Prof. Décio Krause

Research interests

Philosophy of quantum physics. I am interested mainly in the problem of the individuality of quantum entities, the raise of the concept of particle in quantum field theories (to explain “the particle grin” in field theories, in Michael Redhead’s words), so as in the ontologies associated to quantum theories, the logic structure of quantum theories, and the metaphysics associated to quantum theories. Much on these topics can be seen in my book with Steven French, Identity in Physics: A Historical, Philosophical, and Formal Analysis (Oxford Un. Press, 2006), but of course there is still much to be done.

Philosophy of Non-Individuality. Some of the forerunners of quantum mechanics (Heisenberg, Born, Schrödinger) spoke of the “lost of individuality” of quantum objects, so as about their non-individuality. But there are philosophers of science, such as Heinz Post, and physicists such as Yuri Manin, who have suggested that the indiscernibility of quantum objects should be considered right from the start, since, in a sense, there is no identity to lose (the basic entities assumed—even implicitly--by quantum theories simply don’t have individuality, never had individuality). I have pursued this idea from a formal point of view. The main difficulty is that within the framework of standard logic and set theory (the usual frameworks where all physics is usually developed), every object is an individual, in the sense that they can ever be discerned from any other other, even if in principle. Furthermore, in order to speak of non-individuals, we apparently need the concept of identity. This raises interesting philosophical and foundational issues. Usually, in order to speak of non-individuals, physicists make use of a mathematical artifice of restricting the relevant function/vectors to symmetric and anti-symmetric ones, which in certain sense corresponds to the restriction of the discourse to a certain non-rigid structure (structures which can admit indiscernible but not identical individuals). My concern is to avoid this trick (since any structure built in standard set theory can be extended to a rigid one) by means of a distinct logic-mathematical basis, termed quasi-set theory, a mathematical theory which I have been developing and correcting ever since my PhD thesis. (see the chapter 7 of my book with French mentioned above).

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 the reality, but never the reality in totum. According to him, there is no reality per se, but so many `realities’ as 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. 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 in preparation) The Metaphysics of Non-Individuality: Essay on the Indiscernibility of Quanta (written in Portuguese).

There are entities without identity. 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”. 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.

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 (the binary predicate =) may be not used to define well-formed formulas (that is, x=y would be not a well-formed formulas 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 indiscernible but distinct objects. 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 fictions 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, and that they are indiscernible when we have no grounds for ascribing them a difference; 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 Schrödinger ‘s ideas.

---updated in October 2010---