*Philosophy of quantum physics. **I am interested in the logical and foundational approach of a metaphysics of non-individuals, understood as things to which the standard notion of identity fails. It comprises the problem of the individuality of quantum entities, the raise of the concept of particle in quantum field theories and to explain how even when `particles’ are ontologically subsumed by the concept of quantum field, “the particle grin”, in Michael Redhead’s words, still remain. The logic structure of quantum theories, and the metaphysics associated to quantum theories are also parts of my interests. Much on these topics can be seen in my book with Steven French, *Identityin Physics: A Historical, Philosophical, and Formal Analysis (Oxford Un. Press, 2006), but of course there is still much to be done.
**Applications of non-classical logic to the philosophy of science. **I have worked in some applications of paraconsistent logic to questions such as the concept of complementarity, and inductive logic. My interest is to understand the role played by non-classical logics in the foundational aspects (philosophical, metaphysical, logical, epistemological) of scientific theories.
*“Perspectivism” in the philosophy of science. **The Spanish philosopher José Ortega y Gasset presented “perspectivism” as a way to justify his belief that the individual point of view is the only one possible to see the world. According to him, each subject has a special position in the universe, and it is from this “perspective” that she is able of catching certain aspects of reality, but never the reality *in totum. According to him, there is no reality per se, but so many ‘realities’ as there are perspectives. Notwithstanding, his position is contrary both to relativism and subjectivism. I have found in Ortega’s ideas a way of summarizing a conception of science and the scientific theories I ever have. In a sense, Ortega’s ideas are close to Schrödinger’s (who knew Ortega) on the “construction” of reality by the subject. I think that there is still a link with Piaget’s conception about the “construction of the reality by the children”. I am trying to connect these views by sustaining that the view according to which quantum entities can be seen as non-individuals can be considered as one of the possible ‘perspectives’ of the quantum world in a book (still inpreparation) The Metaphysics of Non-Individuality: Essay on the Indiscernibility of Quanta.
There are entities without identity and classical space and time. Quine’s well-known slogan that there are no entities without identity is linked to his ontological criteria. His theses gave rise to a wide literature; for instance, Ruth Barcan Marcus replied that “there is no identity without entity” instead. My claim is that by a suitable change in the underlying logic, we can found regimented languages (thus of course departing from Quine) such that even objects without identity can be values of variables. Of course the main motivation comes from quantum theory, and the reading of some of the above other topics can provide additional information. In particular, I am interested in clarifying the relationship between classical, that is, Newtonian space and time, used to ground non-relagivistic quantum mechanics, does not provide identity for quantum particles.
Non-reflexive (nonreflexive) logics. Non-reflexive logics are logics in which the standard theory of identity (either first-order or higher-order) is in some sense weakened. For instance, the notion of identity (formalized with the use of the binary predicate =) may be not used to define well-formed formulas (that is, x=y would be not a well-formed formula for arbitrary x and y). Logics in this sense were termed Schrödinger Logics, and you may find references to them in some of my works. Another alternative is to construct logical systems where the disputed Leibniz’s Principle of the Identity of Indiscernibles is not valid in general. Thus, we might have collections of indiscernible objects with cardinal greater than one. Still other systems can use a weaker notion of indiscernibility instead of identity, and are called Logics of Indiscernibility. All these topics arose from readings on quantum theories, but my aim is to explore a deeper philosophical idea, namely, that the standard notion of identity is a kinf of useful notion, perhaps suited for mathematics, but which in science would be substituted by a weaker notion of indiscernibility. In short, it suffices to say that two objects are discernible instead that they are different, so avoiding any compromise with a theory of identity; in this case, to say that they are “identical” would be a mistake. My motivation is of course David Hume, but grounded in quantum mechanics, specially on some ideas of Schrödinger .
—updated in November 2016—