In a series of papers, Don Fallis points out that although mathematicians are generally unwilling to accept merely probabilistic proofs, they do accept proofs that are incomplete, long and complicated, or partly carried out by computers. He argues that there are no epistemic grounds on which probabilistic proofs can be rejected while these other proofs are accepted. I defend the practice by presenting a property I call ‘transferability’, which probabilistic proofs lack and acceptable proofs have. I also consider what this (...) says about the similarities between mathematics and, on the one hand natural sciences, and on the other hand philosophy. (shrink)

The philosophical theory of scientific explanation proposed here involves a radically new treatment of causality that accords with the pervasively statistical character of contemporary science. Wesley C. Salmon describes three fundamental conceptions of scientific explanation--the epistemic, modal, and ontic. He argues that the prevailing view is untenable and that the modal conception is scientifically out-dated. Significantly revising aspects of his earlier work, he defends a causal/mechanical theory that is a version of the ontic conception. Professor Salmon's theory furnishes a robust (...) argument for scientific realism akin to the argument that convinced twentieth-century physical scientists of the existence of atoms and molecules. To do justice to such notions as irreducibly statistical laws and statistical explanation, he offers a novel account of physical randomness. The transition from the "reviewed view" of scientific explanation to the causal/mechanical model requires fundamental rethinking of basic explanatory concepts. (shrink)

In 'Two Dogmas of Empiricism', Quine attacks the analytic/synthetic distinction and defends a doctrine that I call epistemological holism. Now, almost fifty years after the article's appearance, what are we to make of these ideas? I suggest that the philosophical naturalism that Quine did so much to promote should lead us to reject Quine's brief against the analytic/synthetic distinction; I also argue that Quine misunderstood Carnap's views on analyticity. As for epistemological holism, I claim that this thesis does not follow (...) from the logical point that Duhem and Quine made about the role of auxiliary assumptions in hypothesis testing, and that the thesis should be rejected. \\\ [Peter Hylton] Section I of this essay discusses Quine's views about reference, contrasting them with those of Russell. For the latter, our language and thought succeed in being about the world because of our acquaintance with objects; the relation of reference-roughly, the relation between a name and its bearer-is thus fundamental. For Quine, by contrast, the fundamental relation by which our language comes to be about the world, and to have empirical content, is that between a sentence and stimulations of our sensory surfaces; reference, while important, is a derivative notion. Section II shows how this view of reference as derivative makes possible the notorious Quinean doctrine of ontological relativity. Section III raises the issue of realism. It argues that somewhat different notions of realism are in play for Quine and for Russell-for Russell, objects, and our knowledge of objects, play the fundamental role, while for quine objectivity and truth are fundamental, with ontology being derivative. (shrink)

In 'Two Dogmas of Empiricism', Quine attacks the analytic/synthetic distinction and defends a doctrine that I call epistemological holism. Now, almost fifty years after the article's appearance, what are we to make of these ideas? I suggest that the philosophical naturalism that Quine did so much to promote should lead us to reject Quine's brief against the analytic/synthetic distinction; I also argue that Quine misunderstood Carnap's views on analyticity. As for epistemological holism, I claim that this thesis does not follow (...) from the logical point that Duhem and Quine made about the role of auxiliary assumptions in hypothesis testing, and that the thesis should be rejected. \\\ [Peter Hylton] Section I of this essay discusses Quine's views about reference, contrasting them with those of Russell. For the latter, our language and thought succeed in being about the world because of our acquaintance with objects; the relation of reference-roughly, the relation between a name and its bearer-is thus fundamental. For Quine, by contrast, the fundamental relation by which our language comes to be about the world, and to have empirical content, is that between a sentence and stimulations of our sensory surfaces; reference, while important, is a derivative notion. Section II shows how this view of reference as derivative makes possible the notorious Quinean doctrine of ontological relativity. Section III raises the issue of realism. It argues that somewhat different notions of realism are in play for Quine and for Russell-for Russell, objects, and our knowledge of objects, play the fundamental role, while for quine objectivity and truth are fundamental, with ontology being derivative. (shrink)

Carnap's inductive logic (or confirmation) project is revisited from an "increase in firmness" (or probabilistic relevance) point of view. It is argued that Carnap's main desiderata can be satisfied in this setting, without the need for a theory of "logical probability." The emphasis here will be on explaining how Carnap's epistemological desiderata for inductive logic will need to be modified in this new setting. The key move is to abandon Carnap's goal of bridging confirmation and credence, in favor of bridging (...) confirmation and evidential support. (shrink)

Kolmogorov''s axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0">.

No mathematical background is necessary to appreciate this classic of probability theory, which remains unsurpassed in its clarity, readability, and sheer charm. Its author, British logician John Venn (1834-1923), popularized the famous Venn Diagrams that are commonly used in teaching elementary mathematics.