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96Lógica, lenguajes formales y modalidadAndamios 20 (53): 45-60. 2023.This paper examines two alleged limitations in the use of formal languages: on the one hand, the trade-offs between expressive and inferential power, and on the other, the phenomenon of system imprisonment. After reconceptualizing the issue, we consider the role played by modality in the understanding of certain aspects of mathematical structures and argue for its centrality.
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120Resisting easy inferencesPhilosophy and Phenomenological Research 102 (3): 729-735. 2021.Amie Thomasson has articulated a novel conception of ontological debates, defending an easy approach to ontological questions as part of the articulation of a deflationary metaphysical view (Thomasson, 2015). After raising some concerns to the approach, we sketch a neutralist alternative to her ontological framework, offering an even easier way of conducting ontological debates.
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73Putnam’s indispensability argument revisited, reassessed, revivedTheoria : An International Journal for Theory, History and Fundations of Science 33 (2): 201-218. 2018.Crucial to Hilary Putnam’s realism in the philosophy of mathematics is to maintain the objectivity of mathematics without the commitment to the existence of mathematical objects. Putnam’s indispensability argument was devised as part of this conception. In this paper, I reconstruct and reassess Putnam’s argument for the indispensability of mathematics, and distinguish it from the more familiar, Quinean version of the argument. Although I argue that Putnam’s approach ultimately fails, I develop a…Read more
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86Scientific Theories, Models and the Semantic ApproachPrincipia: An International Journal of Epistemology 11 (2): 187-201. 2007.According to the semantic view, a theory is characterized by a class of models. In this paper, we examine critically some of the assumptions that underlie this approach. First, we recall that models are models of something. Thus we cannot leave completely aside the axiomatization of the theories under consideration, nor can we ignore the metamathematics used to elaborate these models, for changes in the metamathematics often impose restrictions on the resulting models. Second, based on a paralle…Read more
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90In this first paper of a series of works on the foundations of science, we examine the significance of logical and mathematical frameworks used in foundational studies. In particular, we emphasize the distinction between the order of a language and the order of a structure to prevent confusing models of scientific theories with first-order structures, and which are studied in standard model theory. All of us are, of course, bound to make abuses of language even in putatively precise contexts. Th…Read more
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84Is science inconsistent?Synthese 191 (13): 2887-2889. 2014.There has always been interest in inconsistency in science, not least within science itself as scientists strive to devise a consistent picture of the universe. Some important early landmarks in this history are Copernicus’s criticism of the Ptolemaic picture of the heavens, Galileo’s claim that Aristotle’s theory of motion was inconsistent, and Berkeley’s claim that the early calculus was inconsistent. More recent landmarks include the classical theory of the electron, Bohr’s theory of the atom…Read more
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51Gennaro Chtjerchia, Dynamics of meaning: anaphora, presupposition, and the the of grammar. Chicago and London: The University of Chicago Press, 1995.xv+ 270 pp, £59.95, £31.95 G. Pr...
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Paraconsistent logicIn Susana Nuccetelli, Ofelia Schutte & Otávio Bueno (eds.), A Companion to Latin American Philosophy, Wiley-blackwell. 2009.
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265How Theories RepresentBritish Journal for the Philosophy of Science 62 (4): 857-894. 2011.An account of scientific representation in terms of partial structures and partial morphisms is further developed. It is argued that the account addresses a variety of difficulties and challenges that have recently been raised against such formal accounts of representation. This allows some useful parallels between representation in science and art to be drawn, particularly with regard to apparently inconsistent representations. These parallels suggest that a unitary account of scientific and ar…Read more
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31We present an axiomatic framework for semantics that can be applied to natural and formal languages. Our main goal is to suggest a very simple mathematical model that describes fundamental cognitive aspects of the human brain and that can still be applied to artificial intelligence. One of our main results is a theorem that allows us to infer syntactical properties of a language out of its corresponding semantics. The role of pragmatics in semantics in our mathematical framework is also discusse…Read more
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754Paradox without satisfactionAnalysis 63 (2). 2003.Consider the following denumerably infinite sequence of sentences: (s1) For all k > 1, sk is not true. (s2) For all k > 2, sk is not true. (s3) For all k > 3, sk is not true.
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85Empiricism, conservativeness, and quasi-truthPhilosophy of Science 66 (3): 485. 1999.A first step is taken towards articulating a constructive empiricist philosophy of mathematics, thus extending van Fraassen's account to this domain. In order to do so, I adapt Field's nominalization program, making it compatible with an empiricist stance. Two changes are introduced: (a) Instead of taking conservativeness as the norm of mathematics, the empiricist countenances the weaker notion of quasi-truth (as formulated by da Costa and French), from which the formal properties of conservativ…Read more
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68Is there a zande logic?History and Philosophy of Logic 19 (1): 41-54. 1998.The issue of what consequences to draw from the existence of non-classical logical systems has been the subject of an interesting debate across a diversity of fields. In this paper the matter of alternative logics is considered with reference to a specific belief system and its propositions :the Azande are said to maintain beliefs about witchcraft which, when expressed propositionally, appear to be inconsistent. When the Azande have been presented with such inconsistencies, they either fail to s…Read more
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205On representing the relationship between the mathematical and the empiricalPhilosophy of Science 69 (3): 497-518. 2002.We examine, from the partial structures perspective, two forms of applicability of mathematics: at the “bottom” level, the applicability of theoretical structures to the “appearances”, and at the “top” level, the applicability of mathematical to physical theories. We argue that, to accommodate these two forms of applicability, the partial structures approach needs to be extended to include a notion of “partial homomorphism”. As a case study, we present London's analysis of the superfluid behavio…Read more
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21Why inconsistency is not hell : Making room for inconsistency in scienceIn Erik J. Olsson (ed.), Knowledge and Inquiry: Essays on the Pragmatism of Isaac Levi, Cambridge University Press. pp. 70. 2006.
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38Belief Systems and Partial SpacesFoundations of Science 21 (1): 225-236. 2016.One important role of belief systems is to allow us to represent information about a certain domain of inquiry. This paper presents a formal framework to accommodate such information representation. Three cognitive models to represent information are discussed: conceptual spaces, state-spaces, and the problem spaces familiar from artificial intelligence. After indicating their weakness to deal with partial information, it is argued that an alternative, formulated in terms of partial structures, …Read more
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1What is Semantics? A Brief Note on a Huge QuestionSorites 3 43-47. 1995.After mentioning the cogent connection between pure semantics and the particular set theoretical framework in which it is formulated, some issues regarding the conceptual status of semantics itself, as well as its relationship to logic, are concisely raised.
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48The Drexler-Smalley Debate on Nanotechnology: Incommensurability at Work?Hyle 10 (2). 2004.In a recent debate, Eric Drexler and Richard Smalley have discussed the chemical and physical possibility of constructing molecular assemblers - devices that guide chemical reactions by placing, with atomic precision, reactive molecules. Drexler insisted on the mechanical feasibility of such assemblers, whereas Smalley resisted the idea that such devices could be chemically constructed, because we do not have the required control. Underlying the debate, there are differences regarding the approp…Read more
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3Omnibus Review (review)Journal of Symbolic Logic 62 (2): 683-685. 1997.Reviewed Works:Chris Mortensen, Inconsistent Mathematics.Chris Mortensen, Peter Lavers, Category Theory.William James, Closed Set Sheaves and Their Categories.Chris Mortensen, Joshua Cole, Foundations: Provability, Truth and Sets.
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62Logical non-apriorism and the law of non-contradictionIn Graham Priest, Jc Beall & Bradley P. Armour-Garb (eds.), The Law of Non-Contradiction : New Philosophical Essays, Oxford University Press. pp. 156--175. 2004.A common response to those who question the Law of Non-Contradiction is that it is impossible to debate such a fundamental law of logic. The reasons for this response vary, but what seems to underlie them is the thought that there is a minimal set of logical resources without which rational debate is impossible. This chapter argues that this response is misguided. First, it defends non-apriorism in logic: the view that logic is in the same epistemic boat as other scientific theories. It then off…Read more
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100Styles of reasoning: A pluralist viewStudies in History and Philosophy of Science Part A 43 (4): 657-665. 2012.Styles of reasoning are important devices to understand scientific practice. As I use the concept, a style of reasoning is a pattern of inferential relations that are used to select, interpret, and support evidence for scientific results. In this paper, I defend the view that there is a plurality of styles of reasoning: different domains of science often invoke different styles. I argue that this plurality is an important source of disunity in scientific practice, and it provides additional argu…Read more
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117Defeasible Reasoning + Partial Models: A Formal Framework for the Methodology of Research Programs (review)Foundations of Science 16 (1): 47-65. 2011.In this paper we show that any reasoning process in which conclusions can be both fallible and corrigible can be formalized in terms of two approaches: (i) syntactically, with the use of defeasible reasoning, according to which reasoning consists in the construction and assessment of arguments for and against a given claim, and (ii) semantically, with the use of partial structures, which allow for the representation of less than conclusive information. We are particularly interested in the forma…Read more
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59Realism and Anti-Realism about ScienceInternational Journal for the Study of Skepticism 5 (2): 145-167. 2015.Pyrrhonists provide a way of investigating the world in which conflicting views about a given topic are critically compared, assessed, and juxtaposed. Since Pyrrhonists are ultimately unable to decide between these views, they end up suspending judgment about the issues under examination. In this paper, I consider the question of whether Pyrrhonists can be realists or anti-realists about science, focusing, in particular, on contemporary philosophical discussions about it. Althoughprima faciethe …Read more
Coral Gables, Florida, United States of America
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Mathematics |
General Philosophy of Science |
Areas of Interest
Epistemology |
Metaphysics |
Aesthetics |
Philosophy of Physical Science |