This article elaborates the epistemic indispensability argument, which fully embraces the epistemic contribution of mathematics to science, but rejects the contention that such a contribution is a reason for granting reality to mathematicalia. Section 1 introduces the distinction between ontological and epistemic readings of the indispensability argument. Section 2 outlines some of the main flaws of the first premise of the ontological reading. Section 3 advances the epistemic indispensability argument in view of both applied and pure mathematics. And Sect. 4 (...) makes a case for the epistemic approach, which firstly calls into question the appeal to inference to the best explanation in the defense of the indispensability claim; secondly, distinguishes between mathematical and physical posits; and thirdly, argues that even though some may think that inference to the best explanation works in the postulation of physical posits, no similar considerations are available for postulating mathematicalia. (shrink)

Pierre Duhem, cent ans plus tard. Actes de la journée d’étude internationale tenue à Tunis le 10 mars 2016, suivis de l’édition française de l’Histoire de la physique. [Pierre Duhem, a hundred years later. Proceedings of the International Study Day held in Tunis on March 10, 2016, followed by the French edition of the History of Physics ]. Edited by Jean-François Stoffel, with the collaboration of Souad Ben Ali. Tunis: Université de Tunis, 2017. 412 p. ISBN: 978-9973-06-968-9.

I will contrast two conceptions of the nature of mathematical objects: the conception of mathematical objects as preconceived objects, and heavy duty platonism. I will argue that friends of the indispensability argument are committed to some metaphysical theses and that one promising way to motivate such theses is to adopt heavy duty platonism. On the other hand, combining the indispensability argument with the conception of mathematical objects as preconceived objects yields an unstable position. The conclusion is that the metaphysical commitments (...) of the indispensability argument should be carefully scrutinized. (shrink)

Neo-Fregeanism is a combination of two ideas: logicism, according to which arithmetic can be derived from logic plus definitions, and Platonism, according to which there are mathematical objects. Neo-Fregeans propose a new interpretation of Frege’s principles of abstraction and of the role of reconceptualization and implicit definition for the introduction of numbers into our ontology. I analyze the ontological implications of neo-Fregeanism, not only for mathematics, but for abstract entities in general. After briefly introducing some of the main elements of (...) neo-Fregeanism, I present two possible readings of its ontological implications and I argue that none of them gives the desired results. (shrink)

From early work of N. Goodman to recent approaches by H. Field and D. Lewis, there have been attempts to combine 2nd order languages with calculi of individuals. This paper is a contribution, containing basic definitions and distinctions and some metatheorems, to the development of a general metatheory of such theories.

The Generalized Integration Challenge is the task of providing, for a given domain of discourse, a simultaneously acceptable metaphysics, epistemology and metasemantics and showing them to be so. In this paper, we focus on a metaethical position for which seems particularly acute: the brand of normative realism which takes normative properties to be mind-independent and causally inert. The problem is that these metaphysical commitments seem to make normative knowledge impossible. We suggest that bringing metasemantics into play can help to resolve (...) this puzzle. We propose an independently plausible metasemantic constraint on reference determination and show how it can provide a plausible response to for this brand of normative realism. (shrink)

Mathematical platonism is the view that abstract mathematical objects exist. Ontological pluralism is the view that there are many modes of existence. This paper examines the prospects for...

A complete philosophy of mathematics must address Paul Benacerraf’s dilemma. The requirements of a general semantics for the truth of mathematical theorems that coheres also with the meaning and truth conditions for non-mathematical sentences, according to Benacerraf, should ideally be coupled with an adequate epistemology for the discovery of mathematical knowledge. Standard approaches to the philosophy of mathematics are criticized against their own merits and against the background of Benacerraf’s dilemma, particularly with respect to the problem of understanding the distinction (...) between pure and applied mathematics and the effectiveness of applied mathematics in the natural sciences and engineering. The evaluation of these alternatives provides the basis for articulating a philosophically advantageous Aristotelian inherence concept of mathematical entities. An inherence account solves Benacerraf’s dilemma by interpreting mathematical entities as nominalizations of structural spatiotemporal properties inhering in existent spatiotemporal entities. (shrink)

Chris Daly défend « l'explicationisme », la position selon laquelle l'inférence a la meilleure explication constitue une façon acceptable de justifier une théorie. Il la défend en tentant de justifier la position explicationiste par ses propres ressources, c'est-a-dire par elle-même. Je soutiens que dans le contexte de la métaphysique, cette défense échoue. L'explicationiste échoue à se justifier par ses propres ressources et l'une de ses premisses centrales ne peut pas être justifiée uniquement de façon externaliste.

Dans cet article je propose d'exprimer et de défendre une conception des pratiques et du domaine de discours mathématiques qui soit sensible, d'une part, au pluralisme des relations entre pratiques inférentielles et intérêts, et d'autre part, à la structure objective et déterminante des concepts mathématiques. J'ébauche tout d'abord une caractérisation générale des pratiques, pour ensuite préciser certains phénomènes propres aux pratiques mathématiques. Suit un recensement des idées qui se dégagent des arguments pluralistes, et de celles qui sont à retenir. Mais (...) je défends par la suite la nécessité d'une forme de réalisme mathématique, qui toutefois ne peut être le réalisme d'objets que prônent les partisans de l'argument d'indispensabilité. Je défends plutôt un réalisme des concepts, soutenu par ce que je baptise l'« argument de la contrainte ». (shrink)

In both the historical and contemporary literature on the metaphysics of space, a core dispute is that between relationism and substantivalism. One version of the latter is supersubstantivalism, according to which space is the only kind of substance, such that what we think of as individual material objects are actually just parts of spacetime which instantiate certain properties. If those parts are ontologically dependent on spacetime as a whole, then we arrive at an ontology with only a single genuinely independent (...) substance, namely the entire spacetime manifold. This is monist supersubstantivalism. A view on which the parts of spacetime are ontologically prior to the whole has been called pluralistic supersubstantivalism. As currently formulated, supersubstantivalism carries significant advantages and encounters major difficulties. I argue that some of the latter motivate... (shrink)

The paper raises some difficulties for the typical motivations behind set reductionism, the view that sets are reducible to entities identified independently of set theory.

There are important differences among those philosophers who would call themselves nominalists and thus claim to disbelieve in the existence of numbers, properties, propositions, and their ilk. Some are non-concessive, and would deny that sentences such as following can be true.

The modal antirealist, as presented here, aims to secure at least some of the benefits associated with talking in genuine modal realist terms while avoiding commitment to a plurality of Lewisian (or ersatz) worlds. The antirealist stance of agnosticism about other worlds combines acceptance of Lewis's account of what world‐talk means with refusal to assert, or believe in, the existence of other worlds. Agnosticism about other worlds does not entail a comprehensive agnosticism about modality, but where such agnosticism about modality (...) is enforced, the aim of the agnostic programme is to show that it is not detrimental to our modal practices. The agnostic programme consists in an attempt to demonstrate the rational dispensability of that disputed class of modal beliefs which the agnostic eschews, but which are held by the realist and the folk. Here I attempt to motivate, describe, and illustrate such an agnostic antirealist programme in modal philosophy. (shrink)

Impure systems contain Objects and Subjects: Subjects are human beings. We can distinguish a person as an observer (subjectively outside the system) and that by definition is the Subject himself, and part of the system. In this case he acquires the category of object. Objects (relative beings) are significances, which are the consequence of perceptual beliefs on the part of the Subject about material or energetic objects (absolute beings) with certain characteristics.The IS (Impure System) approach is as follows: Objects are (...) perceptual significances (relative beings) of material or energetic objects (absolute beings). The set of these objects will form an impure set of the first order. The existing relations between these relative objects will be of two classes: transactions of matter and/or energy and inferential relations. Transactions can have alethic modality: necessity, possibility, impossibility and contingency. Ontic existence of possibility entails that inferential relations have Deontic modality: obligation, permission, prohibition, faculty and analogy. We distinguished between theorems (natural laws) and norms (ethical, legislative and customary rules of conduct). (shrink)

From the perspective of mathematical practice, I examine positions claiming that mathematical objects are introduced by human agents. I consider in particular mathematical fictionalism and a recent position on social ontology formulated by Cole (2013, 2015). These positions are able to solve some of the challenges that non-realist positions face. I argue, however, that mathematical entities have features other than fictional characters and social institutions. I emphasise that the way mathematical objects are introduced is different and point to the multifaceted (...) role that relations and interconnections play in this context. Finally, I argue that mathematical entities can be considered to be pragmatically real. (shrink)

If you put chimpanzees from different communities together you can expect mayhem - they are not keen on treating each other nicely. There is closely related species of apes, however, whose members have countless encounters with unrelated specimen on a daily basis and yet almost all get through the day in one piece - that species is us, homo sapiens. But what makes us get along, most of the time? Morality as such is, perhaps surprisingly, not a mainstream research topic (...) in social psychology. Most textbooks in the field do not even mention the term morality at all (and focus on 'prosociality' instead). This relative lack of 'coverage' might have to do with the difficulty of operationalising 'morality' in a fitting way (more on this below). However, morality certainly is a social phenomenon and therefore the collection of Fargas, Jussim, and Van Lange is certainly a step in the right direction; it offers an extensive overview of the field and is suggestive of the vast potential of studying morality through the lens of social psychology. (shrink)

In this paper, I argue for three main claims. First, that there are two broad sorts of error theory about a particular region of thought and talk, eliminativist error theories and non-eliminativist error theories. Second, that an error theory about rule following can only be an eliminativist view of rule following, and therefore an eliminativist view of meaning and content on a par with Paul Churchland’s prima facie implausible eliminativism about the propositional attitudes. Third, that despite some superficial appearances to (...) the contrary, non-eliminativist error theory does not provide a plausible vehicle for understanding the ‘sceptical solution’ to the sceptical paradox about rule - following developed in Saul Kripke’s Wittgenstein on Rules and Private Language. (shrink)

ABSTRACTStandard theories treat A→C and A→D as equivalent when C and D coincide on A. However, Yablo's incremental conditional does not behave in this way. Consider the following: a = b→Fa. a = b→Fb.According to Yablo, the real content of is Fb and the real content of is Fa. In worlds where a = b is true, both and have the same truth-value. However, ‘Fa can come apart truth-value-wise from Fb in worlds where a isn't b.’ In this paper, I (...) argue that this feature of Yablo's incremental conditional makes his if-thenism incompatible with fictionalism. (shrink)

An emphasis on explanatory contribution is central to a recent formulation of the indispensability argument for mathematical realism. Because scientific realism is argued for by means of inference to the best explanation, it has been further argued that being a scientific realist entails a commitment to IA and thus to mathematical realism. It has, however, gone largely unnoticed that the way that IBE is argued to be truth conducive involves citing successful applications of IBE and tracing this success over time. (...) This in turn involves identifying those constituents of scientific theories that are responsible for their predictive success and showing that these constituents are retained across theory change in science. I argue that even if mathematics can be shown to feature in best explanations, the role of mathematics in scientific theories does not satisfy the condition that mathematics is always retained across theory change. According to a scientific realist, this condition needs to be met for making ontological claims on the basis of explanatory contribution. Thus scientific realists are not committed to mathematical realism on the basis of this recent formulation of IA. (shrink)

Baker claims to provide an example of mathematical explanation of an empirical phenomenon which leads to ontological commitment to mathematical objects. This is meant to show that the positing of mathematical entities is necessary for satisfactory scientific explanations and thus that the application of mathematics to science can be used, at least in some cases, to support mathematical realism. In this paper I show that the example of explanation Baker considers can actually be given without postulating mathematical objects and thus (...) cannot be used by the mathematical realist. I also show that, despite this, mathematics keeps playing an important methodological role in the explanation and does not reduce to a merely computational or descriptive framework. (shrink)

Mathematical platonism is the view that abstract mathematical objects exist. Ontological pluralism is the view that there are many modes of existence. This paper examines the prospects for plural platonism, the view that results from combining mathematical platonism and ontological pluralism. I will argue that some forms of platonism are in harmony with ontological pluralism, while other forms of platonism are in tension with it. This shows that there are some interesting connections between the platonism–antiplatonism dispute and recent debates over (...) ontological pluralism. (shrink)

sBuilding models as a practical aspect of ecological theory has as a principal purpose the determination of relations in formal language. In this paper, the authors provide a formalization of ecological models based on impure systems theory. Impure systems contain objects and subjects: subjects are human beings. We can distinguish a person as an observer that by definition is the subject himself and part of the system. In this case he acquires the category of object. Objects are significances, which are (...) the consequence of perceptual beliefs on the part of the subject about material or energetic objects with certain characteristics. The impure system approach is as follows: objects are perceptual significances of material or energetic objects. The set of these objects will form an impure set of the first order. The existing relations between these relative objects will be of two classes: transactions of matter and/or energy and inferential relations. Transactions can have alethic modality: necessity, possibility, impossibility and contingency. In this work we define measures which let us choose the more suitable variables to relate both the model with the ecosystem and with different models. In this way we define different comparison indexes. (shrink)

Approaches to truth and the Liar paradox seem invariably to face a dilemma: either appeal to some sort of hierarchy, or declare apparently perfectly coherent concepts incoherent. But since both options lead to severe expressive restrictions, neither seems satisfactory. The aim of this paper is a new approach, which avoids the dilemma and the resulting expressive restrictions. Previous approaches tend to appeal to some new sort of semantic value for the truth predicate to take. I argue that such approaches inevitably (...) lead to the dilemma in question. In contrast, the present proposal sticks with classical semantic values, but allows the compositional rules associated with these to admit of exceptions. I show how such an approach can be developed systematically. (shrink)

Batterman raises a number of concerns for the inferential conception of the applicability of mathematics advocated by Bueno and Colyvan. Here, we distinguish the various concerns, and indicate how they can be assuaged by paying attention to the nature of the mappings involved and emphasizing the significance of interpretation in this context. We also indicate how this conception can accommodate the examples that Batterman draws upon in his critique. Our conclusion is that ‘asymptotic reasoning’ can be straightforwardly accommodated within the (...) inferential conception. 1 Introduction2 Immersion, Inference and Partial Structures3 Idealization and Surplus Structure4 Renormalization and the Stability of Mathematical Representations5 Explanation and Eliminability6 Requirements for Explanation7 Interpretation and Idealization8 Explanation, Empirical Regularities and the Inferential Conception9 Conclusion. (shrink)

This paper offers an exposition of Husserl's mature philosophy of mathematics, expounded for the first time in Logische Untersuchungen and maintained without any essential change throughout the rest of his life. It is shown that Husserl's views on mathematics were strongly influenced by Riemann, and had clear affinities with the much later Bourbaki school.

This paper analyzes the logical truths as (very roughly) those truths that would still have been true under a certain range of counterfactual perturbations.What’s nice is that the relevant range is characterized without relying (overtly, at least) upon the notion of logical truth. This approach suggests a conception of necessity that explains what the different varieties of necessity (logical, physical, etc.) have in common, in virtue of which they are all varieties of necessity. However, this approach places the counterfactual conditionals (...) in an unfamiliar foundational role. (shrink)

In Grundgesetze, Vol. II, §91, Frege argues that ‘it is applicability alone which elevates arithmetic from a game to the rank of a science’. Many view this as an in nuce statement of the indispensability argument later championed by Quine. Garavaso has questioned this attribution. I argue that even though Frege's applicability argument is not a version of ia, it facilitates acceptance of suitable formulations of ia. The prospects for making the empiricist ia compatible with a rationalist Fregean framework appear (...) thus much less dim than expected. Nonetheless, those arguing for such compatibility eventually face an hardly surmountable dilemma. (shrink)

The access problem for mathematics arises from the supposition that the referents of mathematical terms inhabit a realm separate from us. Quine’s approach in the philosophy of mathematics dissolves the access problem, though his solution sometimes goes unrecognized, even by those who rely on his framework. This paper highlights both Quine’s position and its neglect. I argue that Michael Resnik’s structuralist, for example, has no access problem for the so-called mathematical objects he posits, despite recent criticism, since he relies on (...) an indispensability argument. Still, Resnik’s structuralist does not provide an account of our access to traditional mathematical objects, and this may be seen as a problem. (shrink)

In this special issue, we put together papers that explore the theme “objectivity, space, and mind” from various angles. In the introduction we minimally discuss what are involved in this theme.

In recent years some archaeological commentators have suggested moving away from an exclusively anthropocentric view of social reality. These ideas endorse elevating objects to the same ontological level as humans – thus creating a symmetrical view of reality. However, this symmetry threatens to force us to abandon the human subject and theories of meaning. This article defends a different idea. It is argued here that an archaeology of the social, based on human intentionality, is possible, while maintaining an ontology that (...) does not involve dualistic conceptions of reality. Building upon the philosophical work of Vincent Descombes, it is contended that humans are intentional actors and society is predicated on triadic relations that involve humans, objects and meanings. These relations can only be understood holistically, given that these relations are merely parts of a meta-narrative. These meta-narratives contain specific historical and social settings, and it is only within these settings that social relations are intelligible. (shrink)