Lately, philosophers of mathematics have been exploring the notion of mathematical explanation within mathematics. This project is supposed to be analogous to the search for the correct analysis of scientific explanation. I argue here that given the way philosophers have been using “ explanation,” the term is not applicable to mathematics as it is in science.

The Quine-Putnam Indispensability argument is the argument for treating mathematical entities on a par with other theoretical entities of our best scientific theories. This argument is usually taken to be an argument for mathematical realism. In this chapter I will argue that the proper way to understand this argument is as putting pressure on the viability of the marriage of scientific realism and mathematical nominalism. Although such a marriage is a popular option amongst philosophers of science and mathematics, in light (...) of the indispensability argument, the marriage is seen to be very unstable. Unless one is careful about how the Quine-Putnam argument is disarmed, one can be forced to either mathematical realism or, alternatively, scientific instrumentalism. I will explore the various options: (i) finding a way to reconcile the two partners in the marriage by disarming the indispensability argument (Jody Azzouni [2], Hartry Field [13, 14], Alan Musgrave [18, 19], David Papineau [21]); (ii) embracing mathematical realism (W.V.O. Quine [23], Michael Resnik [25], J.J.C. Smart [27]); and (iii) embracing some form of scientific instrumentalism (Ot´ avio Bueno [7, 8], Bas van Fraassen [30]). Elsewhere [11], I have argued for option (ii) and I won’t repeat those arguments here. Instead, I will consider the difficulties for each of the three options just mentioned, with special attention to option (i). In relation to the latter, I will discuss an argument due to Alan Musgrave [19] for why option (i) is a plausible and promising approach. From the discussion of Musgrave’s argument, it will emerge that the issue of holist versus separatist theories of confirmation plays a curious role in the realism–antirealism debate in the philosophy of mathematics. I will argue that if you take confirmation to be an holistic matter—it’s whole theories (or significant parts thereof) that are confirmed in any experiment—then there’s an inclination to opt for (ii) in order to resolve the marital tension outlined above.. (shrink)

For fifty years Hubert Dreyfus has done pioneering work which brings phenomenology and existentialism to bear on the philosophical and scientific study of the mind. This is a selection of his most influential essays, developing his critique of the representational model of the mind in analytical philosophy of mind and mainstream cognitive science.

The spectre of the repugnant conclusion and the search for a population axiology that avoids it has endured as a focus of population ethics. This is in part because the repugnant conclusion is often interpreted as a defining problem for totalism, while the implications of averagism and related views are taken to illustrate the theoretical cost of avoiding the repugnant conclusion. However, we show that this interpretation cannot be sustained unless one focuses only on a special case of the repugnant (...) conclusion: namely, the subset of instances of the repugnant conclusion where there is no portion of the population unaffected by the choice between population outcomes (as in Derek Parfit’s original illustration). To avoid an inappropriate focus on only this proper subset of instances of the repugnant conclusion, we formulate a general characterization of the repugnant conclusion. We then prove formally that all leading welfarist axiologies imply this conclusion, including averagism and Ng’s Theory X0 , including probabilistic and ‘very repugnant’ variants that involve the addition of negative lives. We then prove that the full range of axiologies considered by population ethics each imply an extended version of the repugnant conclusion, including axiologies that are incomplete, intransitive, rank-dependent, person-affecting, and/or pluralist. The upshot is that the repugnant conclusion does not ultimately tell against any approach to axiology, and the methodological requirement to avoid the repugnant conclusion should be dropped from population axiology. (shrink)

Persons are biological beings who participate in social environments. Is human sociality different from that of insects? Is human sociality different from that of a computer or robot with elaborate rules for social interaction in its program memory? What is the relationship between the biology of humans and the sociality of persons? I argue that persons constitute an emergent ontological level that develops out of the biological and psychological realm, but that is largely social in its own constitution. This requires (...) a characterization of the relationships between the bio/psychological and the social, and of the developmental process of emergence. It also requires a framework for modeling the bio/psychological level that makes any such emergence possible. Neither attachment theory nor information processing frameworks, for example, will do — the major orientations toward human sociality today make understanding that sociality ultimately impossible. Only an action framework, such as that of Peirce or Piaget2, suffices. (shrink)

neglected aspect: knowledge of error, or ‘‘negative’’ knowledge. The development of knowledge of what counts as error occurs via a kind of internal variation and selection, or quasi-evolutionary, process. Processes of reflection generate a hierarchy of principles of error.

Dieser Aufsatz analysiert Leibniz' Begriff der Expression. Er ist eine Vorstudie zu einer umfassenden Untersuchung der Lehre, daß jede einfache Substanz das ganze Weltall ausdrückt. Leibnizens Beispiele und Definitionen von Expression werden besprochen, und dann wird die Analyse des Begriffs in zwei Stufen entwickelt.

The paper presents an account of the concept of existence that is based on Brentano’s work. In contrast to Frege and Russell, Brentano took ‘exists’ to express a that subsumes objects and explained it with recourse to the non-propositional attitude of acknowledgment. I argue that the core of Brentano’s view can be developed to a defensible alternative to the Frege-Russell view of existence.

Formal arguments have proven that avoiding the Repugnant Conclusion is impossible without rejecting one or more highly plausible population principles. To many, such proofs establish not only a deep challenge for axiology, but also pose an important practical problem of how policymaking can confidently proceed without resolving any of the central questions of population ethics. Here we offer deflationary responses: first to the practical challenge, and then to the more fundamental challenge for axiology. Regarding the practical challenge, we provide an (...) overview of recent literature that explores the implications for public policy of the Repugnant Conclusion and related puzzles within population ethics, and shows that there is more commonality in the implications of different population axiologies than is generally recognized. The upshot is that uncertainty about population ethics presents no important problem for policymaking, and the importance of population ethics to policymaking has been overstated. We then turn to more fundamental issues about axiology, and describe a new series of formal proofs that undermine the idea that any plausible axiology could avoid the Repugnant Conclusion, including those that are assumed to avoid it in the literature. The philosophical upshot is that the Repugnant Conclusion cannot plausibly be avoided, and so it is a mistake to assume as a constraint on a plausible axiology that it must be avoided, as is assumed by most of the literature in population ethics, including by all of the fundamental impossibility theorems. (shrink)

Many people have been enraged lately by the enormous increases in certain generic prescription drugs. But free marketeers defend these prices by arguing that they simply represent what the market will bear, and in a capitalist society there is accordingly nothing wrong with charging them. This paper argues that such a defense is actually contrary to the very principles that free marketeers claim to embrace. These prices are not only unjust and exploitative, but government interference with them would not render (...) the market less free, at least if what it means for a market to be “free” is properly understood. Everyone, even free marketeers with a libertarian or neoliberal bent, should accordingly be against this kind of profiteering. (shrink)

We have used fMRI to measure responses to chromatic and achromatic contrast in retinotopically defined regions of macaque and human visual cortex. We make four observations. Firstly, the relative amplitudes of responses to color and luminance stimuli in macaque area V1 are similar to those previously observed in human fMRI experiments. Secondly, the dorsal and ventral subdivisions of macaque area V4 respond in a similar way to opponent (L j M)-cone chromatic contrast suggesting that they are part of a single (...) functional area. Thirdly, we find that macaque area V4, like area V1, responds preferentially to chromatic contrast compared to luminance contrast and the degree of preference is strongly influenced by the temporal frequency of the stimulus. Finally, we observe that while macaque V4d is a region on the dorsal surface of the macaque visual cortex that responds robustly to chromatic stimuli, human chromatic responses to identical stimuli are largely confined to the ventral surface suggesting a fundamental difference in the topographical organization of higher visual areas between humans and macaques. (shrink)

ABSTRACT We consider several ways in which a good understanding of modern techniques and principles in physics can elucidate ecology, and we focus on analogical reasoning between these two branches of science. Analogical reasoning requires an understanding of both sciences and an appreciation of the similarities and points of contact between the two. In the current ecological literature on the relationship between ecology and physics, there has been some misunderstanding about the nature of modern physics and its methods. Physics is (...) seen as being much cleaner and tidier than ecology. When compared to this idealized, fictional version of physics, ecology looks very different, and the prospect of ecology and physics learning from one another is questionable. We argue that physics, once properly understood, is more like ecology than ecologists have thus far appreciated. Physicists and ecologists can and do learn from each other, and, in this paper, we outline how analogical reasoning can facilitate such exchanges. (shrink)

As with the problem of universals, late medieval thinkers were very concerned with the ontological status of relations, for they were central to numerous theological and philosophical problems. These relations were of various types: relations of identity, qualitative similarity, quantitative equality, causal relations, and intentional relations, such as those between knower and the object known. Each of these relations was taken to be an Aristotelian accident. Does it differ from the substance which is related? Broadly speaking, I have discovered four (...) alternative theories: as sentence of the form "a is related by a real relation R to b" is true only if the relation R is an extra-mental thing really distinct from a and b ; R only exists as a concept in a mind ; a and b exist in a certain real way ; the term "R" is connotative, signifying a directly and connoting b . Using printed sources and my critical edition of various codices, I ask the following thinkers whether a real relation is distinct from that which is related: Thomas Aquinas, Giles of Rome, Henry of Ghent, Richard of Middleton, John Duns Scotus, Henry of Harclay, Hervaeus Natalis, and Peter Aurioli. (shrink)

Time is perceived very differently from different vantage points. A year in the life of a primary-school student, for instance, is a very long time—somewhere between 1/5 and 1/ 12 of a primary-school child’s life. When you tlirow in the massive amount a child learns in any one year, compared with the diminishing returns that conspire against us later in life, a child’s year is more like a decade in adult years. But for a primary-school teacher, a school year is (...) just another ten or so months spent trying to remember names, delivering lessons, writing report cards, and endeavoring to shepherd students through the educational system. And, of course, the classroom is just one part of a teacher’s life. Teachers are juggling other serious and timeconsuming matters such as relationships, mortgages, further study, family and so forth. The best teachers, however, don’t let on about these asymmetries between the child’s world and their own; they conceal the differences in temporal perception and they give no clue that each student is just a small part of their life. Such sleight of hand can’t be easy, yet all my primary school teachers pulled it off to perfection. One, however, deserves special mention: Mr. Williams. In 1969 I turned 11 and was in 6th class at the Armidale Demonstration.. (shrink)

In this book Noel Curran suggests that considerations in the philosophy of mathematics—in particular, the proper interpretation of quaternions—leads to a “new” philosophy of space and time. According to Curran: space is Euclidean; time is absolute, flows and has a beginning; and God created the universe at the beginning of time.

This book is a must-read for researchers interested in taking a high-level, non-mechanistic approach to answering age-old fundamental questions in the brain ...

Values Education in Schools is a new resource for teachers involved in values and ethics education. It provides a range of 'practical philosophy' resources for secondary school teachers that can be used in English, religious education, citizenship, personal development and social science subjects. The materials include narratives to engage students in philosophical inquiry, doing ethics through the activity of philosophy, not simply learning about it.

With Fermat’s Last Theorem finally disposed of by Andrew Wiles in 1994, it’s only natural that popular attention should turn to arguably the most outstanding unsolved problem in mathematics: the Riemann Hypothesis. Unlike Fermat’s Last Theorem, however, the Riemann Hypothesis requires quite a bit of mathematical background to even understand what it says. And of course both require a great deal of background in order to understand their significance. The Riemann Hypothesis was first articulated by Bernhard Riemann in an address (...) to the Berlin Academy in 1859. The address was called “On the Number of Prime Numbers Less Than a Given Quantity” and among the many interesting results and methods contained in that paper was Riemann’s famous hypothesis: all non-trivial zeros of the zeta function, ζ(s) = ∞ n=1 n−s, have real part 1/2. Although the zeta function as stated and considered as a real-valued function is defined only for s > 1, it can be suitably extended. It can, as a matter of fact, be extended to have as its domain all the complex numbers (numbers of the form x + yi, where x and y √ −1) with the exception of 1 + 0i (at which point are real numbers and i =. (shrink)

It is an excellent companion to Plato's Dialogues.

Hegel thinks the state is so important to our identity that we should be willing to give our lives for it. He characterizes the state as our ethical "substance." It is sometimes inferred from this that he thinks members of a modern state form a tightly-knit, culturally and ethnically homogeneous community. A close reading of his texts shows, rather, that Hegel does not think they must be a "community," or of the same race or ethnicity, or speak the same language, (...) or practice the same religion. I explore Hegel's view of the ties that bind members of a state, arguing that what he thinks members must share are social practices. I conclude by considering whether in his effort to forge a common identity Hegel resorts to ties too weak to justify the claims he makes about the state being our substance, something worth dying for. (shrink)

In the 1990s a rise of populist or regionalist parties in Western democracies has challenged the ruling centrist consensus.1 There are, however, only a few similarities between them. Thus it is impossible to equate, e.g., Austria's Jörg Haider or France's Jean-Marie Le Pen with Canada's Preston Manning. Diverse political cultures produce different political figures, programs and ideologies. When all is said and done, Manning's Reform Party remains idiosyncratically Canadian, and it is necessary to examine the Canadian context within which it (...) arose in order to understand it. Generally speaking, the Reform Party offers little to traditionalists, while its “populism” often…. (shrink)