Re: syllogism

From: patty (pattyNO_at_SPAMicyberspace.net)
Date: 10/11/04 

Date: Mon, 11 Oct 2004 15:15:15 GMT

patty wrote:
> David Longley wrote:
>

>> The law of extensionality is what's missing in this discussion, and I
>> suspect Patty of a little obfuscation or at least a little foggy writing
>> here as I suspect she does know the intensional nature of properties.
>>
>
> Well one thing i know for sure is that if i use the word "property" i
> will get a lecture from Longley. Thing is that if an investigator takes
> some measurements on individuals and records them in a database, the
> records in the database will be the same whether she thinks of them as
> properties or classes. The triple "X memberOf ClassP" codes the same
> information as the triple "X hasProperty P". I think this is a tempest
> in a tea pot.
>
> patty
>

I would like to register my objection above to Quine's avoidance of
properties below. However there is another objection that should also
be noted. When an engineer designs a mechanism to classify objects, she
does not design from a exemplar of the extension of the class; no she
will design the mechanism from the *intension* of the class. She will
of course test the mechanism against a subclass by extension - but that
is beside the point. What is the logical distinction between a property
and the intension of a class? None, right? There is no mistake in
recognizing properties of objects and defining classes by intension - in
fact it is unavoidable. Perhaps someone can put me out of my misery and
explain the point of the Longley\Quine tirade against "property" below.

patty

> ---- Quine's lecture included below ----
>
>> 'The notion of a property is one of various notions,
>> called INTENSIONAL, that depend thus on the nebulous
>> notion of meaning. Other examples are necessity,
>> possibility, and idioms of propositional attitude such
>> as belief, hope, regret.'
>>
>> Quine (1985)
>> The Time of My Life
>> Quine does a nice comparison of properties vs classes in Quiddities:
>>
>> 'If it makes sense to speak of properties, it should
>> make clear sense to speak of sameness and differences of
>> properties; but it does not. If a thing has this
>> property and not that, then certainly this property and
>> that are different properties. But what if everything
>> that has this property has that one as well, and vice
>> versa? Should we say that they are the same property? If
>> so, well and good; no problem. But people do not take
>> that line. I am told that every creature with a heart
>> has kidneys, and vice versa; but who will say that the
>> property of having a heart is the same as that of having
>> kidneys?
>>
>> In short, coextensiveness of properties is not seen as
>> sufficient for their identity. What then is? If an
>> answer is given, it is apt to be that they are identical
>> if they do not just happen to be coextensive, but are
>> necessarily coextensive. But NECESSITY, q.v., is too
>> hazy a notion to rest with.
>>
>> We have been able to go on blithely all these years
>> without making sense of identity between properties,
>> simply because the utility of the notion of property
>> does not hinge on identifying or distinguishing them.
>> That being the case, why not clean up our act by just
>> declaring coextensive properties identical? Only because
>> it would be a disturbing breach of usage, as seen in the
>> case of the heart and kidneys. To ease that shock, we
>> change the word; we speak no longer of properties, but
>> of CLASSES......
>>
>> We must acquiesce in ordinary language for ordinary
>> purposes, and the word 'property' is of a piece with it.
>> But also the notion of property or its reasonable
>> facsimile that takes over, since these contexts never
>> hinge on distinguishing coextensive properties. One
>> instance among many of the use of classes in mathematics
>> is seen under DEFINITION, in the definition of number.
>>
>> For science it is classes SI, properties NO.'
>>
>> W. V. O. Quine (1987)
>> Classes versus Properties
>> QUIDDITIES:
>>
>> See "Fragments..." for more details, but the following should give the
>> basic idea:
>>
>> 'The new logic is distinguished from the old not only by the
>> form in which it is presented but chiefly also by the
>> increase of its range....The only form of statements
>> (sentences) in the old logic was the predicative form:
>> "Socrates is a man," "All (or some) Greeks are men." A
>> predicate-concept or property is attributed to a subject-
>> concept. Leibniz had already put forward the demand that
>> logic should consider sentences of relational form. In a
>> relational sentence such as, for example, "a is greater than
>> b," a relation is attributed to two or more objects, (or, as
>> it might be put, to several subject-concepts). Liebniz's idea
>> of a theory of relations has been worked out in the new
>> logic. The old logic conceived relational sentences as
>> sentences of predicative form. However, many inferences
>> involving relational sentences thereby become impossible. To
>> be sure, one can interpret the sentence "a is greater than b"
>> in such a way that the predicate "greater than b" is
>> attributed to the subject a. But the predicate then becomes a
>> unity; one cannot extract b by any rule of inference.
>> Consequently, the sentence "b is smaller than a" cannot be
>> inferred from this sentence. In the new logic, this inference
>> takes place in the following way: The relation "smaller than"
>> is defined as the "converse" of the relation "greater than."
>> The inference in question then rests on the universal
>> proposition: If a relation holds between x and y, its
>> converse holds between y and x. A further example of a
>> statement that cannot be proved in the old logic: "Wherever
>> there is a victor someone is vanquished." In the new logic,
>> this follows from the logical proposition: If a relation has
>> a referent, it also has a relatum. Relational statements are
>> especially indispensable for the mathematical sciences. Let
>> us consider as an example the geometrical concept of the
>> three-place relation "between" (on an open straight line).
>> The geometrical axioms "If a lies between b and c, b does not
>> lie between c and a" can be expressed only in the new logic.
>> According to the predicative view, in the first case we would
>> have the predicates "lying between b and c" and "lying
>> between c and a". If these are left unanalyzed, there is no
>> way of showing how the first is transformed into the second.
>> If one takes the objects b and c out of the predicate, the
>> statement "a lies between b and c" no longer serves to
>> characterise only one object, but three. It is therefore a
>> three-place relational statement....
>>
>> Restriction to predicate-sentences has had disastrous effects
>> on subjects outside logic. Perhaps Russell is right when he
>> made this logical failing responsible for certain
>> metaphysical errors.....Above all, we may well assume that
>> this logical error is responsible for the concept of absolute
>> space. Because the fundamental form of a proposition had to
>> be predicative, it could only consist in the specification of
>> the position of a body. Since Leibniz had recognized the
>> possibility of relational sentences, he was able to arrive at
>> a correct conception of space: the elementary fact is not
>> position of a body but its positional relations relative to
>> other bodies. He upheld the view on epistemological grounds:
>> there is no way of determining the absolute position of a
>> body, but only its positional relations. His campaign in
>> favor of the relativistic view of space, as against the
>> absolutistic views of the followers of Newton, had as little
>> success as his program for logic.
>>
>> Only after two hundred years were his ideas on both subjects
>> taken up and carried through: in logic with the theory of
>> relations (De Morgan 1858; Pierce 1870), in physics with the
>> theory of relativity (anticipatory ideas in Mach 1883;
>> Einstein 1905).'
>>
>> R. Carnap
>> The Old and the New Logic (1930)
>> In A.J. Ayer (ed) Logical Positivism (1959)
>>
>> '.. consists in characterizing the predicates by their
>> extension instead of according to their content. To each
>> predicate corresponds a certain "class" of objects,
>> consisting of all objects for which the predicate holds. The
>> case of a class containing no object is of course not
>> excluded here. Classes are now to be taken as the entities
>> dealt with by the calculus, which in this interpretation will
>> be called the calculus of classes.
>>
>> D. Hilbert & W. Ackermann (1950)
>> The Principles of Mathematical Logic p.46
>>
>>
>> 'We think of a science as comprising those truths which are
>> expressible in terms of 'and', 'not', quantifiers, variables,
>> and certain predicates appropriate to the science in
>> question....To specify a science, within the described mold,
>> we still have to say what the predicates are to be, and what
>> the domain of objects is to be over which the variables of
>> quantification range.'
>>
>> W.V.O. Quine (1954)
>> The Scope and Language of Science
>> The Ways of Paradox and other essays p.242
>>
>>
>> 'Thus we have arrived at something fundamental: our
>> conventions regarding the use of the words "not" and "or" is
>> such that in asserting the two propositions "object A is
>> either red or blue" and "object A is not red," I have
>> implicitly already asserted "object A is blue." This is the
>> essence of so-called *logical deduction*. It is not then, in
>> any way based on real connections between states of affairs,
>> which we apprehend in thought. On the contrary, it has
>> nothing at all to do with the nature of things, but drives
>> from our manner of speaking about things. A person who
>> refused to recognize logical deduction would not thereby
>> manifest a different belief from mine about the behaviour of
>> things, but he would refuse to speak about things according
>> to the same rules as I do. I could not convince him, but I
>> could refuse to speak with him any longer, just as I should
>> refuse to play chess with a partner who insisted on moving
>> the bishop orthogonally.
>>
>> What logical deduction accomplishes, then, is this: it makes
>> us aware of all that we have implicitly asserted - on the
>> basis of conventions regarding the use of language - in
>> asserting a system of propositions, just as, in the above
>> example, "object A is blue" is implicitly asserted by the
>> assertion of the two propositions "object A is red or blue"
>> and "object A is not red."
>>
>> In saying this we have already suggested the answer to the
>> question, which naturally must have forced itself on the mind
>> of every reader who has followed our argument: if it is
>> really the case that the propositions of logic are
>> tautologies, that they say nothing about objects, what
>> purpose does logic serve?
>>
>> ..logical propositions, though being purely tautologous, and
>> logical deductions, though being nothing but tautological
>> transformations, have significance for us because we are not
>> omniscient. Our language is so constituted that in asserting
>> such and such propositions we implicitly assert such and such
>> other propositions - but we do not see immediately all that
>> we have implicitly asserted in this manner. It is only
>> logical deduction which makes us conscious of it.
>>
>> If I have succeeded in clarifying somewhat the role of logic,
>> I may now be brief about the role of mathematics. The
>> propositions of mathematics are of exactly the same kind as
>> the propositions of logic: they are tautologous, they say
>> nothing at all about the objects we want to speak about, but
>> concern only the manner in which we want to speak of
>> them....We become aware of meaning the same by "2+3" and by
>> "5", by going back to the meanings of "2," "3," "5," "+," and
>> making tautological transformations until we just see that
>> "2+3" means the same as "5". It is such successive
>> tautological transformation that is meant by "calculating";
>> the operations of addition and multiplication which are
>> learned in school are directives for such tautological
>> transformation; every mathematical proof is a succession of
>> such tautological transformations. Their utility, again, is
>> due to the fact that, for example, we do not by any means see
>> immediately that we mean by "24 x 31" the same as by "744";
>> but if we calculate the product "24 x 31", then we transform
>> it step by step, in such a way that in each individual
>> transformation we recognize that on the basis of the
>> conventions regarding the use of the signs involved (in this
>> case numerals and the signs "+" and "x") what we mean after
>> the transformation is still the same as what we meant before
>> it, until finally we became consciously aware of meaning the
>> same by "744" and by "24 x 31."
>>
>> ..at first glance it is difficult to believe that the whole
>> of mathematics, with its theorems that it cost such labour to
>> establish, with its results that so often surprise us, should
>> admit of being resolved into tautologies. But there is just
>> one little point which this argument overlooks: it overlooks
>> the fact that we are not omniscient. An omniscient being,
>> indeed, would at once know everything that is implicitly
>> contained in the assertion of a few propositions. IT would
>> know immediately that on the basis of the conventions
>> concerning the use of the numerals and the multiplication
>> sign, "24 x 31" is synonymous with "744". An omniscient being
>> has no need for logic and mathematics. We ourselves, however,
>> first have to make ourselves conscious of this by successive
>> tautological transformations, and hence it may prove quite
>> surprising to us that in asserting a few propositions we have
>> implicitly also asserted a proposition which seemingly is
>> entirely different from them, or that we do mean the same by
>> two complexes of symbols which are externally altogether
>> different.'
>>
>> H Hahn (1933)
>> Logic, Mathematics and Knowledge of Nature
>> In Ayer (Ed) Logical Positivism (1959)
>>
>>
>>
>> 'At first the problem of mind was ontological and linguistic.
>> With the passing of mind as substance, there remained a
>> twofold problem of mentalistic language: syntactic and
>> semantic. The distinctive syntactic trait of mentalistic
>> discourse was the content clause 'that p'. This obstructed
>> extensionality: that is, the substitutivity of identity and
>> more generally the interchangeability of all coextensive
>> terms and clauses salva veritate. It obstructed classical
>> predicate logic as a universal theoretical framework. Now
>> this quarter of the mind problem is in a fair way to
>> dissolution. Quotational treatment of propositional attitudes
>> de dicto delivers them to the extensional domain of predicate
>> logic, thanks to the reduction of quotation to spelling.
>> Propositional attitudes de re, on the other hand, we
>> downgraded.
>>
>> So we see the attitudes de dicto reconciled syntactically
>> with extensional logic. A single language, regimented in
>> predicate logic, can take them in stride along with natural
>> science. The residual oddity of these mentalistic predicates
>> de dicto is purely semantic: they do not interlock
>> productively with the self-sufficient concepts and causal
>> laws of natural science.
>>
>> Still the mentalistic predicates, for all their vagueness,
>> have long interacted with one another, engendering age-old
>> strategies for predicting and explaining human action. They
>> complement natural science in their incommensurable way, and
>> are indispensable both to the social sciences and our
>> everyday dealings. Read Dennett and Davidson.'
>>
>> W. V. O. Quine (1992)
>> Intension
>> The Pursuit of Truth p.72-73
>>
>> Note - "incommensurable way" - this is the part of "the double standard"
>> of anomalous monism (and research) that few really grasp the
>> significance of - hence my frequent references to "Two Dogmas of
>> Empiricism".
>>
>> I thought the following worth repeating too:
>>
>> 'The first-order predicate calculus is an extensional logic
>> in which Leibniz's Law is taken as an axiomatic principle.
>> Such a logic cannot admit 'intensional' or 'referentially
>> opaque' predicates whose defining characteristic is that they
>> flout that principle.'
>>
>> U. T. Place (1987)
>> Skinner Re-Skinned P. 244
>> In B.F. Skinner Consensus and Controversy
>> Eds. S. Modgil & C. Modgil
>>
>> But I bet none of this will make any difference to what is posted by
>> most folk here. It has all been posted in the past, as has much else
>> besides but they insist on having it rehashed. Here's just one example:
>>
>> <http://groups.google.com/groups?selm=spr961206123219-4437@kauri.vuw.ac.n
>> z>
>>
>> What does this tell one other than that people have very short memories
>> and aren't really here for much more than post to post verbal jousting?
>> <g>
>>
>> Kind regards,

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