-
34Décio Krause 2002: Introdução aos fundamentos axiomáticos da ciênciaNatureza Humana 5 (1): 257-264. 2003.
-
68Structuralism and the Applicability of MathematicsGlobal Philosophy 20 (2-3): 229-253. 2010.In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.
-
13The Axioms of Set TheoryGlobal Philosophy 13 (2): 107-126. 2002.In this paper I argue for the view that the axioms of ZF are analytic truths of a particular concept of set. By this I mean that these axioms are true by virtue only of the meaning attached to this concept, and, moreover, can be derived from it. Although I assume that the object of ZF is a concept of set, I refrain from asserting either its independent existence, or its dependence on subjectivity. All I presuppose is that this concept is given to us with a certain sense as the objective focus of…Read more
-
74On the Principle of Excluded MiddlePrincipia: An International Journal of Epistemology 15 (2): 333. 2011.I carry out in this paper a philosophical analysis of the principle of excluded middle (or, as it is often called in the version I favor here, principle of bivalence: any meaningful assertion is either true or false). This principle has been criticized, and sometimes rejected, on the charge that its validity depends on presuppositions that are not, some believe, universally obtainable; in particular, that any well-posed problem is solvable. My goal here is to show that, although excluded middle …Read more
-
60Husserl on Geometry and Spatial RepresentationAxiomathes 22 (1): 5-30. 2012.Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally …Read more
-
62Husserl's Phenomenology and Weyl's PredictivismSynthese 110 (2). 1997.In this paper I discuss the version of predicative analysis put forward by Hermann Weyl in "Das Kontinuum". I try to establish how much of the underlying motivation for Weyl's position may be due to his acceptance of a phenomenological philosophical perspective. More specifically, I analyze Weyl's philosophical ideas in connexion with the work of Husserl, in particular "Logische Untersuchungen" and "Ideen I". I believe that this interpretation of Weyl can clarify the views on mathematical existe…Read more
-
903This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal scie…Read more
-
Husserl on the Principle of the Excluded MiddleIn Gary Banham (ed.), Husserl and the Logic of Experience, Palgrave-macmillan. 2005.
-
30Resenha 'Husserl or Frege: meaning, objectivity and mathematics' (Claire Ortiz Hill & Guillermo E. Rosado Haddock)Manuscrito 23 (2): 351-372. 2000.
-
10A phenomenological inquiry into the concept of setManuscrito 28 (2): 291-316. 2005.The main concern of this paper is the justification of the axioms of Zermelo-Fraenkel set theory, either as true statements about a concept of set or, alternatively, as true statements about abstract objects . I want to argue here that, in either case, set theory can be seen as a body of knowledge largely built on intuitive foundations . I call this inquiry “phenomenological” for it approaches its subject from the perspective of the intentional acts that originate sets as doubly dependent object…Read more
-
15On proofs in mathematicsManuscrito 31 (1): 185-196. 2008.In his book Chateaubriand points out some differences between the mathematical and the formal notions of proof. I argue here that the contrast between both cannot be exaggerated, and that the latter fails to represent essential aspects of the former. I also sketch a view of the nature of mathematics that can accommodate one particular feature of mathematical proofs the formal notion, by its very nature, cannot: their freedom.Em seu livro, Chateaubriand aponta algumas diferenças entre a noção for…Read more
-
27The many senses of completenessManuscrito 23 (2): 41-60. 2000.In this paper I study the variants of the notion of completeness Husserl pre-sented in “Ideen I” and two lectures he gave in Göttingen in 1901. Introduced primarily in connection with the problem of imaginary numbers, this notion found eventually a place in the answer Husserl provided for the philosophically more im-portant problem of the logico-epistemological foundation of formal knowledge in sci-ence. I also try to explain why Husserl said that there was an evident correlation between his and…Read more
-
A Phenomenological Inquiry Into The Concept Of SetManuscrito 29 (2): 291-316. 2006.The main concern of this paper is the justification of the axioms of Zermelo-Fraenkel set theory, either as true statements about a concept of set or, alternatively, as true statements about abstract objects. I want to argue here that, in either case, set theory can be seen as a body of knowledge largely built on intuitive foundations. I call this inquiry “phenomenological” for it approaches its subject from the perspective of the intentional acts that originate sets as doubly dependent objects.…Read more
-
19On the nature of the propositionManuscrito 27 (1): 141-146. 2004.I present here my criticism of Chateaubriand’s account of propositions as having an identifying character with respect to reality. I claim that propositions are better understood as pictures of possible states-of-affairs, and that this account is more natural considering the acts of judgment that are at the origin of propositions. I also present a possible way of understanding the notion of a possible state-of-affairs that takes care of the seemingly absurd case of necessarily false, but meaning…Read more
Areas of Specialization
Science, Logic, and Mathematics |
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Mathematics |