How far should our realism extend? For many years philosophers of mathematics and philosophers of ethics have worked independently to address the question of how best to understand the entities apparently referred to by mathematical and ethical talk. But the similarities between their endeavours are not often emphasised. This book provides that emphasis. In particular, it focuses on two types of argumentative strategies that have been deployed in both areas. The first—debunking arguments—aims to put pressure on realism by emphasising the (...) seeming redundancy of mathematical or moral entities when it comes to explaining our judgements. In the moral realm this challenge has been made by Gilbert Harman and Sharon Street; in the mathematical realm it is known as the 'Benacerraf-Field' problem. The second strategy—indispensability arguments—aims to provide support for realism by emphasising the seeming intellectual indispensability of mathematical or moral entities, for example when constructing good explanatory theories. This strategy is associated with Quine and Putnam in mathematics and with Nicholas Sturgeon and David Enoch in ethics. Explanation in Ethics and Mathematics addresses these issues through an explicitly comparative methodology which we call the 'companions in illumination' approach. By considering how argumentative strategies in the philosophy of mathematics might apply to the philosophy of ethics, and vice versa, the papers collected here break new ground in both areas. For good measure, two further companions for illumination are also broached: the philosophy of chance and the philosophy of religion. Collectively, these comparisons light up new questions, arguments, and problems of interest to scholars interested in realism in any area. (shrink)

We address the following questions in this paper: (1) Which set or number existence axioms are needed to prove the theorems of ‘ordinary’ mathematics? (2) How should Frege’s theory of numbers be adapted so that it works in a modal setting, so that the fact that equivalence classes of equinumerous properties vary from world to world won’t give rise to different numbers at different worlds? (3) Can one reconstruct Frege’s theory of numbers in a non-modal setting without mathematical primitives such (...) as “the number of Fs” ( $$\#F$$ ) or mathematical axioms such as Hume’s Principle? Our answer to question (1) is ‘None’. Our answer to question (2) begins by defining ‘x numbers G’ as: x encodes all and only the properties F such that being-actually-F is equinumerous to G with respect to discernible objects. We answer (3) by showing that the mere existence of discernible objects allows one to reconstruct Frege’s derivation of the Dedekind-Peano axioms in a non-modal setting. (shrink)

Commentators provide two different accounts of desires in Kant: “feeling-based” accounts stress their connection with feelings, while “action-based” accounts view them as causes of action. I argue that “feeling-based” accounts blur the feeling-desire distinction, while the “action-based” accounts conflict with Kantian desires that do not cause action. On my alternative, Kantian desires are dispositions to action normally directed at producing future objects, and so they differ from the feelings they are connected to, which refer to the way we are affected (...) by objects. This account preserves the feeling-desire distinction, is compatible with desires that do not cause action, and anticipates holistic theories of desire that combine dispositional, hedonic, and evaluative components. (shrink)

Descartes claimed that the Cogito is ‘so firm and sure that all the most extravagant suppositions of the sceptics were incapable of shaking it’. This paper aims to demonstrate that this claim is false by presenting a sceptical scenario for the Cogito. It is argued that the story ‘The Circular Ruins’ by J. L. Borges illustrates that one can doubt one’s own existence and that pace Descartes (and many others) the claim ‘I am, I exist, is necessarily true whenever it (...) is put forward by me or conceived in my mind’ is false. (shrink)

We discuss the problem of finding forcing posets which introduce closed unbounded subsets to a given stationary set.

We present two experiments that cast doubt on existing evidence suggesting that it is impossible to suspend belief in a comprehended proposition. In Experiment 1, we found that interrupting the encoding of a statement's veracity decreased memory for the statement's falsity when the false version of the statement was uninformative, but not when the false version was informative. This suggests that statements that are informative when false are not represented as if they were true. In Experiment 2, participants made faster (...) lexical decisions to words implied by preceding statements when they were told that the statements were true than when the veracity of the statements was unknown or when the statements were false. The findings suggest that comprehending a statement may not require believing it, and that it may be possible to suspend belief in comprehended propositions. (shrink)

Commentators disagree about Kant’s view on the proper treatment of emotions. In contrast to a tendency in this literature to treat them uniformly, I argue that, according to Kant, feelings (but not affects) require cultivation, and inclinations – although they can and perhaps may be cultivated – generally require discipline. The appropriate treatment for emotions depends on their susceptibility to rational constraint and on the threat they pose to rational deliberation. Although I read Kant as recommending that we cultivate certain (...) emotions, I argue that my reading is not vulnerable to Thomason’s recent pertinent objections to such readings. (shrink)

In this paper I assess the viability of a particularist explanation of moral knowledge. First, I consider two arguments by Sean McKeever and Michael Ridge that purport to show that a generalist, principle-based explanation of practical wisdom—understood as the ability to acquire moral knowledge in a wide range of situations—is superior to a particularist, non-principle-based account. I contend that both arguments are unsuccessful. Then, I propose a particularist-friendly explanation of knowledge of particular moral facts. I argue that when we are (...) careful to keep separate the various explanatory tasks at hand we can see that a particularist-friendly explanation of the fact that Jane knows that A is morally right might not be so difficult to come by. Moreover, I suggest that a particularist approach to explaining knowledge of particular moral facts may go some way towards discharging the challenge of moral scepticism. (shrink)

In this essay I offer a new particularist reading of Aristotle’s Nicomachean Ethics. I argue that the interpretation I present not only helps us to resolve some puzzles about Aristotle’s goals and methods, but it also gives rise to a novel account of morality—an account that is both interesting and plausible in its own right. The goal of this paper is, in part, exegetical—that is, to figure out how to best understand the text of the Nicomachean Ethics. But this paper (...) also aims to contribute to the current exciting and controversial debate over particularism. By taking the first steps towards a comprehensive particularist reading of Aristotle’s Ethics I hope to demonstrate that some of the mistrust of particularism is misplaces and that what is, perhaps, the most influential moral theory in the history of philosophy is, arguably, a particularist moral theory. (shrink)

We investigate the form of mathematical structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to criticisms recently, and our view is that the problems raised are resolved by proper, mathematics-free theoretical foundations. Starting with an axiomatic theory of abstract objects, we identify a mathematical structure as an abstract object encoding the truths of a mathematical theory. From such foundations, we derive consequences that address the main questions and issues that (...) have arisen. Namely, elements of different structures are different. A structure and its elements ontologically depend on each other. There are no haecceities and each element of a structure must be discernible within the theory. These consequences are not developed piecemeal but rather follow from our definitions of basic structuralist concepts. (shrink)

According to Alix Cohen, Kant defines emotions as ‘feelings’. Although I find her account of Kantian feelings compelling, I provide three reasons to doubt that it is an account of emotions: (1) it is unclear why Cohen identifies emotions with Kantian feelings; (2) some Kantian feelings are not emotions; (3) some Kantian desires may be emotions. I propose, however, that with some qualifications Cohen’s account may be upheld, provided its extra-textual assumptions about emotions are explicated. Against her claim that Kantian (...) feelings have a derived intentionality, I argue that the text is compatible with their being intrinsically intentional. (shrink)

The lambda model of Feldman & Levin for intentional hand movement is compared with a hemispheric motor model (IIMM). Both models imply similar conclusions independently. This increases the validity of both models.

Dans plusieurs passages, Épicure mentionne des durées infraperceptibles saisies par la raison, ce qui conduit à envisager un atomisme du temps, c’est-à-dire l’existence de durées indivisibles ou quanta de temps. Cette hypothèse, nulle part explicite chez Épicure et Lucrèce, a été évoquée par quelques doxographes. L’objet de cet article est de l’étayer et de la préciser, en lisant les textes épicuriens sur le temps à la lumière des trois grandes objections antiatomistes de la Physique. Notre analyse conclut que l’atomisme du (...) temps permet de répondre aux objections d’Aristote, mais doit être limité au seul niveau des atomes, par opposition à celui des agrégats. Il permet alors en effet de justifier l’isotachie des atomes, de rendre concevable la communauté de structure de la grandeur, du mouvement et du temps, et de garantir le caractère fini de la vitesse atomique. Deux lignes argumentatives se superposent : une conception proprement atomiste du mouvement et une reprise des termes de la physique aristotélicienne destinée à mieux en réfuter les objections. (shrink)

The knowledge of an object under observation will have no concrete meaning unless we can work out a logical model the similarities of which are known in relation to the analysed structures. The logical model, when dealing with complex structures, is drawn out by similarity starting from an analogical model worked out in relating local dimensions in the object to physical dimensions of a different nature which restrict the number of variables and can be arranged and modified as required.Any operating (...) similarity and behaviour comparisons come actually down to an apparent functional analogy. The difference between the thin structure of the natural and artificial systems makes it illusive to hope that a strict isomorphism between these two fields may thus be sorted out. However, the fact of achieving analogical models widens our knowledge and shows new possibilities to the human creative mind. (shrink)

Any model of ZFC + GCH has a generic extension (made with a poset of size ℵ 2 ) in which the following hold: MA + 2 ℵ 0 = ℵ 2 +there exists a Δ 2 1 -well ordering of the reals. The proof consists in iterating posets designed to change at will the guessing properties of ladder systems on ω 1 . Therefore, the study of such ladders is a main concern of this article.

Monists, pluralists, and particularists disagree about the structure of the best explanation of the rightness (wrongness) of actions. In this paper I argue that the availability of good moral advice gives us reason to prefer particularist theories and pluralist theories to monist theories. First, I identify two distinct roles of moral theorizing—explaining the rightness (wrongness) of actions, and providing moral advice—and I explain how these two roles are related. Next, I explain what monists, pluralists, and particularists disagree about. Finally, I (...) argue that particularists and pluralists are better situated than monists to explain why it is a good idea to think before we act, and that this gives us reason to favor particularism and pluralism over monism. (shrink)

We examine how degrees of computably enumerable equivalence relations under computable reduction break down into isomorphism classes. Two ceers are isomorphic if there is a computable permutation of ω which reduces one to the other. As a method of focusing on nontrivial differences in isomorphism classes, we give special attention to weakly precomplete ceers. For any degree, we consider the number of isomorphism types contained in the degree and the number of isomorphism types of weakly precomplete ceers contained in the (...) degree. We show that the number of isomorphism types must be 1 or ω, and it is 1 if and only if the ceer is self-full and has no computable classes. On the other hand, we show that the number of isomorphism types of weakly precomplete ceers contained in the degree can be any member of $[0,\omega ]$. In fact, for any $n \in [0,\omega ]$, there is a degree d and weakly precomplete ceers ${E_1}, \ldots,{E_n}$ in d so that any ceer R in d is isomorphic to ${E_i} \oplus D$ for some $i \le n$ and D a ceer with domain either finite or ω comprised of finitely many computable classes. Thus, up to a trivial equivalence, the degree d splits into exactly n classes.We conclude by answering some lingering open questions from the literature: Gao and Gerdes [11] define the collection of essentially FC ceers to be those which are reducible to a ceer all of whose classes are finite. They show that the index set of essentially FC ceers is ${\rm{\Pi }}_3^0$-hard, though the definition is ${\rm{\Sigma }}_4^0$. We close the gap by showing that the index set is ${\rm{\Sigma }}_4^0$-complete. They also use index sets to show that there is a ceer all of whose classes are computable, but which is not essentially FC, and they ask for an explicit construction, which we provide.Andrews and Sorbi [4] examined strong minimal covers of downwards-closed sets of degrees of ceers. We show that if $\left$ is a uniform c.e. sequence of non universal ceers, then $\left\{ {{ \oplus _{i \le j}}{E_i}|j \in \omega } \right\}$ has infinitely many incomparable strong minimal covers, which we use to answer some open questions from [4].Lastly, we show that there exists an infinite antichain of weakly precomplete ceers. (shrink)

The randomization of a complete first-order theory [Formula: see text] is the complete continuous theory [Formula: see text] with two sorts, a sort for random elements of models of [Formula: see text] and a sort for events in an underlying atomless probability space. We study independence relations and related ternary relations on the randomization of [Formula: see text]. We show that if [Formula: see text] has the exchange property and [Formula: see text], then [Formula: see text] has a strict independence (...) relation in the home sort, and hence is real rosy. In particular, if [Formula: see text] is o-minimal, then [Formula: see text] is real rosy. (shrink)

Biological phenomena can be investigated at multiple levels, from the molecular to the cellular to the organismic to the ecological. In typical biology instruction, these levels have been segregated. Yet, it is by examining the connections between such levels that many phenomena in biology, and complex systems in general, are best explained. We describe a computation-based approach that enables students to investigate the connections between different biological levels. Using agent-based, embodied modeling tools, students model the microrules underlying a biological phenomenon (...) and observe the resultant aggregate dynamics. We describe 2 cases in which this approach was used. In both cases, students framed hypotheses, constructed multiagent models that incorporate these hypotheses, and tested these by running their models and observing the outcomes. Contrasting these cases against traditionally used, classical equation-based approaches, we argue that the embodied modeling approach connects more directly to students’ experience, enables extended investigations as well as deeper understanding, and enables “advanced” topics to be productively introduced into the high school curriculum. (shrink)

Assuming the existence of a supercompact cardinal and a weakly compact cardinal above it, we provide a generic extension where there are no Aronszajn trees of height ω 2 or ω 3 . On the other hand we show that some large cardinal assumptions are necessary for such a consistency result.

We say that a theory [Formula: see text] satisfies arithmetic-is-recursive if any [Formula: see text]-computable model of [Formula: see text] has an [Formula: see text]-computable copy; that is, the models of [Formula: see text] satisfy a sort of jump inversion. We give an example of a theory satisfying arithmetic-is-recursive non-trivially and prove that the theories satisfying arithmetic-is-recursive on a cone are exactly those theories with countably many [Formula: see text]-back-and-forth types.

We show that the theory of the partial order of computably enumerable equivalence relations (ceers) under computable reduction is 1-equivalent to true arithmetic. We show the same result for the structure comprised of the dark ceers and the structure comprised of the light ceers. We also show the same for the structure of L-degrees in the dark, light, or complete structure. In each case, we show that there is an interpretable copy of (N, +, \times) .

The Cnidaria represent the most ancient eumetazoan phylum. Members of this group possess typical animal cells and tissues such as sensory cells, nerve cells, muscle cells and epithelia. Due to their unique phylogenetic position, cnidarians have traditionally been used as a reference group in various comparative studies. We propose the colonial marine hydroid, Hydractinia, as a convenient, versatile platform for basic and applied research in developmental biology, reproduction, immunology, environmental studies and more. In addition to being a typical cnidarian representative, (...) Hydractinia offers many practical and theoretical advantages: studies that are feasible in Hydra like regeneration, pattern regulation, and cell renewal from stem cells, can be supplemented by genetic analyses and classical embryology in Hydractinia. Metamorphosis of the planula larva of Hydractinia can be used as a model for cell activation and communication and the presence of a genetically controlled allorecognition system makes it a suitable model for comparative immunology. Most importantly, Hydractinia may be manipulated at most aspects of its (short) life cycle. It has already been the subject of many studies in various disciplines, some of which are discussed in this essay. BioEssays 23:963–971, 2001. © 2001 John Wiley & Sons, Inc. (shrink)

Moral philosophers are, among other things, in the business of constructing moral theories. And moral theories are, among other things, supposed to explain moral phenomena. Consequently, one’s views about the nature of moral explanation will influence the kinds of moral theories one is willing to countenance. Many moral philosophers are (explicitly or implicitly) committed to a deductive model of explanation. As I see it, this commitment lies at the heart of the current debate between moral particularists and moral generalists. In (...) this paper I argue that we have good reasons to give up this commitment. In fact, I show that an examination of the literature on scientific explanation reveals that we are used to, and comfortable with, non-deductive explanations in almost all areas of inquiry. As a result, I argue that we have reason to believe that moral explanations need not be grounded in exceptionless moral principles. (shrink)

It is known that every non-universal self-full degree in the structure of the degrees of computably enumerable equivalence relations (ceers) under computable reducibility has exactly one strong minimal cover. This leaves little room for embedding wide partial orders as initial segments using self-full degrees. We show that considerably more can be done by staying entirely inside the collection of non-self-full degrees. We show that the poset can be embedded as an initial segment of the degrees of ceers with infinitely many (...) classes. A further refinement of the proof shows that one can also embed the free distributive lattice generated by the lower semilattice as an initial segment of the degrees of ceers with infinitely many classes. (shrink)

The methodology of physics is discussed. The limitations of the empirical method are exposed, and it is argued that these limitations are related to our sensory input. The limitations of mathematics and of the representation of physical theories by mathematical models are also examined. An alternative methodology, the establishing of physical models on neuropsychology, is suggested and demonstrated. A cognitive psychological model of the genesis and the termination of time is explored.

A methodological problem may distort the implications derived from the metabolism scans of the brain, but Posner & Raichle may have found neural networks which underlie the analytical and synthetical hemispheric data processing mechanism. This methodological problem is that a large regional consumption of energy, detected by the PET technique, is not necessarily related to more data processing. It may be related to the inefficiency of the neural system at this region.

This study analyzes the triple relation between cognitive biological psychology, philosophy and quantum mechanics. It discusses the findings of Treisman according to which there exists a pre-conscious cerebral mechanism that manipulates the sensory input and transfers it to our consciousness only after correcting it to suit our logic and expectations. This experimental finding was predicted two centuries ago by Kant. It is observed that during the primary pre-conscious level of perception the macroscopic physical world is not perceived as behaving according (...) to the laws of classical physics but rather according to the laws of quantum mechanics, like the microscopic world. (shrink)

Name der Zeitschrift: Naharaim Jahrgang: 8 Heft: 2 Seiten: 210-226.

This article deals with a tripartite structure applied to a Tannaitic source. This structure is designed in the form of a difficulty and a short resolution, bringing one example for each of the three parts of the Tannaitic source. The uniform formative-stylistic phrasing gives the discussion of the Tannaitic source's three parts a tripartite form. The Tannaitic source utilises a chaining of examples from the first to the second part and from the second to the third part.

If one answers the question ‘What is G-ness?’ with a biconditional of the form ‘x is G iff x is F,’ one can ask whether x is G because it is F, or whether x is F because it is G. This question, known as The Euthyphro Question, invites one to choose between one of two options which are presented as mutually exclusive and jointly exhaustive: either x is G because it is F, or x is F because it is (...) G but not both. Each answer has its attractions and difficulties. The _Euthyphro Problem_ is the problem of choosing one rather than the other. This paper argues that holism in the theory of reasons — a view developed by Jonathan Dancy in a different context and for a different purpose — provides a novel and elegant solution to this age-old problem. (shrink)