Re: SUO: Thoughts and judgments
John,
At 05:21 AM 1/18/2002 -0500, John F. Sowa wrote:
>Pierluigi, Adam, and Chris,
>
>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.
>
>As I have said many times, I believe that the structure of the ontology
>is far more important than any particular axiom.
Yes, you've said this often, and I don't even disagree with this up to a
point. Just writing axioms willy-nilly is pointless, but so is discussion
without formalization. We can't create a standard by discussion of Peirce
and Frege unless someone takes the time to make concrete proposals in
standards words derived from those discussions.
Adam
>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:
>
> http://www.jfsowa.com/pubs/signproc.htm
>
>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:
>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)?
>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?
>
>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.
>
>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.
>
>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.
>
>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....
>
>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:
>
> 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)
>
>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.
>
>By the way, the full references for all citations are in my combined
>bibliography:
>
> http://www.jfsowa.com/bib.htm
>
>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.
>
>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.
>
>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.
>
>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.
>
>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:
>
> 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.
>
>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....
>
>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.
>
>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
>
> 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.
>
>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.
>
>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.
>
>John Sowa
>______________________________________________________________________
>
>Source: 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."
>
>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.
Adam Pease
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