Online research in philosophy

Can identity be vague? More exactly, can there be objects x and y such that it is vague whether x = y, and the vagueness is due to the objects themselves as opposed to vagueness in language used to denote the objects? The question has been extensively discussed since Evans (1978) where it was claimed that an affirmative answer was a necessary condition for the thesis that there could be vague objects. A recent, ingenious argument in Pinillos (2003) seeks to establish the negative and show that it cannot be de re vague whether x = y. The argument depends crucially on count claims concerning objects whose identity conditions are de re vague, and so we must learn how to count such objects — clouds, persons and much else besides. When that has been accomplished we can see a way out of Pinillos’s argument, and claim that de re vague identity remains coherent.

In this paper I present a new argument against vague identity — one that is more fundamental than existing arguments — and I also try to explain why we find the idea of vague identity puzzling, in a way that will dispel the puzzlement. In brief, my argument is this: to make clear sense of something, one must at least model it set-theoretically; but due to the special place of identity in set-theoretic models, any vague relation that one does model set-theoretically will not be identity, for real identity will already be there, built into the background of the model, and perfectly precise.

The supporter of vague objects has been long challenged by the following ‘Argument from Identity’: 1) if there are vague objects, then there is ontically indeterminate identity; 2) there is no ontically indeterminate identity; therefore, 3) there are no vague objects. Some supporters of vague objects have argued that 1) is false. Noonan (Analysis 68: 174–176, 2008) grants that 1) does not hold in general, but claims that ontically indeterminate identity is indeed implied by the assumption that there are vague objects of a certain special kind (i.e. vague objects*). One can therefore formulate a ‘New Argument from Identity’: 1′) if there are vague objects*, then there is ontically indeterminate identity; 2) there is no ontically indeterminate identity; therefore, 3′) there are no vague objects*. Noonan’s strategy is to argue that premiss 1′) is inescapable, and, as a consequence, that Evans’s alleged defence of 2) is a real challenge for any supporter of vague objects. I object that a supporter of vague objects who grants the validity of Evans’s argument allegedly in favour of 2) should reject premiss 1′). The threat of the New Argument from Identity is thus avoided.

The concept of indiscernibility in a structure is analysed with the aim of emphasizing that in asserting that two objects are indiscernible, it is useful to consider these objects as members of (the domain of) a structure. A case for this usefulness is presented by examining the consequences of this view to the philosophical discussion on identity and indiscernibility in quantum theory.

In this paper we try to justify our way of looking for an alternative approach to quantum mechanics, which is based on a non-classical logic. We consider two specific questions related to quantum theory, namely, entanglement and the indiscernibility of quanta. We characterize individuals, and then explain in what sense entanglement is a concept which can be applied to individuals in a restricted sense only. Then, we turn to indiscernibility and, after realizing that this concept is of a fundamental importance, we mention the ‘traditional’ theory of identity (TTI) of standard logic and mathematics, which underly the basic formalism of quantum theory. Then we propose to call the Problem of Identity the question whether identity of objects can be justified, and under what conditions. As in the Hume’s celebrated Problem of Induction, we conclude that the attribution of transtemporal identity to an object (either a macroscopic or a microscopic one) has no logic justification, and must be considered as a metaphysical hypothesis. Numerical identity is also put aside for similar reasons. Then we guess that identity is just an useful concept, but which in certain fields, mainly in the quantum realm, could be substituted by a weaker concept of indiscernibility. This assumption motivates us to look for an interpretation of quantum mechanics based on a non-classical logic, termed non-reflexive, and the corresponding mechanics is called non-reflexive quantum mechanics.

The concept of indiscernibility in a structure is analysed with the aim of emphasizing that in asserting that two objects are indiscernible, it is useful to consider these objects as members of (the domain of) a structure. A case for this usefulness is presented by examining the consequences of this view to the philosophical discussion on identity and indiscernibility in quantum theory.