Identity笔记
这个议题确实有元形而上学的重要性。
https://plato.stanford.edu/entries/identity/
两个极端立场Peter Geach: the notion of absolute identity they presuppose has no application; there is only relative identity.
Lewis: Identity is an utterly unproblematic notion.
2. The Logic of Identity
Numerical identity的名字就暗示了the controversial view that it is the only identity relation in accordance with which we can properly count (or number) things: x and y are to be properly counted as one just in case they are numerically identical (Geach 1973).
通常用Leibniz’s Law来定义同一性, the principle of the indiscernibility of identicals, that if x is identical with y then everything true of x is true of y.但是“what is true of x” is understood to include “being identical with x”，所以该定义是循环的。But often it is read with “what is true of x” restricted, e.g., to qualitative, non-relational, properties of x. It then becomes philosophically controversial.
any two predicates which can be regarded as expressing identity (i.e., any predicates satisfying the two schemata “for all x, Rxx” and “for all x, for all y, Rxy → (Fx → Fy)” for any one-place predicate in place of “F”) will be extensionally equivalent. They do not, however, ensure that any two-place predicate does express identity within a particular theory, for it may simply be that the descriptive resources of the theory are insufficiently rich to distinguish items between which the equivalence relation expressed by the predicate holds (“Identity” in Geach 1972). Geach由此得到的教训是，不能对所有概念进行量化的一阶语言总是不足以identify对象。Identity is only second-order definable.
3. Relative Identity
Geach从而认为absolute identity不存在，只有relative identity。具体而言，他所拒绝的是whenever a term “A” is interpretable as a sortal term in a language L (a term which makes (independent) sense following “the same”) the expression (interpretable as) “x is the same A as y” in language L will be satisfied by a pair <x,y> only if the I-predicate of L is satisfied by <x,y>.
Quine’s proposal that an I-predicate in a first-order theory may always be interpreted as expressing absolute identity (even if such an interpretation is not required).
Geach对蒯因的反驳在于it leads to an out-and-out logical absurdity, the existence of what he calls “absolute surmen” (entities for which having the same surname constitutes a criterion of absolute identity, ie., entails indiscernibility in all respects).
具体而言First, that there are sentences of English supplemented by the predicate “is the same surman as” (explained to mean “is a man and has the same surname as”), which are evidently true and which, considered as sentences of that fragment of English in which “is the same surman as” is an I-predicate, when this is interpreted in the way Quine suggests, can be true only if absolute surmen exist. And secondly, that the existence of absolute surmen is absurd.但是这个论证在蒯因的整体论下是失败的。
另一个反驳：Suppose a cat, Tibbles, is sitting on a mat. Now consider that portion of Tibbles that includes everything except its tail – its “tail complement” – and call it “Tib”. Tibbles and Tib都可以是猫，它们似乎是不同的个体，但又是同一的，因此这里面临一个困难。这个反驳并非是决定性的，但可能导致这样的结果：the linguistic data provide no basis for a decision for or against.
4. Criteria of identity
弗雷格会认为The criterion of identity for numbers is equinumerosity of concepts, that is, the number of As is identical with the number of Bs if and only if there are exactly as many As as Bs.这是一种二阶定义，更一般的，二阶同一性定义会采取这种形式：
If x is a G and y is a G then d(x) = d(y) iff Rxy
（隐定义了算子d，对于弗雷格而言，d的指称从而也就被定义了）
Lowe (1997: section 6)的批评: two-level criteria of identity are neither definitions of identity, nor of identity restricted to a certain sort (for identity is universal), nor even of the sortal terms denoting the sorts for which they provide criteria. They merely constrain, but not to uniqueness, the possible referents of the functor “d” they implicitly define and they thus give a merely necessary condition for falling under the sortal predicate “is an F”
a one-level criterion for objects of sort F takes the form:
If x is an F and y is an F then x=y iff Rxy
Lowe (1997) and Wright and Hale (2001) any two-level criterion can be restated in a one-level form.
Lewis 1986: one-level criterion of identity merely specifies a necessary condition of being an object of sort “F”.而这就足够了。
觉得剩下的部分不算重要（
