Develops a structuralist understanding of mathematics, as an alternative to set- or type-theoretic foundations, that respects classical mathematical truth while ...

Moral theorists like Singer and Greene argue that we should discount intuitions about ‘up-close-and-personal’ moral dilemmas because they are more likely than intuitions about ‘impersonal’ dilemmas to be artifacts of evolution. But by that reasoning, it seems we should ignore the evolved, ‘up-close-and-personal’ intuition to save a drowning child in light of the too-new-to-be-evolved, ‘impersonal’ intuition that we need not donate to international famine relief. This conclusion seems mistaken and horrifying, yet it cannot be the case both that ‘up-close-and-personal’ intuitions (...) are more reliable than ‘impersonal’ intuitions, and vice versa. Thus, Singer’s evolutionary debunking argument proves too much, and should not be taken seriously. However, Singer’s debunking argument is typical of an entire class of arguments that seeks to debunk normative principles by reference to evolution. This entire class of argument, I argue, therefore also proves too much to be taken seriously. (shrink)

This groundbreaking book revisits the writings of classic theorists in an effort re-evaluate the importance and influence the psychology of esteem has on the economy. The authors explore ways the economy of esteem may be reshaped to improve overall social outcomes and offer new ways of thinking about how society works and may be made to work.

Category theory and topos theory have been seen as providing a structuralist framework for mathematics autonomous vis-a-vis set theory. It is argued here that these theories require a background logic of relations and substantive assumptions addressing mathematical existence of categories themselves. We propose a synthesis of Bell's many-topoi view and modal-structuralism. Surprisingly, a combination of mereology and plural quantification suffices to describe hypothetical large domains, recovering the Grothendieck method of universes. Both topos theory and set theory can be carried out (...) relative to such domains; puzzles about ‘large categories’ and ‘proper classes’ are handled in a uniform way, by relativization, sustaining insights of Zermelo. (shrink)

Three principal varieties of mathematical structuralism are compared: set-theoretic structuralism (‘STS’) using model theory, Shapiro's ante rem structuralism invoking sui generis universals (‘SGS’), and the author's modal-structuralism (‘MS’) invoking logical possibility. Several problems affecting STS are discussed concerning, e.g., multiplicity of universes. SGS overcomes these; but it faces further problems of its own, concerning, e.g., the very intelligibility of purely structural objects and relations. MS, in contrast, overcomes or avoids both sets of problems. Finally, it is argued that the modality (...) of MS or a close cousin appears at crucial junctures in both STS and SGS, so that the above outcome is not obviously tendentious. (shrink)

Gender dysphoria (GD) is marked by an incongruence between a person’s biological sex at birth, and their felt gender (or gender identity). There is continuing debate regarding the benefits and drawbacks of physiological treatment of GD in children, a pathway, beginning with endocrine treatment to suppress puberty. Currently, the main alternative to physiological treatment consists of the so-called “wait-and-see” approach, which often includes counseling or other psychotherapeutic treatment. In this paper, we argue in favor of a “third pathway” for the (...) diagnosis and treatment of GD in youths. To make our case, we draw on a recent development in bioethics: the phenomenological approach. Scholars such as Slatman and Svenaeus have argued that the extent to which the body can (or should be) manipulated or reconstructed through medical intervention is not only determined by consideration of ethical frameworks and social and legal norms. Rather, we must also take account of patients’ personal experience of their body, the personal and social values associated with it, and their understanding of its situation in their life: their narrative identities. We apply this phenomenological approach to medicine and nursing to the diagnosis and treatment of GD in youth. In particular, we discuss Zahavi and Martiny’s conception of the phenomenological interview, in order to show that narrative techniques can assist in the process of gender identification and in the treatment of youth presenting with GD. We focus on two case studies that highlight the relevance of a narrative-based interview in relations between patients, HCPs, and family, to expose the influence of social ideologies on how young people presenting with GD experience their bodies and gender. (shrink)

This paper makes a comparison between enactivism and Levinas’ philosophy. Enactivism is a recent development in philosophy of mind and cognitive science that generally defines cognition in terms of a subject’s natural interactions with the physical environment. In recent years, enactivists have been focusing on social and ethical relations by introducing the concept of participatory sensemaking, according to which ethical know-how spontaneously emerges out of natural relations of participation and communication, that is, through the exchange of knowledge. This paper will (...) argue first that, although participatory sensemaking is a valuable concept in that it offers a practical and realistic way of understanding ethics, it nevertheless downplays the significance of otherness for understanding ethics. I will argue that Levinas’ work demonstrates in turn that otherness is significant for ethics in that we cannot completely anticipate others through participation or know-how. We cannot live the other’s experiences or suffering, which makes ethical relation so difficult and serious (e.g. care for a terminally ill person always falls short to a certain extent). I will argue next that enactivism and Levinas’ philosophy nevertheless do not exclude each other insofar they share a similar concept of subjectivity as a quality of naturally interacting with the external world to gain knowledge (Levinas speaks of dwelling). Finally, I will argue that enactivism’s notion of participatory sensemaking also offers something which Levinas’ insufficiently defines, namely a concept of social justice, based on equality and participation, that emerges out of natural relations. (shrink)

Some remarks on determination, physicalism, model theory, and logical truth.//An attempt to defend physicalism against objections that its bases are indeterminate.

We develop a point-free construction of the classical one- dimensional continuum, with an interval structure based on mereology and either a weak set theory or logic of plural quantification. In some respects this realizes ideas going back to Aristotle,although, unlike Aristotle, we make free use of classical "actual infinity". Also, in contrast to intuitionistic, Bishop, and smooth infinitesimal analysis, we follow classical analysis in allowing partitioning of our "gunky line" into mutually exclusive and exhaustive disjoint parts, thereby demonstrating the independence (...) of "indecomposability" from a non-punctiform conception. It is surprising that such simple axioms as ours already imply the Archimedean property and that they determine an isomorphism with the Dedekind-Cantor structure of R as a complete, separable, ordered field. We also present some simple topological models of our system, establishing consistency relative to classical analysis. Finally, after describing how to nominalize our theory, we close with comparisons with earlier efforts related to our own. (shrink)

Standard proofs of generalized Bell theorems, aiming to restrict stochastic, local hidden-variable theories for quantum correlation phenomena, employ as a locality condition the requirement of conditional stochastic independence. The connection between this and the no-superluminary-action requirement of the special theory of relativity has been a topic of controversy. In this paper, we introduce an alternative locality condition for stochastic theories, framed in terms of the models of such a theory (§2). It is a natural generalization of a light-cone determination condition (...) that is essentially equivalent to mathematical conditions that have been used to derive Bell inequalities in the deterministic case. Further, it is roughly equivalent to a condition proposed by Bell that, in one investigation, needed to be supplemented with a much stronger assumption in order to yield an inequality violated by some quantum mechanical predictions. It is shown here that this reflects a very general situation: from the proposed locality condition, even adding the strict anticorrelation condition and the auxiliary hypotheses needed to derive experimentally useful (and theoretically telling) inequalities, no Bell-type inequality is derivable. (These independence claims are the burden of §4.) A certain limitation on the scope of the proposed stochastic locality condition is exposed (§5), but it is found to be rather minor. The conclusion is thus supported that conditional stochastic independence, however reasonable on other grounds, is essentially stronger than what is required by the special theory.Our results stand in apparent contradiction with a class of derivations purporting to obtain generalized Bell inequalities from locality alone. It is shown in Appendix (B) that such proofs do not achieve their goal. This fits with our conclusion that generalized Bell theorems are not straightforward generalizations of theorems restricting deterministic hidden-variable theories, and that, in fact, such generalizations do not exist. This leaves open the possibility that a satisfactory, non-deterministic account of the quantum correlation phenomena can be given within the framework of the special theory. (shrink)

Several leading topics outstanding after John Earman's Bayes or Bust? are investigated further, with emphasis on the relevance of Bayesian explication in epistemology of science, despite certain limitations. (1) Dutch Book arguments are reformulated so that their independence from utility and preference in epistemic contexts is evident. (2) The Bayesian analysis of the Quine-Duhem problem is pursued; the phenomenon of a "protective belt" of auxiliary statements around reasonably successful theories is explicated. (3) The Bayesian approach to understanding the superiority of (...) variety of evidence is pursued; a recent challenge (by Wayne) is converted into a positive result on behalf of the Bayesian analysis, potentially with far-reaching consequences. (4) The condition for applying the merger-of-opinion results and the thesis of underdetermination of theories are compared, revealing significant limitations in applicability of the former. (5) Implications concerning "diachronic Dutch Book" arguments and "non-Bayesian shifts" are drawn, highlighting the incompleteness, but not incorrectness, of Bayesian analysis. (shrink)

With developments in the 19th and early 20th centuries, structuralist ideas concerning the subject matter of mathematics have become commonplace. Yet fundamental questions concerning structures and relations themselves as well as the scope of structuralist analyses remain to be answered. The distinction between axioms as defining conditions and axioms as assertions is highlighted as is the problem of the indefinite extendability of any putatively all-embracing realm of structures. This chapter systematically compares four main versions: set-theoretic structuralism, a version taking structures (...) as sui generis universals, structuralism based on category theory, and a quasi-nominalist modal-structuralism. While none of the approaches is problem-free, it appears that some synthesis of the category-theoretic approach with modal-structuralism can meet the challenges set out, given the notion of “logical possibility.”. (shrink)

China, India, Brazil and other major Third World nations have long refused to sign the Nuclear Non‐proliferation Treaty. This position might at first sight appear to be without any question morally unjustified and even irrational. Yet their claim that the treaty is ‘discriminatory’ merits the serious attention which it has not received. Only if certain aspects of this claim are accepted by the nuclear weapons signatories does a moral and rational onus to sign become unquestionable.

A remarkable development in twentieth-century mathematics is smooth infinitesimal analysis ('SIA'), introducing nilsquare and nilpotent infinitesimals, recovering the bulk of scientifically applicable classical analysis ('CA') without resort to the method of limits. Formally, however, unlike Robinsonian 'nonstandard analysis', SIA conflicts with CA, deriving, e.g., 'not every quantity is either = 0 or not = 0.' Internally, consistency is maintained by using intuitionistic logic (without the law of excluded middle). This paper examines problems of interpretation resulting from this 'change of logic', (...) arguing that standard arguments based on 'smoothness' requirements are question-begging. Instead, it is suggested that recent philosophical work on the logic of vagueness is relevant, especially in the context of a Hilbertian structuralist view of mathematical axioms (as implicitly defining structures of interest). The relevance of both topos models for SIA and modal-structuralism as appled to this theory is clarified, sustaining this remarkable instance of mathematical pluralism. (shrink)

This paper considers on what basis justice may require that people be treated as equals. It begins with an examination of the argument that people are to be treated as equals because they are equals, and suggests reasons for thinking that such an argument is unlikely to succeed. The remainder of the paper considers, and tries to make plausible, the argument that justice requires people be treated as equals because they are individuals. Thus the paper offers some support for the (...) view that the proper foundation of egalitarianism is individualism. (shrink)

It is often supposed that there is a relationship between desert and responsibility: that to be deserving we must be responsible for that which makes us deserving. Indeed, there seems little doubt that a supposed relationship between desert and responsibility, combined with a growing tendency to view less and less as the responsibility of the individual, contributed to the reluctance to appeal to desert which has been a feature of much recent moral and political philosophy. Certainly, if to be deserving (...) we need to be responsible for that which makes us deserving ‘all the way down,’ it is not easy to see how anyone could ever be deserving of anything.I will argue that the claim that we can deserve only on the basis of that for which we are responsible — the desert-responsibility thesis — is false. There is no conceptual connection between desert and responsibility. Nevertheless, it is true that many claims to deserve are undermined if there is a lack of responsibility. (shrink)

To what extent can constructive mathematics based on intuitionistc logic recover the mathematics needed for spacetime physics? Certain aspects of this important question are examined, both technical and philosophical. On the technical side, order, connectivity, and extremization properties of the continuum are reviewed, and attention is called to certain striking results concerning causal structure in General Relativity Theory, in particular the singularity theorems of Hawking and Penrose. As they stand, these results appear to elude constructivization. On the philosophical side, it (...) is argued that any mentalist-based radical constructivism suffers from a kind of neo-Kantian apriorism. It would be at best a lucky accident if objective spacetime structure mirrored mentalist mathematics. the latter would seem implicitly committed to a Leibnizian relationist view of spacetime, but is it doubtful if implementation of such a view would overcome the objection. As a result, an anti-realist view of physics seems forced on the radical constructivist. (shrink)

Two EPR arguments are reviewed, for their own sake, and for the purpose of clarifying the status of "stochastic" hidden variables. The first is a streamlined version of the EPR argument for the incompleteness of quantum mechanics. The role of an anti-instrumentalist ("realist") interpretation of certain probability statements is emphasized. The second traces out one horn of a central foundational dilemma, the collapse dilemma; complex modal reasoning, similar to the original EPR, is used to derive determinateness (of all spin components (...) of two spin- 1 / 2 particles in the singlet state) from just (a form of) weak locality, result definiteness, and an assumption on propensities based on conservation. Theories meeting these conditions are therefore constrained by the Bell inequalities. Neither controversial assumptions of "strong locality" ("factorability") nor of determinism are employed in the derivation. The categories of "stochastic hidden variables" are then analyzed; one can focus on "quasi-definite" theories, without loss of generality. A means of excluding these is proposed, based on a demand that certain ideal cases be accurately treated. Theorems from quantum measurement theory, sometimes cited as showing that such cases are not physically possible, are found inapplicable. (shrink)

This paper aims to show that Paul Ricoeur’s hermeneutical phenomenology has significance for philosophy of mind, in particular for recent theories of enactivism, one of the most significant latest developments in cognitive theory. While philosophy of mind often finds its inspiration in hermeneutics and phenomenology, especially in Husserl’s and Merleau-Ponty’s, the later development of hermeneutical phenomenology under the influence of Gadamer and Ricoeur, as it evolved into the theory of the interpretation of narratives and lived existence, is often lost sight (...) of in recent debates about embodied cognition. I defend the thesis, however, that combining Ricoeur’s phenomenology with enactivism shows that embodied cognition has an intrinsic ethico-political aspect. The central argument is that, if we take that imagination and narrative lie at the heart of basic embodied cognition as interaction with the world (planning, motor skills, coordination), as both recent theories of enactivism and Ricoeur hold, then embodied cognition or the way in which we experience and gain knowledge in embodied cognitive relations with the world is ethically and politically significant in that it gets shaped by the ethical and political contexts in which these relations take place (e.g., cultural body images and morals in subcultures). These contexts contain ethical and political narratives and our imaginations are influenced by and work with these narratives in order to gain knowledge. This essay thus attempts to explore some of the possibilities of phenomenological hermeneutics for the philosophy of mind today. Keywords: phenomenology, hermeneutics, philosophy of mind, embodied cognition, ethico- political world. (shrink)

We list, with discussions, various principles of scientific realism, in order to exhibit their diversity and to emphasize certain serious problems of formulation. Ontological and epistemological principles are distinguished. Within the former category, some framed in semantic terms (truth, reference) serve their purpose vis-a-vis instrumentalism (Part 1). They fail, however, to distinguish the realist from a wide variety of (constructional) empiricists. Part 2 seeks purely ontological formulations, so devised that the empiricist cannot reconstruct them from within. The main task here (...) is to characterize "independence of mind". A pair of notions, "physical invariance" and "anti-determination", seem to work. They enable us to assess anew "the problem of constructing the physical out of the phenomenal" (yielding certain clarifications demanded by Goodman). Modern cosmology, especially, is seen to present insuperable obstacles to such empiricist approaches to science. The final section on epistemological principles reveals a morass better avoided in favor of an elementary claim about perception, together with a rejection of any absolute observation/theory dichotomy. Finally, a positive, realist notion of "observable-in-principle" is sketched, and it is suggested that, from the perspective of relativistic cosmology, even this defines no boundary to potential knowledge. (shrink)

The paper discusses some of the key factors that shaped Friedrich Kittler’s anglophone reception. Four points are of special importance: the truncated appropriation of Kittler’s ‘middle period’ by American academics; the structural and ideological reasons for the failure of North American German Studies to capitalize on the growing interest in Kittler; the charges of technodeterminism; and Kittler’s difficult role in the debate over posthumanism.

As argued in Hellman (1993), the theorem of Pour-El and Richards (1983) can be seen by the classicist as limiting constructivist efforts to recover the mathematics for quantum mechanics. Although Bridges (1995) may be right that the constructivist would work with a different definition of 'closed operator', this does not affect my point that neither the classical unbounded operators standardly recognized in quantum mechanics nor their restrictions to constructive arguments are recognizable as objects by the constructivist. Constructive substitutes that may (...) still be possible necessarily involve additional 'incompleteness' in the mathematical representation of quantum phenomena. Concerning a second line of reasoning in Hellman (1993), its import is that constructivist practice is consistent with a 'liberal' stance but not with a 'radical', verificationist philosophical position. Whether such a position is actually espoused by certain leading constructivists, they are invited to clarify. (shrink)

This paper explores strengths and limitations of both predicativism and nominalism, especially in connection with the problem of characterizing the continuum. Although the natural number structure can be recovered predicatively (despite appearances), no predicative system can characterize even the full predicative continuum which the classicist can recognize. It is shown, however, that the classical second-order theory of continua (third-order number theory) can be recovered nominalistically, by synthesizing mereology, plural quantification, and a modal-structured approach with essentially just the assumption that an (...) -sequence of concrete atoms be possible. Predicative flexible type theory may then be used to carry out virtually all of scientifically applicable mathematics in a natural way, still without ultimate need of the platonist ontology of classes and relations. (shrink)

Literary criticism is neither more nor less important today than it has been since the becoming an accepted activity in the Renaissance. The humanists of the sixteenth and seventeenth centuries created the institution of criticism as we know it: the recovery and analysis of works of art. They printed, edited, and interpreted texts that dated from antiquity and which had been lost or disheveled. Evangelical in their fervor, avid in their search for lost or buried riches, they also put into (...) circulation certain influential ideas. Perhaps the most important of these was that the authoritative version of a book is the original version, freed from interpolation and accretion. A correlative idea was that, similarly, one could rely on an original or natural light in the interpreter, an intuitive good sense that helped him to a true understanding of a text if it was a genuine text. . . . There are signs that we are now nearing the end of this Renaissance humanism. Not because of a determinist or providential march of history, but ideas eventually exhaust what influence they may have. Today, after all, there is no dearth of ancient texts, or of new ones. Editing, moreover, has become only too conscious of the difficulty of recovering an "original" version or edition: in Wordsworth scholarship, for example, the authority of the 1850 Prelude, the text approved by the poet shortly before his death, was challenged by the 1805-6 Prelude printed by de Sélincourt in the 1920s; and the authority of this is in turn being eroded by antecedent manuscripts, the so-called "Five-Books Prelude" and "Two-Part Prelude." It is equally precarious to establish the text of Emily Dickinson's poems—which of the variants are to be chosen as definitive? Or, from another angle, Melville's Billy Budd has become a mine for genetic speculation. Even when no editorial problem exists, a philosophical issue arises as to the concept of originality itself.1 · 1. For the time being, it is enough to quote Hegel's provocative attack on all "Ur-Metaphysics": "What comes later is more concrete and richer; the first is abstract, and least differentiated." Geoffrey Hartman, professor of English and comparative literature at Yale University, is the author of The Unmediated Vision, Andre Malraux, Wordsworth's Poetry, Beyond Formalism, and most recently The Fate of Reading. He is currently working on a book to be published in late 1977, Criticism in the Wilderness. (shrink)

Wallace Martin's response to "Literary Criticism and Its Discontents" is anything but naive. Its most sophisticated device is to posit my invention of a "naive reader" and to suggest that I would place the New Critics and their heirs in that category. But when I see the movement of criticism after Arnold as exhibiting an anti-self-consciousness principle or being so worried about a hypertrophy of the critical spirit that the spirit is acknowledged only by refusing its seminal or creative force, (...) I am not alleging naiveté but "organized innocence," or the privileged assignment of some given, intuitive power of creation to the area of art which excludes the area of philosophy or philosophically-minded commentary. This defensive partition of the critical and the creative spirit, which recognizes the intelligence of the creative writer but refuses the obverse proposition that there may be creative force in the critical writer, I have elsewhere named the Arnoldian concordat. Geoffrey Hartman, professor of English and comparative literature at Yale University, is the author of Criticism in the Wilderness. (shrink)

This paper explores the status of the von Neumann-Luders state transition rule (the "projection postulate") within "real-logic" quantum logic. The entire discussion proceeds from a reading of the Luders rule according to which, although idealized in applying only to "minimally disturbing" measurements, it nevertheless makes empirical claims and is not a purely mathematical theorem. An argument (due to Friedman and Putnam) is examined to the effect that QL has an explanatory advantage over Copenhagen and other interpretations which relativize truth-value assignments (...) to experimental arrangements. Two versions of QL, the lattice-theoretic (LT) and partial-Boolean-algebra (PBA), are considered. It turns out that the projection postulate is intimately connected with the choice of conditional connective for QL. The effect of the projection postulate is obtained with the Sasaki conditional. However, this choice is found to require extra assumptions, on both the LT and PBA versions, which are either just as ad hoc as the projection postulate itself or indefensible from within the real-logic QL framework. (shrink)