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Identity, Aristotle informs us in Metaphysics, is oneness,
in matter or substance.
En sentido esencial, las cosas son idénticas
del mismo modo en que son unidad, ya que son idénticas cuando es
una sola su materia (en especie o en número) o cuando su sustancia
es una
(Met., V, 9, 1018 a 7. Cited in N. Abbagano,
Diccionario
de Filosofía, Fondo de Cultura Económica, México,
1986, p. 640). 10
Concerning Aristotle's view of identity as a kind of oneness, Nicholas
White observes:
[...] it is clear that in saying that X
and Y are one, Aristotle does not simply mean that [X
and Y] are parts of the same compound entity; he also means
that [X and Y] are in some sense the same, as each
other.(White [1971], p. 187)
Aristotle is thus not "keeping separate the use of X and Y
are one to mean that they are in some way identical from its use to say
that they make up a unitary entity". (ibid.)
Now, if identity is oneness in substance, Hesperus = Phosphorus and
Hesperus = Hesperus assert different things. Thus, suppose that X
= Y iff X and Y are one in substance. Suppose also
that X and Y are one in substance iff for some Z, X and Y
are parts of Z. Then X = Y iff for some Z, X
and Y are parts of Z.11
Therefore, if identity is oneness in substance, material identity is a
relation that relates one part of a compound entity to another such part.
Not so formal identity. Consider. Since X = Y iff X
and Y are one in substance, Y = Y iff Y and Y are one
in substance. Similarly, since X and Y are one in substance iff for some
Z, X and Y are parts of Z, Y and Y
are one in substance iff for some Z, Y is a part
of
Z. Hence Y = Y iff for some Z, Y is a
part of Z. Thus, unlike material identity, which relates one
part of a compound entity to another, formal identity relates each part
of such an entity to itself.
To sum up so far: If identity is oneness in substance, the ground of
the cognitive difference between Hesperus = Phosphorus and Hesperus
= Hesperus is not a mode of presentation, or an individual concept, or
a criterion for a word's application, or an incomplete state of affairs,
or a context in which a reference is found in the world, or a function
or mathematical mapping of any kind. The ground of this difference is simply
the circumstance in the world which makes each assertion true: in the case
of Hesperus = Phosphorus, that there is some compound entity of which
Hesperus and Phosphorus are parts; and in the case of Hesperus = Hesperus,
that there is some compound entity of which Hesperus is a part.
An ontological foundation is now taking shape for Aristotle's statement
at Met., V, 9, 1018 a 7.
[...] la identidad de cualquier modo es una unidad,
ya sea que la unidad se refiere a pluralidad de cosas, ya sea que se refiera
a una única cosa, considerada como dos, como resulta cuando se dice que
la cosa es idéntica a sí misma.12
(ibid.)
As we will see, the road--from a foundation for Aristotle's statement,
to the shipwreck of Sense, to a solution for the problem
of identity--the road from the return of extensions to the Garden of Meaning,
to the twilight of Fregean semantics, to a reconciliation of the theory
of meaning and theory of reference--this road passes by way of structured
individuals. |
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