(still under construction)

Research interests

Philosophy and metaphysics of quantum physics.

I am interested in the logical and foundational approach to a metaphysics of non-individuals, understood as things to which the standard notion of identity fails. By the "standard notion of identity" I mean the theory of identity of classical logic and standard mathematics (STI, although there are different versions of it). STI, in whatever version, defines identity by means of indiscernibility; indiscernible things, that is, things having exactly the same properties, or attributes, are identical, are the very same thing, and (obviously) conversely. A theory encompassing STI is a theory of individuals, of entities that can always (at least in principle) be differentiated from any other individual by a property. This idea is grounded in our preferred metaphysics, which has been incorporated in classical physics, traditional logic, and standard mathematics. The objects we meet in our everyday experience are individuals in this sense. Non-individuals would be entities which might be absolutely indiscernible, having all their characteristics in common, but even so not being the very same entity, as implied by STI. So, in order to admit non-individuals, STI must be modified. My approach uses a weaker relation of indiscernibility, which holds for all objects, even to those to which identity holds. Of course identity implies indiscernibility, but not the other way around. Non-individuals can be indiscernible in the sense of satisfying the relation of indiscernibility, but not that of identity. The two concepts are separated. Of course we can consider indiscernibility relative to some properties; probably, if you are reading this, we are indiscernible regarding the attibributes "interested in logic, in philosophy, in mathematics", among others). But this is not only what non-individuals are; they cannot be ordered - any order among them makes no sense, for whatever permutation of two non-individuals conduces to "the same" collection, to an ordered set that cannot the discerned from the former one, before the permutation. 

The field par excellence where non-individuals seem to leave is quantum mechanics. The possibility of associating to QM a metaphysics of non-individuals has interested me from a long time ago, and I have investigated this topic from a good number of perspectives, in most times in collaboration with colleagues and former students. My publications give an idea of the resulting works. 

Applications of non-classical logics to the foundations of science

Firstly, it is necessary to link science with logic. By "science", here, I mean "scientific theories", and I assume (to me at least) the thesis that every scientific theory can be analysed from a logical point of view, even those theories which until today have not being axiomatized adequately from a logical point of view; I am thinking of some of the theories of present day physics, such as the Standard Model of particle physics, but biology and the human sciences perhaps can offer more adequate examples. The logical analyses, according to me, would conduce to the study of the kinds of inference which are enabled by the theory, so the structure of the theories themselves, in the sense of their mathematical counterparts: does a theory need to assume individuals or can be erected based on relations only? This of course has interest for the defenders of the ontic structural realism. 

Obviously, the scientist does not use just deductive logic. She uses also induction an non-monotonic reasoning in several ways. Can we legitimate this use in the final presentation of her theory, or should we restrict the description of the theory in terms of deductive logic only? In doing that, we are explicitly distinguishing discovery from presentation. Is it right? 

In what regards other logics than the classical one ("classical logic" is also a wide field, and several systems can be regarded as "classical"), I have worked in some applications of paraconsistent logics to questions such as the concept of complementarity (in the sense of Bohr, if we can say that there is a sense he has privileged), 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, and in particular the use of paraconsistent systems, for we need to understand what a paraconsistent negation really means. That is, if we found a scientific theory in a paraconsistent logic because we believe that the theory should deal with some form of inconsistencies, which forms are them? Inconsistencies mean the presence of a statement A and its negation not-A. But what the "not" means? 

Perspectivism in the philosophy of science: the objectivation of the world

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 possibility to see the world. According to him, each subject has a special position in the universe, and it is from her “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 even without realizing it.  In a sense, Ortega’s ideas are close to Schrödinger’s (who knew Ortega and perhaps was influenced by him) on the “construction” of reality by the subject (according to his book What is life? Mind and Matter ). 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 hypothesis according to which quantum entities can be seen as non-individuals can be considered as one of the possible ‘perspectives’ of the quantum world, that is, a possible metaphysics. 

Space, time, and individuation: a non-Hausdorff topology for quantum mechanics 

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 things need to viewed from another perspective: the case is that “there is no identity without entity”, she said.  My claim is that  by a suitable change of 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 (this may be the language of quasi-set theory, for instance). 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 why we still use classical, that is, Newtonian space and time to ground non-relativistic quantum mechanics, since Newtonian space and time provide identity to quantum particles, contrary to the quantum hypothesis that in the most interesting situations, quanta are indiscernible. I have published a paper in 2018 dealing with this idea, but the subject must be explored further. 

The more difficult question is as follows. Newtonian space and time, when treated mathematically, are described by a manifold that can be identified with the Euclidean space R^4. The underlying topology is Hausdorff, separable. So, if we have two objects whatever, represented by distinct points in this manifold, it is always possible to consider open balls centered in these points which are disjoined. This enable us to say that the objects are individuals in a sense explained above. But take quantum entities. Sometimes it is the case that nothing, not even God, can discern them. Their wave-functions ever overlap, and we don't have strict "separation" (the lovers of some form of Hinduism like this conclusion). So, the topology could not be Hausdorff. I am looking for constructing a non-Hausdorff topology using quasi-set theory in order to apply it to quantum physics.

Measurement

I am learning a lot from my PhD student Felix Flores Pinheiro about measurement theory, something I have read a long time ago but without paying attention to the details he is calling my attention to. Just to mention one of them, I have put above the objectivation of the world as a primary topic in my interests (see above about Perspectivism). My interests in Schrödinger's philosophy of objectivation is due to this.  But know we have perhaps a way to deal with the question; roughly speaking, the possibility of measurement is a way to say that the world is there to be inquired. As I use to say, what there exists is that what kicks you back. Felix and I are investigating several topics related to these ideas.