S. SHAPIRO (ed.), Intensional Mathematics (Studies in Logic and the Foundations of Mathematics, vol. 11 3). Amsterdam: North-Holland, 1985. v + 230 pp. $38.50/100Df.

Review of John Burgess' and Gideon Rosen's A Subject with no Object.

An Essay on Mathematical Instrumentalism M. Detlefsen. THE PHILOSOPHICAL FUNDAMENTALS OF HILBERT'S PROGRAM 1. INTRODUCTION In this chapter I shall attempt to set out Hilbert's Program in a way that is more revealing than ...

In this paper I have considered various attempts to attribute significance to Gödel's second incompleteness theorem (G2 for short). Two of these attempts (Beth-Cohen and the position maintaining that G2 shows the failure of Hilbert's Program), I have argued, are false. Two others (an argument suggested by Beth, Cohen and ??? and Resnik's Interpretation), I argue, are groundless.

Duality has often been described as a means of extending our knowledge with a minimal additional outlay of investigative resources. I consider possible arguments for this view. Major elements of this argument are out of keeping with certain widely held views concerning the nature of axiomatic theories (both in projective geometry and elsewhere). They also require a special form of consistency requirement.

Introduction to a special issue of Philosophia Mathematica on the mechanization of reasoning. Authors include: M. Detlefsen, D. Mundici, S. Shanker, S. Shapiro, W. Sieg and C. Wright.

SOME suggestions are here made for improvement of the text and understanding of Pliny's Eastern Aegean geography. The editions studied for the purpose are Detlefsen's special edition of the geographical books and Mayhoff's Teubner vol. i . The citations of MSS. readings given below are normally taken from Mayhoff's apparatus, which gives a fuller coverage than Detlefsen's. The MSS. are cited by the letters given them in Mayhoff's edition and the Budé Pliny book i , pp. 37 f. (...) One further MS., hitherto not collated in the geographical books, is here cited. Following Campbell, who first drew attention to it, I cite it as c. This MS., formerly in the Phillipps collection in Cheltenham and now in the Pierpont Morgan Library , is assigned to Lorsch and said to be of the first half of the ninth century. It seems thus to be somewhat older than A and E, and in that case is the oldest known surviving MS. of the geographical books. (shrink)

SOME suggestions are here made for improvement of the text and understanding of Pliny's Eastern Aegean geography. The editions studied for the purpose are Detlefsen's special edition of the geographical books and Mayhoff's Teubner vol. i. The citations of MSS. readings given below are normally taken from Mayhoff's apparatus, which gives a fuller coverage than Detlefsen's. The MSS. are cited by the letters given them in Mayhoff's edition and the Budé Pliny book i, pp. 37 f. One further (...) MS., hitherto not collated in the geographical books, is here cited. Following Campbell, who first drew attention to it, I cite it as c. This MS., formerly in the Phillipps collection in Cheltenham and now in the Pierpont Morgan Library, is assigned to Lorsch and said to be of the first half of the ninth century. It seems thus to be somewhat older than A and E, and in that case is the oldest known surviving MS. of the geographical books. (shrink)

According to Margaret Cavendish the entire natural world is essentially rational such that everything thinks in some way or another. In this paper, I examine why Cavendish would believe that the natural world is ubiquitously rational, arguing against the usual account, which holds that she does so in order to account for the orderly production of very complex phenomena (e.g. living beings) given the limits of the mechanical philosophy. Rather, I argue, she attributes ubiquitous rationality to the natural world in (...) order to ground a theory of the ubiquitous freedom of nature, which in turn accounts for both the world's orderly and disorderly behavior. (shrink)

Between 1653 and 1655 Margaret Cavendish makes a radical transition in her theory of matter, rejecting her earlier atomism in favour of an infinitely-extended and infinitely-divisible material plenum, with matter being ubiquitously self-moving, sensing, and rational. It is unclear, however, if Cavendish can actually dispense of atomism. One of her arguments against atomism, for example, depends upon the created world being harmonious and orderly, a premise Cavendish herself repeatedly undermines by noting nature’s many disorders. I argue that her supposed difficulties (...) with atomism expose a deeper tension in her work between two fundamental metaphysical commitments each of which has substantial philosophical support: her monist theory of the material world (which maintains that there exists just one natural substance which is the single principal cause) and her occasional theory of causation (which requires multiple finite principal causes in nature -- causes that might be considered individual substances). Her monism undermines atomism while her theory of occasional cause seems to rest on a conception of nature that would be especially friendly to atomism. I argue further that we can solve this tension within a Cavendishian framework in such a way as to preserve her theory of causation and her monism, but that this solution depends upon our taking her monism in a particular (and weak) form. I finally note that we can best make sense of her unique and interesting form of monism by acknowledging her social-political motivations in addition to her motivations in natural philosophy. (shrink)

In this paper, I consider Descartes’ Sixth Meditation dropsy passage on the difference between the human body considered in itself and the human composite of mind and body. I do so as a way of illuminating some features of Descartes’ broader thinking about teleology, including the role of teleological explanations in physiology. I use the writings on teleology of some ancient authors for the conceptual (but not historical) help they can provide in helping us to think about the Sixth Meditation (...) passage. From this, I draw several points, most notably that the Sixth Meditation passage is primarily concerned with the natures of body and composites, and that the issue of teleological explanation is derivative of this primary interest. So, we – and Descartes – must come to terms with what he takes the nature of the composite to be such that it has an intrinsic end-referred nature which grounds teleological explanations. I consider three possibilities: the human composite is a third type of substance – a hylomorphic substance; there is a sort of “satisfaction” relationship between mind and body (each of which retains its own distinct nature in the composite) such that the mind confers teleological value on the body; and there is a sort of “satisfaction” relationship between mind and body (each of which retains its own distinct nature in the composite) such that the mind recognizes teleological value in the body. None of these interpretations is without problems. So in the concluding section, I sketch a program for future research, specifically, trying to render Descartes’ teleological thinking consistent by distinguishing between the metaphysical natures of things (the concern of his Sixth Meditation passage) and the physical natures of things (his concern in his physiological writings). (shrink)

In this chapter, I examine similarities and divergences between Du Châtelet and Descartes on their endorsement of the use of hypotheses in science, using the work of Condillac to locate them in his scheme of systematizers. I conclude that, while Du Châtelet is still clearly a natural philosopher, as opposed to modern scientist, her conception of hypotheses is considerably more modern than is Descartes’, a difference that finds its roots in their divergence on the nature of first principles.

This study described the relationships between academic class and student moral sensitivity and reasoning and between curriculum design components for ethics education and student moral sensitivity and reasoning. The data were collected from freshman (n = 506) and senior students (n = 440) in eight baccalaureate nursing programs in South Korea by survey; the survey consisted of the Korean Moral Sensitivity Questionnaire and the Korean Defining Issues Test. The results showed that moral sensitivity scores in patient-oriented care and conflict were (...) higher in senior students than in freshman students. Furthermore, more hours of ethics content were associated with higher principled thinking scores of senior students. Nursing education in South Korea may have an impact on developing student moral sensitivity. Planned ethics content in nursing curricula is necessary to improve moral sensitivity and moral reasoning of students. (shrink)

In this chapter, I examine similarities and divergences between Du Châtelet and Descartes on their endorsement of the use of hypotheses in science, using the work of Condillac to locate them in his scheme of systematizers. I conclude that, while Du Châtelet is still clearly a natural philosopher, as opposed to modern scientist, her conception of hypotheses is considerably more modern than is Descartes’, a difference that finds its roots in their divergence on the nature of first principles.

There have been many different historical-intellectual accounts of the shaping and development of concepts of liberty in pre-Enlightenment Europe. This volume is unique for addressing the subject of liberty principally as it is discussed in the writings of women philosophers, and as it is theorized with respect to women and their lives, during this period. The volume covers ethical, political, metaphysical, and religious notions of liberty, with some chapters discussing women's ideas about the metaphysics of free will, and others examining (...) the topic of women's freedom in their moral and personal lives as well as in the public socio-political domain. In some cases, these topics are situated in relation to the emergence of the concept of autonomy in the late eighteenth century, and in others, with respect to recent feminist theorizing about relational autonomy and internalized oppression. Many of the chapters draw upon a wide range of genres, including polemical texts, poetry, plays, and other forms of fiction, as well as standard philosophical treatises. Taken as a whole, this volume shows how crucial it is to recover the too-long forgotten views of female and women-friendly male philosophers of the seventeenth and eighteenth centuries. In the process of recovering these voices, our understanding of philosophy in the early modern period is not only expanded, but also significantly enhanced, toward a more accurate and gender-inclusive history of our discipline. (shrink)

This paper is an update of the documents we have concerning the Acts of the Christian martyrs, focused on three main aspects: 1) the kind of acts we know of and their classification from the point of view of their historic value; 2) the versions or editions of the texts that are most accepted by scholars; 3) the relevance of the different parts that make up these documents in order to discern the original text from passages that were rewritten or (...) underwent later variations. In this way, the article offers an exhaustive list of the documents for use in researching Christian martyrs in the Roman period. (shrink)

In 2020, the University of Pennsylvania instituted a graduate certificate in public philosophy. In many ways, this certificate formalized and recognized the public engagement work that graduate students in the philosophy department and beyond had been involved with for some years. One element of the certificate, however, was pivotal in moving our work in public philosophy forward in important ways. This element is the research seminar in public philosophy. In this paper, we recount the motivation for the creation of the (...) certificate and especially the motivation for the inclusion of the research seminar. We also explore ways in which such a certificate, along with the deliberately self-reflective work of the research seminar, might help us reimagine the nature and value of philosophy and its connection with human life and flourishing. We focus on metaphilosophical themes such as the very nature of philosophy and the philosopher as well as the importance of cultivating a new generation of academic philosophers committed to transcending the distinction between the academy and the public and, relatedly, between academic philosophy and public philosophy. (shrink)

First published in the most ambitious international philosophy project for a generation; the _Routledge Encyclopedia of Philosophy_. _Logic from A to Z_ is a unique glossary of terms used in formal logic and the philosophy of mathematics. Over 500 entries include key terms found in the study of: * Logic: Argument, Turing Machine, Variable * Set and model theory: Isomorphism, Function * Computability theory: Algorithm, Turing Machine * Plus a table of logical symbols. Extensively cross-referenced to help comprehension and add (...) detail, _Logic from A to Z_ provides an indispensable reference source for students of all branches of logic. (shrink)

In recent literature, panpsychism has been defended by appeal to two main arguments: first, an argument from philosophy of mind, according to which panpsychism is the only view which successfully integrates consciousness into the physical world (Strawson 2006; Chalmers 2013); second, an argument from categorical properties, according to which panpsychism offers the only positive account of the categorical or intrinsic nature of physical reality (Seager 2006; Adams 2007; Alter and Nagasawa 2012). Historically, however, panpsychism has also been defended by appeal (...) to a third argument based on considerations about the nature and observability of causation. This argument has not been much discussed in recent times. Here is a concise version from William James: "… the concrete perceptual flux, taken just as it comes, offers in our own activity-situations perfectly comprehensible instances of causal agency … If we took these experiences as the type of what actual causation is, we should have to ascribe to cases of causation outside of our life, to physical cases also, an inwardly experiential nature. In other words, we should have to espouse a so-called “pan-psychic” philosophy" (James 1911: 218). James here suggests that we have direct experience of causation in our own agency. He thereby directly contradicts David Hume, who famously denied that we have any experience of causation. James goes on to claim that if this experience is representative of causation in general, it follows that all causation is mental, and that panpsychism is true. This kind of argument for panpsychism can be called the argument from (experience of) causation. This chapter offers, first, a history of this argument and arguments closely related to it, and second, an analysis of the argument – is it valid, are its premises in any way defensible, and how does it relate to the other, more popular arguments for panpsychism from philosophy of mind and categorical properties? (shrink)

Ibn al-ʻArabī, 1165-1240; views on freedom; Sufism; Islamic philosophy.

Throughout history, mathematicians have expressed preference for solutions to problems that avoid introducing concepts that are in one sense or another “foreign” or “alien” to the problem under investigation. This preference for “purity” (which German writers commonly referred to as “methoden Reinheit”) has taken various forms. It has also been persistent. This notwithstanding, it has not been analyzed at even a basic philosophical level. In this paper we give a basic analysis of one conception of purity—what we call topical purity—and (...) discuss its epistemological significance. (shrink)

A comprehensive historical overview of formalist ideas in the philosophy of mathematics.

An outstanding reference source for the wide range of philosophical contributions made by women writing in Europe from about 1560 to 1780. It shows the range of genres and methods used by women writing in these centuries in Europe, thus encouraging an expanded understanding of our historical canon.

The aims of this paper are twofold: firstly, to say something about that philosophy of mathematics known as 'intuitionism' and, secondly, to fit these remarks into a more general message for the philosophy of mathematics as a whole. What I have to say on the first score can, without too much inaccuracy, be compressed into two theses. The first is that the intuitionistic critique of classical mathematics can be seen as based primarily on epistemological rather than on meaning-theoretic considerations. The (...) second is that the intuitionist's chief objection to the classical mathematician's use of logic does not center on the use of particular logical principles (in particular, the law of excluded middle and its ilk). Rather on the role the classical mathematician assigns (or at least extends) generally (i.e. regardless of the particular principles used) to the use of logic in the production mathematical proofs. Thus, the intuitionist critique of logic that we shall be presenting is far more radical than that which has commonly been presented. -/- Concerning the second, more general, theme, my claim is this: some restriction of the role of logical inference in mathematical proof such as that mentioned above is necessary if one is to account for the seeming difference in the epistemic conditions of provers whose reasoning is based on genuine insight into the subject-matter being investigated, and would-be provers whose reasoning is based not on such insight, but rather on principles of inference which hold of every subject-matter indifferently. (shrink)

Poincaré was a persistent critic of logicism. Unlike most critics of logicism, however, he did not focus his attention on the basic laws of the logicists or the question of their genuinely logical status. Instead, he directed his remarks against the place accorded to logical inference in the logicist's conception of mathematical proof. Following Leibniz, traditional logicist dogma (and this is explicit in Frege) has held that reasoning or inference is everywhere the same — that there are no principles of (...) inference specific to a given local topic. Poincaré, a Kantian, disagreed with this. Indeed, he believed that the use of non-logical reasoning was essential to genuinely mathematical reasoning (proof). In this essay, I try to isolate and clarify this idea and to describe the mathematical epistemology which underlies it. Central to this epistemology (which is basically Kantian in orientation, and closely similar to that advocated by Brouwer) is a principle of epistemic conservation which says that knowledge of a given type cannot be extended by means of an inference unless that inference itself constitutes knowledge belonging to the given type. (shrink)

I criticize a recent paper by Thomas Tymoczko in which he attributes fundamental philosophical significance and novelty to the lately-published computer-assisted proof of the four color theorem (4CT). Using reasoning precisely analogous to that employed by Tymoczko, I argue that much of traditional mathematical proof must be seen as resting on what Tymoczko must take as being "empirical" evidence. The new proof of the 4CT, with its use of what Tymoczko calls "empirical" evidence is therefore not so novel as he (...) maintains. Finally, without attempting to give a full account of the notion of empirical mathematical evidence, I sketch a view showing how the use of calculation injects an empirical ingredient into proof. (shrink)

In this paper, I argue that Margaret Cavendish’s account of freedom, and the role of education in freedom, is better able to account for the specifics of women’s lives than are Thomas Hobbes’ accounts of these topics. The differences between the two is grounded in their differing conceptions of the metaphysics of human nature, though the full richness of Cavendish’s approach to women, their minds and their freedom can be appreciated only if we take account of her plays, accepting them (...) as philosophical texts alongside her more standard philosophical treatises. (shrink)