We show here that the first order theory of the positive integers equipped with multiplication remains decidable when one adds to the language the usual order restricted to the prime numbers. We see moreover that the complexity of the latter theory is a tower of exponentials, of height O(n).

We show in this paper that the theory of ordinal addition of any fixed ordinal ωα, with α less than ωω, admits a quantifier elimination. This in particular gives a new proof for the decidability result first established in 1965 by R. Büchi using transfinite automata. Our proof is based on the Ehrenfeucht games, and we show that quantifier elimination go through generalized power.RésuméOn montre ici que, pour tout ordinal α inférieur à ωω, la théorie additive de ωα admet une (...) élimination des quantificateurs. On obtient ainsi une nouvelle preuve de la décidabilité de ces théories . On utilise ici les jeux d'Ehrenfeucht, avec un formalisme à la Ferrante et Rackoff, et on montre que le fait d'admettre une élimination des quantificateurs se transmet par produit généralisé. (shrink)

: Françoise Dastur describes her efforts to practice history of philosophy in a (paradoxically) non-historical fashion. She discusses her concept of the historical, and argues that the only true way to be of one's time is to be against one's time.

Françoise Dastur describes her efforts to practice history of philosophy in a non-historical fashion. She discusses her concept of the historical, and argues that the only true way to be of one's time is to be against one's time.

The treatise attempts to approach and deal with some of the most fundamental problems facing anyone who wishes to uphold some version of the so-called theory of tropes. Three assumptions serve as a basis for the investigation: tropes exist, only tropes exist, and a one-category trope-theory along these lines should be developed so that the tropes it postulates are able to serve as truth-makers for all kinds of atomic propositions. Provided that these assumptions are accepted, it is found that the (...) trope-theorist will have to deal with two important problems. First, some atomic propositions seem to require universal truth-makers. Second, some atomic propositions seem to require concrete truth-makers. As tropes are abstract particulars, it follows that the trope-theorist, in order to fulfil assumption, must provide an account of exactly how he or she could construct universality and concreteness from his or her basic stock of tropes. In the treatise such constructions are attempted and some basic problems with such constructions are revealed. Although these problems are serious enough it is argued that it is nevertheless possible to deal with these basic issues while staying squarely within the boundaries of a one-category trope-ontology. (shrink)

That there could be ontologically complex concrete particulars is self-evidently true. A reductio may however be formulated which contradicts this truth. In this paper I argue that all of the reasonable ways in which we might refute this reductio will require the existence of at least some tropes.

Grounding theorists insist that grounding and explanation are intimately related. This claim could be understood as saying either that grounding ‘inherits’ its properties from explanation or it could be interpreted as saying that grounding plays an important—possibly an indispensable—role in metaphysical explanation. Or both. I argue that saying that grounding ‘inherits’ its properties from explanation can only be justified if grounding is explanatory by nature, but that this view is untenable. We ought therefore to be ‘separatists’ and view grounding and (...) explanation as distinct. As it turns out, though, once grounding has been in this sense distinguished from the explanation it backs, the view that the role grounding plays in explanation justifies its introduction ends up in serious trouble. I conclude that the role grounding plays in explanation does not justify attributing to grounding whatever nature we think it has, and it most likely does not give us any special reason to think grounding exists. (shrink)

Donald Davidson claims that, by studying the most general aspects of natural language, we will also be studying the most general aspects of reality.In particular, this means that, through the application of a systematic truththeory to natural language, we will be able to reveal its basic structure, its true logical form. Once this logical form has been spelled out, we will be able to determine the finite stock of important constituents of which sentences are built, and also the specific roles (...) these “atoms” play in the relevant structure. Since the structure of language can be said to “mirror” the structure of reality, this also means that we can now say something about the basic constituents of the world. We will be able to tell which kinds of entities exist and which do not. If, by spelling out the logical form, we find that there is a sentence (or several sentences) committing us to the existence of a certain (kind of) object (i.e. a sentence where an object (of this kind)serves as the value of a quantified variable) and, if we know the sentence to be true, then we have good reason to suppose that there is an object (of that kind) rather than not. This will hold given that there is no other way of spelling out the logical form of the sentence in question that is compatible with the nonexistence of that (kind of) object. So what exists is what, according to the (complete) theory, functions as values of the quantified variables, once thelogical form, the basic structure, of all the sentences of the language has been spelled out. Davidson has claimed that what all this quantificational structure will demand from ontology is the existence of objects and particular events. This should be taken somewhat at faith. In order to reach valid conclusions concerning the logical form of natural language, Davidson would have to examine allof its true sentences, and state allof their truth conditions, which he has not done. For practical reasons he has only been able to look at small segments of language, to consider how they normally function, to attempt to exhibit their logical structure by looking at entailment-relations, etc., and it is from this that he has drawn his ontological conclusions. In this paper, I concentrate on some of the likely consequences of the adoption of this method of reaching ontological conclusions. In particular, I will try to show that Davidson’s own way of arguing for the existence of events can be applied to cases where he seemingly would have to commit himself to the existence of properties too. To demonstrate this, I begin by considering whether the fact that Davidson spells out the logical form of natural language in first-order logic raises a serious objection to my claim or not. I then proceed by making a case for properties using an argument based on what Davidson has to say about the existence of events. What I will try to show is that, if Davidson is to be true to his general method of reaching conclusions regarding existence, which he claims to be, then he must go where this method leads him. This means that he has to keep his mind open as to the kinds of entities he should or should not allow. Finally, assuming that I have shown properties to be one of the different kinds of entities that a Davidsonian would have to allow, I conclude the paper by indicating what the consequence(s) of this may be. (shrink)

This article is the text of an interview with D. H. Mellor conducted in Cambridge on 30 May 2001 by Anna-Sofia Maurin and Johannes Persson for the philosophical journal Theoria.

Trope theory is the view that the world is a world of abstract particular qualities. But if all there is are tropes, how do we account for the truth of propositions ostensibly made true by some concrete particular? A common answer is that concrete particulars are nothing but tropes in compresence. This answer seems vulnerable to an argument (first presented by F. H. Bradley) according to which any attempt to account for the nature of relations will end up either in (...) contradiction, nonsense, or will lead to a vicious infinite regress. I investigate Bradley’s argument and claim that it fails to prove what it sets out to. It fails, I argue, because it does not take all the different ways in which relation and relata may depend on one another into account. If relations are entities that are distinct from yet essentially dependent upon their relata, the Bradleyan problem is solved. We are then free to say that tropes in compresence are what make true propositions ostensibly made true by concrete particulars. (shrink)

Françoise Dastur describes her efforts to practice history of philosophy in a (paradoxically) non-historical fashion. She discusses her concept of the historical, and argues that the only true way to be of one's time is to be against one's time.

Françoise Dastur describes her efforts to practice history of philosophy in a non-historical fashion. She discusses her concept of the historical, and argues that the only true way to be of one's time is to be against one's time.

Trope theory is the view that the world consists (wholly or partly) of particular qualities, or tropes. This admittedly thin core assumption leaves plenty of room for variation. Still, most trope theorists agree that their theory is best developed as a one-category theory according to which there is nothing but tropes. Most hold that ‘sameness of property’ should be explained in terms of resembling tropes. And most hold that concrete particulars are made up from tropes in compresence (for an overview, (...) including an introduction to some alternative versions of the view, cf. Maurin, 2014). D. M. Armstrong disagrees. He thinks the world is a world of immanent universals, the thin particulars in which those universals are instantiated, and the states of affairs that—thereby—exist. He holds that ‘sameness of property’ should be explained in terms of numerically identical universals or—if the resembling things are the universals themselves—in terms of partially identical universals. And he believes that concrete particulars are made up from ‘thin particulars’ in which a (sufficient) number of universals are instantiated. In spite of their disagreements, proponents of tropes owe Armstrong a debt of gratitude. First, for being one of the theory’s earliest, most serious, and—not least—most prominent, critics (Armstrong for the first time considers, and rejects, what he then labels ‘particularism’, in his 1978a). But also for being one of the theory’s most ardent champions. Already in his 1989a, Armstrong regrets his 1978-rejection of the view. Equivalence classes of exactly resembling tropes, he now admits, for most purposes “serve as an excellent substitute for universals” (Armstrong 1989a, 122). But then why isn’t Armstrong a trope theorist? In this paper, Armstrong’s main reasons for rejecting the trope view are critically scrutinized. All of them, it is maintained, fail to convince. If this argument is accepted, Armstrong seems to have no—or, at least, no good—reason for not accepting the existence of tropes. But, then, ought Armstrong to have been a trope theorist? If the ‘best’ version of the trope view turns out to be ontologically more parsimonious than Armstrong’s own theory of universals, then, yes. That there is a version of the trope view, a version that is not (or, at least not seriously) considered by Armstrong, that is ontologically more parsimonious than the universals view, is argued in the next section. Why none of Armstrong’s reasons for preferring universals to tropes manage to convince, is explained in the section after that. First, however, and in order to avoid a common misunderstanding of the trope view and, as a consequence, of why one ought to reject it, a few more words about the core-difference between tropes and universals, and about how this difference matters (as well as does not matter) to what—and how well—these theories explain. (shrink)

We use genomic information to tell us stories of evolutionary origins. But what does it mean when different genomes report wildly different accounts of lineage history? This genomic “discordance” can be a consequence of a fascinating suite of natural history and evolutionary phenomena, from the different inheritance mechanisms of nuclear versus cytoplasmic (mitochondrial and plastid) genomes to hybridization and introgression to horizontal transfer. Here, we explore how we can use these distinct genomic stories to provide new insights into the maintenance (...) of sexual reproduction, one of the most important unanswered questions in biology. We focus on the strikingly distinct nuclear versus mitochondrial versions of the story surrounding the origin and maintenance of asexual lineages in Potamopyrgus antipodarum, a New Zealand freshwater snail. While key questions remain unresolved, these data inspire multiple testable hypotheses that can be powerfully applied across a broad range of taxa toward a deeper understanding of the causes and consequences of mitonuclear discordance, the maintenance of sex, and the origin of new asexual lineages. (shrink)

Ever since F. H. Bradley first formulated his famous regress argument philosophers have been hard at work trying to refute it. The argument fails, it has been suggested, either because its conclusion just does not follow from its premises, or it fails because one or more of its premises should be given up. In this paper, the Bradleyan argument, as well as some of the many and varied reactions it has received, is scrutinized.

Paper responding to critique of Maurin (2002) presented by Herbert Hochberg in his “Relations, Properties and Particulars” (2004).

In this chapter, we introduce the perennial and sometimes sprawling topic of properties, with a brief historical sketch from Ancient to Modern philosophy throughout various cultures and traditions. We argue that the importance of properties can be shown by explaining what explanatory work they can do in philosophical theorising across many areas of philosophy. The chapters in this volume do just that in their specific ways. We also outline the structure of the volume and summarise each Part, first describing the (...) larger context of each Part and then the upshot of each chapter. (shrink)

oise Baylis, 1234 Le Marchant Street, Halifax, Nova Scotia, Canada B3H 3P7. Tel.: (902)-494–2873; Fax: (902)-494-2924; Email: francoise.baylis{at}dal.ca ' + u + '@' + d + ' '//--> . Abstract Recently, there has been a growing interest in public health and public health ethics. Much of this interest has been tied to efforts to draw up national and international plans to deal with a global pandemic. It is common for these plans to state the importance of drawing upon a (...) well-developed ethics framework and we argue that this framework should reflect the values and insights of feminist relational theory. More specifically, we argue that pandemic planning must be squarely situated in the larger realm of public health and that an ethics framework for public health will be one that recognizes the need to pay particular attention to the vulnerability of subpopulations lacking in social and economic power. We propose an ethics framework for public health that builds on the notions of relational personhood (including relational autonomy and social justice) and relational solidarity. In this way, we aim for a public health ethics that, as appropriate, promotes the public interest and the common good. CiteULike Connotea Del.icio.us What's this? (shrink)

Most philosophers adopt an etiological conception of functions, but not one that uniformly explains the functions attributed to material entities irrespective of whether they are natural or man-made. Here, I investigate the widespread idea that a combination of the two current etiological theories, SEL and INT, can offer a satisfactory account of the proper functions of both organisms and artifacts.. Making explicit what a realist theory of function supposes, I first show that SEL offers a realist theory of biological functions (...) in which these are objective properties of a peculiar sort. I argue next that an artifact function demonstrates the same objective nature as a biological function when it is accounted for by SEL, but not when it is accounted for by INT. I explain why a dual theory of artifact functions admitting both INT and SEL functions is to be dismissed. I establish that neither INT nor SEL alone can account for all artifact functions. Drawing the conclusion that we need a new etiological theory of function, I show how one can overcome the apparent inevitability of INT for some artifact functions. Finally, I outline a new etiological theory of functions that applies equally to biological entities and to artifacts. (shrink)

How, asks Françoise Dastur, can philosophy account for the sudden happening and the factuality of the event? Dastur asks how phenomenology, in particular the work of Heidegger, Husserl, and Merleau-Ponty, may be interpreted as offering such an account. She argues that the "paradoxical capacity of expecting surprise is always in question in phenomenology," and for this reason, she concludes, "We should not oppose phenomenology and the thinking of the event. We should connect them; openness to phenomena must be identified with (...) openness to unpredictability." The article offers reflections in these terms on a phenomenology of birth. (shrink)

How, asks Françoise Dastur, can philosophy account for the sudden happening and the factuality of the event? Dastur asks how phenomenology, in particular the work of Heidegger, Husserl, and Merleau-Ponty, may be interpreted as offering such an account. She argues that the “paradoxical capacity of expecting surprise is always in question in phenomenology,” and for this reason, she concludes, “We should not oppose phenomenology and the thinking of the event. We should connect them; openness to phenomena must be identified with (...) openness to unpredictability.” The article offers reflections in these terms on a phenomenology of birth. (shrink)

In this paper I critically investigate an unorthodox attempt to metaphysically explain in virtue of what there are states of affairs. This is a suggestion according to which states of affairs exist thanks to, rather than, as is the common view, in spite of, the infinite regress their metaphysical explanation seems to engender. I argue that, no matter in which form it is defended, or in which theoretical framework it is set, this suggestion cannot provide us with the explanation we (...) crave. (shrink)

In this paper I argue that the infinite regress of resemblance is vicious in the guise it is given by Russell but that it is virtuous if generated in a (contemporary) trope theoretical framework. To explain why this is so I investigate the infinite regress argument. I find that there is but one interesting and substantial way in which the distinction between vicious and virtuous regresses can be understood: The Dependence Understanding. I argue, furthermore, that to be able to decide (...) whether an infinite regress exhibits a dependence pattern of a vicious or a virtuous kind, facts about the theoretical context in which it is generated become essential. It is precisely because of differences in context that he Russellian resemblance regress is vicious whereas its trope theoretical counterpart is not. (shrink)

Chronique/critique de Françoise Favretto parue dans la revue L'intranquille. Revue de littérature, n° 20, St-Quentin-de-Caplong, L'Atelier de l'Agneau, 2021, p. 83. - Recensions.

How, asks Françoise Dastur, can philosophy account for the sudden happening and the factuality of the event? Dastur asks how phenomenology, in particular the work of Heidegger, Husserl, and Merleau-Ponty, may be interpreted as offering such an account. She argues that the “paradoxical capacity of expecting surprise is always in question in phenomenology,” and for this reason, she concludes, “We should not oppose phenomenology and the thinking of the event. We should connect them; openness to phenomena must be identified with (...) openness to unpredictability.” The article offers reflections in these terms on a phenomenology of birth. (shrink)

THERE WAS A TIME when many philosophers agreed that metaphysics was dead. Anyone aquatinted with the works of D.H. Mellor knows that the subject is alive and well. Two young philosophers who are familiar with his work, Anna-Sofia Maurin and Johannes Persson, met him in Cambrige for an interview.

We outline a number of ethical objections to genetic technologies aimed at enhancing human capacities and traits. We then argue that, despite the persuasiveness of some of these objections, they are insufficient to stop the development and use of genetic enhancement technologies. We contend that the inevitability of the technologies results from a particular guiding worldview of humans as masters of the human evolutionary future, and conclude that recognising this worldview points to new directions for ethical thinking about genetic enhancement (...) technologies. (shrink)

This work was supported, in part, by a Stem Cell Network grant to Françoise Baylis and Jason Scott Robert and a CIHR grant to Françoise Baylis. We sincerely thank Alan Fine, Rich Campbell, Cynthia Cohen, and Tim Krahn for helpful comments on an earlier draft of this paper. Thanks are also owed to Tim Krahn for his research assistance. An earlier version of this paper was presented to the Department of Bioethics and the Novel Tech Ethics research team. We thank (...) the participants at each of these meetings for their helpful comments. (shrink)

Eklund vs. Bradley : Regress, Relation, Explanation.

This article probes the visual spatial représentations underlying the creative conceptual design of complex objects.

According to Johansson (2009: 22) an infinite regress is vicious just in case “what comes first [in the regress-order] is for its definition dependent on what comes afterwards.” Given a few qualifications (to be spelled out below (section 3)), I agree. Again according to Johansson (ibid.), one of the consequences of accepting this way of distinguishing vicious from benign regresses is that the so-called Russellian Resemblance Regress (RRR), if generated in a one-category trope-theoretical framework, is vicious and that, therefore, the (...) existence of tropes only makes sense if trope-theory is understood (minimally) as a two-category theory which accepts, besides the existence of tropes, also the existence of at least one universal: resemblance.1 I disagree. But how can that be? How can Johansson and I agree about what distinguishes a vicious from a benign regress, yet disagree about which regresses are vicious and which are benign? In this paper I attempt to answer that question by first setting out and defending the sense of viciousness which both Johansson and I accept, only to then argue that to be able to determine if a particular regress is vicious in this sense, more than features intrinsic to the regress itself must be taken into account. This is why, although the RRR as originally set out by Russell is vicious, the seemingly identical resemblance regress which ensues in a one-category (standard) trope-theoretical context is not (provided, that is, that we accept certain views about how the nature of tropes relates to the resemblance between tropes, and given that we set our theory in a truthmaker theoretical framework – all of which are standard assumptions for proponents of (the standard-version of) the trope-theory).2. (shrink)