In this paper we introduce the Wholeness Axiom , which asserts that there is a nontrivial elementary embedding from V to itself. We formalize the axiom in the language {∈, j } , adding to the usual axioms of ZFC all instances of Separation, but no instance of Replacement, for j -formulas, as well as axioms that ensure that j is a nontrivial elementary embedding from the universe to itself. We show that WA has consistency strength strictly between I 3 (...) and the existence of a cardinal that is super- n -huge for every n . ZFC + WA is used as a background theory for studying generalizations of Laver sequences. We define the notion of Laver sequence for general classes E consisting of elementary embeddings of the form i :V β → M , where M is transitive, and use five globally defined large cardinal notions – strong, supercompact, extendible, super-almost-huge, superhuge – for examples and special cases of the main results. Assuming WA at the beginning, and eventually refining the hypothesis as far as possible, we prove the existence of a strong form of Laver sequence for a broad range of classes E that include the five large cardinal types mentioned. We show that if κ is globally superstrong, if E is Laver-closed at beth fixed points, and if there are superstrong embeddings i with critical point κ and arbitrarily large targets such that E is weakly compatible with i , then our standard constructions are E -Laver at κ . , there is an extendible Laver sequence at κ .) In addition, in most cases our Laver sequences can be made special if E is upward λ -closed for sufficiently many λ. (shrink)

Versions of Laver sequences are known to exist for supercompact and strong cardinals. Assuming very strong axioms of infinity, Laver sequences can be constructed for virtually any globally defined large cardinal not weaker than a strong cardinal; indeed, under strong hypotheses, Laver sequences can be constructed for virtually any regular class of embeddings. We show here that if there is a regular class of embeddings with critical point κ, and there is an inaccessible above κ, then it is consistent for (...) there to be a regular class that admits no Laver sequence. We also show that extendible cardinals are Laver-generating, i.e., that assuming only that κ is extendible, there is an extendible Laver sequence at κ. We use the method of proof to answer a question about Laver-closure of extendible cardinals at inaccessibles. Finally, we consider Laver sequences for super-almost-huge cardinals. Assuming slightly more than super-almost-hugeness, we show that there are super-almost-huge Laver sequences, improving the previously known upper bound for such Laver sequences. We also describe conditions under which the canonical construction of a Laver sequence fails for super-almost-huge cardinals. (shrink)

In 1970, K. Kunen, working in the context of Kelley–Morse set theory, showed that the existence of a nontrivial elementary embedding j:V→V is inconsistent. In this paper, we give a finer analysis of the implications of his result for embeddings V→V relative to models of ZFC. We do this by working in the extended language , using as axioms all the usual axioms of ZFC , along with an axiom schema that asserts that j is a nontrivial elementary embedding. Without (...) additional axiomatic assumptions on j, we show that that the resulting theory is weaker than an ω-Erdös cardinal, but stronger than n-ineffables. We show that natural models of ZFC+BTEE give rise to Schindler’s remarkable cardinals. The approach to inconsistency from ZFC+BTEE forks into two paths: extensions of ZFC+BTEE+Cofinal Axiom and ZFC+BTEE+¬Cofinal Axiom, where Cofinal Axiom asserts that the critical sequence is cofinal in the ordinals. We describe near-minimal inconsistent extensions of each of these theories. The path toward inconsistency from ZFC+BTEE+¬Cofinal Axiom is paved with a sequence of theories of increasing large cardinal strength. Indeed, the extensions of the theory ZFC +“j is a nontrivial elementary embedding” form a hierarchy of axioms, ranging in strength from Con to the existence of a cardinal that is super-n-huge for every n, to inconsistency. This hierarchy is parallel to the usual hierarchy of large cardinal axioms, and can be used in the same way. We also isolate several intermediate-strength axioms which, when added to ZFC+BTEE, produce theories having strengths in the vicinity of a measurable cardinal of high Mitchell order, a strong cardinal, ω Woodin cardinals, and n-huge cardinals. We also determine precisely which combinations of axioms, of the form result in inconsistency. (shrink)

The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended language $\{\in,j\}$ , and that asserts the existence of a nontrivial elementary embedding $j:V\to V$ . The well-known inconsistency proofs are avoided by omitting from the schema all instances of Replacement for j-formulas. We show that the theory ZFC + V = HOD + WA is consistent relative to the existence of an $I_1$ embedding. This answers a question about the (...) existence of Laver sequences for regular classes of set embeddings: Assuming there is an $I_1$ -embedding, there is a transitive model of ZFC +WA + “there is a regular class of embeddings that admits no Laver sequence.”. (shrink)

We suggest a new approach for addressing the problem of establishing an axiomatic foundation for large cardinals. An axiom asserting the existence of a large cardinal can naturally be viewed as a strong Axiom of Infinity. However, it has not been clear on the basis of our knowledge of ω itself, or of generally agreed upon intuitions about the true nature of the mathematical universe, what the right strengthening of the Axiom of Infinity is—which large cardinals ought to be derivable? (...) It was shown in the 1960s by Lawvere that the existence of an infinite set is equivalent to the existence of a certain kind of structure-preserving transformation from V to itself, not isomorphic to the identity. We use Lawvere's transformation, rather than ω, as a starting point for a reasonably natural sequence of strengthenings and refinements, leading to a proposed strong Axiom of Infinity. A first refinement was discussed in later work by Trnková—Blass, showing that if the preservation properties of Lawvere's tranformation are strengthened to the point of requiring it to be an exact functor , such a transformation is provably equivalent to the existence of a measurable cardinal. We propose to push the preservation properties as far as possible, short of inconsistency. The resulting transformation V→V is strong enough to account for virtually all large cardinals, but is at the same time a natural generalization of an assertion about transformations V→V known to be equivalent to the Axiom of Infinity. (shrink)

We describe a fairly general procedure for preserving I3 embeddings j: Vλ → Vλ via λ-stage reverse Easton iterated forcings. We use this method to prove that, assuming the consistency of an I3 embedding, V = HOD is consistent with the theory ZFC + WA where WA is an axiom schema in the language {∈, j} asserting a strong but not inconsistent form of “there is an elementary embedding V → V”. This improves upon an earlier result in which consistency (...) was established assuming an I1 embedding. (shrink)

We improve results of Marczewski, Frankiewicz, Brown, and others comparing the σ-ideals of measure zero, meager, Marczewski measure zero, and completely Ramsey null sets; in particular, we remove CH from the hypothesis of many of Brown's constructions of sets lying in some of these ideals but not in others. We improve upon work of Marczewski by constructing, without CH, a nonmeasurable Marczewski measure zero set lacking the property of Baire. We extend our analysis of σ-ideals to include the completely Ramsey (...) null sets relative to a Ramsey ultrafilter and obtain all 32 possible examples of sets in some ideals and not others, some under the assumption of MA, but most in ZFC alone. We also improve upon the known constructions of a Marczewski measure zero set which is not Ramsey by using a set theoretic hypothesis which is weaker than those used by other authors. We give several consistency proofs: one concerning the relative sizes of the covering numbers for the meager sets and the completely Ramsey null sets; another concerning the size of non(CRU 0); and a third concerning the size of add(CRU 0). We also study those classes of perfect sets which are bases for the class of always first category sets. (shrink)

We describe a fairly general procedure for preserving I3 embeddings j: V λ → V λ via λ-stage reverse Easton iterated forcings. We use this method to prove that, assuming the consistency of an I3 embedding, V = HOD is consistent with the theory ZFC + WA where WA is an axiom schema in the language {∈, j} asserting a strong but not inconsistent form of “there is an elementary embedding V → V”. This improves upon an earlier result in (...) which consistency was established assuming an I1 embedding. (shrink)

In this paper I shall focus on Castaneda's notion of quasi-indicators and I shall defend the following theses: (i) Essential indexicals (‘I’, ‘here’ and ‘now’) are intrinsically perspectival mechanisms of reference and, as such, they are not reducible to any other mechanism reference...

SummaryAgainst an externalist view popularized, among others, by Evans and McDowell I shall show fiat object‐dependent thoughts are psychologically spurious. This version of externalism is contrasted with the picture that thoughts are object‐independent. It is argued that object‐independent thoughts are perspectival and context‐sensitive and that these perspectival thoughts, unlike object‐dependent thoughts: deal with delusion in an intuitive and elegant way; support psychological generalizations in a straightforward way; do not need to be fully articulated and, as such, fit with an economical (...) rule governing our thinking activity. To state my point I shall mainly concentrate on perceptual thoughts and emphasize how they are contextually related to the external world. (shrink)

SummaryAgainst an externalist view popularized, among others, by Evans and McDowell I shall show fiat object‐dependent thoughts are psychologically spurious. This version of externalism is contrasted with the picture that thoughts are object‐independent. It is argued that object‐independent thoughts are perspectival and context‐sensitive and that these perspectival thoughts, unlike object‐dependent thoughts: deal with delusion in an intuitive and elegant way; support psychological generalizations in a straightforward way; do not need to be fully articulated and, as such, fit with an economical (...) rule governing our thinking activity. To state my point I shall mainly concentrate on perceptual thoughts and emphasize how they are contextually related to the external world. (shrink)

We defend the view that an indexical uttered by an actor works on the model of deferred reference. If it defers to a character which does not exist, it is an empty term, just as‘Hamlet’and‘Ophelia’are. The utterance in which it appears does not express a proposition and thus lacks a truth value. We advocate an ontologically parsimonious, anti‐realist, position. We show how the notion of truth in our use and understanding of indexicals as they appear within a fiction is not (...) a central issue. We claim that our use and understanding of indexicals rests on the fact that their cognitive contribution is not exhausted by their semantic contribution. (shrink)

According to proponents of the continuity hypothesis, metaphors represent one end of a spectrum of linguistic phenomena, which includes various forms of loosening/broadening, such as category extensions and approximations, as well as hyperbolic interpretations. The continuity hypothesis is used to establish that the inferences derived from the set of linguistic expressions mentioned above result from the same or nearly similar pragmatic processes. In this paper, we want to challenge that particular aspect of the continuity hypothesis. We do so based on (...) considerations and analysis of an understudied linguistic phenomenon that we call the metaphorical uses of proper names (MPNs). We first explain how MPNs represent a unique linguistic class distinguishable from, for example, nicknames. In addition, we offer some remarks on how MPNs can be understood against the background of current debates between referentialists and predicativists about names. Our discussion leads us to conclude that MPNs are categorically different from literal interpretations of proper names. We spell out the consequences that the results of our analysis have for the continuity hypothesis. (shrink)

In some previous work, I tried to give a concept-based account of the nature of our entitlement to certain very basic inferences (see the papers in Part III of Boghossian 2008b). In this previous work, I took it for granted, along with many other philosophers, that we understood well enough what it is for a person to infer. In this paper, I turn to thinking about the nature of inference itself. This topic is of great interest in its own right (...) and surprisingly understudied by philosophers. A correct understanding of inference promises to shed light on a number of important topics. In particular, it threatens to undermine the sort of concept-based story about entitlement to which I had previously been attracted. (shrink)

Eliminative materialism is the thesis that our common-sense conception of psychological phenomena constitutes a radically false theory, a theory so fundamentally defective that both the principles and the ontology of that theory will eventually be displaced, rather than smoothly reduced, by completed neuroscience. Our mutual understanding and even our introspection may then be reconstituted within the conceptual framework of completed neuroscience, a theory we may expect to be more powerful by far than the common-sense psychology it displaces, and more substantially (...) integrated within physical science generally. My purpose in this paper is to explore these projections, especially as they bear on (1) the principal elements of common-sense psychology: the propositional attitudes (beliefs, desires, etc.), and (2) the conception of rationality in which these elements figure. (shrink)

Whilst it may seem strange to ask to whom “I” refers, we show that there are occasionswhen it is not always obvious. In demonstratingthis we challenge Kaplan's assumptionthat the utterer, agent and referent of “I” arealways the same person.We begin by presenting what weregard to be the received view about indexicalreference popularized by David Kaplan in hisinfluential 1972 “Demonstratives” before goingon, in section 2, to discuss Sidelle'sanswering machine paradox which may be thoughtto threaten this view, and his deferredutterance method of (...) resolving this puzzle. Insection 3 we introduce a novel version of theanswering machine paradox which suggests that,in certain cases, Kaplan's identification ofutterer, agent and referent of “I” breaks down.In the fourth section we go on to consider arecent revision of Kaplan's picture by Predelliwhich appeals to the intentions of the utterer,before arguing that this picture is committedto unacceptable consequences and, therefore,should be avoided if possible. Finally, insection 5, we present a new revision ofKaplan's account which retains much of thespirit of his original proposal whilst offeringa intuitively acceptable way to explain all ofthe apparently problematic data. In doing so,we also show how this picture is able toexplain the scenario which motivated Predelli'saccount without appealing to speakerintentions. (shrink)

Summary The present work focuses on the transformations of the psychotherapeutic field through the relationship dynamics which occur within it. The first part of this article starts with a brief outline of the Gestalt psychological understanding of the field concept, also in its application to the psychotherapeutic situation, followed by a brief review of the introduction of the field concept into the psychoanalytic theory formation. After this, the first author first presents the theoretical concept underlying a new approach he has (...) developed for observing the relationship dynamics in psychotherapy. Mirroring a formation of both psychoanalytic and Gestalt theory of the main author, this new approach is based on the combination of psychoanalytic and Gestalt psychological concepts. According to the clinical experience and insights of the author, the phenomenological and relational approach of Gestalt theory fits well with the psychoanalytic approach; on this basis, a criterion for recording the progress of therapy can be developed. This criterion is the phenomenology of the development of the qualities of the relationships of the client, as they become visible in his dream narrations and the subsequent associations in the analysis room and continue to develop during the session and the further course of therapy. The relationship dynamics in the dream narration is thus compared with those which develop in the course of the subsequent associations. This is demonstrated and further elaborated in the second part of this article on the basis of a clinical case. The clinical example shows how the relationship dynamics develop in this sense in the individual therapy sessions and over a longer course of therapy. The associated transformations of the therapeutic field give a good indication of the progress of therapy. The main author gained such insights into the transformations of the therapeutic field and the progression of therapy, which are visible in the course of therapy, from the careful application of the criterion “MDAC of relational dynamics”. In the specific case, there was also a high degree of correspondence between the results of the application of this phenomenological criterion and the empirical evidence of the symptom questionnaire, a self-report measure requested by the patient himself during the course of the therapy. (shrink)

Este ensaio tem como objetivo afirmar a leitura e a escrita enquanto processo ativo tradutório, por meio da reimaginação do Texto de Partida As cidades invisíveis, redigido em 1972 pelo autor italiano Ítalo Calvino. O ensaio é tecido mediante a noção de fragmentos, tal como entendido por Tavares, em que a escrita se constitui como uma experimentação do pensamento. Toma como ponto de partida as pistas deixadas pelo viajante Marco Polo, na obra de Calvino, a qual foi lida e reinventada (...) pelos acadêmicos do Curso de Pedagogia de uma Instituição de Ensino Superior localizada no interior do Rio Grande do Sul. Um Roteiro de Procedimentos Escrileitores – escritura e leitura – das Cidades de Calvino foi disponibilizado aos estudantes, tendo como proposição mostrar nove regras, cujo objetivo consistiu em servir à operação tradutório-inventiva. A partir delas, os estudantes arriscaram uma leitura ativa e uma escritura viva, ou seja, uma escritura tradutória, que não visa à recuperação literal do texto, mas privilegia uma escrileitura inventiva e traduções-reinvenções. Como aporte teórico, o texto aproxima-se do pensamento da diferença, de Roland Barthes, de Gilles Deleuze, além das teorizações da tradução literária propostas por Haroldo de Campos. Trata-se de experimentar a prática da leitura e o ensaio da escrita gerando novas interpretações ao Texto de Partida. Nesse sentido, ler-e-escrever configuram-se como uma prática aberta, jamais definitiva e tampouco estática. Em síntese, o texto propõe defender que os Textos de Partida são sempre fisgados pelos processos tradutórios e, por isso, novamente reinventados via leitura e escrita em Textos de Chegada. Palavras-chave: Tradução. Recriação. Pedagogia. Educação. (shrink)

Eros Corazza presents a fascinating investigation of the role that indexicals play in our thought. Indexicality is crucial to the understanding of such puzzling issues as the nature of the self, the nature of perception, social interaction, psychological pathologies, and psychological development. Corazza draws on work from philosophy, linguistics, and psychology to illuminate this key aspect of the relation between mind and world. By highlighting how indexical thoughts are irreducible and intrinsically perspectival, Corazza shows how we can (...) depict someone else's indexical thought from a third-person perspective. The phenomenon of quasi-indexicality is introduced here: to represent Jane saying, "I am prosperous", we use what Castañeda termed a quasi-indicator in a report of the form "Jane said that she is prosperous". Corazza argues that quasi-indicators play such an important role in our linguistic, social, and psychological life that they have a cognitive primacy over other mechanisms of reference. Quasi-indexicality also emerges as a key notion when we come to consider our ability to understand other minds. Corazza argues that indexicality and quasi-indexicality are two sides of the same coin, best understood within the framework of direct reference. (shrink)

Summary The present work focuses on the transformations of the psychotherapeutic field through the relationship dynamics that occur within it. The first part of this article starts with a brief outline of the Gestalt psychological understanding of the field concept, also in its application to the psychotherapeutic situation, followed by a brief review of the introduction of the field concept into the psychoanalytic theory formation. After this, the first author first presents the theoretical concept underlying a new approach he has (...) developed for observing the relationship dynamics in psychotherapy. Mirroring a formation both psychoanalytic and gestaltic of the main author, this new approach is based on the combination of psychoanalytic and Gestalt psychological concepts. According to the clinical experience and insights of the author, the phenomenological and relational approach of Gestalt theory fits well with the psychoanalytic approach; on this basis, a criterion for recording the progress of therapy can be developed. This criterion is the phenomenology of the development of the qualities of the relationships of the client, as they become visible in his dream narrations and the subsequent associations in the analysis room, and continue to develop during the session and the further course of therapy. The relationship dynamics in the dream narration is thus compared with those that develop in the course of the subsequent associations. This is demonstrated and further elaborated in the second part of this paper on the basis of a clinical case. The clinical example shows how the relationship dynamics develop in this sense in the individual therapy sessions and over a longer course of therapy. The associated transformations of the therapeutic field give a good indication of the progress of therapy. The main author gained such insights into the transformations of the therapeutic field and the progression of therapy, which are visible in the course of therapy, from the careful application of the criterion “manifest dream/associations comparison of relational dynamics”. In the specific case, there was also a high degree of correspondence between the results of the application of this phenomenological criterion and the empirical evidence of the symptom questionnaire, a self-report measure requested by the patient himself during the course of the therapy. (shrink)

Dieses historische Buch kann zahlreiche Tippfehler und fehlende Textpassagen aufweisen. Kaufer konnen in der Regel eine kostenlose eingescannte Kopie des originalen Buches vom Verleger herunterladen (ohne Tippfehler). Ohne Indizes. Nicht dargestellt. 1910 edition. Auszug:...endliche als durch sie erzeugt; oder diese in jener involviert und aus ihr sich evolvierend. Der wahre Erzeuger der endlichen Grosse ist nicht die unendlichkleine" Grosse (das Unendlichkleine ware dem Grossenwert nach vielmehr Null), sondern es ist das Gesetz der Grosse (als Veranderlicher), das man sich nun wie (...) in einen Punkt zusammengezogen, d. h. fur den einzelnen Punkt ausgedruckt, oder an einer endlichen Erstreckung sich darstellend denken kann, das aber dem letzten Sachgehalt nach dasselbe ist fur den Punkt und die endliche Erstreckung, wenn es auch in Bezug auf beide verschiedene, im allgemeinen auseinander ableitbare Ausdrucke erhalten muss. Da aber die endliche Grosse uberhaupt von Punkt zu Punkt entstehend (d. h. veranderlich) gedacht wird, so ist insofern der punktuelle, d. h. infinitesimale Ausdruck der fundamentale, aus dem der extensionale gleichsam erst hervorwachst. Die Differenz entsteht eben von der Null an; nicht aus ihr; aus Null wird keine extensive Grosse; wohl aber von der Null, d. h. dem Nichtsein dessen, was werden soll, oder ganz schlicht1) vom Ausgangs wert an; woraus? Aus dem Gesetz; eine andere Antwort ist nicht zu geben und nicht zu verlangen. Durch dies Gesetz aber ist die Grosse als Eines, Identisches, im Unterschied von den sukzessiven Grossenwerten, also in ihrem Gattungsausdruck definiert. i) Vgl. oben S. 122. Fragt man also: wie soll aus der Null gewordenen, verschwundenen" Grosse die endliche Grosse wiederentstehen? so ist zu antworten: die Grosse zwar (yuantitas). (shrink)

A study of how syntax relates to meaning by a leader of the new generation of philosopher-linguists.

Recreational Drugs European Network (ReDNet) project aims to use the Psychonaut Web Mapping Project database (Psychonaut Web Mapping Group, 2009) containing novel psychoactive compounds usually not mentioned in the scientific literature and thus unknown to clinicians as a unique source of information. The database will be used to develop an integrated ICT prevention approach targeted at vulnerable individuals and focused on novel synthetic and herbal compounds and combinations. Particular care will be taken in keeping the health professionals working directly with (...) young people showing problematic behaviors regularly updated in terms of novel compounds and combinations as well. A user-friendly project website will be developed aimed primarily at delivering the information/prevention approaches, but will also be a way of communicating with project partners and relevant stakeholders (e.g. thematic forum facilities, instant messages, blogs, video chat, wikiblog, newsletters distributed via mailing list). The website will support various ICT prevention tools, including an SMS alert service. Different areas and sections will be aimed specifically at the different target groups. -/- . (shrink)

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox, a challenge to 'classical' mathematics from a world-famous mathematician, a new foundational school, and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection (...) brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field. (shrink)

In this chapter, we analyze the relationships between the Internet and its users in terms of situated cognition theory. We first argue that the Internet is a new kind of cognitive ecology, providing almost constant access to a vast amount of digital information that is increasingly more integrated into our cognitive routines. We then briefly introduce situated cognition theory and its species of embedded, embodied, extended, distributed and collective cognition. Having thus set the stage, we begin by taking an embedded (...) cognition view and analyze how the Internet aids certain cognitive tasks. After that, we conceptualize how the Internet enables new kinds of embodied interaction, extends certain aspects of our embodiment, and examine how wearable technologies that monitor physiological, behavioral and contextual states transform the embodied self. On the basis of the degree of cognitive integration between a user and Internet resource, we then look at how and when the Internet extends our cognitive processes. We end this chapter with a discussion of distributed and collective cognition as facilitated by the Internet. (shrink)

In a recent book, Jeffrey King (King 2001) argues that complexdemonstratives, i.e., noun phrases of the form `this/that F, are not singular terms. As such,they are not devices of direct reference contributing the referent to the proposition expressed.In this essay I challenge King's position and show how a direct reference view can handle the datahe proposes in favor of the quantificational account. I argue that when a complex demonstrativecannot be interpreted as a singular term, it is best understood as a (...) case of deferredreference – in which case it should be viewed as an anaphora inheriting its value from a quantifiedterm – or as an emphatic description. (shrink)

It is argued that, in order to account for examples where the indexicals `now' and `here' do not refer to the time and location of the utterance, we do not have to assume (pace Quentin Smith) that they have different characters (reference-fixing rules), governed by a single metarule or metacharacter. The traditional, the fixed character view is defended: `now' and `here' always refer to the time and location of the utterance. It is shown that when their referent does not correspond (...) to the time and/or location of the utterance, `now' and `here' work in an anaphoric way, inheriting their reference from another noun phrase. The latter may be explicit or implicit in the discourse. It is also shown that `now' and `here' can inherit their reference from a presupposed or tacit reference. In that case, they are coreferential with what will be labeled a `tacit initiator'. This anaphoric interpretation has the merit of fitting within the Kaplanian distinction between pure indexicals (`now', `here', `today', etc.) and demonstratives (`this', `that', `she', etc.). (shrink)

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, (...) and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field. (shrink)

Supporters of G.W.F. Hegel's philosophy have largely shied away from relating his logic to modern symbolic or mathematical approaches. While it has predominantly been the non-Greek discipline of algebra that has informed modern mathematical logic, philosopher Paul Redding argues that the approaches of Plato and Aristotle to logic were deeply shaped by the arithmetic and geometry of classical Greek culture. And by ignoring the fact that Hegel's logic also has this deep mathematical dimension, conventional Hegelians have missed some of (...) Hegel's greatest insights. In Conceptual Harmonies, Redding develops an account of Hegel's logic against a classical and modern historical background that is rarely considered. He stresses Hegel's attention to the Platonic background of Aristotle's original syllogistic and beyond. He then links these Platonic elements to Leibniz's modern revitalization of the logical tradition and then to new forms of algebraic geometry emerging in Hegel's lifetime. Redding thereby reestablishes aspects of Hegel's philosophy that are essential if Hegel is to be taken as a thinker relevant not only to contemporary philosophy, but also to current philosophical conceptions of logic. (shrink)

The first study of this ancient text in over 70 years, Rituals of the Way explores how the Xunzi influenced Confucianism and other Chinese philosophies through its emphasis on "the Way.".

For over twenty years, Paul Weithman has explored the thought of John Rawls to ask how liberalism can secure the principled allegiance of those people whom Rawls called 'citizens of faith'. This volume brings together ten of his major essays, which reflect on the task and political character of political philosophy, the ways in which liberalism does and does not privatize religion, the role of liberal legitimacy in Rawls's theory, and the requirements of public reason. The essays reveal Rawls (...) as a thinker deeply engaged with political and existential questions that trouble citizens of faith, and explore how - in firm opposition to political realism - he tries to show that the possibility of liberal democracy and the natural goodness of humanity are objects of reasonable faith. The volume will be of interest to political philosophers, political theorists, moral theologians, and religious ethicists. (shrink)

In this paper I challenge the common wisdom (see Dummett and Davidson) that sentences are the minimal units with which one can perform a speech act or make a move in the language game. I thus sit with Perry and Stainton in arguing that subsentences can be used to perform full-fledged speech acts. In my discussion I assume the traditional framework which distinguishes between the proposition expressed and the thought or mental state (possibly a sentence in Mentalese) one comes to (...) grasp when using/understanding an utterance (or sentence-in-a-context) expressing a proposition. Unlike Stainton, I will argue that the proposition expressed by a subsentential assertion and its corresponding thought are not the end product of a pragmatic process of free enrichment. I shall defend the view that a thought may concern something without the thinker having to represent that very thing. This should help us to resist the view that with the utterance of a subsentence enrichment is mandatory. I will further argue that subsentences and their corresponding thoughts are situated. Because of that we can successfully interact and engage in joint ventures using subsentences and be guided by thoughts without having to enrich them. The fact that the actors’ unenriched thoughts are co-situated may suffice to explain the positive outcome of their joint project. Last but not least, I will also show how the picture I propose gains further support by taking on board Perry’s distinction between reflexive truth conditions and incremental truth conditions (or official content). Since competent speakers can grasp an utterance’s reflexive truth conditions without having to grasp its official content (roughly, the proposition expressed) they can successfully interact without their thoughts having to undergo a process of free enrichment. Moreover, if I’m right in arguing that an utterance’s reflexive truth conditions are the best tool to classify the semantic features of one’s mental state (or sentence in Mentalese), we can further explain mental causation and linguistic communication without appealing to free enrichment. (shrink)

After discussing some difficulties that contextualism and minimalism face, this paper presents a new account of the linguistic exploitation of context, situationalism. Unlike the former accounts, situationalism captures the idea that the main intuitions underlying the debate concern not the identity of propositions expressed but rather how truth-values are situation-dependent. The truth-value of an utterance depends on the situation in which the proposition expressed is evaluated. Hence, like in minimalism, the proposition expressed can be truth-evaluable without being enriched or expanded. (...) Along with contextualism, it is argued that an utterance’s truth-value is context dependent. But, unlike contextualism and minimalism, situationalism embraces a form of relativism in so far as it maintains that semantic content must be evaluated vis-à-vis a given situation and, therefore, that a proposition cannot be said to be true/false eternally. (shrink)

It is argued that the pronouns `she' and `he' are disguised complexdemonstratives of the form `that female/male'. Three theories ofcomplex demonstratives are examined and shown to be committed to theview that `s/he' turns out to be an empty term when used to refer toa hermaphrodite. A fourth theory of complex demonstratives, one thatis hermaphrodite friendly, is proposed. It maintains that complexdemonstratives such as `that female/male' and the pronoun `s/he' can succeed in referring to someone independently of his or her gender.This (...) theory incorporates: (i) a multiple proposition view, i.e., theview that an utterance of a sentence containing a complex demonstrativeexpresses two (or more) propositions, namely the background proposition(s)and the official one; (ii) that the referent of a complex demonstrativeis a component of the official proposition expressed whether it satisfiesthe nominal part of the demonstrative expression or not; (iii) that thenominal part of a complex demonstrative only affect the background proposition(s) and (iv) that the utterance inherits its truth-value onlyfrom the official proposition. (shrink)

According to the subset account of realization, a property, F, is realized by another property, G, whenever F is individuated by a non-empty proper subset of the causal powers by which G is individuated (and F is not a conjunctive property of which G is a conjunct). This account is especially attractive because it seems both to explain the way in which realized properties are nothing over and above their realizers, and to provide for the causal efficacy of realized properties. (...) It therefore seems to provide a way around the causal exclusion problem. There is reason to doubt, however, that the subset account can achieve both tasks. The problem arises when we look closely at the relation between properties and causal powers, specifically, at the idea that properties confer powers on the things that have them. If realizers are to be ontically prior to what they realize, then we must regard the conferral of powers by properties as a substantive relation of determination. This relation of conferral is at the heart of a kind of exclusion problem, analogous to the familiar causal exclusion problem. I argue that the subset account cannot adequately answer this new exclusion problem, and is for that reason ill-suited to be the backbone of a non-reductive physicalism. (shrink)

Although thinkers of the past might have started from presumptions of fundamental difference and inequality between (say) the genders, or people of different races, this is no longer the case. At least in mainstream political philosophy, we are all now presumed to be, in some fundamental sense, basic equals. Of course, what follows from this putative fact of basic equality remains enormously controversial: liberals, libertarians, conservatives, Marxists, republicans, and so on, continue to disagree vigorously with each other, despite all presupposing (...) some kind of basic equality. They may argue about who gets what, how much, and why, but the starting point - that all people are in some sense deserving of prima facie equal consideration - has become an axiom of our moral and political thinking. But why? Why are we basic equals? The trouble is that as soon as one asks for an explanation of this foundational premise, it begins to look shaky. After all, on any conceivable metric human beings are notably unequal, and often to striking degrees. Philosophers in this area tend to talk of equal worth, but often without trying to specify what exactly that means. Philosophically, basic equality is neither acceptable nor rejectable. It is not rejectable because we appear to be, as a matter of fact, profoundly committed to the truth of the claim that we are all one another's basic equals. But to the extent that there appear to be no philosophical arguments for believing in the truth of basic equality, it is not acceptable either. The aim of this book is to try and show why basic equality is acceptable. To do so, however, it will also contend that we need to approach the question rather differently to how it has mostly been handled so far. What's required is an exercise in what Bernard Williams called 'impure philosophy': it must include insights from other areas of human intellectual endeavour, whether psychology and history or even what we learn from how we go about practicing basic equality in our collective lives. (shrink)

Describing his creative process, David Bowie stated: “I’ll take articles out of newspapers, poems that I’ve written, pieces of other people’s books, and put them all into this little warehouse, thi...

Free Will & The Tragic Predicament : Making Sense of Williams -/- The discussion in this paper aims to make better sense of free will and moral responsibility by way of making sense of Bernard Williams’ significant and substantial contribution to this subject. Williams’ fundamental objective is to vindicate moral responsibility by way of freeing it from the distortions and misrepresentations imposed on it by “the morality system”. What Williams rejects, in particular, are the efforts of “morality” to further “deepen” (...) or “refine” the notion of the voluntary, with a view to securing “ultimate justice”. It is these aims and aspirations, he argues, that take us to the precipice of scepticism. In Shame and Necessity (1993) Williams advances a vindicatory genealogy that unmasks the “illusions” and “fantasies” of our current ethical ideas as they relate to agency and responsibility. What we are then left with is the task of “recasting our ethical conceptions” . It is here that Williams is especially insistent on the importance and value of historical consciousness and reflection. The role of our reflections about the Greeks and tragedy is precisely to show that in order to move forward, into the future, we need to first look back at where we have come from. The value of these “untimely” observations is that they provide us with alternatives and options that we might otherwise lack. What we discover, when we consider the Greeks, is their commitment to a “pessimism of strength” that rests on rejecting scepticism. It is this two-sided perspective on our ethical predicament that delivers a more truthful account of our human situation, one that will help us discard those illusions and fantasies of "morality" that we are “better off” without. An account of this kind refuses to accept an optimism that insists that any form of responsible ethical life must be one that is immune to the influence of luck and fate. This is the fundamental lesson that we can learn from the ancient Greeks and that Williams seeks to “recover” for us. (shrink)

It is argued that, contrary to appearances, description-names (e.g.: "The Roman Empire", "The Beatles", "The Holy Virgin",...) do conform to Millianism, i.e. the view that proper names are directly referential expressions, referring regardless of whether the relevant individual satisfies some associated description or not. However, description-names name and describe. Some arguments supporting this peculiarity and a logic to handle description-names are proposed. It will be shown that the best framework with which to accommodate description-names is a multiple-proposition theory, according to (...) which a given utterance may express several propositions. (shrink)

In combining a pluri‐propositionalist framework (Bach‐style) concerning alleged conventional implicatures, and a pluri‐propositionalist framework (Perry‐style) distinguishing various levels of content associated with a single utterance, I defend a Grice‐inspired model of communication. In so doing, I rely on the distinction between what is said, i.e. what is semantically encoded, and what is pragmatically implicated. I show how the notion of same‐saying plays a central role in dealing with problems pertaining to communication insofar as it permits us to posit a stability (...) of content among interlocutors. I also show how people can be classified as same‐sayers in different ways, viz. if they express the same (minimal) proposition/content or if they utter the same sentence. If A utters ‘I'm happy’ and B replies: ‘C said that too’, what B said can mean either that C said that A is happy—thus C and A expressed the same proposition—or that C utters the same words—they both utter ‘I'm happy’ and in so doing express different propositions, i.e. that A is happy and that C is happy respectively. (shrink)

In this paper, we put forward a position we call “situationalism” (or “situated minimalism”), which is a middle-ground view between minimalism and contextualism in recent philosophy of language. We focus on the notion of free enrichment, which first arose within contextualism as underlying the claim that what is said is typically enriched relative to the logical form of the uttered sentence. However, minimalism also acknowledges some process of pragmatic intrusion in its claim that what is thought and communicated is typically (...) enriched relative to what is said. We show that situationalism dispenses with free enrichment both at the level of what is said (proposition expressed) and of what is thought (mental level). According to situationalism, an alleged underdetermined utterance can, pace minimalism, be true in one situation while false in another, and two people using the same alleged underdetermined sentence can be characterized, pace contextualism, as having said the same thing. (shrink)

This is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann's classic treatise with this title. Fundamental non-classical features of quantum mechanics-indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entanglement, nonlocality-are explicated and analysed using the tools of operational quantum theory. The book is divided into four parts: 1. Mathematics provides a systematic exposition of the Hilbert space and (...) operator theoretic tools and relevant measure and integration theory leading to the Naimark and Stinespring dilation theorems; 2. Elements develops the basic concepts of quantum mechanics and measurement theory with a focus on the notion of approximate joint measurability; 3. Realisations offers in-depth studies of the fundamental observables of quantum mechanics and some of their measurement implementations; and 4. Foundations discusses a selection of foundational topics (quantum-classical contrast, Bell nonlocality, measurement limitations, measurement problem, operational axioms) from a measurement theoretic perspective. The book is addressed to physicists, mathematicians and philosophers of physics with an interest in the mathematical and conceptual foundations of quantum physics, specifically from the perspective of measurement theory. (shrink)