This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...) providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)

European Journal of Philosophy, EarlyView.

What has become generally known as the Berlin School of Logical Empiricism constitutes a philosophical movement that was erected on foundations laid by Albert Einstein. His revolutionary work in physics had a profound impact on philosophers interested in scientific issues, prominent among them Paul Oppenheim and Hans Reichenbach, the founding fathers of the school, who joined in viewing him as their hero among philosopher-scientists. Overall the membership of this school falls into three groups. The founding generation was linked by the (...) circumstance that both Grelling and Reichenbach were collaborators of Oppenheim; the middle generation by the fact that both Hempel and Helmer were students of Reichenbach's in Berlin; and the younger generation by the fact that all of its members were students and disciples either of Reichenbach's or of Hempel's in the USA. Three stages are at issue: an initial phase in Berlin, a transatlantic migration, and a continuation in the U.S.A.--principally in Pittsburgh. (shrink)

Inconsistency toleration is the phenomenon of working with inconsistent information without threatening one’s rationality. Here I address the role that ignorance plays for the tolerance of contradictions in the empirical sciences. In particular, I contend that there are two types of ignorance that, when present, can make epistemic agents to be rationally inclined to tolerate a contradiction. The first is factual ignorance, understood as temporary undecidability of the truth values of the conflicting propositions. The second is what I call “ignorance (...) of theoretical structure”, which is lack of knowledge of relevant inference patterns within a specific theory. I argue that these two types of ignorance can be explanatory of the scientists’ rational disposition to be tolerant towards contradictions, and I illustrate this with a case study from neutrino physics. (shrink)

A transformative decision rule transforms a given decision probleminto another by altering the structure of the initial problem,either by changing the framing or by modifying the probability orvalue assignments. Examples of decision rules belonging to thisclass are the principle of insufficient reason, Isaac Levi'scondition of E-admissibility, the de minimis rule, andthe precautionary principle. In this paper some foundationalissues concerning transformative decision rules are investigated,and a couple of formal properties of this class of rules areproved.

Nietzsche sometimes praises the drive to order—to simplify, organize, and draw clear boundaries—as expressive of a vital "classical" style, or an Apollonian artistic drive to calmly contemplate forms displaying "epic definiteness and clarity." But he also sometimes harshly criticizes order, as in the pathological dialectics or "logical schematism" that he associates paradigmatically with Socrates. I challenge a tradition that interprets Socratism as an especially one-sided expression of, or restricted form of attention to, the Apollonian: they are more radically disparate. Beyond (...) strengthening the case for this basic point, I develop a distinctive account of what, exactly, distinguishes the Apollonian-classical and Socratic forms of order. To this end, I advance interrelated interpretations of Apollonian-classical simplicity and the "cold" calm that it elicits, by contrast to superficially similar Socratic phenomena. This illuminates Nietzsche's broader ambivalence toward science, in part by clarifying the nature and value of an idealized Apollonian science. (shrink)

Some philosophers have recently argued that contrary to the traditional view, good scientific theories can in fact be logically inconsistent. The literature is now full of case-studies that are taken to support this claim. I will argue however that as of yet no-one has managed to articulate a philosophically interesting view about the role of logically inconsistent theories in science that genuinely goes against tradition, is plausibly true, and is supported by any of the case studies usually given.

One of the key events in the relations between the Central European philosophers and those of the Nordic countries was the Second International Congress for the ...

It has recently been argued by Davey (2014) that inconsistency is never tolerated in science, but only discretely isolated. But when talking about inconsistencies in science, not much attention has been paid to the inconsistencies between theory and observation. Here I will argue that inconsistency toleration actually takes place in science, and that when we examine actual inconsistent theories, inconsistencies between theory and observation look anything but homogeneous. I will argue, appealing to certain properties of empirical theories, especially holism, that (...) at least two sub-types of inconsistencies regarding theory and observation can be distinguished: those that satisfy a criterion of observational independence and those that do not. (shrink)