Online research in philosophy

This paper introduces, as an alternative to the (absolutely) lawless sequences of Kreisel and Troelstra, a notion of choice sequence lawless with respect to a given class D of lawlike sequences. For countable D, the class of D-lawless sequences is comeager in the sense of Baire. If a particular well-ordered class F of sequences, generated by iterating definability over the continuum, is countable then the F-lawless, sequences satisfy the axiom of open data and the continuity principle for functions from lawless to lawlike sequences, but fail to satisfy Troelstra's extension principle. Classical reasoning is used.

This paper defends the claim that there is a deep tension between the principle of countable additivity and the one-third solution to the Sleeping Beauty problem. The claim that such a tension exists has recently been challenged by Brian Weatherson, who has attempted to provide a countable additivity-friendly argument for the one-third solution. This attempt is shown to be unsuccessful. And it is argued that the failure of this attempt sheds light on the status of the principle of indifference that underlies the tension between countable additivity and the one-third solution.

The theoretical system Lyell presented in 1830 was composed of three requirements or principles: 1) the Uniformity Principle which states that past geological events must be explained by the same causes now in operation; 2) the Uniformity of Rate Principle which states that geological laws operate with the same force as at present; 3) the Steady-state Principle which states that the earth does not undergo any directional change. The three principles form a single thesis called uniformitarianism which has been repeatedly questioned and which has been reputed to be unable to face the competing directional synthesis based on the theory of the earth's cooling down. As a result, the significance of Lyell's system has been reduced to a simple actualism which admits the validity of the only Uniformity Principle. I believe that the only way to understand Lyell's role in the history of science is to maintain the unity of his synthesis. To show the Newtonian roots of this synthesis I will compare Lyell's principles and Newton's Rules of Reasoning. I will conclude with an analysis of the methodological function of principles in Lyell's scientific endeavour.

The form of nominalism known as 'mathematical fictionalism' is examined and found wanting, mainly on grounds that go back to an early antinominalist work of Rudolf Carnap that has unfortunately not been paid sufficient attention by more recent writers.

The form of nominalism known as 'mathematical fictionalism' is examined and found wanting, mainly on grounds that go back to an early antinominalist work of Rudolf Carnap that has unfortunately not been paid sufficient attention by more recent writers.

While there are several arguments on either side, it is far from clear as to whether or not countable additivity is an acceptable axiom of subjective probability. I focus here on de Finetti's central argument against countable additivity and provide a new Dutch book proof of the principle, To argue that if we accept the Dutch book foundations of subjective probability, countable additivity is an unavoidable constraint.

The form of nominalism known as 'mathematical fictionalism' is examined and found wanting, mainly on grounds that go back to an early antinominalist work of Rudolf Carnap that has unfortunately not been paid sufficient attention by more recent writers.

In this paper an outline of a metaphysical conception of modern science is presented in which a fundamental distinction is drawn between scientific principles, laws and theories. On this view, ontologicalprinciples, rather than e.g. empirical data, constitute the core of science. The most fundamental of these principles are three in number, being, more particularly (A) the principle of the uniformity of nature, (B) the principle of the perpetuity of substance, and (C) the principle of causality.These three principles set basic constraints on the methodology of both empirical and theoretical science. The uniformity principle is central to the empirical aspect of science, suggesting a methodology consisting in the attempt to discover empiricallaws, while the causality principle is central to the theoretical aspect of science, suggesting the postulation of scientifictheories capable of indicating the causal basis of the laws. And the perpetuity principle functions so as to form a bridge between the theories and the laws.