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A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms...
Three things are presented: How Hilbert changed the original construction postulates of his geometry into existential axioms; In what sense he formalized geometry; How elementary geometry is formalized to present day's standards.
A reading is given of Curie's Principle that the symmetry of a cause is always preserved its effects. The truth of the principle is demonstrated and its importance, under the proposed reading, is defended.“As far as I see, all a priori statements in physics have their origin in symmetry.” (Weyl, Symmetry, p. 126)
The transition from the traditional to the representational theory of measurement around the turn of the century was accompanied by little sustained criticism of the former. The most forceful critique was Bertrand Russell's 1897 Mind paper, ‘On the relations of number and quantity’. The traditional theory has it that real numbers unfold from the concept of continuous quantity. Russell's critique identified...
This paper attempts an interpretation of Everett's relative state formulation of quantum mechanics that avoids the commitment to new metaphysical entities like ‘worlds’ or ‘minds’. Starting from Everett's quantum mechanical model of an observer, it is argued that an observer's belief to be in an eigenstate of the measurement (corresponding to the observation of a well-defined measurement outcome)...
In 1912, Henri Poincaré published an argument which apparently shows that the hypothesis of quanta is both necessary and sufficient for the truth of Planck's experimentally corroborated law describing the spectral distribution of radiant energy in a black body. In a recent paper, John Norton has reaffirmed the authority of Poincarés argument, setting it up as a paradigm case in which empirical data...
This paper aims at a partial rehabilitation of E. A. Moody's characterization of the 14th century as an age of rising empiricism, specifically by contrasting the conception of the natural science of psychology found in the writings of a prominent 13th-century philosopher (Thomas Aquinas) with those of two 14th-century philosophers (John Buridan and Nicole Oresme). What emerges is that if the meaning...
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 argue that indirect quotation in the first person simple present tense (“self-quotation”) provides a class of infallible assertions. The defense of this conclusion examines the joint descriptive and constitutive functions of performative utterances and argues that a parallel treatment of belief ascription is in order. The parallel account yields a class of infallible belief ascriptions that makes...
In this paper, I analyze the particular conception of reciprocal justification proposed by Nelson Goodman and incorporated by John Rawls into what he called “reflective equilibrium”. I propose a way of avoiding the twin dangers which threaten to push this idea to either of two extremes: the reliance on epistemically privileged observation reports (or moral judgments in Rawls’ version), which tends...
Proponents of the language of thought (LOT) thesis are realists when it comes to syntactically structured representations, and must defend their view against instrumentalists, who would claim that syntactic structures may be useful in describing cognition, but have no more causal powers in governing cognition than do the equations of physics in guiding the planets. This paper explores what it will...
In his book, Contemporary Theories of Knowledge, John Pollock argues that all externalist theories of justification should be rejected on the grounds that they do not do justice to the action-guiding character of epistemic norms. I reply that Pollock’s argument is ineffective -- because not all externalisms are intended to involve action-guiding norms, and because Pollock does not give a good reason...
Currently there is hardly any connection between philosophy of science and Artificial Intelligence research. We argue that both fields can benefit from each other. As an example of this mutual benefit we discuss the relation between Inductive-Statistical Reasoning and Default Logic. One of the main topics in AI research is the study of common-sense reasoning with incomplete information. Default logic...
Despite various attempts to rectify matters, the internalism-externalism (I-E) debate in epistemology remains mired in serious confusion. I present a new account of this debate, one which fits well with entrenched views on the I-E distinction and illuminates the fundamental disagreements at the heart of the debate. Roughly speaking, the I-E debate is over whether or not certain of the necessary conditions...
Quine’s ontological relativity is related to Tarski’s theory of truth in two ways: Quine “repudiates term-by-term-correspondence”, as does Tarski’s rule of truth; and Quine’s proxy argument in support of relativity finds exact formulation in Tarski’s truth definition.Unfortunately, relativity is threatened by the fact that the proxy argument doesn’t comply with the rule of truth (Tarski’s celebrated...
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