|Identity: Two objects are never identical. Identity is a single object, to which may be referred to with two different terms. The fact that two descriptions mean a single object may be discovered only in the course of an investigation._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
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Identity/Bigelow/Pargetter: we understand this here as a 2-digit predicate, we do not need to expand the language.
A19. (x)(x = x)
A20. (a u ~a (σ/λ) > σ unequal λ)
Everyday language translation: if something is true of something and not true of something, then these two things cannot be identical.
Contingent Identity/Bigelow/Pargetter: these two axioms have a surprising consequence: namely that all identity is necessary. There is then no contingent identity. Non-identity is then also necessary. So the following can be proved as theorems:
NI. (x = y) > N(x = y)
NNI. (x unequal y) > N(x unequal y)
Semantic rule: then causes an identity statement to be true in all possible worlds or true in none.
Valuation rule/identity/Bigelow/Pargetter: V (=) (c, c) = W
W: is the set of all possible worlds.
Identity statements/Bigelow/Pargetter: are then either necessary or impossible.
This is surprising and shows another illustration of the interplay between semantics and ontology.
Ontology/Bigelow/Pargetter: is what is suggested to us by a streamlined and plausible semantics.
Identity/Science/Bigelow/Pargetter: in the history of science there have often been discoveries that have shown us that things we thought were different are identical.
Now one should think that these are contingent identities.
Contingent Identity/Semantics/Bigelow/Pargetter: if they like contingent identity, they would have to change the semantics. And that is not hard:
Definition Diversity/new: instead of saying that two things are different, if something is true of one but not true of the other, we could say that something non-modal is true of one, but not true of the other.
That brings out some new systems.
It is interesting to note that some of these systems verify NNI while they continue to falsify NI.
For example, it is more difficult to allow New York and Miami to be one and the same city than to allow Miami to be two cities.
Identity/BigelowVsContingent Identity/Bigelow/Pargetter: we should let the semantics decide and say that there is simply no contingent identity.
Contingent Identity/Bigelow/Pargetter: instead of changing the semantics and then to allow it nevertheless, we should rather explain why they seem to exist: e.g.
Theory of descriptions/Russell/Bigelow/Pargetter: provides a means to reconcile contingently with necessary identities: assertions of the form
the F = the G
can be analyzed as contingent by saying that the properties F and G are co-instantiated by a single thing. This is still compatible with the necessary self-identity.
Bigelow/Pargetter: through descriptions most contingent identities are explained away.
Introverted Realism/Bigelow/Pargetter: (see above Chapter 1) introverted realism, as can be seen here, can reinforce the extroverted realism from which it originated._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990