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2010a, “Evolution without Naturalism
 Studies in Philosophy of Religion
"... Does evolutionary theory have implications about the existence of supernatural entities? This question concerns the logical relationships that hold between the theory of evolution and different bits of metaphysics. There is a distinct question that I also want to address; it is epistemological in ch ..."
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Does evolutionary theory have implications about the existence of supernatural entities? This question concerns the logical relationships that hold between the theory of evolution and different bits of metaphysics. There is a distinct question that I also want to address; it is epistemological in character. Does the evidence we have for evolutionary theory also provide evidence concerning the existence of supernatural entities? An affirmative answer to the logical question would entail an affirmative answer to the epistemological question if the principle in confirmation theory that Hempel (1965, p. 31) called the special consequence condition were true: The special consequence condition: If an observation report confirms a hypothesis H, then it also confirms every consequence of H. According to this principle, if evolutionary theory has metaphysical implications, then whatever confirms evolutionary theory also must confirm those metaphysical implications. But the special consequence is false. Here‟s a simple example that illustrates why. You are playing poker and would dearly like to know whether the card you are about to be dealt will be the Jack of Hearts. The dealer is a bit careless and so you catch a glimpse of the card on top of the deck before it is dealt to you. You see that it is red. The fact that it is red confirms the hypothesis that the card is the Jack of Hearts, and the hypothesis that it is the Jack of Hearts entails that the card will be a Jack. However, the fact that the card is red does not confirm the hypothesis that the card will be a Jack. 2 Bayesians gloss these facts by understanding confirmation in terms of probability raising: The Bayesian theory of confirmation: O confirms H if and only if Pr(H│O)> Pr(H). The general reason why Bayesianism is incompatible with the special consequence
Conceptions of the Continuum
"... Abstract: A number of conceptions of the continuum are examined from the perspective of conceptual structuralism, a view of the nature of mathematics according to which mathematics emerges from humanly constructed, intersubjectively established, basic structural conceptions. This puts into question ..."
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Abstract: A number of conceptions of the continuum are examined from the perspective of conceptual structuralism, a view of the nature of mathematics according to which mathematics emerges from humanly constructed, intersubjectively established, basic structural conceptions. This puts into question the idea from current set theory that the continuum is somehow a uniquely determined concept. Key words: the continuum, structuralism, conceptual structuralism, basic structural conceptions, Euclidean geometry, Hilbertian geometry, the real number system, settheoretical conceptions, phenomenological conceptions, foundational conceptions, physical conceptions. 1. What is the continuum? On the face of it, there are several distinct forms of the continuum as a mathematical concept: in geometry, as a straight line, in analysis as the real number system (characterized in one of several ways), and in set theory as the power set of the natural numbers and, alternatively, as the set of all infinite sequences of zeros and ones. Since it is common to refer to the continuum, in what sense are these all instances of the same concept? When one speaks of the continuum in current settheoretical
On the calculating power of Laplace’s demon (Part I)
, 2006
"... We discuss several ways of making precise the informal concept of physical determinism, drawing on ideas from mathematical logic and computability theory. We outline a programme of investigating these notions of determinism in detail for specific, precisely articulated physical theories. We make a s ..."
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We discuss several ways of making precise the informal concept of physical determinism, drawing on ideas from mathematical logic and computability theory. We outline a programme of investigating these notions of determinism in detail for specific, precisely articulated physical theories. We make a start on our programme by proposing a general logical framework for describing physical theories, and analysing several possible formulations of a simple Newtonian theory from the point of view of determinism. Our emphasis throughout is on clarifying the precise physical and metaphysical assumptions that typically underlie a claim that some physical theory is ‘deterministic’. A sequel paper is planned, in which we shall apply similar methods to the analysis of other physical theories. Along the way, we discuss some possible repercussions of this kind of investigation for both physics and logic. 1
Indispensability Arguments and Their Quinean Heritage
"... Indispensability arguments (IA) for mathematical realism are commonly traced back to Quine. We identify two different Quinean strands in the interpretation of IA, what we label the ‘logical point of view ’ and the ‘theorycontribution ’ point of view. Focusing on each of the latter, we offer two min ..."
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Indispensability arguments (IA) for mathematical realism are commonly traced back to Quine. We identify two different Quinean strands in the interpretation of IA, what we label the ‘logical point of view ’ and the ‘theorycontribution ’ point of view. Focusing on each of the latter, we offer two minimal versions of IA. These both dispense with a number of theoretical assumptions commonly thought to be relevant to IA (most notably confirmational holism and naturalism). We then show that the attribution of both minimal arguments to Quine is controversial, and stress the extent to which this is so in both cases, in order to attain a better appreciation of the Quinean heritage of IA.
Naturalising Mathematics: A Critical Look at the QuineMaddy Debate
"... This paper considers Maddy’s strategy for naturalising mathematics in the context of Quine’s scientific naturalism. The aim of this proposal is to account for the acceptability of mathematics on scientific grounds without committing to revisionism about mathematical practice entailed by the QuinePu ..."
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This paper considers Maddy’s strategy for naturalising mathematics in the context of Quine’s scientific naturalism. The aim of this proposal is to account for the acceptability of mathematics on scientific grounds without committing to revisionism about mathematical practice entailed by the QuinePutnam indispensability argument. It has been argued that Maddy’s mathematical naturalism makes inconsistent assumptions on the role of mathematics in scientific explanations to the effect that it cannot distinguish mathematics from pseudoscience. I shall clarify Maddy’s arguments and show that the objection can be overcome. I shall then reformulate a novel version of the objection and consider a possible answer, and I shall conclude that mathematical naturalism does not ultimately provide a viable strategy for accommodating an antirevisionary stance on mathematics within a Quinean naturalist framework.