This paper looks at how the idea of pointless topology itself evolved during its pre-localic phase by analyzing the definitions of the concept of topological space of Menger and Nöbeling. Menger put forward a topology of lumps in order to generalize the definition of the real line. As to Nöbeling, he developed an abstract theory of posets so that a topological space becomes a particular case of topological poset. The analysis emphasizes two points. First, Menger's geometrical perspective was superseded by (...) an algebraic one, a lattice-theoretical one to be precise. Second, Menger's bottom–up approach was replaced by a top–down one. (shrink)
Faculty plagiarism and fraud are widely documented occurrences but little analysis has been conducted. This article addresses the question of why faculty plagiarism and fraud occurs and suggests approaches on how to develop an environment where faculty misconduct is socially inappropriate. The authors review relevant literature, primarily in business ethics and student cheating, developing action steps that could be applied to higher education. Based upon research in these areas, the authors posit some actions that would be appropriate in higher education (...) and suggest topics for continued study. (shrink)
In this paper, I introduce the idea that some important parts of contemporary pure mathematics are moving away from what I call the extensional point of view. More specifically, these fields are based on criteria of identity that are not extensional. After presenting a few cases, I concentrate on homotopy theory where the situation is particularly clear. Moreover, homotopy types are arguably fundamental entities of geometry, thus of a large portion of mathematics, and potentially to all mathematics, at least according (...) to some speculative research programs. (shrink)
Nietzsche, in his work On the Genealogy of Morals, argues that human cognition is analogous in certain significant respects to the perspectival nature of optical vision. Because of this analogy, his account of human cognition is often referred to as perspectivism. Brian Leiter argues that Nietzsche’s use of this optical perspective metaphor undermines interpretations that take perspectivism to have radically skeptical implications. In this paper, I examine Leiter’s argument and show that the considerations he raises based on the optical perspective (...) metaphor are insufficient to undermine the claim that perspectivism entails radical skepticism. (shrink)
According to Carson Strong, the future of value account of the wrongness of killing is subject to counterexamples. Ezio Di Nucci has disagreed. Their disagreement turns on whether the concepts of a future of value and a future like ours are equivalent. Unfortunately, both concepts are fuzzy, which explains, at least in part, the disagreement. I suggest that both concepts can be clarified in ways that seem plausible and that makes them equivalent. Strong claims that better accounts of the wrongness (...) of killing exist. I show that those alternative accounts are unsatisfactory. (shrink)
In this paper, I present and discuss critically the main elements of Mario Bunge’s philosophy of mathematics. In particular, I explore how mathematical knowledge is accounted for in Bunge’s systemic emergent materialism.To Mario, with gratitude.
We model the forgetting of propositional variables in a modal logical context where agents become ignorant and are aware of each others' or their own resulting ignorance. The resulting logic is sound and complete. It can be compared to variable-forgetting as abstraction from information, wherein agents become unaware of certain variables: by employing elementary results for bisimulation, it follows that beliefs not involving the forgotten atom(s) remain true.
A Study of the History and Philosophy of Category Theory Jean-Pierre Marquis. to say that objects are dispensable in geometry. What is claimed is that the specific nature of the objects used is irrelevant. To use the terminology already ...
We model the forgetting of propositional variables in a modal logical context where agents become ignorant and are aware of each others’ or their own resulting ignorance. The resulting logic is sound and complete. It can be compared to variable-forgetting as abstraction from information, wherein agents become unaware of certain variables: by employing elementary results for bisimulation, it follows that beliefs not involving the forgotten atom(s) remain true.
The aim of this paper is to put into context the historical, foundational and philosophical significance of category theory. We use our historical investigation to inform the various category-theoretic foundational debates and to point to some common elements found among those who advocate adopting a foundational stance. We then use these elements to argue for the philosophical position that category theory provides a framework for an algebraic in re interpretation of mathematical structuralism. In each context, what we aim to show (...) is that, whatever the significance of category theory, it need not rely upon any set-theoretic underpinning. (shrink)
This essay is a response to Julian Savulescu’s objections to the future of value argument for the immorality of abortion published in the Journal of Medical Ethics, June 2002. Firstly, Savulescu’s claim that the future of value argument has implausible implications is considered. The author argues that the argument does not have these implications. Secondly, properties which, according to Savulescu, could underwrite the wrongness of killing and that are acquired only after implantation, are considered. It is argued that none of (...) these properties is an adequate basis for the distinction between wrongful and permissible killing. (shrink)
In this issue of the journal Mark Brown has offered a new argument against my potential future of value theory. I argue that even though the premises of this new argument are far more defensible than the premises of his old argument, the new argument does not show that the potential future of value theory of the wrongness of killing is false. If the considerations to which Brown appeals are used, not to show that the potential future of value theory (...) is false, but to show that abortion is morally permissible, they are also unsuccessful. I also argue that Brown's clarified self-represented future of value account and Simon Parsons's account of the wrongness of killing are both subject to major difficulties. Finally, I show, in an appendix, that Brown's assertion that my discussion of his views suffers from major logical errors is false. (shrink)
In this paper, the problem of purifying an assumption-based theory KB, i.e., identifying the right extension of KB using knowledge-gathering actions (tests), is addressed. Assumptions are just normal defaults without prerequisite. Each assumption represents all the information conveyed by an agent, and every agent is associated with a (possibly empty) set of tests. Through the execution of tests, the epistemic status of assumptions can change from "plausible" to "certainly true", "certainly false" or "irrelevant", and the KB must be revised so (...) as to incorporate such a change. Because removing all the extensions of an assumption-based theory except one enables both identifying a larger set of plausible pieces of information and renders inference computationally easier, we are specifically interested in finding out sets of tests allowing to purify a KB (whatever their outcomes). We address this problem especially from the point of view of computational complexity. (shrink)
In my essay, Why abortion is immoral, I criticised discussions of the morality of abortion in which the crucial issue is whether fetuses are human beings or whether fetuses are persons. Both argument strategies are inadequate because they rely on indefensible assumptions. Why should being a human being or being a person make a moral difference? I argued that the correct account of the morality of abortion should be based upon a defensible account of why killing children and adults is (...) wrong. I claimed that what makes killing us wrong is that our premature deaths deprive us of our futures of value, that is, the goods of life we would have experienced had we survived. This account of the wrongness of killing explains why killing is one of the worst of crimes and how killing greatly harms the victim. It coheres with the attitudes of those with cancer or HIV facing premature death. It explains why we believe it is wrong to kill infants (as personhood theories do not). It does not entail that it wrongs a human being to end her life if she is in persistent vegetative state or if her future must consist only of unbearable physical suffering and she wants to die (as sanctity of human life theories do not). This account of the wrongness of killing implies (with some defensible additional assumptions) that abortion is immoral because we were fetuses once and we know those fetuses had futures of value. Mark Brown claims that this potential future of value account is unsound because it implies that we have welfare rights to what we need to stay alive that most people would reject. I argue that Brown is incorrect in two ways: a welfare right to what we need to stay alive is not directly implied by my account and, in addition, most of us do believe that dependent human beings have substantial welfare rights to what they need to stay alive. Brown argues that depriving us of a future of value of which we have mental representations both is a better explanation of the wrongness of killing and does not imply that abortion is immoral. I reply that (a) if Brown's arguments against my view were sound, those arguments could be easily adapted to show that his view is unsound as well and (b) Brown's view is both ambiguous and unsound on any interpretation. The most popular class of pro-choice argument strategies appeals to the view that some or all fetuses lack either a mental state or function or a capacity for a mental state or function necessary for possession of the right to life. Desires, interests, sentience, various concepts, moral agency, and rationality have all been suggested as candidates for this crucial mental role. Brown's analysis is one member of this class of strategies. I believe that it is possible to show that none of these strategies is reasonable. However, there are so many of these strategies that the required argument demands something more like a book and less like a short essay. The argument of the following essay is a piece of this larger argument. (shrink)
In this paper, I introduce and examine the notion of “mathematical engineering” and its impact on mathematical change. Mathematical engineering is an important part of contemporary mathematics and it roughly consists of the “construction” and development of various machines, probes and instruments used in numerous mathematical fields. As an example of such constructions, I briefly present the basic steps and properties of homology theory. I then try to show that this aspect of contemporary mathematics has important consequences on our conception (...) of mathematical knowledge, in particular mathematical growth. (shrink)
In this paper, we try to establish that some mathematical theories, like K-theory, homology, cohomology, homotopy theories, spectral sequences, modern Galois theory (in its various applications), representation theory and character theory, etc., should be thought of as (abstract) machines in the same way that there are (concrete) machines in the natural sciences. If this is correct, then many epistemological and ontological issues in the philosophy of mathematics are seen in a different light. We concentrate on one problem which immediately follows (...) the recognition of the particular status of these theories: the demarcation problem between ‘natural kinds’ and ‘artefacts’. (shrink)