A phenomenological insight in the debate on empathy is that it is possible to directly perceive other people’s emotions in their expressive bodily behaviour. Contrary to what is suggested by many phenomenologists, namely that this perceptual skill is immediately available if one has vision, this paper argues that the perceptual skill for empathy is acquired. Such a skill requires that we have undergone certain emotional experiences ourselves and that we have had the experience of seeing the world differently, which is (...) a form of pretence. By investigating how we retain knowledge of what is real while pretending, that is, how we anchor the experience of pretence in something that is not pretended, the paper argues that we split our experiential perspective into a double perspective, which differs from the cognitive act of understanding what a perspective is. With this notion in hand, we can return to the debate on empathy. It is argued that in order to have the capacity for direct empathic perception, one must have undergone experiences involving a double perspective. (shrink)

The most recent studies concerning the compositional structure of Seneca's dialogues all agree in stating that its basic organization is due to rhetorical criteria. From this perspective, the article analyzes the general nature of refutation in Consolatio ad Helviam matrem as well as different passages from the dialogue, traditionally considered to be digressions, in order to establish its functionality. We can see from this that the apparently deliberative tenor of the Consolation is endowed with judicial and epideictic elements, and can (...) thus clarify its compositional sequence and lines of thought. (shrink)

Attention-deficit hyperactivity disorder is one of the most common neurodevelopmental disorders in children and adolescents. People who have this disorder are characterized by presenting difficulties in the processes of sustained attention, being very active, and having poor control of their impulses. Despite the high prevalence of this disorder and the existence of various tests used for its diagnosis, few data are available regarding the usefulness and diagnostic validity of these tools. Given the difficulties that these subjects present in executive functions, (...) the aim of this study was to evaluate whether the Neuropsychological Assessment of Executive Functions battery for Children allows to establish specific profiles of executive performance for people with attention-deficit hyperactivity disorder. The sample was made up of 197 participants of both sexes, aged between 6 and 12 years age. A nonexperimental design was followed, using a comparative descriptive study method. The results indicated that the scales of phonological fluency, color path, rings, and interference are the most associated with the diagnosis of ADHD, providing data on inhibition, mental flexibility, sustained and selective attention, planning, verbal fluency, and working memory, among others. The practical implication of these results is in line with providing support in the clinical diagnosis that is carried out in children’s mental health units. In addition, the ENFEN tool can be valued as a suitable psychometric instrument in the psychoeducational field, helping professionals in a school environment to be more aware of the areas of cognitive development in which a student diagnosed with ADHD will have more difficulties and, in doing so, providing more adjusted and effective psychopedagogical measures when it comes to supporting students in their adaptation to the school environment. (shrink)

Objective: Parental influence during children’s “everyday” pain events is under-explored, compared to clinical or experimental pains. We trialed two digital reporting methods for parents to record the real-world context surrounding their child’s everyday pain events within the family home.Methods: Parents completed a structured e-diary for 14 days, reporting on one pain event experienced by their child each day, and describing child pain responses, parental supervision, parental estimates of pain severity and intensity, and parental catastrophizing, distress, and behavioral responses. During (...) the same 2-week period, a subsample of parent-child pairs completed digital ecological momentary assessments, immediately after any chosen pain event. Children reported their current pain while parents estimated the child’s pain and indicated their own distress.Results: “Everyday” pain events frequently featured minor injuries to the child’s head, hands or knees, and child responses included crying and non-verbal comments. Pain events occurred less frequently when parents had been supervising their child, and supervising parents reported lower levels of worry and anxiety than non-supervising parents. Child sex was significantly associated with parental estimates of pain intensity, with parents of girls giving higher estimates than parents of boys. Child age was significantly associated with both the number of pain events and with parental estimates of pain intensity and child distress: the youngest children experienced the fewest pain events but received higher pain and distress estimates from parents than older children. Hierarchal Linear Modeling revealed that parental estimates of pain severity were significant positive predictors of parental distress and catastrophizing in response to a specific pain event. Furthermore, higher levels of parental catastrophic thinking in response to a specific pain event resulted in increased distress, solicitousness, and coping-promoting behaviors in parents. The EMA data revealed that children reported significantly higher pain intensity than their parents.Conclusion: The electronic pain diary provided a key insight into the nature of “everyday” pain experiences around the family home. Digital daily reporting of how the family copes with “everyday” events represents a viable means to explore a child’s everyday pains without disrupting their home environment. (shrink)

Keywords: Elementary Submodel; Real Line; Order-Isomorphic.

It is widely taken for granted that physical lines are real lines, i.e., that the arithmetical structure of the real numbers uniquely matches the geometrical structure of lines in space; and that other number systems, like Robinson's hyperreals, accordingly fail to fit the structure of space. Intuitive justifications for the consensus view are considered and rejected. Insofar as it is justified at all, the conviction that physical lines are real lines is a scientific hypothesis which we may (...) one day reject. /// En general se asume que las líneas físicas son líneas reales, esto es, que la estructura aritmética de los números reales corresponde de manera única a la estructura geométrica de líneas en el espacio, y que otros sistemas de números, como los hiperreales de Robinson, no logran corresponder a la estructura del espacio. En este artículo se examinan y rechazan las justificaciones intuitivas de la posición de consenso. En la medida en que pueda estar justificada, la convicción de que las líneas físicas son líneas reales es una hipótesis científica que algún día podríamos rechazar. (shrink)

We investigate some relations between omitting types of a countable theory and some notions defined in terms of the real line, such as for example the ideal of meager subsets ofR. We also try to express connections between the logical structure of a theory and the existence of its countable models omitting certain families of types.It is well known that assuming MA we can omit (...) to be able to omit real line cannot be covered by less thanmeager sets; and this is in fact the weakest possible condition. It is worth pointing out that by means of forcing we can easily obtain the model of ZFC in whichRcannot be covered by shrink)

We investigate, within the framework of Zermelo-Fraenkel set theory ZF, the interrelations between weak forms of the Axiom of Choice AC restricted to sets of reals.

This paper is devoted to discussing the topological structure of the arrow of time. In the literature, it is often accepted that its algebraic and topological structures are that of a one-dimensional Euclidean space \, although a critical review on the subject is not easy to be found. Hence, leveraging on an operational approach, we collect evidences to identify it structurally as a normed vector space \\), and take a leap of abstraction to complete it, up to isometries, to the (...) real line. During the development of the paper, the space-time is recognized as a fibration, with the fibers being the sets of simultaneous events. The corresponding topology is also exposed: open sets naturally arise within our construction, showing that the classical space-time is non-Hausdorff. The transition from relativistic to classical regimes is explored too. (shrink)

We consider decompositions of the real line into pairwise disjoint Borel pieces so that each piece is closed under addition. How many pieces can there be? We prove among others that the number of pieces is either at most 3 or uncountable, and we show that it is undecidable in and even in the theory if the number of pieces can be uncountable but less than the continuum. We also investigate various versions: what happens if we drop the (...) Borelness requirement, if we replace addition by multiplication, if the pieces are subgroups, if we partition (0, ∞), and so on. (shrink)

We prove that S4 is complete with respect to Boolean combinations of countable unions of convex subsets of the real line, thus strengthening a 1944 result of McKinsey and Tarski 45 141). We also prove that the same result holds for the bimodal system S4+S5+C, which is a strengthening of a 1999 result of Shehtman 369).

It is shown that AC, the axiom of choice for families of non-empty subsets of the real line ℝ, does not imply the statement PW, the powerset of ℝ can be well ordered. It is also shown that the statement “the set of all denumerable subsets of ℝ has size 2math image” is strictly weaker than AC and each of the statements “if every member of an infinite set of cardinality 2math image has power 2math image, then the (...) union has power 2math image” and “ℵ ≠ ℵω” is Hartogs' aleph, the least ℵ not ≤ 2math image), is strictly weaker than the full axiom of choice AC. (shrink)

An ordered field is said to be Scott complete iff it is complete with respect to its uniform structure. Zakon has asked whether nonstandard real lines are Scott complete. We prove in ZFC that for any complete Boolean algebra B which is not (ω, 2)-distributive there is an ultrafilter U of B such that the Boolean ultrapower of the real line modulo U is not Scott complete. We also show how forcing in set theory gives rise to (...) examples of Boolean ultrapowers of the real line which are not Scott complete. (shrink)

We expand our effective framework for weak convergence of measures on the real line by showing that effective convergence in the Prokhorov metric is equivalent to effective weak convergence. In addition, we establish a framework for the study of the effective theory of vague convergence of measures. We introduce a uniform notion and a non-uniform notion of vague convergence, and we show that both these notions are equivalent. However, limits under effective vague convergence may not be computable even (...) when they are finite. We give an example of a finite incomputable effective vague limit measure, and we provide a necessary and sufficient condition so that effective vague convergence produces a computable limit. Finally, we determine a sufficient condition for which effective weak and vague convergence of measures coincide. As a corollary, we obtain an effective version of the equivalence between classical weak and vague convergence of sequences of probability measures. (shrink)

We find a characterization of the covering number $cov({\mathbb R})$ , of the real line in terms of trees. We also show that the cofinality of $cov({\mathbb R})$ is greater than or equal to ${\mathfrak n}_\lambda$ for every $\lambda \in cov({\mathbb R}),$ where $\mathfrak n_\lambda \geq add({\mathcal L})$ ( $add( {\mathcal L})$ is the additivity number of the ideal of all Lebesgue measure zero sets) is the least cardinal number k for which the statement: $(\exists{\mathcal G}\in [^\omega \omega (...) ]^{\leq \lambda })(\forall{\mathcal F}\in [^\omega \omega ]^{\leq k})(\exists g\in{\mathcal G})(\exists h\in ^\omega \omega )(\forall f\in{\mathcal F})(\forall ^\infty n)(\exists u\in [g(n),g(n+1))(f(u)=h(u))$ fails. (shrink)

We present a proof of a Ramsey-type theorem for infinite metric spaces due to Matoušek. Then we show that for every K>1 every uncountable Polish space has a perfect subset that K-bi-Lipschitz embeds into the real line. Finally we study decompositions of infinite separable metric spaces into subsets that, for some K>1, K-bi-Lipschitz embed into the real line.

In the topological semantics for modal logic, S4 is well known to be complete for the rational line and for the real line: these are special cases of S4’s completeness for any dense-in-itself metric space. The construction used to prove completeness can be slightly amended to show that S4 is not only complete but strongly complete, for the rational line. But no similarly easy amendment is available for the real line. In an earlier paper, (...) we proved a general theorem: S4 is strongly complete for any dense-in-itself metric space. Strong completeness for the real line is a special case. In the current paper, we give a proof of strong completeness tailored to the special case of the real line: the current proof is simpler and more accessible than the proof of the more general result and involves slightly different techniques. We proceed in two steps: first, we show that S4 is strongly complete for the space of finite and infinite binary sequences, equipped with a natural topology; and then we show that there is an interior map from the real line onto this space. (shrink)

We prove that the cofinality of the smallest covering of R by meager sets is bigger than the additivity of measure.

We study the role the axiom of choice plays in the existence of some special subsets of ℝ and its power set ℘.

The main purpose of this dissertation is to apply and develop new forcing techniques to obtain models where several cardinal characteristics are pairwise different as well as force many (even more, continuum many) different values of cardinal characteristics that are parametrized by reals. In particular, we look at cardinal characteristics associated with strong measure zero, Yorioka ideals, and localization and anti-localization cardinals.In this thesis we introduce the property “F-linked” of subsets of posets for a given free filter F on the (...) natural numbers, and define the properties “ $\mu $ -F-linked” and “ $\theta $ -F-Knaster” for posets in a natural way. We show that $\theta $ -F-Knaster posets preserve strong types of unbounded families and of maximal almost disjoint families. These kinds of posets led to the development of a general technique to construct $\theta $ - $\textrm {Fr}$ -Knaster posets (where $\textrm {Fr}$ is the Frechet ideal) via matrix iterations of ${<}\theta $ -ultrafilter-linked posets (restricted to some level of the matrix). The latter technique allows proving consistency results about Cichoń’s diagram (without using large cardinals) and to prove the consistency of the fact that, for each Yorioka ideal, the four cardinal characteristics associated with it are pairwise different. Another important application is to show that three strongly compact cardinals are enough to force that Cichoń’s diagram can be separated into 10 different values. Later on, it was shown by Goldstern, Kellner, Mejía, and Shelah that no large cardinals are needed for Cichoń’s maximum (J. Eur. Math. Soc. 24 (2022), no. 11, p. 3951–3967).On the other hand, we deal with certain types of tree forcings including Sacks forcing, and show that these increase the covering of the strong measure zero ideal $\mathcal {SN}$. As a consequence, in Sacks model, such covering number is equal to the size of the continuum, which indicates that this covering number is consistently larger than any other classical cardinal characteristics of the continuum. Even more, Sacks forcing can be used to force that $\operatorname {\mathrm{non}}(\mathcal {SN})<\operatorname {\mathrm{cov}}(\mathcal {SN})<\operatorname {\mathrm{cof}}(\mathcal {SN})$, which is the first consistency result where more than two cardinal characteristics associated with $\mathcal {SN}$ are pairwise different. To obtain another result in this direction, we provide bounds for $\operatorname {\mathrm{cof}}(\mathcal {SN})$, which generalizes Yorioka’s characterization of $\mathcal {SN}$ (J. Symbolic Logic 67.4 (2002), p. 1373–1384). As a consequence, we get the consistency of $\operatorname {\mathrm{add}}(\mathcal {SN})=\operatorname {\mathrm{cov}}(\mathcal {SN})<\operatorname {\mathrm{non}}(\mathcal {SN})<\operatorname {\mathrm{cof}}(\mathcal {SN})$ with ZFC (via a matrix iteration forcing construction).We conclude this thesis by combining creature forcing approaches by Kellner and Shelah (Arch. Math. Logic 51.1–2 (2012), p. 49–70) and by Fischer, Goldstern, Kellner, and Shelah (Arch. Math. Logic 56.7–8 (2017), p. 1045–1103) to show that, under CH, there is a proper $\omega ^\omega $ -bounding poset with $\aleph _2$ -cc that forces continuum many pairwise different cardinal characteristics, parametrized by reals, for each one of the following six types: uniformity and covering numbers of Yorioka ideals as well as both kinds of localization and anti-localization cardinals, respectively. This answers several open questions from Klausner and Mejía (Arch. Math. Logic 61 (2022), pp. 653–683).Abstract prepared by Miguel Antonio Cardona-MontoyaE-mail: [email protected]: https://repositum.tuwien.at/handle/20.500.12708/19629. (shrink)

We show: iff every countable product of sequential metric spaces (sequentially closed subsets are closed) is a sequential metric space iff every complete metric space is Cantor complete. Every infinite subset X of has a countably infinite subset iff every infinite sequentially closed subset of includes an infinite closed subset. The statement “ is sequential” is equivalent to each one of the following propositions: Every sequentially closed subset A of includes a countable cofinal subset C, for every sequentially closed subset (...) A of, is a meager subset of, for every sequentially closed subset A of,, every sequentially closed subset of is separable, every sequentially closed subset of is Cantor complete, every complete subspace of is Cantor complete. (shrink)

We will give a simple philosophical "proof" of the negation of Cantor's continuum hypothesis (CH). (A formal proof for or against CH from the axioms of ZFC is impossible; see Cohen [1].) We will assume the axioms of ZFC together with intuitively clear axioms which are based on some intuition of Stuart Davidson and an old theorem of Sierpinski and are justified by the symmetry in a thought experiment throwing darts at the real number line. We will in (...) fact show why there must be an infinity of cardinalities between the integers and the reals. We will also show why Martin's Axiom must be false, and we will prove the extension of Fubini's Theorem for Lebesgue measure where joint measurability is not assumed. Following the philosophy--if you reject CH you are only two steps away from rejecting the axiom of choice (AC)--we will point out along the way some extensions of our intuition which contradict AC. (shrink)

This paper begins an analysis of the real line using an inconsistency-tolerant (paraconsistent) logic. We show that basic field and compactness properties hold, by way of novel proofs that make no use of consistency-reliant inferences; some techniques from constructive analysis are used instead. While no inconsistencies are found in the algebraic operations on the real number field, prospects for other non-trivializing contradictions are left open.

The aim of this paper is to reconstruct the historical evolution of the so-called Measurement Theory. MT has two clearly different periods, the formation period and the mature theory, whose borderline coincides with the publication in 1951 of Suppes' foundational work, ‘A set of independent axioms for extensive quantities’. In this paper two previous research traditions on the foundations of measurement, developed during the formation period, come together in the appropriate way. These traditions correspond, on the one hand, to Helmholtz's, (...) Campbell's and Hölder's studies on axiomatics and real morphisms and, on the other, to the work undertaken by Stevens and his school on scale types and transformations. These two lines of research are complementary in the sense that neither of them is enough taken alone, but together they contain all that is necessary to develop the theory, and it is in Suppes that these complementary approaches converge and all the elements of the theory are appropriately integrated for the first time. With Suppes' work, then, begins what may be called the ‘mature’ theory, which was to develop rapidly later on, especially during the 1960s. Our historical reconstruction is divided into two parts, each part devoted to one of the periods mentioned. Part I also contains a conceptual introduction which aims to establish the use of some notions, specifically those of measurement and metrization. Although the reconstruction is not exhaustive, it intends to be quite complete and up to date compared to what is available in measurement literature; in this sense the aim of this paper is mainly historical but, although secondarily, it also attempts to make some conceptual and metascientific clarifications on the subject of the theory. (shrink)

This paper surveys some ways of distinguishing Quasi-Realism in metaethics from Non-naturalist Realism, including ‘Explanationist’ methods of distinguishing, which characterize the Real by its explanatory role, and Inferentialist methods. Rather than seeking the One True Distinction, the paper adopts an irenic and pragmatist perspective, allowing that different ways of drawing the line are best for different purposes.

There's a student in my philosophy class who has "real potential." I might express this thought in any of the following ways: "She is potentially a philosopher"; "She is a potential philosopher"; "She has the potential to be a philosopher." The first way uses a cognate of "potential" as an adverb to modify "is." The second ways uses "potential" as an adjective to modify "philosopher." However, the third way uses "potential" as a noun to refer to something that the (...) student has. What kind of thing is this potential? One worry about even asking this question is that this nominalization of the adjective "potential" suggests a metaphysical picture that is an artifact of language. This is even more strongly suggested by the less ambiguous nominalization "potentiality." Once we have the term "potentiality," we have a new kind of entity to countenance, and questions about its nature arise. One might argue, just because we use the word "potentiality," we should not think that it refers to a "thing" that someone can "have." There is something disingenuous about such an argument. It proceeds as if the adverbial and adjectival uses of "potential" are unproblematic, and questions only arise with the nominalization. But it is not obvious what it means to potentially be something, or what it means to be a potential something. To say that someone "is potentially" a philosopher is to talk about a way of being that falls short of actuality. And a "potential philosopher" is not a kind of philosopher at all. So what is it? Each of the three above formulations is a modal claim. If there is anything philosophical puzzling about a potentiality claim, it is not going to go away by translating it into an equivalent modal claim. In this chapter I defend the existence of potentialities against anti-realist arguments, and make a proposal as to their nature. The proposal, in short, is that potentialities are properties, specifically dispositions, though more needs to be said about properties and dispositions. I will do this in Part I. In Part II, I will address two lines of argument against potentialities: that they are reducible, and that they are causally inert. (shrink)

We show that it is consistent with ZFC that the additivity number add of the ideal of meager sets of the real line is strictly greater than the tower number t of the reals. MSC: 03E35, 54D20.

W. E. B. Du Bois never felt so at home as when he was a student at the University of Berlin. But Du Bois was also American to his core, scarred but not crippled by the racial humiliations of his homeland. In Lines of Descent, Kwame Anthony Appiah traces the twin lineages of Du Bois' American experience and German apprenticeship, showing how they shaped the great African-American scholar's ideas of race and social identity. At Harvard, Du Bois studied with such (...) luminaries as William James and George Santayana, scholars whose contributions were largely intellectual. But arriving in Berlin in 1892, Du Bois came under the tutelage of academics who were also public men. The economist Adolf Wagner had been an advisor to Otto von Bismarck. Heinrich von Treitschke, the historian, served in the Reichstag, and the economist Gustav von Schmoller was a member of the Prussian state council. These scholars united the rigorous study of history with political activism and represented a model of real-world engagement that would strongly influence Du Bois in the years to come. With its romantic notions of human brotherhood and self-realization, German culture held a potent allure for Du Bois. Germany, he said, was the first place white people had treated him as an equal. But the prevalence of anti-Semitism allowed Du Bois no illusions that the Kaiserreich was free of racism. His challenge, says Appiah, was to take the best of German intellectual life without its parochialism--to steal the fire without getting burned. (shrink)

The aim of this paper is to argue that the adoption of an unrestricted principle of bivalence is compatible with a metaphysics that (i) denies that the future is real, (ii) adopts nomological indeterminism, and (iii) exploits a branching structure to provide a semantics for future contingent claims. To this end, we elaborate what we call Flow Fragmentalism, a view inspired by Kit Fine (2005)’s non-standard tense realism, according to which reality is divided up into maximally coherent collections of (...) tensed facts. In this way, we show how to reconcile a genuinely A-theoretic branching-time model with the idea that there is a branch corresponding to the thin red line, that is, the branch that will turn out to be the actual future history of the world. (shrink)

Governments, companies, and citizens all think trust is important. Especially today, in the networked era, where we make use of all sorts of e-services and increasingly interact and buy online, trust has become a necessary condition for society to thrive. But what do we mean when we talk about trust and how does the rise of the Internet transform the functioning of trust? This books starts off with a thorough conceptual analysis of trust, drawing on insights from - amongst others (...) philosophy and sociology - to sharpen our understanding of the topic. The book explains how the arrival of large systems - such as the internet - has changed the character of trust which today is no longer based on interpersonal interactions but has become completely mediated by technologies. Based on the layered building plan of the Internet itself, a new conceptual lens called 4 Cs is developed to analyse and understand trust in the networked era. The 4Cs refer to the 4 layers which all have to be taken into account to assess trust online, namely: context, code, codification, and curation. The 4Cs bring together the firsthand experiences of the user (context), the sort of technology that is being used (code), the legal implication (codification) and business interests (curation) in order to get a clear picture of the trust issues that may arise. In the final part of the book some real-life cases are discussed (digital hotel keys, Airbnb, online personalization) to illustrate how trust -analysed through the 4 Cs lens- might flourish or be challenged in our current networked era. (shrink)

New technologies in germ–line engineering have raised many questions about obligations to future generations. In this article, I focus on the importance of increasing freedom and the equality of freedom for present and future generations, because these two ideals are necessary for a just society and because they are most threatened by the wide–scale privatisation of GLE technologies. However, there are ambiguities in applying these ideals to the issue of genetic technologies. I argue that Amartya Sen's capability theory can (...) be used as a framework to ensure freedom and equality in the use of GLE technology. Capability theory articulates the goal of equalising real freedom by bringing all people up to a threshold of basic human capabilities. Sen's capability theory can clarify the proper moral goal of GLE insofar as this technology could be used to bring people up to certain basic human capabilities, thereby increasing their real freedom. And by increasing the freedom of those who lack basic human capabilities, GLE can aid in decreasing the inequalities of freedom among classes of people. (shrink)

Just how realistic about human nature and real possibilities must a theory of justice, or a moral theory, more generally, be? Lines have been drawn, with some holding that idealizing away from reality is indispensable and others maintaining that utopian thinking is not just useless but irrelevant. In Utopophobia David Estlund defends the value of utopian theory. At his most modest, Estlund claims that it is a legitimate approach, not ruled out of court by anti-idealists on entirely inadequate grounds—merely (...) “by assumption or definition” as he puts it. Yet he also argues against what we call real world theory, which takes account of human imperfection and feasible options. It invites complacency and undermines aspiration, he argues, and he accepts Rawls’ claim that it will of necessity be unsystematic, thanks to its realism. We accept that the utopian approach is neither useless nor irrelevant. Yet we press hard against the charges against real world theory, maintaining that, properly understood, it invites neither complacency nor aspiration and can perfectly well offer a systematic and principled account of normative concepts, including justice specifically. (shrink)

Of all the crew to serve on a starship Enterprise, none has had such a convoluted line of existence as the venerable Mr. Spock. This chapter explores what the various incarnations of Mr. Spock can tell us about the nature of reality, existence, and personal identity. Lewis argues for the metaphysical theory of modal realism: all possible worlds are as real as the actual world. In science fiction parlance, this philosophical concept of world is more often called a (...) universe. Thus, Earth and Vulcan are both part of the same world depicted in Star Trek. The central question Lewis addresses is whether our world is the only real world, or whether other possible worlds could also be considered real. Lewis argues for the metaphysical theory of modal realism, all possible worlds are as real as the actual world. (shrink)

This study addresses the conceptual affinities between F. W. J. Schelling and Félix RavaissonRavaisson-Mollien, Félix by focusing on the genesis of the link between nature and thought in their respective philosophies. To achieve this, it considers the role of diagrammatic representation in depicting this link—particularly in the figure of the spiral. I argue that, for Schelling, the spiral is a real pattern that suggests the polarity of the mental and the physical whereas, for RavaissonRavaisson-Mollien, Félix, it is a memory (...) of the condition of action and a condition of grace. I cash out this argument by considering not only Schelling’s philosophy of nature, where the spiral is manifest in the vortex of the First Outline of the System of the Philosophy of Nature, and RavaissonRavaisson-Mollien, Félix’s OfHabitHabit, but also RavaissonRavaisson-Mollien, Félix’s essays on fine art, Leonardo da Vinci and the serpentine line. (shrink)

Most philosophical accounts of the foundations of economics have assumed that economics is intended to be an empirical science concerned with human behaviour, though they have, of course, differed over the extent to which it has been or can be successful as such an enterprise. A prominent source of dissent against this consensus is Alexander Rosenberg. In his recent book, Rosenberg summarizes and completes his statement of a position that he has been developing for some time. He argues that although (...) economists evaluate one another's work according to shared and rigorous standards of adequacy, these standards are strictly internal, like those of mathematics, instead of being derived from discoveries about contingent relationships between theoretical statements and empirical facts. Economics, that is to say, is essentially conceptual rather than empirical inquiry. In the following discussion, I will provide grounds for resisting Rosenberg's conclusion. The point of this criticism, however, is not mainly negative. Most of the historical preoccupations of the philosophy of economics, like those of the philosophy of science in general, have been epistemological. Careful attention to Rosenberg's argument, however, redirects our attention to ontological questions about the objects of economics, and this redirection, I will maintain, is to be welcomed. I will argue that while the majority of philosophers of economics is correct, as against Rosenberg, in regarding economics as an empirical science, the conventional view as to the identity of its empirical objects should be substantially revised under the pressure of Rosenberg's criticisms. My critical analysis of the implications of Rosenberg's work for the ontological commitments of economics is intended to furnish one line of argument towards my own conception of the objects of economics. This conception, which is still preliminary in many respects, will be briefly sketched toward the end of the present paper; a detailed account of it is given in Ross and LaCasse. (shrink)

When it comes to Wittgenstein's philosophy of mathematics, even sympathetic admirers are cowed into submission by the many criticisms of influential authors in that field. They say something to the effect that Wittgenstein does not know enough about or have enough respect for mathematics, to take him as a serious philosopher of mathematics. They claim to catch Wittgenstein pooh-poohing the modern set-theoretic extensional conception of a real number. This article, however, will show that Wittgenstein's criticism is well grounded. A (...) real number, as an 'extension', is a homeless fiction; 'homeless' in that it neither is supported by anything nor supports anything. The picture of a real number as an 'extension' is not supported by actual practice in calculus; calculus has nothing to do with 'extensions'. The extensional, set-theoretic conception of a real number does not give a foundation for real analysis, either. The so-called complete theory of real numbers, which is essentially an extensional approach, does not define (in any sense of the word) the set of real numbers so as to justify their completeness, despite the common belief to the contrary. The only correct foundation of real analysis consists in its being 'existential axiomatics'. And in real analysis, as existential axiomatics, a point on the real line need not be an 'extension'. (shrink)

Most philosophical accounts of the foundations of economics have assumed that economics is intended to be an empirical science concerned with human behaviour, though they have, of course, differed over the extent to which it has been or can be successful as such an enterprise. A prominent source of dissent against this consensus is Alexander Rosenberg. In his recent book, Rosenberg summarizes and completes his statement of a position that he has been developing for some time. He argues that although (...) economists evaluate one another's work according to shared and rigorous standards of adequacy, these standards are strictly internal, like those of mathematics, instead of being derived from discoveries about contingent relationships between theoretical statements and empirical facts. Economics, that is to say, is essentially conceptual rather than empirical inquiry. In the following discussion, I will provide grounds for resisting Rosenberg's conclusion. The point of this criticism, however, is not mainly negative. Most of the historical preoccupations of the philosophy of economics, like those of the philosophy of science in general, have been epistemological. Careful attention to Rosenberg's argument, however, redirects our attention to ontological questions about the objects of economics, and this redirection, I will maintain, is to be welcomed. I will argue that while the majority of philosophers of economics is correct, as against Rosenberg, in regarding economics as an empirical science, the conventional view as to the identity of its empirical objects should be substantially revised under the pressure of Rosenberg's criticisms. My critical analysis of the implications of Rosenberg's work for the ontological commitments of economics is intended to furnish one line of argument towards my own conception of the objects of economics. This conception, which is still preliminary in many respects, will be briefly sketched toward the end of the present paper; a detailed account of it is given in Ross and LaCasse. (shrink)

This book presents vigorous and wide-ranging arguments in defense of an Aristotelian metaphysical scheme along fairly orthodox Thomistic lines. The central claim is that the items that populate the world have real essences – natures that mind-independently define what each such item is. This Aristotelian essentialism, Oderberg begins by telling us, is a different doctrine from what has recently been called ‘essentialism’, and a more powerful one . For recent essentialism has treated a thing's essence as merely all those (...) properties that the thing takes with it across all possible worlds – and here modality gets presupposed in order to explain essentialness, when the order should be reversed.We can observe essences, Oderberg holds, even though the observation is indirect, and even though knowing what to make of our observations requires applying metaphysical knowledge. Positivism-inspired worries that there is something unfactual about modal claims, and hence about essences, are unfounded . Claims about essences do have factual content, but not because they merely express our concepts or our grammar, and not because they simply report empirical findings . True reports of the essences of objects articulate a metaphysical insight from Aristotle: an object's essence is a compound of its substantial form and its prime matter . Its form actuates potentialities of its matter . The laws of nature derive from essences, and hence are necessary rather than contingent . Artifacts are ‘accidental unities’ of individual substances and …. (shrink)

Frege's definition of the real numbers, as envisaged in the second volume of Grundgesetze der Arithmetik, is fatally flawed by the inconsistency of Frege's ill-fated Basic Law V. We restate Frege's definition in a consistent logical framework and investigate whether it can provide a logical foundation of real analysis. Our conclusion will deem it doubtful that such a foundation along the lines of Frege's own indications is possible at all.

It is commonly thought, in line with the position defended in an influential paper by David Lewis, that the decision problems faced in the prisoner’s dilemma and the Newcomb situation are essentially the same problem. José Luis Bermúdez has recently attacked the case Lewis makes for this claim. While I think the claim is false, I contend that Bermúdez’s reason for rejecting Lewis’s argument is inadequate, and then outline what I take to be a better reason for doing so.

Do there exist real numbers d with d2 = 0? The question is formulated provocatively, to stress a formalist view about existence: existence is consistency, or better, coherence.Also, the provocation is meant to challenge the monopoly which the number system, invented by Dedekind et al., is claiming for itself as THE model of the geometric line. The Dedekind approach may be termed “arithmetization of geometry”.We know that one may construct a number system out of synthetic geometry, as Euclid (...) and followers did : “geometrization of arithmetic”..Starting from the geometric side, nilpotent elements are somewhat reasonable, although Euclid excluded them. The sophist Protagoras presented a picture of a circle and a tangent line; the apparent little line segment D which tangent and circle have in common, are, by Pythagoras' Theorem, precisely the points, whose abscissae d have d2 = 0. Protagoras wanted to use this argument for destructive reasons: to refute the science of geometry.A couple of millenia later, the Danish geometer Hjelmslev revived the Protagoras picture. His aim was more positive: he wanted to describe Nature as it was. According to him, the Real Line, the Line of Sensual Reality, had many nilpotent infinitesimals, which we can see with our naked eyes. (shrink)

Once we have distinguished between beauty and aesthetic value, we are faced with the question of whether beauty is a thing of value in itself. A number of theorists have suggested that the answer might be no. They have thought that the pursuit of beauty is just the indulgence of one particular taste: a taste that has, for contingent historical reasons, been privileged. This paper attempts to resist a line of thought that leads to that conclusion. It does so (...) by arguing that there really are objective facts about beauty. To do this, the paper draws distinctions between objectivity and subjectivity, and between realism and anti-realism. It argues that, regarding attributions of beauty, we should be realists and objectivists. This is shown to be compatible with taking the semantic content of such attributions to vary between contexts. This form of context sensitivity is able to account of those features of beauty-attributions that have been taken as evidence for its subjectivity. (shrink)