The Uses of ‘Is’ are not Quantifiers
November 23rd, 2008, search relatedRelated posts :: The Uses of ‘Is’ are not Quantifiers :: Isness, Nominata and Quantifiers :: The Uses of ‘Is’ are not Quantifiers :: Truth and Validity
GEVANS613 at aol.com wrote:
>20/11/2008 jPolanikwrites:
>[Joe]: Jud, your recent posts concerning the natural language
>quantifiers ‘is’ and ‘exists’ display a fundamental confusion insofar
>as they suggest that there is a relationship between natural language
>quantifiers and logical quantifiers.
>[Jud]: Let me attempt to *de-confuse* you Joe. First of all there is
>no right which reserves the term *quantifier* exclusively for use by
>predicational logicians. The term was only introduced in the early
>nineteenth century as a term in logic. It has been in use in NL for
>centuries and comes from the Medieval Latin quantificre : Latin
>quantus, how great; see quantity + Latin -ficre, -fy. Literally in the
>sense of “determine the quantity of, the measure of* etc.
[Joe (new)]: hold onto that thought about quantity.
there are two uses of ‘is’ involved in this discussion: the is of
predication and the is of isness.
there are two logical quantifiers, the universal and the existential.
each of these specifies a quantity — the quantity of cases (within the
designated universe of discourse) for which a statement of predication
must hold before the statement in question can be considered true. thus,
*both* quantifiers assert/use the is of predication.
where C = is a crow and B = is black
[1] (x)(Cx -> Bx) = for any x that is, if x is a crow then x is black
(or, colloquially, all crows are black).
as a universally quantified statement, [1] is false if and only if there
is at least one non-black crow; meanining; that [1] is true if either
(a) there are crows in the universe of discourse AND all such crows are
black; or, (b) there are no crows at all in the universe of discourse.
(in case ‘b’, the assertion may be vacuous; but, it is not false; so, as
long as we use a binary logic, it has to be true).
[2] (Ex)(Cx & Bx) = there is an x such that x is a crow and x is black
(or, colloquially, some crows are black).
as an existentially quantified statement, [2] is true if and only if
*there is* at least one black crow in the universe of discourse. hence,
[2] asserts the is of isness — its truth conditions require that there
is an instance of a black crow; whereas, [1] can be true even if there
are no black crows (as long as there are no crows at all).
>What I am claiming is that *is* and *exist* are (God forbid!) not the
>SAME as the predicate logic (all and some) version of the UQ and the
>EQ, but act as the *some or none* NL VERSION or VARIANT manifested
>linguistically as sentential tools in the quantification of the
>presence or non-presence of matter, material, matergy, (call it what
>you will.)
as you well know, mathematicians consider ‘an even prime number exists’
a true statement; and, thus, the logical quantifiers are not limited to
situations where the subject of the predication is a material object.
Joe
–
Philosophy is, after all, done ultimately in the first person for the
first person. — H-N Castaneda
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http://what-am-i.net
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