Georg Cantor's absolute infinity, the paradoxical Burali-Forti class Ω of all ordinals, is a monstrous non-entity for which being called a "class" is an undeserved dignity. This must be the ultimate vexation for mathematical philosophers who hold on to some residual sense of realism in set theory. By careful use of Ω, we can rescue Georg Cantor's 1899 "proof" sketch of the Well-Ordering Theorem––being generous, considering his declining health. We take the contrapositive of Cantor's suggestion (...) and add Zermelo's choice function. This results in a concise and uncomplicated proof of the Well-Ordering Theorem. (shrink)

Ortega y Gasset is known for his philosophy of life and his effort to propose an alternative to both realism and idealism. The goal of this article is to focus on an unfamiliar aspect of his thought. The focus will be given to Ortega’s interpretation of the advancements in modern mathematics in general and Cantor’s theory of transfinite numbers in particular. The main argument is that Ortega acknowledged the historical importance of the Cantor’s Set Theory, analyzed it and (...) articulated a response to it. In his writings he referred many times to the advancements in modern mathematics and argued that mathematics should be based on the intuition of counting. In response to Cantor’s mathematics Ortega presented what he defined as an ‘absolute positivism’. In this theory he did not mean to naturalize cognition or to follow the guidelines of the Comte’s positivism, on the contrary. His aim was to present an alternative to Cantor’s mathematics by claiming that mathematicians are allowed to deal only with objects that are immediately present and observable to intuition. Ortega argued that the infinite set cannot be present to the intuition and therefore there is no use to differentiate between cardinals of different infinite sets. (shrink)

Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty ordinal construction and his fundamental powerset description of the continuum, Cantor has also left to us his obsessive presumption that the universe of sets should be subjected to laws similar to those governing the set of natural numbers, including the universal principles (...) of cardinal comparability and well-ordering -- and implying an ordinal re-creation of the continuum. During the last hundred years, the mainstream set-theoretical research -- all insights and adjustments due to Kurt G\"odel's revolutionary insights and discoveries notwithstanding -- has compliantly centered its efforts on ad hoc axiomatizations of Cantor's intuitive transfinite design. We demonstrate here that the ontological and epistemic sustainability} of this design has been irremediably compromised by the underlying peremptory, Reductionist mindset of the XIXth century's ideology of science. (shrink)

The mathematician Georg Cantor strongly believed in the existence of actually infinite numbers and sets. Cantor’s “actualism” went against the Aristotelian tradition in metaphysics and mathematics. Under the pressures to defend his theory, his metaphysics changed from Spinozistic monism to Leibnizian voluntarist dualism. The factor motivating this change was two-fold: the desire to avoid antinomies associated with the notion of a universal collection and the desire to avoid the heresy of necessitarian pantheism. We document the changes in (...) Cantor’s thought with reference to his main philosophical-mathematical treatise, the Grundlagen (1883) as well as with reference to his article, “Über die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche” (“Concerning Various Perspectives on the Actual Infinite”) (1885). (shrink)

Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician (...) Georg Cantor (1845-1918) says that between the realm of the finite and the absolute infinite, there is an intermediate realm partaking in properties in a certain sense of both the finite and the infinite: the transfinite realm. Like the finite, the transfinite realm is a realm of mathematical objects, numbers, and knowledge. Like the absolute infinite, the transfinite is a form of infinity insofar as transfinite sets and numbers transcend any finite number. Echoing Cusanus and neo-Platonism, Cantor says that the transfinite sequence of all ordinals is a symbol of the absolutely infinite, that is, God. This paper considers how the doctrine of symbolism and the philosophers' different commitments to the laws of logic, especially the Law of Non-Contradiction (LNC), enables these thinkers to articulate a transcendental apophatic approach to divinity. (shrink)

Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician (...) Georg Cantor (1845-1918) says that between the realm of the finite and the absolute infinite, there is an intermediate realm partaking in properties in a certain sense of both the finite and the infinite: the transfinite realm. Like the finite, the transfinite realm is a realm of mathematical objects, numbers, and knowledge. Like the absolute infinite, the transfinite is a form of infinity insofar as transfinite sets and numbers transcend any finite number. Echoing Cusanus and neo-Platonism, Cantor says that the transfinite sequence of all ordinals is a symbol of the absolutely infinite, that is, God. Moreover, Cantor envisioned his transfinite set theory (Mengenlehre) as providing the analytical methods and techniques necessary for a comprehensive, organic, non-reductive description of nature, a Naturphilosophie. Thus Cantor’s novel mathematics is presented as part of a long tradition, to which Cusanus, Bruno, Spinoza, Leibniz and others belong, in which the infinity and infinite character of organic life forms is appreciated, and is in some sense a mirror or symbol of the divine. The doctrine of symbolism and their different approach to the laws of logic present in both the work of Cusanus and Cantor enables these thinkers to articulate a transcendental apophatic approach to divinity. (shrink)

What is so special and mysterious about the Continuum, this ancient, always topical, and alongside the concept of integers, most intuitively transparent and omnipresent conceptual and formal medium for mathematical constructions and the battle field of mathematical inquiries ? And why it resists the century long siege by best mathematical minds of all times committed to penetrate once and for all its set-theoretical enigma ? -/- The double-edged purpose of the present study is to save from the transfinite deadlock of (...) higher set theory the jewel of mathematical Continuum -- this genuine, even if mostly forgotten today raison d'etre of all set-theoretical enterprises to Infinity and beyond, from Georg Cantor to W. Hugh Woodin to Buzz Lightyear, by simultaneously exhibiting the limits and pitfalls of all old and new reductionist foundational approaches to mathematical truth: be it Cantor's or post-Cantorian Idealism, Brouwer's or post-Brouwerian Constructivism, Hilbert's or post-Hilbertian Formalism, Goedel's or post-Goedelian Platonism. -/- In the spirit of Zeno's paradoxes, but with the enormous historical advantage of hindsight, we claim that Cantor's set-theoretical methodology, powerful and reach in proof-theoretic and similar applications as it might be, is inherently limited by its epistemological framework of transfinite local causality, and neither can be held accountable for the properties of the Continuum already acquired through geometrical, analytical, and arithmetical studies, nor can it be used for an adequate, conceptually sensible, operationally workable, and axiomatically sustainable re-creation of the Continuum. -/- From a strictly mathematical point of view, this intrinsic limitation of the constative and explicative power of higher set theory finds its explanation in the identified in this study ultimate phenomenological obstacle to Cantor's transfinite construction, similar to topological obstacles in homotopy theory and theoretical physics: the entanglement capacity of the mathematical Continuum. (shrink)

The original purpose of the present study, 2011, started with a preprint «On the Probable Failure of the Uncountable Power Set Axiom», 1988, is to save from the transfinite deadlock of higher set theory the jewel of mathematical Continuum — this genuine, even if mostly forgotten today raison d’être of all traditional set-theoretical enterprises to Infinity and beyond, from Georg Cantor to David Hilbert to Kurt Gödel to W. Hugh Woodin to Buzz Lightyear.

The topic of a priori knowledge is approached through the theory of evidence. A shortcoming in traditional formulations of moderate rationalism and moderate empiricism is that they fail to explain why rational intuition and phenomenal experience count as basic sources of evidence. This explanatory gap is filled by modal reliabilism -- the theory that there is a qualified modal tie between basic sources of evidence and the truth. This tie to the truth is then explained by the theory of concept (...) possession: this tie is a consequence of what, by definition, it is to possess (i.e., to understand) one’s concepts. A corollary of the overall account is that the a priori disciplines (logic, mathematics, philosophy) can be largely autonomous from the empirical sciences. (shrink)

Functionalism would be mistaken if there existed a system of deviant relations (an “anti-mind”) that had the same functional roles as the standard mental relations. In this paper such a system is constructed, using “Quinean transformations” of the sort associated with Quine’s thesis of the indeterminacy of translation. For example, a mapping m from particularistic propositions (e.g., that there exists a rabbit) to universalistic propositions (that rabbithood is manifested). Using m, a deviant relation thinking* is defined: x thinks* p iff (...) x thinks m(p). Such deviant relations satisfy the commonly discussed functionalist psychological principles. Finally, a more complicated system of deviant relations is constructed, one satisfying sophisticated principles dealing with the self-conscious rational mind. (shrink)

Modal intuitions are not only the primary source of modal knowledge but also the primary source of modal error. An explanation of how modal error arises — and, in particular, how erroneous modal intuitions arise — is an essential part of a comprehensive theory of knowledge and evidence. This chapter begins with a summary of certain preliminaries: the phenomenology of intuitions, their fallibility, the nature of concept-understanding and its relationship to the reliability of intuitions, and so forth. It then identifies (...) two sources of modal error: the first has to do with the failure to distinguish between metaphysical possibility and various kinds of epistemic possibility; the second, with the local misunderstanding of one's concepts. The first source of error is widely misunderstood; the second source has not been discussed in philosophical literature. This source of modal error, and the potential to overcome it, has wide-ranging implications for philosophical method. The failure to understand these sources of modal error has recently led to sceptical accounts of intuition and modal error, which are, ultimately self-defeating. (shrink)

In this article I examine language used to define, express, and exploit “National Socialism”. These different uses vary in time and purpose, and need to be understood in context. The Nazis did not create much of the language most closely associated with National Socialism, but their use of certain language, symbols, and images has been so firmly established that we immediately recognize them even when partially spoken or indirectly referenced. This easy recognition, combined with the emotional charge of anger and (...) horror, lends itself to commercial and political exploitation. I discuss this with examples from scholarly publishing and current events, and also discuss possibilities for crowd manipulation made possible by political use of interactive social networks. (shrink)

This paper examines the nature of friendship and the nature of exploitation, and the intersection of the two phenomena. It argues that because vulnerability is an essential aspect of friendship, the possibility of exploitation is ineliminable in friendship. Considers how we might, nonetheless, reduce our exposure to unfair treatment in friendships.

A surprising feature of the White Rose anti-Nazi resistance pamphlets is their appeal to a foundational classical Chinese text, the Laozi (otherwise known as the Daodejing), to buttress their critique of fascism and authoritarianism. I argue that from the perspective of a 1942 educated readership, the act of quoting the Laozi functioned as a subtle and pointed nod to anti-fascist intellectuals in pre-war Germany, many of whom had interpreted the Laozi as an anti-authoritarian and pacifist text. To a sympathetic reader, (...) the Laozi therefore constituted an apt reference point for critiquing National Socialism. I then introduce a complication for this wartime reading of the Laozi from the perspective of its ambiguous reception in ancient Chinese political thought. I more specifically discuss an ancient line of interpretation of the Laozi that points in the direction of authoritarianism — in stark tension with the White Rose message of passive resistance and popular revolt. (shrink)

The phenomenology of a priori intuition is explored at length (where a priori intuition is taken to be not a form of belief but rather a form of seeming, specifically intellectual as opposed to sensory seeming). Various reductive accounts of intuition are criticized, and Humean empiricism (which, unlike radical empiricism, does admit analyticity intuitions as evidence) is shown to be epistemically self-defeating. This paper also recapitulates the defense of the thesis of the Autonomy and Authority of Philosophy given in the (...) author’s “A Priori Knowledge and the Scope of Philosophy” (Philosophical Studies, 1996). (shrink)

This study provides a unified theory of properties, relations, and propositions (PRPs). Two conceptions of PRPs have emerged in the history of philosophy. The author explores both of these traditional conceptions and shows how they can be captured by a single theory.

Past research has identified a number of asymmetries based on moral judgments. Beliefs about what a person values, whether a person is happy, whether a person has shown weakness of will, and whether a person deserves praise or blame seem to depend critically on whether participants themselves find the agent's behavior to be morally good or bad. To date, however, the origins of these asymmetries remain unknown. The present studies examine whether beliefs about an agent's “true self” explain these observed (...) asymmetries based on moral judgment. Using the identical materials from previous studies in this area, a series of five experiments indicate that people show a general tendency to conclude that deep inside every individual there is a “true self” calling him or her to behave in ways that are morally virtuous. In turn, this belief causes people to hold different intuitions about what the agent values, whether the agent is happy, whether he or she has shown weakness of will, and whether he or she deserves praise or blame. These results not only help to answer important questions about how people attribute various mental states to others; they also contribute to important theoretical debates regarding how moral values may shape our beliefs about phenomena that, on the surface, appear to be decidedly non-moral in nature. (shrink)

The paper begins with a clarification of the notions of intuition (and, in particular, modal intuition), modal error, conceivability, metaphysical possibility, and epistemic possibility. It is argued that two-dimensionalism is the wrong framework for modal epistemology and that a certain nonreductionist approach to the theory of concepts and propositions is required instead. Finally, there is an examination of moderate rationalism’s impact on modal arguments in the philosophy of mind -- for example, Yablo’s disembodiment argument and Chalmers’s zombie argument. A less (...) vulnerable style of modal argument is defended, which nevertheless wins the same anti-materialist conclusions sought by these other arguments. (shrink)

This paper provides a defense of two traditional theses: the Autonomy of Philosophy and the Authority of Philosophy. The first step is a defense of the evidential status of intuitions (intellectual seemings). Rival views (such as radical empiricism), which reject the evidential status of intuitions, are shown to be epistemically self-defeating. It is then argued that the only way to explain the evidential status of intuitions is to invoke modal reliabilism. This theory requires that intuitions have a certain qualified modal (...) tie to the truth. This result is then used as the basis of the defense of the Autonomy and Authority theses. The paper closes with a defense of the two theses against a potential threat from scientific essentialism. (shrink)

Radical empiricism is the view that a person's experiences (sensory and introspective), or a person's observations, constitute the person's evidence. This view leads to epistemic self-defeat. There are three arguments, concerning respectively: (1) epistemic starting points; (2) epistemic norms; (3) terms of epistemic appraisal. The source of self-defeat is traced to the fact that empiricism does not count a priori intuition as evidence (where a priori intuition is not a form of belief but rather a form of seeming, specifically intellectual (...) as opposed to sensory). Moderate rationalism, by contrast, avoids self-defeat. (shrink)

This paper constructs a model of metaphysical indeterminacy that can accommodate a kind of ‘deep’ worldly indeterminacy that arguably arises in quantum mechanics via the Kochen-Specker theorem, and that is incompatible with prominent theories of metaphysical indeterminacy such as that in Barnes and Williams (2011). We construct a variant of Barnes and Williams's theory that avoids this problem. Our version builds on situation semantics and uses incomplete, local situations rather than possible worlds to build a model. We evaluate the resulting (...) theory and contrast it with similar alternatives, concluding that our model successfully captures deep indeterminacy. (shrink)

Scientific essentialism is the view that some necessities can be known only with the aid of empirical science. The thesis of the paper is that scientific essentialism does not extend to the central questions of philosophy and that these questions can be answered a priori. The argument is that the evidence required for the defense of scientific essentialism is reliable only if the intuitions required by philosophy to answer its central questions is also reliable. Included is an outline of a (...) modal reliabilist theory of basic evidence and a concept-possession account of the reliability of a priori intuition. (shrink)

Recent work in philosophy of language has raised significant problems for the traditional theory of propositions, engendering serious skepticism about its general workability. These problems are, I believe, tied to fundamental misconceptions about how the theory should be developed. The goal of this paper is to show how to develop the traditional theory in a way which solves the problems and puts this skepticism to rest. The problems fall into two groups. The first has to do with reductionism, specifically attempts (...) to reduce propositions to extensional entities-either extensional functions or sets. The second group concerns problems of fine grained content-both traditional 'Cicero'/'Tully' puzzles and recent variations on them which confront scientific essentialism. After characterizing the problems, I outline a non-reductionist approach-the algebraic approach-which avoids the problems associated with reductionism. I then go on to show how the theory can incorporate non-Platonic (as well as Platonic) modes of presentation. When these are implemented nondescriptively, they yield the sort of fine-grained distinctions which have been eluding us. The paper closes by applying the theory to a cluster of remaining puzzles, including a pair of new puzzles facing scientific essentialism. (shrink)

The paper elaborates upon various points and arguments in the author’s “A Priori Knowledge and the Scope of Philosophy” (Philosophical Studies, 1993), in which the author defends the autonomy of philosophy from the empirical sciences. It provides, for example, an extended defense of the modal reliabilist theory of basic evidence, including a new argument against evolutionary explanations of the reliability of intuitions. It also contains a fuller discussion of how to neutralize the threat of scientific essentialism to the autonomy of (...) philosophy. (shrink)

Criticism and recommendations are very much welcome. Please don't hesitate to contact me with them. -/- .

It is argued that, because of scientific essentialism, two currently popular arguments against the mind-body identity thesis -- the multiple-realizability argument and the Nagel-Jackson knowledge argument -- are unsatisfactory as they stand and that their problems are incurable. It is then argued that a refutation of the identity thesis in its full generality can be achieved by weaving together two traditional Cartesian arguments -- the modal argument and the certainty argument. This argument establishes, not just the falsity of the identity (...) thesis, but also the metaphysical possibility of disembodiment. (shrink)

Presented here is an argument for the existence of universals. Like Church's translation- test argument, the argument turns on considerations from intensional logic. But whereas Church's argument turns on the fine-grained informational content of intensional sentences, this argument turns on the distinctive logical features of 'that'-clauses embedded within modal contexts. And unlike Church's argument, this argument applies against truth-conditions nominalism and also against conceptualism and in re realism. So if the argument is successful, it serves as a defense of full (...) ante rem realism. The argument emphasizes the need for a unified treatment of intensional statements -- modal statements as well as statements of assertion and belief. The larger philosophical moral will be that ante rem universals are uniquely suited to carry a certain kind of modal information. Linguistic entities, mind-dependent universals, and instance-dependent universals are incapable of serving that function. (shrink)

This paper provides a new approach to a family of outstanding logical and semantical puzzles, the most famous being Frege's puzzle. The three main reductionist theories of propositions (the possible-worlds theory, the propositional-function theory, the propositional-complex theory) are shown to be vulnerable to Benacerraf-style problems, difficulties involving modality, and other problems. The nonreductionist algebraic theory avoids these problems and allows us to identify the elusive nondescriptive, non-metalinguistic, necessary propositions responsible for the indicated family of puzzles. The algebraic approach is also (...) used to defend antiexistentialism against existentialist prejudices. The paper closes with a suggestion about how this theory of content might enable us to give purely semantic (as opposed to pragmatic) solutions to the puzzles based on a novel formulation of the principle of compositionality. (shrink)

In this chapter we explore two important questions that we believe should be central to any discussion of the ethics and politics of cultural heritage: What are the harms associated with appropriation and commodification, specifically where the heritage of Indigenous peoples is concerned? And how can these harms best be avoided? Archaeological concerns animate this discussion; we are ultimately concerned with fostering postcolonial archaeological practices. But we situate these questions in a broader context, addressing them as they arise in connection (...) with the appropriation of Indigenous cultural heritage, both past and present. (shrink)

Philosophical interest in state power has tended to focus on the state’s coercive powers rather than its expressive powers. I consider an underexplored aspect of the state’s expressive capacity: its capacity to use symbols (such as monuments, memorials, and street names) to promote political ends. In particular, I argue that the liberal state’s deployment of symbols to promote its members’ commitment to liberal ideals is in need of special justification. This is because the state’s exercise of its capacity to use (...) symbols may be in tension with respecting individual autonomy, particularly in cases in which the symbols exert influence without engaging citizens’ rational capacities. But despite the fact that the state’s deployment of symbols may circumvent citizens’ rational capacities, I argue that it may nonetheless be permissible when surrounded by certain liberal institutions and brought about via democratic procedures. (shrink)

This paper argues that participation in an intimate relationship can generate additional or stronger reasons for one to act paternalistically toward the intimate. Moreover, participation in such a relationship can also weaken or cancel some of the presumptive reasons of respect one would otherwise have not to interfere. The paper also reflects, more generally, on the nature of intimate relationships, the normative significance of paternalism, and the normative differences between paternalism in larger-scale institutional contexts and paternalism in closer, interpersonal ones. (...) -/- . (shrink)

The paper begins with an argument against eliminativism with respect to the propositional attitudes. There follows an argument that concepts are sui generis ante rem entities. A nonreductionist view of concepts and propositions is then sketched. This provides the background for a theory of concept possession, which forms the bulk of the paper. The central idea is that concept possession is to be analyzed in terms of a certain kind of pattern of reliability in one’s intuitions regarding the behavior of (...) the concept. The challenge is to find an analysis that is at once noncircular and fully general. Environmentalism, anti-individualism, holism, analyticity, etc. provide additional hurdles. The paper closes with a discussion of the theory’s implications for the Wittgenstein-Kripke puzzle about rule-following and the Benacerraf problem concerning mathematical knowledge. (shrink)

This is the only complete logic for properties, relations, and propositions (PRPS) that has been formulated to date. First, an intensional abstraction operation is adjoined to first-order quantifier logic, Then, a new algebraic semantic method is developed. The heuristic used is not that of possible worlds but rather that of PRPS taken at face value. Unlike the possible worlds approach to intensional logic, this approach yields a logic for intentional (psychological) matters, as well as modal matters. At the close of (...) the paper, the origin of incompleteness in logic is investigated. The culprit is found to be the predication relation, a relation on properties and relations that is expressed in natural language by the copula. (shrink)

_Socrates_ presents a compelling case for some life-changing conclusions that follow from a close reading of Socrates' arguments. Offers a highly original study of Socrates and his thought, accessible to contemporary readers Argues that through studying Socrates we can learn practical wisdom to apply to our lives Lovingly crafted with humour, thought-experiments and literary references, and with close reading sof key Socratic arguments Aids readers with diagrams to make clear complex arguments.

Hilbert's ε-calculus is based on an extension of the language of predicate logic by a term-forming operator εx. Two fundamental results about the ε-calculus, the first and second epsilon theorem, play a rôle similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential (...) theorems obtained by this elimination procedure. (shrink)

Professor Fletcher challenges the traditional account of the development of tort doctrine as a shift from an unmoral standard of strict liability for directly causing harm to a moral standard based on fault. He then sets out two paradigms of liability to serve as constructs for understanding competing ideological viewpoints about the proper role of tort sanctions. He asserts that the paradigm of reciprocity, which looks only to the degree of risk imposed by the parties to a lawsuit on each (...) other, and to the existence of possible excusing conditions, provides greater protection of individual interests than the paradigm of reasonableness, which assigns liability instrumentally on the basis of a utilitarian calculus. Finally, Professor Fletcher examines stylistic differences between the two paradigms which may explain the modern preference for the paradigm of reasonableness. (shrink)

Revised and reprinted; originally in Dov Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic, Volume IV. Kluwer 133-251. -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented in the (...) course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

Revised and reprinted in Handbook of Philosophical Logic, volume 10, Dov Gabbay and Frans Guenthner (eds.), Dordrecht: Kluwer, (2003). -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented in the (...) course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

This paper demonstrates that there is an inconsistency in functionalism in psychology and philosophy of mind. Analogous inconsistencies can be expected in functionalisms in biology and social theory. (edited).

Das deutsche Gesundheitswesen steht durch die schnell steigende Anzahl an CO- VID-19-Erkrankten vor erheblichen Herausforderungen. In dieser Krisensituation sind alle Beteiligten mit ethischen Fragen konfrontiert, beispielsweise nach gerech- ten Verteilungskriterien bei begrenzten Ressourcen und dem gesundheitlichen Schutz des Personals angesichts einer bisher nicht therapierbaren Erkrankung. Daher werden schon jetzt klinische und ambulante Ethikberatungsangebote verstärkt mit Anfragen nach Unterstützung konfrontiert. Wie können Ethikberater*innen Entscheidungen in der Krankenversorgung im Rahmen der COVID-19-Pandemie unterstützen? Welche Grenzen von Ethikberatung sind zu beachten? Bislang liegen hierzu (...) noch wenige praktische Erfahrungen vor. Angesichts der dynamischen Entwicklung erscheint es der Akademie für Ethik in der Medizin (AEM) wichtig, einen Diskurs über die angemessene Rolle der Ethikberatung bei der Bewältigung der vielfachen Heraus- forderungen durch die COVID-19-Pandemie zu führen und professionelle Hinweise zu geben. Mit dem vorliegenden Diskussionspapier möchte die AEM einen Beitrag zur Beantwortung wesentlicher Fragen leisten, die sich für die Ethikberatung in den verschiedenen Bereichen des Gesundheitswesens stellen. Sie regt an, diesen Dis- kurs weiter zu führen und hat ein Online-Forum (s. unten) eingerichtet, in dem Ethikberater*innen ihre Erfahrungen teilen und die professionelle Selbstreflexion der Ethikberatung in Pandemiezeiten mit Anregungen fördern können. (shrink)

Modal intuitions are the primary source of modal knowledge but also of modal error. According to the theory of modal error in this paper, modal intuitions retain their evidential force in spite of their fallibility, and erroneous modal intuitions are in principle identifiable and eliminable by subjecting our intuitions to a priori dialectic. After an inventory of standard sources of modal error, two further sources are examined in detail. The first source - namely, the failure to distinguish between metaphysical possibility (...) and various kinds of epistemic possibility - turns out to be comparatively easy to untangle and poses little threat to intuition-driven philosophical investigation. The second source is the local misunderstanding of one's concepts . This pathology may be understood on analogy with a patient who is given a clean bill of health at his annual check-up, despite his having a cold at the time of the check-up: although the patient's health is locally disrupted, his overall health is sufficiently good to enable him to overcome the cold without external intervention. Even when our understanding of certain pivotal concepts has lapsed locally, our larger body of intuitions is sufficiently reliable to allow us, without intervention, to ferret out the modal errors resulting from this lapse of understanding by means of dialectic and/or a process of a priori reflection. This source of modal error, and our capacity to overcome it, has wide-ranging implications for philosophical method - including, in particular, its promise for disarming skepticism about the classical method of intuition-driven investigation itself. Indeed, it is shown that skeptical accounts of modal error are ultimately self-defeating. (shrink)

ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be equivalent; (...) but, when regarded as consequence systems (ibid., p. 157), one diverges from the others in a fashion which suggests that two standard measures of semantic complexity may not be as closely linked as previously thought. -/- This 1974 paper uses the linear notation for natural deduction presented in [2]: each two-dimensional deduction is represented by a unique one-dimensional string of characters. Thus obviating need for two-dimensional trees, tableaux, lists, and the like—thereby facilitating electronic communication of natural deductions. The 1969 paper presents a (modal, sentential) logic which may be thought of as a partial systematization of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of this logic coincides those of standard formalizations of Lewis’s S4. Among the paper's innovations is its treatment of modal logic in the setting of natural deduction systems--as opposed to axiomatic systems. The author’s apologize for the now obsolete terminology. For example, these papers speak of “a proof of a sentence from a set of premises” where today “a deduction of a sentence from a set of premises” would be preferable. 1. Corcoran, John. 1969. Three Logical Theories, Philosophy of Science 36, 153–77. J P R -/- 2. Corcoran, John and George Weaver. 1969. Logical Consequence in Modal Logic: Natural Deduction in S5 Notre Dame Journal of Formal Logic 10, 370–84. MR0249278 (40 #2524). 3. Weaver, George and John Corcoran. 1974. Logical Consequence in Modal Logic: Some Semantic Systems for S4, Notre Dame Journal of Formal Logic 15, 370–78. MR0351765 (50 #4253). (shrink)

Self-consciousness constitutes an insurmountable obstacle to functionalism. Either the standard functional definitions of mental relations wrongly require the contents of self-consciousness to be propositions involving “realizations” rather than mental properties and relations themselves. Or else these definitions are circular. The only way to save functional definitions is to expunge the standard functionalist requirement that mental properties be second-order and to accept that they are first-order. But even the resulting “ideological” functionalism, which aims only at conceptual clarification, fails unless it incorporates (...) the thesis that the mental properties are fully “natural” universals. Accordingly, mental properties are sui generis: first-order, nonphysical, natural universals. (shrink)

I develop an account of the nature and value of being supportive in interpersonal relationships. In particular, I argue that the virtue of being supportive, construed as a modally demanding value, facilitates the autonomy of one's intimate and promotes a sense of unity in one's relationship. Moreover, the practice of being supportive plays an important role with regard to the familiar need to reconcile the normative demands of one's own projects with one's responsibilities to intimates.

Draft Chapter for Chinese Philosophy and Its Thinkers: From Ancient Times to the Present Day .

Arguments are given against the thesis that properties and propositional functions are identical. The first shows that the familiar extensional treatment of propositional functions -- that, for all x, if f(x) = g(x), then f = g -- must be abandoned. Second, given the usual assumptions of propositional-function semantics, various propositional functions (e.g., constant functions) are shown not to be properties. Third, novel examples are given to show that, if properties were identified with propositional functions, crucial fine-grained intensional distinctions would (...) be lost. (shrink)

We revisit the Marxist debate on the commodity form. By following the thought of Alfred Sohn-Rethel and Slavoj Žižek, we attempt to understand the commodity form through the Kantian categories a priori. Sohn-Rethel explores the proposition that there can be no cognition independent of its historical and social conditions and puts forward the daring conclusion of an ontological unity between knowledge and commodity exchange. We suggest that Sohn-Rethel’s thought finds new relevance nowadays, under the prevalence of a cognitive capitalism. We (...) discuss the reformulation of relations of production and consumption under cognitive capitalism and show how knowledge-led immaterial and affective labour adds a higher value to the commodities into which it is embodied. Above all, the commodity form in cognitive capitalism becomes biopolitical. (shrink)

What is the role of faith in the familiar practice of supporting intimates in their personal projects? Is there anything distinctly valuable about such faith-based support? I argue that the virtue of being supportive, a characteristic of the good friend or lover, involves a distinctive kind of faith: faith in another persons’ chosen self-expressive pursuit. Support based on such faith enables the supported party to enjoy a more meaningful and autonomous exercise of agency in self-expressive arenas, and engenders a sense (...) of relational unity or solidarity, deepening the normative and emotional bonds of the relationship. (shrink)