Articles by two American mathematicians, E. V. Huntington and Oswald Veblen, are discussed as examples of a movement in foundational research in the period 1900-1930 called American postulate theory. This movement also included E. H. Moore, R. L. Moore, C. H. Langford, H. M. Sheffer, C. J. Keyser, and others. The articles discussed exemplify American postulate theorists' standards for axiomatizations of mathematical theories, and their investigations of such axiomatizations with respect to metatheoretic properties such as independence, completeness, and consistency.
Articles by two American mathematicians, E. V. Huntington and Oswald Veblen, are discussed as examples of a movement in foundational research in the period 1900-1930 called American postulate theory. This movement also included E. H. Moore, R. L. Moore, C. H. Langford, H. M. Sheffer, C. J. Keyser, and others. The articles discussed exemplify American postulate theorists' standards for axiomatizations of mathematical theories, and their investigations of such axiomatizations with respect to metatheoretic properties such as independence, completeness, and consistency.
Jonathan Lear has suggested that Aristotle attempts to demonstrate a proof-theoretic analogue of a compactness theorem in Posterior analyticsI, chs. 19?22. Aristotle argues in these chapters that there cannot be in finite series of predications of terms. Lear's analysis of Aristotle's arguments are shown to be based on confusions about the nature of infinite orderings. Three distinct confusions are identified. In final remarks, it is suggested that a compactness claim is irrelevant to the issues which motivate Aristotle's arguments.
This article outlines the work of a group of US mathematicians called the American Postulate Theorists and their influence on Tarski's work in the 1930s that was to be foundational for model theory. The American Postulate Theorists were influenced by the European foundational work of the period around 1900, such as that of Peano and Hilbert. In the period roughly from 1900???1940, they developed an indigenous American approach to foundational investigations. This made use of interpretations of precisely formulated axiomatic theories (...) to prove such metatheoretic properties as independence, consistency, categoricity and, in some cases, completeness of axiom sets. This approach to foundations was in many respects similar to that later taken by Tarski, who frequently cites the work of American Postulate Theorists. Their work served as paradigm examples of the theories and concepts investigated in model theory. The article also examines the possibility of a more specific impetus to Tarski's model theoretic investigation, arising from his having studied in 1927???1929 a paper by C. H. Langford proving completeness for various axiom sets for linear orders. This used the method of elimination of quantifiers. The article concludes with an examination of one example of Langford's methods to indicate how their correct formulation seems to call for model-theoretic concepts. (shrink)
A case from 1996 in Oregon in which citizens' legally publicmotor vehicle information was disseminated on a World Wide Website is considered. The case evoked widespread moral outrageamong Oregonians and led to changes in the Oregon records laws.The application of either consequentialist ornon-consequentialist moral theories to this and otherinformational privacy cases is found to be inadequate.Adjudication of conflicting desires is offered as the appropriateanalytical model for moral disputes. The notion of adjudicationoffered here diverges from traditional moral theories in itsindeterminate nature.
We present a memorial summary of the professional life and contributions to logic of John Corcoran. We also provide a full list of his many publications.Courtesy of Lynn Corcoran.
Although it is eommon to attribute to Wittgenstein in the Tractatus a treatment of general propositions as equivalent to eonjunctions and disjunctions of instance propositions, the evidence for this is not perfeetly clear. This article considers Wittgenstein’s comments in 5.521, which can be read as rejecting such a treatment. It argues that properly situating the Tractatus historically allows for a revised reading of 5.521 and other parts of the Tractatus relevant to Wittgenstein’s theory of generality. The result is that 5.521 (...) does not conflict with the view that general propositions are truth-functions of instance propositions. Common problems with such a view are to some extent obviated by the fact that Wittgenstein, following Russell and Moore, was not concerned with a syntactically defined language, but with propositions conceived as independent of a fixed language. (shrink)
Although it is eommon to attribute to Wittgenstein in the Tractatus a treatment of general propositions as equivalent to eonjunctions and disjunctions of instance propositions, the evidence for this is not perfeetly clear. This article considers Wittgenstein’s comments in 5.521, which can be read as rejecting such a treatment. It argues that properly situating the Tractatus historically allows for a revised reading of 5.521 and other parts of the Tractatus relevant to Wittgenstein’s theory of generality. The result is that 5.521 (...) does not conflict with the view that general propositions are truth-functions of instance propositions. Common problems with such a view are to some extent obviated by the fact that Wittgenstein, following Russell and Moore, was not concerned with a syntactically defined language, but with propositions conceived as independent of a fixed language. (shrink)
