SUO: Re: *Date 18 Jan 2002
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JA's Projects, Queries, Replies for 18 Jan 2002
Pr_1: Abstract & Concrete
Re_1: John Sowa, Thoughts & Judgments
AP = Adam Pease
CM = Chris Menzel
JS = John Sowa
PM = Pierluigi Miraglia
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Pr_1: Abstract & Concrete
I am going to focus on the distinction between abstract and concrete for a while,
but I will be viewing this spectral dimension in two distinct lights, first, for
it's own sake, as a distinction that we draw between and mark as affecting other
objects, next, as a typical example of a very important distinction that we draw,
but one to be studied in comparison with many other distinctions of its same ilk.
But first, a token bit of deference to standard usage:
| Abstract. (Latin 'ab' = from, 'trahere' = to draw).
| A designation applied to a partial aspect or quality
| considered in isolation from a total object, which is,
| in contrast, designated concrete. (Ledger Wood, in Runes).
Cf. Abstracta, Abstractio Imaginationis,
Abstractio Intellectus Seu Rationis,
Abstraction, Abstractionism, Abstractum.
| Concrete. [Latin 'com-' = together, 'crescere' = to grow].
| Anything that is specific or individual. The term is opposed
| to "general" or to "abstract", terms which stress common
| characteristics or qualities considered apart from
| their specific setting. (Vergilius Ferm, in Runes).
Cf. Concrete Universal, Concretion.
I plan to look into the distinctions between form and matter, logos and physis,
and the top-level categorical distinction between the abstract and the physical
that John Sowa makes in his 'Knowledge Representation', to see if I can see if
they are related in some enlightening way, or not.
But sufficient unto the day are the rations thereof.
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Re_1: John Sowa, Thoughts & Judgments
Subj: Thoughts and Judgments
Date: Fri, 18 Jan 2002 05:21:01 -0500
From: John F Sowa <sowa@bestweb.net>
To: Pierluigi Miraglia <miraglia@cyc.com>,
Chris Menzel <cmenzel@philebus.tamu.edu>,
Adam Pease <apease@ks.teknowledge.com>
JS: Pierluigi, Adam, and Chris,
JS: Before getting into the details, I should first respond to Adam Pease:
AP: Can you relate the issues about physical existence and observers
to either of the two starter documents? This discussion started
off with a title referring to SUMO but doesn't currently specify
any term or axiom in the current document along with a proposed
change as far as I can see.
JS: As I have said many times, I believe that the structure of the ontology
is far more important than any particular axiom. If you want axioms,
I suggested picking up the IMPS axioms for mathematics as a well-tested,
freely available source. Then Chris Welty asked where mathematics fits
in the ontology and how it relates to the axioms about the physical world.
Those are issues that I discuss in my paper on signs, processes, and
language games:
JS: http://www.jfsowa.com/pubs/signproc.htm
JS: One might agree or disagree my arguments and with the proposals I put
forth in Section 7. But I believe that a rationale at a level such
as that paper is essential for answering the fundamental questions:
JS: What belongs in the upper level? Where does mathematics fit in the ontology?
How do you relate different views that may lead to incompatible axioms (e.g.,
the per- & en-durantism debates)?
JS: How do you relate the categories of the ontology to the word senses
of multiple natural languages? How do multiple microtheories relate
to one another? And most of all, how do you accommodate the open
ended, never ceasing developments in science, technology, business,
politics, and everyday life?
JS: Until these questions are answered, churning out axioms is a waste
of time, unless it is done on a piecemeal basis, such as IMPS,
which is clearly organized as a collection of little theories.
My proposal for an infinite lattice of theories (of which any
implementation is a small excerpt) provides some structure to
the collection in a way that accommodates the Cyc microtheories
plus a whole lot more.
JS: I will admit that some of the philosophical issues may seem to be
getting a bit far afield, but I believe that the choice of philosophy
(explicit, or even worse, unstated) has a major influence on how the
ontology is organized. In Section 2 of the signproc paper, I show how
20th-century analytic philosophy has gone astray; and in Section 3,
I show how AI needs something far richer than what the analytic
philosophers have given us. Sections 4, 5, and 6 summarize the
work of Peirce, Whitehead, and Wittgenstein that is essential
to correcting the imbalance created by Russell, the Vienna Circle,
and other influential philosophers. Finally, Section 7 shows how
I believe the contributions by P., W., & W. can be used to establish
a more suitable foundation for ontology.
JS: How it relates to SUMO and IFF: It would require a major revision
of the SUMO categories and organization, although most of the axioms
could be reused. The IFF organization would be better suited to
accommodating the proposals I suggest.
JS: Now on to Chris Menzel's response to my comments about Frege:
JS: This was a hot topic in the late 19th century, when people like
Peirce and Frege were trying to get rid of "psychologism" in logic.
Frege was only half successful, since he continued to use words
like "Gedanke" (thought) and "Urteil" (judgment).
CM: Frege's success in cleansing logic of psychologism surely shouldn't
be evaluated on the basis of the words that he used, but in terms of
what he intended by those words. I agree that "Gedanke" was a poor
choice of terminology because of its mentalistic connotations, but
it is clear from Frege's writings that what he meant by a Gedanke
was something objective and mind-independent, roughly, the content
of a declarative sentence, the proposition it expresses ...
JS: I agree that Frege understood the difference and that his choice of words
was unfortunate. However, I would like to cite the following paragraph
by Peirce, which is crystal clear on those points:
JS, quoting CSP:
| A proposition, as I have just intimated, is not to be understood as the
| lingual expression of a judgment. It is, on the contrary, that sign of
| which the judgment is one replica and the lingual expression another.
| But a judgment is distinctly more than the mere mental replica of
| a proposition. It not merely expresses the proposition, but it
| goes further and accepts it ... One and the same proposition
| may be affirmed, denied, judged, doubted, inwardly inquired into,
| put as a question, wished, asked for, effectively commanded, taught,
| or merely expressed, and does not thereby become a different proposition.
| (Essential Peirce, vol. 2, pp. 311-312)
JS: By adopting the word "proposition", which was the standard word in every textbook
of traditional, Aristotelian logic since the middle ages, Peirce drew a very clear
distinction. He also summarized in one paragraph Austin's theory of speech acts.
For examples of what the medieval scholastics knew (and published), see the
quotations by William of Ockham at the end of this note.
JS: By the way, the full references for all citations are in my combined bibliography:
JS: http://www.jfsowa.com/bib.htm
JS: Pierluigi Miraglia wrote:
PM: it's curious that you'd regard (contemporary) analytic philosophy
as being greatly indebted to Frege's parsing of these notions,
since in the view of many today Frege's views on these matters
have been more often than not grossly misunderstood, especially
given the neo-empiricist bent of much 20th century Anglo-Saxon
philosophy (compared to Frege's punctilious rejection of empiricism).
There is ongoing and lively debate among Frege interpreters.
JS: I agree with this point. Frege was almost completely ignored by
everybody until Russell rediscovered him around 1903. Even then,
he was still largely ignored until Quine revived interest in Frege
in the 1930s and Dummet published many books about Frege.
JS: Ernst Mach was the chief proponent of positivism (which Einstein
called "the miserable philosophy" that would have made modern physics
impossible). I blame Mach for two of the worst failures of 20th-century
philosophy: positivism and behaviorism.
PM: I disagree. There is no Fregean muddle on this. As to whether medieval
scholastic is clearer on these issues than Frege's own work, anyone can
check for her/himself. A bit of Hegelian hindsight may be in order here:
No knock on Petrus Hispanus, but it's not by chance that logic blossomed
as a scientific discipline after 1879 instead of after 1079.
JS: As I said above, I agree that Frege had a fairly clear idea himself,
but his ignorance of the literature (or his stubborness to accept
his rivals' terminology) led him to an unfortuate choice of words.
JS: But the main reason why symbolic logic wasn't developed until the 19th
century was that it depended on further developments in mathematics.
Frege's version of 1879 was irrelevant to the development of modern
logic, since it was completely ignored. Peano explicitly said that
he based his notation on the work of Peirce and Schroeder, and he
wrote a very negative review of Frege's work. When Frege responded,
Peano insisted that Frege rewrite his diagrams in Peano's notation,
since he said that he found the Begriffsschrift unreadable. For
more historical detail (with citations), see my commentary about
Peirce's EGs:
JS: http://www.jfsowa.com/peirce/ms514.htm
PM: This is not to say that Peirce might have a more sophisticated general semiotics
to propose: however, the precise status of semiotics today seems to me quite
a bit more in question than that of logic.
JS: Of course, because most of the people who talk about semiotics either
haven't read Peirce or don't know logic (which Peirce considered one
of the major parts of semiotics). Umberto Eco, for example, talks
a lot about both Peirce and semiotics, but he doesn't know logic.
It is impossible to say anything intelligent about semiotics without
having a very solid understanding of logic. But logic along is not
enough; the logicians still have to read Peirce to see how everything
fits together.
PM: Bolzano has very insightful things to say about the foundations of logic.
However, his contributions are hardly as systematic and as focussed as Frege's.
JS: I agree. Bolzano's contributions are also much less systematic and
less focussed than the medieval scholastics (who also went into much
more detail on semantics than Frege). See for example William of
Ockham's theory of propositions, which is an excellent introduction
to model theoretic semantics of natural language (i.e., Latin), but
without Montague's formidable notation. See the quotations from
Ockham at the end of this note.
PM: Understanding abstraction and the nature of 'concept' was perhaps the
single most important task Frege set for himself in the Grundlagen.
In fact, Frege thought that, as far as the reduction of arithmetic
to logic was concerned, the Begriffschrift had already done everything
that needed doing. He thought of the later work as a lengthy and more
accessible explanation of the conceptual foundations of the new logic.
JS: I agree that Frege was trying to do that, but he was ignorant of
the vast literature on signs. For the work from Aristotle to the
Stoics to St. Augustine, see
JS: Manetti, Giovanni (1987) _Le Theorie del Segno nell' Antiquita classica_
translated by C. Richardson as _Theories of the Sign in Classical Antiquity_,
Indiana University Press, Bloomington, 1993.
JS: The major point that this history shows is that the foundation of logic
from Aristotle to the middle ages was entirely free of "psychologism".
That disease, which Frege was trying to combat, largely originated in
19th century German philosophy. The medieval scholastics had no need
of Frege's cure.
PM: I don't know much about Husserl, and even less about Brentano.
It seems unquestionable that Husserl at least early on thought
very hard about precisely the same issues that were central to
Frege's work. FWIW, I find Husserl's work considerably less
intelligible than Frege on the whole, but I think Frege's
criticism of it was unfair and unhelpful.
JS: I agree. Neither Husserl nor Frege had read Ockham or Peirce, nor did most
20th century analytic philosophers. See my critique in the signproc.htm
article, in which I discuss Ockham's solution for the baldness of the
present king of France. Ockham's approach was logically equivalent
to Russell's, but it was more general, because it also answered
the criticisms by Strawson and others.
JS, excerpting from JS: http://www.jfsowa.com/peirce/ms514.htm
| Ockham (1323) showed how to determine the truth value of compound
| propositions in terms of the truth or falsity of their components and
| to determine the validity of rules of inference (regulae generales
| consequentiarum) in terms of the truth of their antecendents and
| consequents. Following are three quotations from Part II and two from
| Part III of the Summa Logicae, which Peirce had studied in detail:
|
| 1. "We must posit certain rules which are common to the signs 'every',
| 'any', 'each', and others like them, if there are any others. These
| rules are also common to many propositions which are equivalent to
| hypothetical propositions, e.g. 'Every man is an animal', 'Every
| white thing is running', etc.... It should be noted that for the
| truth of such a universal proposition it is not required that the
| subject and the predicate be in reality the same thing. Rather, it
| is required that the predicate supposit for all those things that
| the subject supposits for, so that it is truly predicated of them."
|
| 2. "A conjunctive proposition is one which is composed of two or more
| categoricals joined by the conjunction 'and' or by some particle
| equivalent to such a conjunction. For example, this is a conjunctive
| proposition: 'Socrates is running and Plato is debating'....
|
| "Now for the truth of a conjunctive proposition, it is required that
| both parts be true. Therefore, if any part of a conjunctive proposition
| is false, then the conjunctive proposition itself is false."
|
| 3. "A disjunctive proposition is one which is composed of two or more
| categoricals joined by the disjunction 'or' or by some equivalent.
| For example, this is a disjunctive proposition: 'You are a man or a
| donkey.' Likewise, this is a disjunctive proposition: 'You are a
| man or Socrates is debating.' Now for the truth of a disjunctive
| proposition, it is required that some part be true....
|
| "It should be noted that the contradictory opposite of a disjunctive
| proposition is a conjunctive proposition composed of the
| contradictories of the parts of the disjunctive proposition."
|
| [Note that this is Ockham's version of DeMorgan's law that the
| negation of (p or q) is (~p and ~q)].
|
| 4. "From truth, falsity never follows. Therefore, when the antecedent
| is true and the consequent is false, the inference is not valid."
|
| 5. "From a false proposition, a true proposition may follow. Hence this
| inference does not hold: 'The antecedent is false; therefore, the
| consequent is false.' But the following inference holds: 'The
| consequent is false; therefore, so is the antecedent.'"
|
| Peirce (1869): "All that the formal logician has to say is, that if
| facts capable of expression in such and such forms of words are true,
| another fact whose expression is related in a certain way to the
| expression of these others is also true.... The proposition 'If A,
| then B' may conveniently be regarded as equivalent to 'Every case of
| the truth of A is a case of the truth of B.'".
|
| Tarski (1936): "In terms of these concepts [of model], we can define
| the concept of logical consequence as follows: The sentence X follows
| logically from the sentences of the class K if and only if every model
| of the class K is also a model of the class X."
JS: Bottom line: Peirce and Tarski had the advantage of modern algebraic
notation, but Ockham's formulation is logically equivalent, although
stated in natural language (Latin). See ms514.htm for Peirce's 1909
version of model theoretic semantics -- based on Ockham's rules as
applied to the existential graph notation. Quine took a major step
backwards by reviving interest in Frege instead of Peirce.
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John,
Thanks for this survey of the issues,
which I will make my diet of thought
over the next few days.
I have noticed this problem of psychologism vs. anti-psychologism rearing
its head recurrently on several different discussion lists that I have
passed through, and I have tried to explain repeatedly the difference
between what Peirce calls his "non-psychological conception of logic"
and the brand of virulent anti-psychologism that most folks seem to
catch from Frege. I have even found myself accused of the dreaded
sins of "agentism", "individualism", "psychologism" for doing no
more than referring to the "interpreter" in the very same way
that Peirce did, as a soppy embodiment of and a way-station
to the more fundamental, but more difficult to explain,
notion of an interpretant sign. So I have had many
occasions, some of them going way back, to reflect
on this point. It seems to me that the crucial
issue is really one of reductionism, and the
distinction between critical and descriptive
sciences. A person does not fall into the
error of psychologism simply by referring
to the interpretive or semiotic agent, or
even by pursuing an interest in this or
that particular species of agent, and
Peirce himself, of course, had many
things to say about psychology,
even inciting James to view it
as an experimental science
rather than a purely
introspective study.
No, I think that the erroneous aspect of psychologism only develops
when a person says that the critical science of logic "reduces to"
the descriptive study of a particular species of sign-bearers.
Anyway, I wish you the best of luck with trying to
instill any sort of clarity in this troubled water.
You will need it!
Jon Awbrey
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