Re: syllogism
From: patty (pattyNO_at_SPAMicyberspace.net)
Date: 10/02/04
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Date: Sat, 02 Oct 2004 12:06:55 GMT
David Longley wrote:
> In article <Quv7d.399761$8_6.328956@attbi_s04>, patty
> <pattyNO@SPAMicyberspace.net> writes
>
>> David Longley wrote:
>>
>>> In article <%z17d.20748$MD5.1110057@news20.bellglobal.com>, Wolf
>>> Kirchmeir <wwolfkir@sympatico.ca> writes
>>>
>>>> patty wrote:
>>>>
>>>> [...]
>>>>
>>>>> Well i see where we are stumbling over the rather ambiguous (A--
>>>>>
>>>>>> B). I was interpreting it as a first order term with *one* property
>>>>>
>>>>>
>>>>> and no quantification (Fa => Fb); but now i see you meant it as
>>>>> (for *all* properties F, Fa <=> Fb) which *is* a coding of the
>>>>> definition of the identity of a and b:
>>>>
>>>>
>>>> Sorry, I thought A-->B was a commonly understood representation
>>>> of "If A, then B", or "A implies B." I also think that since I used
>>>> this
>>>> symbolism in the context of implication, it should've been clear to
>>>> you that's what I intended. I use => only as "equal to or greater
>>>> than", never as a logic operator.
>>>>
>>>> Thus A-->B is false if "A true", and "B false", and true otherwise. If
>>>> A, B are truthfunctions, then sometimes (A-->B ANDF B-->A), and
>>>> sometimes not - depends on A, B. IOW, [(A==B) iff (A-->B AND B--
>>>>
>>>>> A] When it comes to truthfunctions, that does not mean A, B are
>>>>
>>>>
>>>> indistinguishable. It means that either can be transformed into the
>>>> other, but that operation is meaningless unless A, B were
>>>> distinguishable to start with. Right?
>>>>
>>>> Whether it makes sense to say that A, B have the same properties
>>>> in this case I'll leave to other thinkers. I'm getting leery of the
>>>> term
>>>> "property."
>>>>
>>> The law of extensionality is what's missing in this discussion, and
>>> 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
>
>
> It's precisely because you (and others) think it's "a tempest in a tea
> pot" that I started and ended the post as I did. Despite what you tell
> yourself, you still don't appreciate where the above slip takes you,
> even though "the lecture" provides a very clear warning, and despite me
> having written thousands of posts which highlight consequences of the
> failure to see it for what it is. Elevating it from a storm in a teacup
> to a tempest in a teapot really just shows the extent to which you have
> not grasped the scope of the problem. Read Hahn again, look at the date,
> and think about what you're reading it on.
>
What difference does it make? Tell me that ! Give me an example of
where calling something a property or calling it a class will make any
difference whatsoever - all other things equal !
> Have you bought Catania yet?
No.
patty
>
>>
>> ---- 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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