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.

Henry Sheffer’s 1908 Harvard Ph.D. thesis contains an interesting appendix on a central feature of the logical work of his thesis advisor, Josiah Royce. This is the claim in Royce’s 1905 article “The Relations of the Principles of Logic to the Foundations of Geometry” that an unsymmetric ordering relation can be defined on the single symmetric O-relation for which he gives postulates in that paper. Sheffer criticizes Royce’s specific definition from the point of view of the evolving twentieth century conception (...) of axiomatic method and also shows more generally that an unsymmetric1 order relation cannot be defined in the system of the 1905 paper based on the O-relation. In this article I wish to consider the nature.. (shrink)

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.

In lieu of an abstract, here is a brief excerpt of the content:_Russell_ journal (home office): E:CPBRRUSSJOURTYPE2602\REVIEWS.262 : 2007-01-24 01:12 eviews THE DENOTING CENTURY, 1 19 90 05 5– –2 20 00 05 5 Michael Scanlan Philosophy / Oregon State U. Corvallis, or 97331, usa [email protected] Guido Imaguire and Bernard Linsky, eds. On Denoting: 1905–2005. Munich: Philosophia Verlag, 2005. Pp. 451. 98.00. isbn 3-88405-091-5. his anniversary collection of papers connected with Russell’s 1905 publiTcation of “On Denoting” reflects both the almost (...) mythic status that paper has achieved in analytic philosophy and the quite variegated nature of the significance that philosophers have seen in it. The papers in this collection break down roughly into two sorts. There are those which take a historical approach and attempt to explicate various aspects of the content of the OD article. The other sort might be labelled “application” papers in which Russell’s analysis in OD is seen as a tool or a model for subsequent philosophical work, in the spirit of Ramsey’s much quoted “paradigm of philosophy” remark. The volume opens with a reprint of the OD text with pagination indicated for the original Mind printing, for the text in Collected Papers 4 and for the widely referenced Logic and Knowledge Russell collection edited by R. C. Marsh. The Mind and Papers texts use the American convention of single quotation marks within double quotation marks. The Marsh edition (and the text given here) uses the inverse British convention. Readers need to be aware that paper authors here, and elsewhere, vary in which text they cite. The end of the volume has a comprehensive 21-page bibliography of the secondary literature. In between there are thirteen papers. I will be rather brief with the “application” papers, since I believe that Russell readers will tend to favour the more historically oriented papers. Some of the application papers wander quite far afield from Russell’s treatment of definite descriptions. For instance the paper by Thomas Mormann on “Description, Construction and Representation from Russell and Carnap to Stone” takes off from Russell’s assertion that his theory of descriptions was an early version of his subsequent interest in substituting “constructions” for “inferred entities” such as space-time points. The paper is almost exclusively a (worthwhile and mathematically astute) analysis of Russell’s efforts along these lines in Our russell: the Journal of Bertrand Russell Studies n.s. 26 (winter 2006–07): 167–90 The Bertrand Russell Research Centre, McMaster U. issn 0036-01631 _Russell_ journal (home office): E:CPBRRUSSJOURTYPE2602\REVIEWS.262 : 2007-01-24 01:12 168 Reviews Knowledge of the External World and The Analysis of Matter. The author argues that Russell’s constructions did not actually achieve the effects he wanted, but that (curiously) they can be properly developed within the later framework of topological spaces developed by Marshall Stone in 1937. The paper by Guido Imaguire, “Theory of Descriptions and Inferential Semantics”, explicitly eschews an “exegetical” approach and allies itself with a “systematical approach, in which one analyses possible new features and extensions of the proposed theory” (p. 397). The extension considered here is to “inferential semantics”, especially that of Robert Brandom. The spirit of this approach is to take the semantics of a language to be determined by the set of allowed inferences within that language. Imaguire takes as an essential lesson of Russell’s theory of descriptions that definite descriptions and proper names cannot be treated as singular terms of a language in the same manner. He goes on to argue for a criterion for distinguishing proper names from definite descriptions based on inferences allowed between sentences containing them, and he takes this distinction to argue for a modification of Brandom’s treatment of singular terms in his inferential semantics. Elena Tatievskaya’s paper on “Russell’s Theory of Descriptions and Wittgenstein on Internal Properties of Propositions” is another paper that is mainly about something other than Russell and his theory of descriptions. It is a very detailed study of Wittgenstein’s attempt to make good on his claim that the logical symbols of propositional logic notation, such as v and ~, do not correspond to “logical” components of propositions (Tractatus... (shrink)

History and Philosophy of Logic, Volume 32, Issue 4, Page 405, November 2011.

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)

Most readers will consult this volume for one or two of the articles in it. However, reading through the volume as a whole gives an interesting perspective on research in this area. I will briefly...

In lieu of an abstract, here is a brief excerpt of the content:September 25, 2010 (2:45 pm) C:\Users\Milt\Desktop\backup copy of Ken's G\WPData\TYPE3001\russell 30,1 032 red corrected.wpd russell: the Journal of Bertrand Russell Studies n.s. 30 (summer 2010): 69–94 The Bertrand Russell Research Centre, McMaster U. issn 0036-01631; online 1913-8032 eviews RUSSELL VS.z MEINONG, 100 YEARS LATER Michael Scanlan South StraTord, vt 05070, usa [email protected] Nicholas GriUn and Dale Jacquette, eds. Russell vs. Meinong: the Legacy of “On Denoting”. London and New (...) York: Routledge, 2009. Pp. xiii, 384. isbn: 978-0-415-96364-0 (hb); 978-0-203-88802-5 (e-bk). £70.00; us$103.00. The background for the conference in 2005 at McMaster University from which these papers come is a 50-year period in anglophone philosophy during which Russell was portrayed as having put to rest the urge, exempliWed by Meinong, to have an intentional object for every thought. Beginning roughly in the 1970s, analytic philosophers began publishing work more sympathetic to both the speciWcs of Meinong and his general concerns. Some landmark publications in this vein are Terence Parsons, Nonexistent Objects (1980), and Richard Routley, Exploring Meinong’s Jungle and Beyond (1980). The development of more sophisticated accounts of Meinong, along with developments in Russell studies, has resulted in a more nuanced presentation of Meinong’s thought in recent literature, including this volume. There is one article in this collection which is explicitly devoted to comparing the views of the historical Russell and Meinong. This is “Psychological Content and Indeterminacy with Respect to Being” by J. C. Marek. The title indicates the two topics examined. Meinong was in the tradition of Brentano in seeing a mental state of presentation (Vorstellungz) as combining a mental act and a mental content. A presentation may or may not also have a presented object. Russell, famously, thought of the state corresponding to Meinong’s presentations as a relation called “direct acquaintance” that comes to exist, or ceases to exist, between a mind and objects. There is no place here for non-existent objects. There is very little to say about Russell’s theory of direct acquaintance and most of that is familiar to English-speaking readers, so Marek rightly devotes himself to expounding Meinong’s views on presentational content. The problem here is whether such content exists. Meinong averred he could introspect such content, and Russell averred that he could not. Beyond such fruitless personal testimony, Meinong oTered arguments for the explanatory value of presentational content. September 25, 2010 (2:45 pm) C:\Users\Milt\Desktop\backup copy of Ken's G\WPData\TYPE3001\russell 30,1 032 red corrected.wpd 70 Reviews One is as an explanation of how we could have presentations (thoughts ofy) nonexistent objects, e.g. the $1,000 in my pocket. Of course, Russell treats this with his theory of descriptions. Another such argument for mental content by Meinong is that it is needed to account for the diTerence in mental state when presented with diTerent objects. Russell says that when the mind is in relation to the distinct objects the distinctness of the objects guarantees two distinct relations of acquaintance. This leaves unclear what the mental diTerence is between seeing a red patch and seeing a blue patch. The separate discussion ofthe Meinong/Mally “indiTerence” of the “pure object ” or object itself as to whether it exists or not is a topic that is canvassed more in the anglophone literature. In Meinong’s 1904 formulation “the present king of France” doesn’t now exist, but if the French have a revolution then a “present ” king of France might exist in 2011. In either case there is an object of thought/reference, and it has (indiTerently) the character (Soseinz) of being king of France. Marek’s exposition in this area focuses on the various technical devices Meinong introduced in 1915 to mitigate the problems caused by allowing for the being of “impossible” objects such as the round square. In “Meditations on Meinong’s Golden Mountain”, Dale Jacquette oTers the traditional dramatic classroom story about Russell and OD. On this account, prior to 1905 Russell is a committed Meinongian who... (shrink)

This book is intended for an undergraduate student who has taken one introductory course in first-order logic.1 It focuses on great figures and periods: Aristotle, the Stoics, the medieval logician...