The Counterpart Principle of Analogical Support by Structural Similarity

We propose and investigate an Analogy Principle in the context of Unary Inductive Logic based on a notion of support by structural similarity which is often employed to motivate scientific conjectures

Content & Watkins's account of natural axiomatizations

This paper briefly recounts the importance of the notion of natural axiomatizations for explicating hypothetico-deductivism, empirical significance, theoretical reduction, and organic fertility. Problems for the account of natural axiomatizations developed by John Watkins in Science and Scepticism and the revised account developed by Elie Zahar are demonstrated. It is then shown that Watkins's account can be salvaged from various counter-examples in a principled way by adding the demand that every axiom of a natural axiomatization should be part of the content of the theory being axiomatized. The crucial point here is that content cannot simply be identified with the set of logical consequences of a theory, but must be restricted to a proper subset of the consequence set. It is concluded that the revised Watkins account has certain advantages over the account of natural axiomatizations offered in Gemes (1993)

Frege on the Generality of Logical Laws

Frege claims that the laws of logic are characterized by their “generality,” but it is hard to see how this could identify a special feature of those laws. I argue that we must understand this talk of generality in normative terms, but that what Frege says provides a normative demarcation of the logical laws only once we connect it with his thinking about truth and science. He means to be identifying the laws of logic as those that appear in every one of the scientific systems whose construction is the ultimate aim of science, and in which all truths have a place. Though an account of logic in terms of scientific systems might seem hopelessly antiquated, I argue that it is not: a basically Fregean account of the nature of logic still looks quite promising

Comparing theories: the dynamics of changing vocabulary. A case-study in relativity theory

There are several first-order logic (FOL) axiomatizations of special relativity theory in the literature, all looking essentially different but claiming to axiomatize the same physical theory. In this paper, we elaborate a comparison, in the framework of mathematical logic, between these FOL theories for special relativity. For this comparison, we use a version of mathematical definability theory in which new entities can also be defined besides new relations over already available entities. In particular, we build an interpretation of the reference-frame oriented theory SpecRel into the observationally oriented Signalling theory of James Ax. This interpretation provides SpecRel with an operational/experimental semantics. Then we make precise, "quantitative" comparisons between these two theories via using the notion of definitional equivalence. This is an application of logic to the philosophy of science and physics in the spirit of Johan van Benthem's work.Comment: 27 pages, 8 figures. To appear in Springer Book series Trends in Logi

Harnessing Higher-Order (Meta-)Logic to Represent and Reason with Complex Ethical Theories

The computer-mechanization of an ambitious explicit ethical theory, Gewirth's Principle of Generic Consistency, is used to showcase an approach for representing and reasoning with ethical theories exhibiting complex logical features like alethic and deontic modalities, indexicals, higher-order quantification, among others. Harnessing the high expressive power of Church's type theory as a meta-logic to semantically embed a combination of quantified non-classical logics, our work pushes existing boundaries in knowledge representation and reasoning. We demonstrate that intuitive encodings of complex ethical theories and their automation on the computer are no longer antipodes.Comment: 14 page

New remarks on the Cosmological Argument

We present a formal analysis of the Cosmological Argument in its two main forms: that due to Aquinas, and the revised version of the Kalam Cosmological Argument more recently advocated by William Lane Craig. We formulate these two arguments in such a way that each conclusion follows in first-order logic from the corresponding assumptions. Our analysis shows that the conclusion which follows for Aquinas is considerably weaker than what his aims demand. With formalizations that are logically valid in hand, we reinterpret the natural language versions of the premises and conclusions in terms of concepts of causality consistent with (and used in) recent work in cosmology done by physicists. In brief: the Kalam argument commits the fallacy of equivocation in a way that seems beyond repair; two of the premises adopted by Aquinas seem dubious when the terms `cause' and `causality' are interpreted in the context of contemporary empirical science. Thus, while there are no problems with whether the conclusions follow logically from their assumptions, the Kalam argument is not viable, and the Aquinas argument does not imply a caused origination of the universe. The assumptions of the latter are at best less than obvious relative to recent work in the sciences. We conclude with mention of a new argument that makes some positive modifications to an alternative variation on Aquinas by Le Poidevin, which nonetheless seems rather weak.Comment: 12 pages, accepted for publication in International Journal for Philosophy of Religio

Poincaré on the Foundation of Geometry in the Understanding

This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study of groups of operations. In place of the established view I offer a revised view, according to which Poincaré held that axioms in geometry are in fact assertions about invariants of groups. Groups, as forms of the understanding, are prior in conception to the objects of geometry and afford the proper definition of those objects, according to Poincaré. Poincaré’s view therefore contrasts sharply with Kant’s foundation of geometry in a unique form of sensibility. According to my interpretation, axioms are not definitions in disguise because they themselves implicitly define their terms, but rather because they disguise the definitions which imply them