicated matter with too few words.

>ron] I'm still sticking with Corcoran.

I would so too, if I would not have a better semantics in the drawer.I
have to sort that out first.

Some final remarks and more canditates for the ongoing beauty-contest:
who is the greatest logician?

Logic did not stop with Gödel's incompeleteness. Gregory Chaitin
(still alive) extended and quantified Gödel's approach.

He introduced a complexity index for calculi and theorems called
"algorithmic information content". If that index of a theorem you wish
to proof in a certain calculus is lower than the index of the calculus
then the theorem is too complex and you can't prove it. You may add
this theorem as a new axiom however. The complexity index of the new
calculus is now higher that the previous one, but it won't do you much
good.

While Chaitin introduced a quantitative measure of information into
"logic", the logician Dana Scott (also still alive) introduced what he
called, "qualitative information" into logic.For this he received the
Turing award in 1976. I can't explain it in a few words howerver. A
good introduction to all that can be found in "Handbook on the
Philosophy of Information", Ed. J.v. Benthem, P. Advioans, Elsevier,
especially the article by Abramsky. I do not know if this book has
appeard yet, I think it is just in the the process of appearing.

Ron, it was geat fun talking to you!

Thanks!
Claus

On 2 Okt., 09:08, Ron Allen <wavel...@pacbell.net> wrote:

> Hello again aristotle-logic group and Claus in
> particular:

> Last post from me was broken off just as it began to
> get good! What happens is that my email
> provider--AT&T, the huge US telecom
> conglomerate--somehow thinks that quoted reply texts
> only need to be so long...and a post of moderate
> length, such as Claus's recent one, gets cut off. So
> what I have to do is open up the post I'm replying to,
> copy out the entire text to a text editor outside the
> browser, and then reply by pasting in the text and
> putting in my own > marks. A pain.

> Oh well, I'm going to cut out the earlier part of
> Claus's post and insert the part that was chopped by
> AT&T/Yahoo. Just so it's clear, I'll flag my new
> remarks with [ron].

> --- pyrrho <c.brillow...@googlemail.com> wrote:

> > Hallo Ron, hallo Zeno777,

>  [snip]

> > Ron, you only have eyes for  Corcoran the excellent

> tailor:

> >>With Corcoran, you get an interpretation that

> consonant with
>  Aristotle's own logical writings and is logically
> rigorous to >boot.

> >But I happen to see the poor crippled Aristotle. Lets

> straighten him
> up a bit, shall we? The "categories", chapter 3 starts
> as follows:

> >"Whenever one thing is predicated of another as of a

> subject, all
> things said of what is predicated will be said of the
> subject also.
> For example man is predicated of the individual man,
> and animal of
> man; so animal will be predicated of the individual
> man also - for the
> individual man is both man and animal." (Translator:
> J.L. Ackrill, The
> Complete Works of Aristotle, Oxford 1985)

> [ron] Two comments: (1) you have to understand
> Aristotle's "one thing predicated of another as of a
> subject" correctly, and (2) altough the transfer of
> predication works for individuals in the "Categories",
> Aristotle's syllogistic does not allow this, because
> the variables do not stand for individuals, but only
> for sets (species or genera) of individuals.

> [ron] I think Claus is headed towards a mistake...and
> here it comes:

> >Corcoran maps this relation to the subset relation

> between sets. E.g.
> {1} subset {1,2} subset {1,2,3}. Let us instantiate:
> {1,2} is a
> predicate said of the subject {1}, because the set {1}
> is both subset
> of {1,2} as well as of {1}. So far so good. But
> Aristotle said: "all
> things said of what is predicated will be said of the
> subject also."
> And the subset predicate is just one thing (one
> property of sets).

> [ron] OK so far.

> >Now

> let us say another one. "{1,2} has two elements."

> [ron] This ^ is the mistake, a serious one, but it's
> an easy one to make. The predication "has two
> elements" is applies to the *set*, not to the things
> making up the set. It is important to see Aristotle's
> glib statement in the categories as applying to the
> elements of the classes, not to the classes
> themselves.

> [ron] That is "has two elements" is something that
> applies to sets, not to individuals. So "has two
> elements" is not something that would be predicated of
> {1, 2} as subject, because what Aristotle means is to
> predicate it of the elements of the class.

> [ron] Actually, if Claus's interpretation is correct,
> Aristotle is as much a fool as Corcoran. For Aristotle
> could clearly have seen that "contains a pig" is
> predicated of Animal, and so contains a pig is
> predicated of Man as well as of Socrates himself.

> >But {1} of course

> does not have two elements. Therefore Corcoran's
> interpretation is
> simply not consonant with Aristotle's own logical
> writings.

> [ron] Well, no, for the reason I gave above. Corcoran
> maps the logical variables to sets of objects. A valid
> predicate for {1,2,3} would be something that
> describes the individuals in the genus...say "less
> than 4". Then, the predicate "less than 4" applies to
> the genus {1,2,3}, and hence it applies to the species
> {1,2}. This is the limit to how far you can do this in
> Aristotle's syllogistic.

> [ron] If you invoke the remark from the "Categories",
> then you can go further, but you are *outside of the
> syllogistic* in so doing! You can say that "less than
> 4" applies to the individual 1.

> [ron] And I think this mistake is cause to reiterate
> what I said in the previous two posts about taking
> stuff from outside the logic (I mean the "Analytics"
> here, specifically) and then using it to interpret the
> logic. You can find stuff elsewhere that is correct,
> but does not apply to the formal syllogistic...such as
> the predication on individuals. Aristotle does not
> develop his formal logic with individual
> symbols...that would be an extension of syllogistic,
> that, as far as I know, has not been done. But it
> seems kind of straightforward. Anyway, the reason that
> there are not individuals in the syllogistic is that
> then the conversion rules would not work, I believe.
> You would have to say things like "Socrates does not
> apply to Animal", which is nonsense. Only abstractions
> are denoted by variables in Aristotle's logic, not
> individuals (as in modern predicate logic).

> [ron] I'm not saying, don't read the other stuff and
> relate it to the syllogistic. I'm saying that the
> logical works are read largely independently (they are
> "prior", "protera" in Aristotle's sense) to the other
> scientific works, because the logical works can stand
> alone, without the others, e.g. "Nicomachean Ethics",
> "Parts of Animals", etc. And if we consider the others
> as instances of rigorous science, then we should see
> them as depending on, and therefore posterior to, the
> logical works.

> >This looks

> mad, but I insist because this is the touchstone of
> Aristotelian logic
> for the next 2000 years. Later this relation became
> the intension/
> extension relation. A thing like "man" is under
> "animal" (in the
> extent of) because animal" is in "man" (in the
> intension of). And
> there are formal objects where this relation holds
> too. But sets
> aren't.

> >Understanding, according to Plato, requires analyses.

> That, means,
> that problems and things must be broken up at their
> ``natural
> joints'', taking care not to break the natural parts
> themselves,
> ``after the manner of a bad carver''[Phaedrus, 265e.]
> Corcoran carved
> up the problem at rather unnatural places.

> [ron] I'm still sticking with Corcoran. But, we can
> continue this!

> >Just an answer to Ron's Ramblings ...
> >Thanks!
> >Claus

> [ron] Thank you, and sorry to have to split up the
> reply like this. Well, it almost happened at a natural
> place in the text. Maybe I should thank AT&T af