In these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past century: Brouwer, Hilbert, Bernays, Weyl, Gödel, Russell, Quine, Putnam, Wang, and Tait.

The best known and most widely discussed aspect of Kurt Gödel's philosophy of mathematics is undoubtedly his robust realism or platonism about mathematical objects and mathematical knowledge. This has scandalized many philosophers but probably has done so less in recent years than earlier. Bertrand Russell's report in his autobiography of one or more encounters with Gödel is well known:Gödel turned out to be an unadulterated Platonist, and apparently believed that an eternal “not” was laid up in heaven, where virtuous (...) logicians might hope to meet it hereafter.On this Gödel commented:Concerning my “unadulterated” Platonism, it is no more unadulterated than Russell's own in 1921 when in the Introduction to Mathematical Philosophy … he said, “Logic is concerned with the real world just as truly as zoology, though with its more abstract and general features.” At that time evidently Russell had met the “not” even in this world, but later on under the infuence of Wittgenstein he chose to overlook it.One of the tasks I shall undertake here is to say something about what Gödel's platonism is and why he held it.A feature of Gödel's view is the manner in which he connects it with a strong conception of mathematical intuition, strong in the sense that it appears to be a basic epistemological factor in knowledge of highly abstract mathematics, in particular higher set theory. Other defenders of intuition in the foundations of mathematics, such as Brouwer and the traditional intuitionists, have a much more modest conception of what mathematical intuition will accomplish. (shrink)

Setting out to understand “indexicality” and its significance in Ethnomethodology, it is first necessary to trace the history of the ideas of Harold Garfinkel. From his early commitment to find “order” in his Harvard dissertation, Garfinkel finds himself in California defending Parsons’ Structural Functionalism while confronting Goffman and Symbolic Interactionism, based in Simmelian, Schützian Sociology. From the audience of students shared with Goffman, Garfinkel puts aside the “situation” of Symbolic Interaction in favour of a process, “Indexicality”, abandoning theorising in (...) favour of ethnomethodology as the means to understand “order*”. This paper, then, demonstrates how indexicality works and proposes completing the tasks that Garfinkel set out in the Studies to disclose the taken-for-granted, the left out, bounded by caveats like No-Time-Out and For-all-practical purposes. (shrink)

According to Quine, Charles Parsons, Mark Steiner, and others, Russell’s logicist project is important because, if successful, it would show that mathematical theorems possess desirable epistemic properties often attributed to logical theorems, such as aprioricity, necessity, and certainty. Unfortunately, Russell never attributed such importance to logicism, and such a thesis contradicts Russell’s explicitly stated views on the relationship between logic and mathematics. This raises the question: what did Russell understand to be the philosophical importance of (...) logicism? Building on recent work by Andrew Irvine and Martin Godwyn, I argue that Russell thought a systematic reduction of mathematics increases the certainty of known mathematical theorems (even basic arithmetical facts) by showing mathematical knowledge to be coherently organized. The paper outlines Russell’s theory of coherence, and discusses its relevance to logicism and the certainty attributed to mathematics. (shrink)

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model (...) other axioms of Church’s intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin’s intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions. (shrink)

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)

Il est rare, en philosophie, qu'on rencontre un problème ayant reçu une solution définitive. Dans le cadre de la philosophie contemporaine du langage, cependant, la critique de Russell à Meinong fait souvent figure d'exception à la règle - ce que l'on ne peut, eu égard à certains aspects de la philosophie de Meinong, que déplorer. Selon l'interprétation courante, la théorie des descriptions définies de Russell - que Ramsey qualifia de “paradigme de philosophie” - aurait mis hors jeu une (...) fois pour toutes la doctrine ontologique de Meinong, caractérisée par des thèses d’apparence paradoxale telles que : “il y a des choses telles qu’il n’y a pas de telles choses”, “l’objet est au-delà de l’être et du non-être”, “l’être-ainsi [le fait d’avoir des propriétés] précède l’existence (Dasein)”. Récemment pourtant, on a tenté, de toutes parts, de faire revivre la doctrine meinongienne. Je pense ici aux diverses propositions, toutes d’inspiration meinongienne, avancées par Castañeda 1989, Parsons 1980, Rapaport 1978, Routley 1980 et Zalta 1983. Mais bien que toutes ces propositions aient développé certaines intuitions meinongiennes de manière certainement plus raffinée d’un point de vue formel que Meinong lui-même, elles ont été perçues comme de purs modèles théoriques sans aucun doute intéressants, mais incapables en tant que tels de déplacer les termes de la question, comme Russell l’avait fait à l’égard de Meinong. Ainsi naît l’exigence de repenser le thème complet et d’évaluer dans quelle mesure la critique de Russell pose vraiment de sérieuses difficultés aux thèses meinongiennes. Nous verrons ainsi ce qu’il faut, dans ces dernières, considérer comme mort, et ce qui, au contraire, jouit toujours d'une validité objective. Si ce qui suit est plausible, nous découvrirons que ces thèses résistent pour la plupart aux critiques de Russell, à condition qu’on les considère de façon adéquate. (shrink)

Russell's criticisms force Meinong to adopt a distinction between two types of negation. Logical expositions of Meinong's theory show the distinction is easily drawn in formal terms, but that alone does not justify the distinction intuitively.I criticise Routley'streatment of the distinction and argue that only Terence Parsons'theory retains and preserves the tight network of conceptual connections between the notions of negation, contradiction and impossibility. Hence, Parsons' approach best expresses the Meinongian perspective.

The ancient puzzle of the Liar was shown by Tarski to be a genuine paradox or antinomy. I show, analogously, that certain puzzles of contemporary game theory are genuinely paradoxical, i.e., certain very plausible principles of rationality, which are in fact presupposed by game theorists, are inconsistent as naively formulated. ;I use Godel theory to construct three versions of this new paradox, in which the role of 'true' in the Liar paradox is played, respectively, by 'provable', 'self-evident', and 'justifiable'. I (...) also construct in modal operator logic a paradox involving reflexive empirical reasoning. Unlike the paradox of the Liar, the paradox of reflexive reasoning does not depend on self-reference. ;I consider various solutions to the Liar paradox and evaluate how well these solutions cope with the paradox of reflexive reasoning. I then formalize the solution to the paradoxes which I favor: the indexical-hierarchical approach, first sketched out by Charles Parsons and Tyler Burge. In this solution, occurrences of the predicate 'true' in sentence-tokens are contextually relativized to levels of a hierarchy. Drawing also on some brief remarks of Bertrand Russell and Charles Parsons, I develop an account of the kind of schematic generality needed for this theory to be statable. ;Finally, I demonstrate that the principles shown to be paradoxical are in fact presupposed by contemporary game theorists in their reliance on the notion of common knowledge or, more precisely, mutual belief. I create novel analyses of and corresponding solutions to several recalcitrant puzzles within game theory, including the "chain-store paradox". (shrink)

This essay re-examines Meinong's "Über Gegenstandstheorie" and undertakes a clarification and revision of it that is faithful to Meinong, overcomes the various objections to his theory, and is capable of offering solutions to various problems in philosophy of mind and philosophy of language. I then turn to a discussion of a historically and technically interesting Russell-style paradox (now known as "Clark's Paradox") that arises in the modified theory. I also examine the alternative Meinong-inspired theories of Hector-Neri Castañeda and Terence (...) Parsons. (shrink)

Inspired by Cantor's Theorem (CT), orthodoxy takes infinities to come in different sizes. The orthodox view has had enormous influence in mathematics, philosophy, and science. We will defend the contrary view---Countablism---according to which, necessarily, every infinite collection (set or plurality) is countable. We first argue that the potentialist or modal strategy for treating Russell's Paradox, first proposed by Parsons (2000) and developed by Linnebo (2010, 2013) and Linnebo and Shapiro (2019), should also be applied to CT, in a (...) way that vindicates Countabilism. Our discussion dovetails with recent independently developed treatments of CT in Meadows (2015), Pruss (2020), and Scambler (2021), aimed at establishing the mathematical viability, and therefore epistemic possibility, of Countabilism. Unlike these authors, our goal isn't to vindicate the mathematical underpinnings of Countabilism. Rather, we aim to argue that, given that Countabilism is mathematically viable, Countabilism should moreover be regarded as true. After clarifying the modal content of Countabilism, we canvas some of Countabilism's many positive implications, including that Countabilism provides the best account of the pervasive independence phenomena in set theory, and that Countabilism has the power to defuse several persistent puzzles and paradoxes found in physics and metaphysics. We conclude that in light of its theoretical and explanatory advantages, Countabilism is more likely true than not. (shrink)

In line with proponents of 4E cognition, Gallagher [2019] is concerned that many cognitive phenomena are not amenable to decomposition strategies since their very nature is to be constituted extensively. By contrast the received view on causal explanation—the mechanistic account [Craver 2007]—emphasises the necessity for decomposition in explaining natural phenomena and insists on a sharp distinction between causal versus constitutive relations. I propose that removing the requirement that constitutive relations cannot also be causes helps to ease this tension between explanation (...) and Gallagher’s non-decompositional stance, per Leuridan [2012]. Further, I draw on Froese et al.’s [2013] minimal model of social cognition to argue that constitutive relations can and do act as causal difference-makers in the Woodwardian sense [Woodward 2003]. (shrink)

Quantification is haunted by the specter of paradoxes. Since Russell, it has been a persistent idea that the paradoxes show what might have appeared to be absolutely unrestricted quantification to be somehow restricted. In the contemporary literature, this theme is taken up by Dummett (1973, 1993) and Parsons (1974a,b). Parsons, in particular, argues that both the Liar and Russell’s paradoxes are to be resolved by construing apparently absolutely unrestricted quantifiers as appropriately restricted.

Discusses the base from which modern societies developed.

This paper consists principally of selections from a much longer work on the semantics of English. It discusses some problems concerning how to represent grammatical modifiers (e.g. slowly in x drives slowly) in a logically perspicuous notation. A proposal of Reichenbach's is given and criticized; then a new theory (apparently discovered independently by myself, Romain Clark, and Richard Montague and Hans Kamp) is given, in which grammatical modifiers are represented by operators added to a first-order predicate calculus. Finally some problems (...) concerning applications of adjectives to that-clauses and gerundive-clauses are discussed. (shrink)

For a ring R, Hilbert’s Tenth Problem $HTP$ is the set of polynomial equations over R, in several variables, with solutions in R. We view $HTP$ as an enumeration operator, mapping each set W of prime numbers to $HTP$, which is naturally viewed as a set of polynomials in $\mathbb {Z}[X_1,X_2,\ldots ]$. It is known that for almost all W, the jump $W'$ does not $1$ -reduce to $HTP$. In contrast, we show that every Turing degree contains a set W (...) for which such a $1$ -reduction does hold: these W are said to be HTP-complete. Continuing, we derive additional results regarding the impossibility that a decision procedure for $W'$ from $HTP$ can succeed uniformly on a set of measure $1$, and regarding the consequences for the boundary sets of the $HTP$ operator in case $\mathbb {Z}$ has an existential definition in $\mathbb {Q}$. (shrink)

Inhaltsverzeichnis/Table of Contents: Rudolf HALLER: Zwei Vorworte in einem. Evelyn DÖLLING: Alexius Meinong: "Der blinde Seher Theiresias". Jaakko HINTIKKA: Meinong in a Long Perspective. Richard SYLVAN: Re-Exploring Item-Theory. Francesca MODENATO: Meinong's Theory of Objects: An Attempt at Overcoming Psychologism. Jan WOLE??N??SKI: Ways of Dealing with Non-existence. Karel LAMBERT: Substitution and the Expansion of the World. Terence PARSONS: Meinongian Semantics Generalized. Reinhardt GROSSMANN: Thoughts, Objectives and States of Affairs. Peter SIMONS: Meinong's Theory of Sense and Reference. Barry SMITH: More Things (...) in Heaven and Earth. Michele LENOCI: Meinongs unvollständige Gegenstände und das Universalienproblem. Maria E. REICHER: Gibt es unvollständige Gegenstände? Dale JACQUETTE: Meinong's Concept of Implexive Being and Nonbeing. Herbert HOCHBERG:s, Functions, Existence and Relations in the Russell-Meinong Dispute, the Bradley Paradox and the Realism-Nominalism Controversy. Jacek PA_NICZEK: Are Contradictions Still Lurking in Meinongian Theories of Objects? Marie-Luise SCHUBERT KALSI: Apriorische Elemente im Denken. Liliana ALBERTAZZI: Forms of Completion. Johann Ch. MAREK: Zwei Gegenstände und ein Inhalt. Zur Intentionalität bei Meinong. Wolfgang KÜNNE: Some Varieties of Thinking. Reflections on Meinong and Fodor. Alberto VOLTOLINI: Is Meaning Without Actually Existing Reference Naturalizable? Markus S. STEPANIANS: Russells Kritik an Meinongs Begriff des Annahmeschlusses. Nenad MIŠ_EVI_: Imagination and Necessity. R.D. ROLLINGER: Meinong on Perception: Two Questions Concerning Propositional Seeing. Wolfgang G. STOCK: Die Genese der Theorie der Vorstellungsproduktion der Grazer Schule. Rudolf HALLER: Über Meinongs Wissenschaftstheorie. Alfred SCHRAMM: Meinongs Wahrscheinlichkeit. Karl SCHUHMANN: Der Wertbegriff beim frühen Meinong. Wilhelm BAUMGARTNER: Wertpräsentation. Ursula ZEGLÉN: Meinong's Analysis of Lying. Seppo SAJAMA: Hitting Reality: France Veber's Concept of Zadevanje. Matja_ POTR_: Sensation According to Meinong and Veber. Róbert SOMOS: Zwei Schüler Brentanos: Ákos von Pauler und Meinong. J.C. NYÍRI: Palágyis Kritik an der Gegenstandstheorie. David M. ARMSTRONG: Reaction to Meinong. (shrink)

First published in 1923, _The Prospects of Industrial Civilization_ is considered the most ambitious of Bertrand Russell's works on modern society. It offers a rare glimpse into often-ignored subtleties of his political thought and in it he argues that industrialism is a threat to human freedom, since it is fundamentally linked with nationalism. His proposal for one government for the whole world as the ultimate solution, along with his argument that the global village and prevailing political democracy should be (...) its eventual results, is both provocative and thoroughly engaging. (shrink)

Natural languages differ from most formal languages in having a partial, rather than a total, semantic interpretation function; e.g., some noun phrases don't refer. The usual semantics for handling such noun phrases (e.g., Russell, Quine) require syntactic reform. The alternative presented here is semantic expansion, viz., enlarging the range of the interpretaion function to make it total. A specific ontology based on Meinong's Theory of Objects, which can serve as domain on interpretation, is suggested, and related to the work (...) of Castaneda, Frege, Katz and Fodor, Parsons, and Scott. (shrink)

This book offers a comprehensive primer for the study of intensionality. It explores and assesses those key theories of intensionality which have been developed in the twentieth and early twenty-first centuries. Each of the examined theories is tested as to whether it can account for the problems associated with the intersubstitution salva veritate of co-extensional expressions, and existential generalisation. All of these theories are subsequently compared so as to determine which of them comes closest to successfully solving these problems. The (...) book examines four kinds of intensionalist approaches: the Fregean approach ; the possible-worlds approaches of Carnap, Montague and Cresswell; the theory of properties relations and propositions devised by Bealer; and the Meinongian approaches put forward by Zalta and Priest. The book also proposes an alternative to intensionalism: sententialism. Sententialists argue that the problems of intensionality could be solved by appealing to linguistic items rather than intensional entities. Drawing on the works of Quine, Davidson, Scheffler and R. M. Martin, it explores the viability and value of sententialism as an alternative to intensionalism. (shrink)

BackgroundChronic kidney disease is a significant cause of global deaths. Those who progress to end-stage kidney disease often commence dialysis as a life-extending treatment. For cognitively impaired patients, the decision as to whether they commence dialysis will fall to someone else. This scoping review was conducted to map existing literature pertaining to how decisions about dialysis are and should be made with, for, and on behalf of adult patients who lack decision-making capacity. In doing so, it forms the basis of (...) a larger body of work that is exploring how these decisions ought to be made.MethodsTo identify relevant papers, searches were conducted on Ovid MEDLINE(R), Embase, PsychINFO, The Cochrane Library, and Web of Science. Inclusion criteria were then applied, requiring that papers: report on empirical studies about how decisions about dialysis are made and/or discuss how decisions about dialysis should be made with, for, and on behalf of adult patients who lack decision-making capacity; be published from 1961 onwards; and be published in English. This resulted in 27 papers eligible for inclusion.ResultsOf note, the majority of papers originated in the United States. There was wide variation across the included papers. Extracted data were grouped under the following themes: involving various parties (patient involvement, family dominance, and wider communication); objectivity about care options (including difficulties with family detachment); cultural sensitivity; medical versus non-medical factors; managing nonadherent patients; and the role and prevalence of substituted judgement. The literature shows that there is inconsistency in the principles and processes surrounding decisions made about dialysis with, for, and on behalf of adult patients who lack decision-making capacity.ConclusionsThis scoping review demonstrates that there is significant variation in both the practice and theory of dialysis decision making with, for, and on behalf of cognitively impaired adult patients. Complexity arises in considering who should get a say, how influential their say should be in a decision, and what factors are most relevant to the decision. A lack of up-to-date literature exploring this issue is highlighted, with this scoping review providing a useful groundwork from which further research can be undertaken. (shrink)

Natural languages differ from most formal languages in having a partial, rather than a total, semantic interpretation function; e.g., some noun phrases don't refer. The usual semantics for handling such noun phrases (e.g., Russell, Quine) require syntactic reform. The alternative presented here is semantic expansion, viz., enlarging the range of the interpretaion function to make it total. A specific ontology based on Meinong's Theory of Objects, which can serve as domain on interpretation, is suggested, and related to the work (...) of Castaneda, Frege, Katz and Fodor, Parsons, and Scott. (shrink)

The paper explores the view that in mathematics, in particular where the infinite is involved, the application of classical logic to statements involving the infinite cannot be taken for granted. L. E. J. Brouwer’s well-known rejection of classical logic is sketched, and the views of David Hilbert and especially Hermann Weyl, both of whom used classical logic in their mathematical practice, are explored. We inquire whether arguments for a critical view can be found that are independent of constructivist premises and (...) consider the entanglement of logic and mathematics. This offers a convincing case regarding second-order logic, but for first-order logic, it is not so clear. Still, we ask whether we understand the application of logic to the higher infinite better than we understand the higher infinite itself. (shrink)

. The truth conditions that Aristotle attributes to the propositions making up the traditional square of opposition have as a consequence that a particular affirmative proposition such as ‘Some A is not B’ is true if there are no Bs. Although a different convention than the modern one, this assumption remained part of centuries of work in logic that was coherent and logically fruitful.

Presenting key texts in and about pragmatism, this collection of essays explores pragmatism's origins, applications, and weaknesses, as well as its remarkable versatility as an approach not only to issues of truth and knowledge, but to ethics and social philosophy, literature, law, aesthetics, religion, and education. Exploring a wide range of work on topics spanning from the birth of pragmatism in nineteenth century America, to its contemporary revival as an international and multi-disciplinary phenomenon, the collection: * is international in scope, (...) covering a wide range of sources, including key American pragmatists such as Nelson Goodman and Morton White * includes key articles on the contemporary neopragmatism revival * considers pragmatism's influences across disciplines * presents newly translated papers. With an impressive breadth and range of content, the set also includes a both a general introduction and introductions to each volume by the editor, a chronological table of contents, and a full index to provide a valuable and unique research resource for student and scholar alike. (shrink)