display all the ideas for this combination of philosophers
6 ideas
16015 | Problems about identity can't even be formulated without the concept of identity [Noonan] |
Full Idea: If identity is problematic, it is difficult to see how the problem could be resolved, since it is difficult to see how a thinker could have the conceptual resources with which to explain the concept of identity whilst lacking that concept itself. | |
From: Harold Noonan (Identity [2009], §1) | |
A reaction: I don't think I accept this. We can comprehend the idea of a mind that didn't think in terms of identities (at least for objects). I suppose any relation of a mind to the world has to distinguish things in some way. Does the Parmenidean One have identity? |
16017 | Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan] |
Full Idea: Numerical identity is usually defined as the equivalence relation (or: the reflexive relation) satisfying Leibniz's Law, the indiscernibility of identicals, where everything true of x is true of y. | |
From: Harold Noonan (Identity [2009], §2) | |
A reaction: Noonan says this must include 'is identical to x' among the truths, and so is circular |
16016 | Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan] |
Full Idea: Identity can be circularly defined, as 'the relation everything has to itself and to nothing else', …or as 'the smallest equivalence relation'. | |
From: Harold Noonan (Identity [2009], §2) | |
A reaction: The first one is circular because 'nothing else' implies identity. The second is circular because it has to quantify over all equivalence relations. (So says Noonan). |
16020 | Identity can only be characterised in a second-order language [Noonan] |
Full Idea: There is no condition in a first-order language for a predicate to express identity, rather than indiscernibility within the resources of the language. Leibniz's Law is statable in a second-order language, so identity can be uniquely characterised. | |
From: Harold Noonan (Identity [2009], §2) | |
A reaction: The point is that first-order languages only refer to all objects, but you need to refer to all properties to include Leibniz's Law. Quine's 'Identity, Ostension and Hypostasis' is the source of this idea. |
16018 | Indiscernibility is basic to our understanding of identity and distinctness [Noonan] |
Full Idea: Leibniz's Law (the indiscernibility of identicals) appears to be crucial to our understanding of identity, and, more particularly, to our understanding of distinctness. | |
From: Harold Noonan (Identity [2009], §2) | |
A reaction: True, but indiscernibility concerns the epistemology, and identity concerns the ontology. |
16019 | Leibniz's Law must be kept separate from the substitutivity principle [Noonan] |
Full Idea: Leibniz's Law must be clearly distinguished from the substitutivity principle, that if 'a' and 'b' are codesignators they are substitutable salva veritate. | |
From: Harold Noonan (Identity [2009], §2) | |
A reaction: He gives a bunch of well-known problem cases for substitutivity. The Morning Star, Giorgione, and the number of planets won't work. Belief contexts, or facts about spelling, may not be substitutable. |