What is the role of mathematics in scientific explanations? Does it/can it play an explanatory part? This question is at the core of the recent ontological debate in the philosophy of mathematics. My aim in this paper is to argue that the two main approaches to this problem found in recent literature (i.e. the top-down and the bottom-up approaches) are both deeply problematic. This has an important implication for the dispute over the existence of mathematical (...) entities: to make progress possible in this debate, we either have to find a different approach to the problem of the role of mathematics in scientific explanations (one that is not affected by the problems that, as I argue in this paper, plague the existing approaches), or we need to recast it in different terms. (shrink)

The predisposition of the Indispensability Argument to objections, rephrasing and versions associated with the various views in philosophy of mathematics grants it a special status of a “blueprint” type rather than a debatable theme in the philosophy of science. From this point of view, it follows that the Argument has more an epistemic character than ontological.

A way to argue that something plays an explanatory role in science is by linking explanatory relevance with importance in the context of an explanation. The idea is deceptively simple: a part of an explanation is an explanatorily relevant part of that explanation if removing it affects the explanation either by destroying it or by diminishing its explanatory power, i.e. an important part is an explanatorily relevant part. This can be very useful in many ontological debates. My aim in (...) this paper is twofold. First of all, I will try to assess how this view on explanatory relevance can affect the recent ontological debate in the philosophy of mathematics—as I will argue, contrary to how it may appear at first glance, it does not help very much the mathematical realists. Second of all, I will show that there are big problems with it. (shrink)

Utilizing Einstein’s comparison of General Relativity and Descartes’ physics, this investigation explores the alleged conventionalism that pervades the ontology of substantival and relationist conceptions of spacetime. Although previously discussed, namely by Rynasiewicz and Hoefer, it will be argued that the close similarities between General Relativity and Cartesian physics have not been adequately treated in the literature—and that the disclosure of these similarities bolsters the case for a conventionalist interpretation of spacetime ontology.

What is the ontological status of mathematical structures? Michael Resnic, Stewart Shapiro and Gianluigi Oliveri, are contemporaries of American philosophers on mathematics, they give Platonic answers on this question.

Substantialism, which is an extremely common paradigm in Western philosophy, has dominated the sciences over time. Arguing that the authentic structure of existence is fixed and unchangeable; over time, with the development of modern physics, this understanding, which was easily adopted due to the precision of mechanical and mathematical explanations and the ease of categorization, created a school of biology that tried to develop through quantitative propositions; thus, living things were considered static entities that could be understood through reverse (...) engineering. Findings regarding evolution, which has continued uninterrupted for millions of years, have led to the gradual abandonment of essentialism. In addition, when many new data were analyzed, such as the transition from genetics to epigenetics and the mutual interaction in nature and niche creation, it was realized that biology in particular and all natural sciences in general needed a new metaphysical approach, thus process philosophy came to the fore. In process philosophy and metaphysics, it is accepted that every structure in nature consists of processual structures, not substances. The living world is fundamentally dynamic, and the existence of things always depends on the existence of processes, the basic assumption of biology is stability, not change; more precisely, it is argued that it is a stability achieved through constant change. By presenting a methodology, metaphysics and perspective from the process perspective of John Dupré, one of today's most important philosophers of biology, it is aimed to draw attention to the flowing of existence and processes of nature, expressed by Heraclitus as panta rhei (everything flows). (shrink)

Throughout his work, John Dewey seeks to emancipate philosophical reflection from the influence of the classical tradition he traces back to Plato and Aristotle. For Dewey, this tradition rests upon a conception of knowledge based on the separation between theory and practice, which is incompatible with the structure of scientific inquiry. Philosophical work can make progress only if it is freed from its traditional heritage, i.e. only if it undergoes reconstruction. In this study I show that implicit appeals to the (...) classical tradition shape prominent debates in philosophy of mathematics, and I initiate a project of reconstruction within this field. (shrink)

Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio (...) of two heights, for example, is a perceivable and measurable real relation between properties of physical things, a relation that can be shared by the ratio of two weights or two time intervals. Ratios are an example of continuous quantity; discrete quantities, such as whole numbers, are also realised as relations between a heap and a unit-making universal. For example, the relation between foliage and being-a-leaf is the number of leaves on a tree,a relation that may equal the relation between a heap of shoes and being-a-shoe. Modern higher mathematics, however, deals with some real properties that are not naturally seen as quantity, so that the “science of quantity” theory of mathematics needs supplementation. Symmetry, topology and similar structural properties are studied by mathematics, but are about pattern, structure or arrangement rather than quantity. (shrink)

This chapter argues that the standard conception of Spinoza as a fellow-travelling mechanical philosopher and proto-scientific naturalist is misleading. It argues, first, that Spinoza’s account of the proper method for the study of nature presented in the Theological-Political Treatise (TTP) points away from the one commonly associated with the mechanical philosophy. Moreover, throughout his works Spinoza’s views on the very possibility of knowledge of nature are decidedly sceptical (as specified below). Third, in the seventeenth-century debates over proper methods in (...) the sciences, Spinoza sided with those that criticized the aspirations of those (the physico-mathematicians, Galileo, Huygens, Wallis, Wren, etc) who thought the application of mathematics to nature was the way to make progress. In particular, he offers grounds for doubting their confidence in the significance of measurement as well as their piece-meal methodology (see section 2). Along the way, this chapter offers a new interpretation of common notions in the context of treating Spinoza’s account of motion (see section 3). (shrink)

Objective The relations between thought and reality are studied in many fields of philosophy and science. Examples include ontology and metaphysics in general, linguistics, neuroscience and even mathematics. Each one has its postulates, its language, its methods and its own constraints. It would be unreasonable, however, for them to ignore each other. In the pages that follow we will try to identify areas of proximity between the ideas of contemporary philosophers of language and those issued mainly by Ontology (...) of Knowledge but also by mathematics and neuroscience. We will try to take advantage of the clarity and the perfect structuring of the lecture « La philosophie contemporaine du langage » (the contemporary philosophy of language) given by Professor Denis Vernant . We will make use of this lecture, both for the ideas presented and as a reference process. The goal of this article is to bring out, through a benevolent confrontation, new ideas for the benefit of knowledge in general. (shrink)

This paper surveys Bolzano's Beyträge zu einer begründeteren Darstellung der Mathematik (Contributions to a better-grounded presentation of mathematics) on the 200th anniversary of its publication. The first and only published issue presents a definition of mathematics, a classification of its subdisciplines, and an essay on mathematical method, or logic. Though underdeveloped in some areas (including,somewhat surprisingly, in logic), it is nonetheless a radically innovative work, where Bolzano presents a remarkably modern account of axiomatics and the epistemology of the (...) formal sciences. We also discuss the second, unfinished and unpublished issue, where Bolzano develops his views on universal mathematics. Here we find the beginnings of his theory of collections, for him the most fundamental of the mathematical disciplines. Though not exactly the same as the later Cantorian set theory, Bolzano's theory of collections was used in very similar ways in mathematics, notably in analysis. In retrospect, Bolzano's debut in philosophy was a remarkably successful one, though its fruits would only become generally known much later. (shrink)

Du Châtelet holds that mathematical representations play an explanatory role in natural science. Moreover, she writes that things proceed in nature as they do in geometry. How should we square these assertions with Du Châtelet’s idealism about mathematical objects, on which they are ‘fictions’ dependent on acts of abstraction? The question is especially pressing because some of her important interlocutors (Wolff, Maupertuis, and Voltaire) denied that mathematics informs us about the properties of material things. After situating Du Châtelet in (...) this debate, this chapter argues, first, that her account of the origins of mathematical objects is less subjectivist than it might seem. Mathematical objects are non-arbitrary, public entities. While mathematical objects are partly mind-dependent, so are material things. Mathematical objects can approximate the material. Second, it is argued that this moderate metaphysical position underlies Du Châtelet’s persistent claims that mathematics is required for certain kinds of general knowledge, including in natural science. The chapter concludes with an illustrative example: an analysis of Du Châtelet’s argument that matter is continuous. A key premise in the argument is that mathematical representations and material nature correspond. (shrink)

In this paper I wish to connect the recent debate in the philosophy of quantum mechanics concerning the nature of the wave function to the historical debate in the philosophy of science regarding the tenability of scientific realism. Being realist about quantum mechanics is particularly challenging when focusing on the wave function. According to the wave function ontology approach, the wave function is a concrete physical entity. In contrast, according to an alternative viewpoint, namely the primitive (...) ontology approach, the wave function does not represent physical entities. In this paper, I argue that the primitive ontology approach can naturally be interpreted as an instance of the so-called ‘explanationism’ realism, which has been proposed as a response to the pessimistic-meta induction argument against scientific realism. If my arguments are sound, then one could conclude that: (1) contrarily to what is commonly though, if explanationism realism is a good response to the pessimistic-meta induction argument, it can be straightforwardly extended also to the quantum domain; (2) the primitive ontology approach is in better shape than the wave function ontology approach in resisting the pessimistic-meta induction argument against scientific realism. (shrink)

Memory technologies are cultural artifacts that scaffold, transform, and are interwoven with human biological memory systems. The goal of this article is to provide a systematic and integrative survey of their philosophical dimensions, including their metaphysical, epistemological and ethical dimensions, drawing together debates across the humanities, cognitive sciences, and social sciences. Metaphysical dimensions of memory technologies include their function, the nature of their informational properties, ways of classifying them, and their ontological status. Epistemological dimensions include the truth-conduciveness of external (...) memory, the conditions under which external memory counts as knowledge, and the metacognitive monitoring of external memory processes. And lastly, ethical and normative dimensions include the desirability of the effects memory technologies have on biological memory, their effects on self and culture, and their moral status. Whilst the focus in the article is largely philosophical and conceptual, empirical issues such as the way we interact with memory technologies in various contexts are also discussed. We thus take a naturalistic approach in which philosophical and empirical concepts and approaches are seen as continuous. (shrink)

If there is an area of discourse in which disagreement is virtually absent, it is mathematics. After all, mathematicians justify their claims with deductive proofs: arguments that entail their conclusions. But is mathematics really exceptional in this respect? Looking at the history and practice of mathematics, we soon realize that it is not. First, deductive arguments must start somewhere. How should we choose the starting points (i.e., the axioms)? Second, mathematicians, like the rest of us, are fallible. (...) Their ability to recognize whether a putative proof is correct is not infallible. In most cases, disagreement over the correctness of a putative proof is, however, evanescent. Once an error is spotted and communicated, the disagreement disappears. But this is not always the case. Sometimes it is recalcitrant; that is, it persists over time. In order to zoom in on this type of disagreement and explain its very possibility, we focus on a single case study: a decades-long (1921-1949) controversy between Federigo Enriques and Francesco Severi, two prominent exponents of the Italian school of algebraic geometry. We suggest that the instability of the mathematical community to which they belonged can be explained by the gap between an abstract criterion of rigor and local criteria of acceptability. It is this instability that made the existence of recalcitrant disagreement over putative proofs possible. We do not condemn speculative mathematics but rather its pretense of being rigorous mathematics. In this respect, we show that the overly self-confident Severi and the more intuitive, visionary Enriques had a completely different attitude. (shrink)

Mathematical objects are divided into (1) those which are autonomous, i.e., not dependent for their existence upon mathematicians’ conscious acts, and (2) intentional objects, which are so dependent. Platonist philosophy of mathematics argues that all objects belong to group (1), Brouwer’s intuitionism argues that all belong to group (2). Here we attempt to develop a dualist ontology of mathematics (implicit in the work of, e.g., Hilbert), exploiting the theories of Meinong, Husserl and Ingarden on the relations between (...) autonomous and intentional objects. In particular we develop a phenomenology of mathematical works, which has the stratified intentional structure discovered by Ingarden in his study of the literary work. (shrink)

The aim of this thesis is to propose a deflationary approach towards the ontological analysis of physical theories. Such an approach sustains that the development of ontologies for physical theories must be neutral relatively to the debate between realists and anti-realists in philosophy of physics. Mainly, our attention will be oriented towards what we called "quantum domain", which includes the non-relativistic Quantum Mechanics and variants of the Quantum Field Theory. This meta-ontological approach consists in an attempt (...) to provide a methodology for the development of specific ontologies for physical theories. With this aim we suggest the separation between physical phenomena and physical theories on one side, and physical theories and ontologies on the other side. This separation intends to endorse the idea that physical theories can provide all the informative contents required for the development of the ontologies associated with them. The result is a defense of the idea that physical theories can positively contribute for the constitution of the ontologies in physics. Additionally, we present a critical analysis of four different ontological approaches to QM and QFT. Each one of these interpretations deals with a different ontological category (tropes, events and processes). At the end of the thesis we will analyze the concepts of interaction and commutation in QFT in order to exemplify the main lines of the deflationary approach suggested here. (shrink)

The aim of this paper is to investigate the current debate on the state of economics from a methodological perspective. We claim that the majority of contributions criticizing modern economics are not based on clear methodological principles and thus many of them are not correct. We show this with respect to such issues as the problem of realisticness of models and their assumptions, the role of mathematics in economics, the way we conceptualize the relation between economics (theory) and (...) economy (empiria), as well as the general problem of comparing theories. In doing so we use the research apparatus taken form the philosophy of science and also we benefit a lot from recent developments in the philosophy of economics. Finally, we show one of the paradoxes of that debate, namely that many critics of economics accuse economists of using the wrong language (mathematics) while they do not use proper language themselves while criticizing economics, namely the apparatus taken from the philosophy of science. (shrink)

Pluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can (...) cover at most one mathematical universe. Indispensability arguments may thus lose their central role in the debate about mathematical ontology. (shrink)

This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.

The present crisis of truth, the "post-truth" crisis, puts the philosophy of truth in a new light. It calls for a reexamination of the tasks of the philosophy of truth and sets a new adequacy condition on this philosophy. One of the central roles of the philosophy of truth is to explain the importance of truth for human life and civilization. Among other things, it has to explain what is, or will be, lost in a post-truth (...) era. Clearly, the deflationist answer that the role of truth is to serve as a tool of generalization and oblique endorsement will not do. My account of truth in this paper addresses this task. Truth, I argue, is first and foremost a human value. Its importance to our life/civilization lies, not exclusively, but principally, in the centrality of this value to our humanity. I investigate the ramifications of this answer to the issues discussed in the contemporary philosophy of truth, and I end with a comparison of the substantivist and deflationist approaches to truth in light of this new perspective. (shrink)

The question of the applicability of mathematics is an epistemological issue that was explicitly raised by Kant, and which has played different roles in the works of neo-Kantian philosophers, before becoming an essential issue in early analytic philosophy. This paper will first distinguish three main issues that are related to the application of mathematics: indispensability arguments that are aimed at justifying mathematics itself; philosophical justifications of the successful application of mathematics to scientific theories; and discussions (...) on the application of real numbers to the measurement of physical magnitudes. A refinement of this tripartition is suggested and supported by a historical investigation of the differences between Kant’s position on the problem, several neo-Kantian perspectives, early analytic philosophy, and late 19th century mathematicians. Finally, the debate on the cogency of an application constraint in the definition of real numbers is discussed in relation to a contemporary debate in neo-logicism, in order to suggest a comparison not only with Frege’s original positions, but also with the ideas of several neo-Kantian scholars, including Hölder, Cassirer, and Helmholtz. (shrink)

ABSTRACT. May scientists rely on substantive, a priori presuppositions? Quinean naturalists say "no," but Michael Friedman and others claim that such a view cannot be squared with the actual history of science. To make his case, Friedman offers Newton's universal law of gravitation and Einstein's theory of relativity as examples of admired theories that both employ presuppositions (usually of a mathematical nature), presuppositions that do not face empirical evidence directly. In fact, Friedman claims that the use of such presuppositions is (...) a hallmark of "science as we know it." But what should we say about the special sciences, which typically do not rely on the abstruse formalisms one finds in the exact sciences? I identify a type of a priori presupposition that plays an especially striking role in the development of empirical psychology. These are ontological presuppositions about the type of object a given science purports to study. I show how such presuppositions can be both a priori and rational by investigating their role in an early flap over psychology's contested status as a natural science. The flap focused on one of the field's earliest textbooks, William James's Principles of Psychology. The work was attacked precisely for its reliance on a priori presuppositions about what James had called the "mental state," psychology's (alleged) proper object. I argue that the specific presuppositions James packed into his definition of the "mental state" were not directly responsible to empirical evidence, and so in that sense were a priori; but the presuppositions were rational in that they were crafted to help overcome philosophical objections (championed by neo-Hegelians) to the very idea that there can be a genuine science of mind. Thus, my case study gives an example of substantive, a priori presuppositions being put to use—to rational use—in the special sciences. In addition to evaluating James's use of presuppositions, my paper also offers historical reflections on two different strands of pragmatist philosophy of science. One strand, tracing back through Quine to C. S. Peirce, is more naturalistic, eschewing the use of a priori elements in science. The other strand, tracing back through Kuhn and C. I. Lewis to James, is more friendly to such presuppositions, and to that extent bears affinity with the positivist tradition Friedman occupies. (shrink)

Imre Lakatos' views on the philosophy of mathematics are important and they have often been underappreciated. The most obvious lacuna in this respect is the lack of detailed discussion and analysis of his 1976a paper and its implications for the methodology of mathematics, particularly its implications with respect to argumentation and the matter of how truths are established in mathematics. The most important themes that run through his work on the philosophy of mathematics and (...) which culminate in the 1976a paper are (1) the (quasi-)empirical character of mathematics and (2) the rejection of axiomatic deductivism as the basis of mathematical knowledge. In this paper Lakatos' later views on the quasi-empirical nature of mathematical theories and methodology are examined and specific attention is paid to what this view implies about the nature of mathematical argumentation and its relation to the empirical sciences. (shrink)

A primary goal of this chapter is to highlight neglected epistemic parallels between dualism and physicalism. Both dualist and physicalist arguments employ a combination of empirical data and armchair reflection; both rely on considerations stemming from how we conceptualize certain phenomena; and both aim to establish views that are compatible with scientific results but go well beyond the deliverances of empirical science. -/- I begin the chapter by fleshing out the distinctive commitments of dualism, in a way that illuminates the (...) interplay of epistemic and metaphysical elements within the dualist position. Section 2 outlines two influential arguments for dualism and explains how dualists defend those arguments from key criticisms. Sections 3 and 4 examine the most powerful objections to dualism: that it is inferior to physicalism as regards the theoretical virtue of simplicity, and that it cannot explain mental causation. I show that each of these objections to dualism depends on substantial assumptions that cannot be empirically justified. The objection from mental causation additionally rests on an ambitious assumption about how we conceptualize physical phenomena. Section 5 briefly reviews how epistemic considerations inform arguments on both sides of this debate. (shrink)

Why study notations, diagrams, or more broadly the variety of nonverbal “representations” or “signs” that are used in mathematical practice? This chapter maps out recent work on the topic by distinguishing three main philosophical motivations for doing so. First, some work (like that on diagrammatic reasoning) studies signs to recover norms of informal or historical mathematical practices that would get lost if the particular signs that these practices rely on were translated away; work in this vein has the potential to (...) broaden our view of the specific normativity of mathematics beyond logical proof. Second, some work focuses on signs to highlight the open-ended and “nonrigorous” aspects of mathematical practice, and the role of these aspects in the historical development of mathematics. The third motivation is based on the following observation: the reason differences in signs matter in mathematics is that humans are finite agents, with cognitive and computational limitations. Accordingly, studying signs can be a way to study how human computational constraints shape the mathematics that we do, and to tackle the topic of mathematical understanding. (shrink)

One of the many debates in the philosophy of race is whether we should eliminate or conserve discourse, thought, and practices reliant on racial terms and categories (i.e., race-talk). In this paper, I consider this debate in the context of medicine. The recent resurgence in anti-racist activism and the COVID-19 pandemic have prompted philosophers, medical professionals, and the public to (re)consider race, its role in long-standing health disparities, and the utility of race-based medicine. In what follows, I argue (...) that while utility is insufficient for adjudicating permissible uses of race in medicine, eliminativism is neither necessary nor sufficient for dealing with the sort of ills associated with race-based medicine. I, then, use a virtue-based framework to adjudicate morally permissible uses of race in medicine. In doing so, I demonstrate the limitations of eliminativism, offer a decision procedure for determining morally permissible uses of race, and demonstrate that the debate regarding eliminating or preserving race-talk need not depend on conclusive answers to metaphysical questions regarding race. (shrink)

Scholars in the field of environmental and animal ethics have propounded theories that outline what, in their view, ought to constitute an ethical relationship between humans and the environment and humans and nonhuman animals respectively. In the field of animal ethics, the contributions by Western scholars to theorize a body of animal ethics, either as an ethic in its own right or as a branch of the broader field of environmental ethics is clearly seen. Consequently, there are, notably, two main (...) schools of thought in the field of animal ethics. These are the ‘welfarist’ and the ‘rightist’ approaches (Regan, 2006; Owoseni & Olatoye, 2014). Unfortunately, a clearly concerted effort to theorize on animal ethics from an African perspective is at the minimal, although there is a lot written in African environmental ethics, broadly construed. It is within this context that this study locates an African animal ethic within the two main theories in the global animal ethics debate, using traditional Akan ontology and ethics particularly, those that speak to their relationship with the environment and, especially animals. Thus, using Akan ontological worldview and ethics as foundational sources, alongside learned principles from the emerging theories in African environmental ethics, the study seeks to find the place of Akan animal ethics within the rightist and welfarist debates. (shrink)

Notions such as śūnyatā, catuṣkoṭi, and Indra's net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nāgārjuna considered two levels of reality: one called conventional reality, and the other ultimate reality. Within this framework, śūnyatā refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuṣkoṭi refers to the (...) claim that four truth values, including contradiction, are admissible in reasoning. Indra's net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions that are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of śūnyatā. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of catuṣkoṭi. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics. (shrink)

Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: (...) the philosophical mathematician Georg Cantor (1845-1918) says that between the realm of the finite and the absolute infinite, there is an intermediate realm partaking in properties in a certain sense of both the finite and the infinite: the transfinite realm. Like the finite, the transfinite realm is a realm of mathematical objects, numbers, and knowledge. Like the absolute infinite, the transfinite is a form of infinity insofar as transfinite sets and numbers transcend any finite number. Echoing Cusanus and neo-Platonism, Cantor says that the transfinite sequence of all ordinals is a symbol of the absolutely infinite, that is, God. This paper considers how the doctrine of symbolism and the philosophers' different commitments to the laws of logic, especially the Law of Non-Contradiction (LNC), enables these thinkers to articulate a transcendental apophatic approach to divinity. (shrink)

An influential position in the philosophy of biology claims that there are no biological laws, since any apparently biological generalization is either too accidental, fact-like or contingent to be named a law, or is simply reducible to physical laws that regulate electrical and chemical interactions taking place between merely physical systems. In the following I will stress a neglected aspect of the debate that emerges directly from the growing importance of mathematical models of biological phenomena. My main aim (...) is to defend, as well as reinforce, the view that there are indeed laws also in biology, and that their difference in stability, contingency or resilience with respect to physical laws is one of degrees, and not of kind . (shrink)

In this paper I apply the concept of _inter-Model Inconsistency in Set Theory_ (MIST), introduced by Carolin Antos (this volume), to select positions in the current universe-multiverse debate in philosophy of set theory: I reinterpret H. Woodin’s _Ultimate L_, J. D. Hamkins’ multiverse, S.-D. Friedman’s hyperuniverse and the algebraic multiverse as normative strategies to deal with the situation of de facto inconsistency toleration in set theory as described by MIST. In particular, my aim is to situate these positions (...) on the spectrum from inconsistency avoidance to inconsistency toleration. By doing so, I connect a debate in philosophy of set theory with a debate in philosophy of science about the role of inconsistencies in the natural sciences. While there are important differences, like the lack of threatening explosive inferences, I show how specific philosophical positions in the philosophy of set theory can be interpreted as reactions to a state of inconsistency similar to analogous reactions studied in the philosophy of science literature. My hope is that this transfer operation from philosophy of science to mathematics sheds a new light on the current discussion in philosophy of set theory; and that it can help to bring philosophy of mathematics and philosophy of science closer together. (shrink)

This paper examines Hobbes’s criticisms of Robert Boyle’s air-pump experiments in light of Hobbes’s account in _De Corpore_ and _De Homine_ of the relationship of natural philosophy to geometry. I argue that Hobbes’s criticisms rely upon his understanding of what counts as “true physics.” Instead of seeing Hobbes as defending natural philosophy as “a causal enterprise … [that] as such, secured total and irrevocable assent,” 1 I argue that, in his disagreement with Boyle, Hobbes relied upon his understanding (...) of natural philosophy as a mixed mathematical science. In a mixed mathematical science one can mix facts from experience with causal principles borrowed from geometry. Hobbes’s harsh criticisms of Boyle’s philosophy, especially in the _Dialogus Physicus, sive De natura aeris_, should thus be understood as Hobbes advancing his view of the proper relationship of natural philosophy to geometry in terms of mixing principles from geometry with facts from experience. Understood in this light, Hobbes need not be taken to reject or diminish the importance of experiment/experience; nor should Hobbes’s criticisms in _Dialogus Physicus_ be understood as rejecting experimenting as ignoble and not befitting a philosopher. Instead, Hobbes’s viewpoint is that experiment/experience must be understood within its proper place – it establishes the ‘that’ for a mixed mathematical science explanation. (shrink)

Powers, capacities and dispositions (in what follows I will use these terms synonymously) have become prominent in recent debates in metaphysics, philosophy of science and other areas of philosophy. In this paper I will analyse in some detail a well-known argument from scientific practice to the existence of powers/capacities/dispositions. According to this argument the practice of extrapolating scientific knowledge from one kind of situation to a different kind of situation requires a specific interpretation of laws of nature, namely (...) as attributing dispositions to systems. My main interest will be to discuss what characteristics these dispositions need to have in order to account for the scientific practice in question. I will furthermore assess whether the introduction of dispositions in the context of the extrapolation argument can be described as a ‘revitalization’ or as a ‘return’ to those notions repudiated by early modern philosophers. More particularly I will argue for the following claims: I. In repudiating scholastic terminology, including substantial forms with their causal powers, post-cartesian philosophers focussed on a concept of causation that was much stronger than 21st century conceptions of causation. For this reason alone, whatever ‘causal’ is supposed to mean in today’s causal powers, embracing causal powers is not a simple return to a pre-cartesian notion. II. The dispositions presupposed in scientific practice need not (and should not) be construed in causal terms (whether strong or weak). III. While some early modern philosophers contrasted the characterisation of the natural world in terms of substantial forms (and their causal powers) on the one hand and a mathematical characterization on the other and suggested that these approaches are incompatible, the dispositions postulated by the extrapolation argument to account for scientific practice are themselves characterized in mathematical terms. More precisely: The behaviour the systems are disposed to display is – at least in physics – often characterized in mathematical terms. IV. The dispositions assumed in the law-statements in scientific practice are determinable rather than determinate properties. (shrink)

The concept of life plays a crucial role in the debate on synthetic biology. The first part of this chapter outlines the controversial debate on the status of the concept of life in current science and philosophy. Against this background, synthetic biology and the discourse on its scientific and societal consequences is revealed as an exception. Here, the concept of life is not only used as buzzword but also discussed theoretically and links the ethical aspects with the (...) epistemological prerequisites and the ontological consequences of synthetic biology. The second part examines this point of intersection and analyses some of the issues which are discussed in terms of the concept of life. The third part turns to the history of the concept of life. It offers an examination of scientific and philosophical discourses on life at the turn of the 20th century and suggests a surprising result: In the light of this history, synthetic biology leads to well-known debates, arguments, notions and questions. But it is concluded that the concept of life is too ambiguous and controversial to be useful for capturing the actual practice of synthetic biology. In the fourth part I argue that with regard to the ethical evaluation of synthetic biology, the ambiguity of the concept of life is not as problematic as sometimes held because other challenges are more important. The question whether the activity of synthetic biological systems should be conceived as life or not is primarily theoretical. (shrink)

This paper argues for an interpretation of Leibniz’s claim that physics requires both mechanical and teleological principles as a view regarding the interpretation of physical theories. Granting that Leibniz’s fundamental ontology remains non-physical, or mentalistic, it argues that teleological principles nevertheless ground a realist commitment about mechanical descriptions of phenomena. The empirical results of the new sciences, according to Leibniz, have genuine truth conditions: there is a fact of the matter about the regularities observed in experience. Taking this stance, however, (...) requires bringing non-empirical reasons to bear upon mechanical causal claims. This paper first evaluates extant interpretations of Leibniz’s thesis that there are two realms in physics as describing parallel, self-sufficient sets of laws. It then examines Leibniz’s use of teleological principles to interpret scientific results in the context of his interventions in debates in seventeenth-century kinematic theory, and in the teaching of Copernicanism. Leibniz’s use of the principle of continuity and the principle of simplicity, for instance, reveal an underlying commitment to the truth-aptness, or approximate truth-aptness, of the new natural sciences. The paper concludes with a brief remark on the relation between metaphysics, theology, and physics in Leibniz. (shrink)

The question of what ontological insights can be gained from the knowledge of physics (keyword: ontic structural realism) cannot obviously be separated from the view of physics as a science from an epistemological perspective. This is also visible in the debate about 'scientific realism'. This debate makes it evident, in the form of the importance of perception as a criterion for the assertion of existence in relation to the 'theoretical entities' of physics, that epistemology itself is 'ontologically (...) laden'. This is in the form of the assumption that things (or entities) in themselves exist as such and such determined ones (independent of cognition, autonomously). This ontological assumption is not only the basis of our naïve understanding of cognition, but also its indispensable premise, insofar as this understanding is a fundamentally passive, 'receptive' one. Accordingly, just as 'perception' is the foundation, ('objective') description is the aim of cognition, that which cognition is about. In this sense, our idea of cognition and our idea of the things are inseparably linked. Without the ontological premise mentioned we just would not know what cognition is, but it is basically just a kind of image that we have in our minds (an assumption that helps us understand 'cognition'). Epistemology not only shares this basic assumption (which it also shares with metaphysics), but it revolves (unlike metaphysics) entirely around it by making the idea and demand of 'certainty' a condition of 'real' knowledge. As 'certainty' is a subjective criterion this entails the 'remodelling' of the real, holistic cognitive situation (to which metaphysics adheres) into a linear subject-object-relation (which results in the strict 'transcendence' of the objects). And it also establishes, due to its 'expertise' in matters of cognition, the 'primacy of epistemology' over all other sciences. Now, on closer inspection, however, the expertise of epistemology seems not all that dependable, because it basically consists only of paradigms which, from the point of view of the holism of the real cognitive situation itself, are nothing more than relatively simplistic interpretations of this situation. However, we do not yet know what another conception of cognition might look like (which is not surprising given the high rank of the phenomenon of cognition in the hierarchy of phenomena according to their complexity). 'Certainty' as a criterion of cognition is thus excluded from the outset, and thus the linear relational model of cognition appears as what it is, a gross distortion of the real, holistic cognitive situation. The significance of this argumentation with regard to physics is that the linear epistemological model of cognition itself is a major obstacle to an adequate epistemological understanding of physics. This is because it is fixed 'a priori' to an object-related concept of cognition, and to 'description' as the only mode of ('real') cognition. But physics (without questioning our naïve notion of cognition on the level of epistemology) simply works past it and its basic assumptions. Its cognitive concept (alias heuristic) is fundamentally different from that of metaphysics. The acceptance of the real, holistic cognitive situation is, in my opinion, the condition for an adequate understanding of physics' heuristic access to objects, its transcendental, generalizing cognitive concept, as well as its ontological relevance and dimension of its own. (shrink)

Williamson’s “anti-luminosity” argument aims to establish that there are no significant luminous conditions. “Far from forming a cognitive home”, luminous conditions are mere “curiosities”. Even supposing Williamson’s argument succeeds in showing that there are no significant luminous states his conclusion has not thereby been established. When it comes to determining what is luminous, mental events and processes are among the best candidates. It is events and processes, after all, which constitute the stream of consciousness. Judgment, for instance, is plausibly self-conscious. (...) If I am judging then plausibly I must know that I am. Similarly, deliberation is plausibly self-conscious. To be deliberating about some matter I plausibly must know that I am. That one is judging and that one is deliberating are thus plausibly luminous conditions. Furthermore, I argue, Williamson’s anti-luminosity argument fails to speak against this suggestion. This reveals that Williamson’s argument is more limited in scope than has been thought—something likely missed due to a misplaced focus on mental states in the luminosity debate as well as in epistemology and the philosophy of mind more generally. For all Williamson shows, there may be luminous events and processes of a sort apt to constitute a cognitive home. I conclude by considering how the anti-luminosity argument might be reinstated in the judgment case and argue that the natural way to do so fails. (shrink)

Biological individuality is without a doubt a key concept in philosophy of biology. Questions around the individuality of organisms, species, and biological systems can be traced throughout the philosophy of biology since the discipline’s inception, not to mention the sustained attention they have received in biology and philosophy more broadly. It’s high time the topic got its own Cambridge Element. McConwell’s Biological Individuality falls short of an authoritative overview of the debate on biological individuality. However, it (...) sends a welcome message to new and seasoned scholars to reorient the debate towards practically and politically relevant themes. (shrink)

The Polish philosophy of mathematics in the 19th century had its origins in the Romantic period under the influence of the then-predominant idealist philosophies. The decline of Romantic philosophy precipitated changes in general philosophy, but what is less well known is how it triggered changes in the philosophy of mathematics. In this paper, we discuss how the Polish philosophy of mathematics evolved from the metaphysical approach that had been formed during the Romantic (...) era to the more modern positivistic paradigm. These evolutionary changes are attributed to the philosophers Henryk Struve, Antoni Molicki and Julian Ochorowicz, and mathematicians Karol Hertz and Samuel Dickstein. We also show how implicit ideas (i.e., those not declared openly) from the area between the philosophy of science and general philosophy played a crucial role in the paradigm shift in the Polish philosophy of mathematics. (shrink)

I begin by outlining Du Châtelet’s ontology of mathematical objects: she is an idealist, and mathematical objects are fictions dependent on acts of abstraction. Next, I consider how this idealism can be reconciled with her endorsement of necessary truths in mathematics, which are grounded in essences that we do not create. Finally, I discuss how mathematics and physics relate within Du Châtelet’s idealism. Because the primary objects of physics are partly grounded in the same kinds of acts as (...) yield mathematical objects, she thinks we are sometimes licensed in drawing conclusions about physical things from mathematical premises. (shrink)

There has been much recent debate over the meaning of the claim that God is good and loving. Although the participants in this debate strongly disagree over the correct analysis of the claim, there is nonetheless agreement across all parties that there is a single correct analysis. This paper aims to overthrow this consensus, by showing that sentences such as ‘There is a good and loving God’ are often used to express a variety of beliefs with quite different (...) logico-grammatical characteristics. Belief in a good and loving God might range from being an evidentially grounded and empirically falsifiable ontological hypothesis, all the way to being a belief which is both ungrounded and unfalsifiable, and more akin to an attitude than to an hypothesis. The logical variety exhibited by the belief in a good and loving God often gives rise, in turn, to people holding that belief in a way that is indeterminate, mixed, or fluid between those different varieties. That is, someone’s belief in a good and loving God may hover indeterminately between more than one logical variety of the belief; or it may mix together some of the logical characteristics of different varieties of the belief; or it may change from having one logical character to another and perhaps back again. These properties are often masked by the fact that the belief is always expressed by the same sentence regardless of any indeterminacy, mixedness, or fluidity. Though these properties are rarely discussed by analytic philosophers of religion, logico-grammatical variety, indeterminacy, mixedness, and fluidity are pervasive in religious beliefs and utterances, and account for much of those beliefs and utterances' real-life complexity. This paper will make a start at an examination of these important properties by using the belief in a good and loving God as a representative case study. (shrink)

Bertrand Russell’s _Principles of Mathematics_ (1903) gives rise to several interpretational challenges, especially concerning the theory of denoting concepts. Only relatively recently, for instance, has it been properly realised that Russell accepted denoting concepts that do not denote anything. Such empty denoting concepts are sometimes thought to enable Russell, whether he was aware of it or not, to avoid commitment to some of the problematic non-existent entities he seems to accept, such as the Homeric gods and chimeras. In this paper, (...) I argue first that the theory of denoting concepts in _Principles of __Mathematics_ has been generally misunderstood. According to the interpretation I defend, if a denoting concept shifts what a proposition is about, then the aggregate of the denoted terms will also be a constituent of the proposition. I then show that Russell therefore could not have avoided commitment to the Homeric gods and chimeras by appealing to empty denoting concepts. Finally, I develop what I think is the best understanding of the ontology of _Principles of __Mathematics_ by interpreting some difficult passages. (shrink)

It has become increasingly common to talk about the second person in the theory of mind debate. While theory theory and simulation theory are described as third person and first person accounts respectively, a second person account suggests itself as a viable, though wrongfully neglected third option. In this paper I argue that this way of framing the debate is misleading. Although defenders of second person accounts make use of the vocabulary of the theory of mind debate, (...) they understand some of the core expressions in a different way. I will illustrate this claim by focusing on Reddy’s and Gallagher’s accounts and argue that these authors use the notions of knowing and of understanding other minds differently than traditionally assumed. As a consequence, second person accounts thus conceived do not directly address the questions that gave rise to the theory of mind debate. They invite us, however, to critically reflect upon the way the debate has been set up. (shrink)

Philosophy can shed light on mathematical modeling and the juxtaposition of modeling and empirical data. This paper explores three philosophical traditions of the structure of scientific theory—Syntactic, Semantic, and Pragmatic—to show that each illuminates mathematical modeling. The Pragmatic View identifies four critical functions of mathematical modeling: (1) unification of both models and data, (2) model fitting to data, (3) mechanism identification accounting for observation, and (4) prediction of future observations. Such facets are explored using a recent exchange between two (...) groups of mathematical modelers in plant biology. Scientific debate can arise from different modeling philosophies. (shrink)

This essay explores the use of platonist and nominalist concepts, derived from the philosophy of mathematics and metaphysics, as a means of elucidating the debate on spacetime ontology and the spatial structures endorsed by scientific realists. Although the disputes associated with platonism and nominalism often mirror the complexities involved with substantivalism and relationism, it will be argued that a more refined three-part distinction among platonist/nominalist categories can nonetheless provide unique insights into the core assumptions that underlie spatial (...) ontologies, but it also assists in critiquing alternative uses of nominalism, platonism, and both ontic and epistemic structural realism. (shrink)

There is a lively debate in contemporary Analytic Philosophy of Religion about the consistency of the Trinitarian doctrine. In this context, the notion of ‘mystery’ has become crucial. However, although it is currently considered the main challenge of Trinitarian theology, its definition remains rather partial and superficial. After a brief description of today’s Mysterianism, I analyse three ‘emblematic’ positions in light of the current debate: Aquinas, Leibniz and Hegel present three ways to believe in a mysterious Trinity. (...) I will point out a few possible weaknesses in the positions of the first two authors in order to better highlight the usefulness of the Hegelian position, often underestimated in the contemporary analytic debate. I will also analyse the connection between the three positions and their respective metaphysics, showing the epistemological premises (e.g., analogy and univocity) that need to be better investigated in the future. (shrink)

In the Fifth Meditation, Descartes makes a remarkable claim about the ontological status of geometrical figures. He asserts that an object such as a triangle has a 'true and immutable nature' that does not depend on the mind, yet has being even if there are no triangles existing in the world. This statement has led many commentators to assume that Descartes is a Platonist regarding essences and in the philosophy of mathematics. One problem with this seemingly natural (...) reading is that it contradicts the conceptualist account of universals that one finds in the Principles of Philosophy and elsewhere. In this paper, I offer a novel interpretation of the notion of a true and immutable nature which reconciles the Fifth Meditation with the conceptualism of Descartes' other work. Specifically, I argue that Descartes takes natures to be innate ideas considered in terms of their so-called 'objective being'. (shrink)

What are words? What makes two token words tokens of the same word-type? Are words abstract entities, or are they (merely) collections of tokens? The ontology of words tries to provide answers to these, and related questions. This article provides an overview of some of the most prominent views proposed in the literature, with a particular focus on the debate between type-realist, nominalist, and eliminativist ontologies of words.

It is discerned what light can bring the recent historical reconstructions of maxwellian optics and electromagnetism unification on the following philosophical/methodological questions. I. Why should one believe that Nature is ultimately simple and that unified theories are more likely to be true? II. What does it mean to say that a theory is unified? III. Why theory unification should be an epistemic virtue? To answer the questions posed genesis and development of Maxwellian electrodynamics are elucidated. It is enunciated that the (...) Maxwellian Revolution is a far more complicated phenomenon than it may be seen in the light of Kuhnian and Lakatosian epistemological models. Correspondingly it is maintained that maxwellian electrodynamics was elaborated in the course of the old pre-maxwellian programmes’ reconciliation: the electrodynamics of Ampére-Weber, the wave theory of Young-Fresnel and Faraday’s programme. To compare the different theoretical schemes springing from the different language games James Maxwell had constructed a peculiar neutral language. Initially it had encompassed the incompressible fluid models; eventually – the vortices ones. The three programmes’ encounter engendered the construction of the hybrid theory at first with an irregular set of theoretical schemes. However, step by step, on revealing and gradual eliminating the contradictions between the programmes involved, the hybrid set is “put into order” (Maxwell’s term). A hierarchy of theoretical schemes starting from ingenious crossbreeds (the displacement current) and up to usual hybrids is set up. After the displacement current construction the interpenetration of the pre-maxwellian programmes begins that marks the commencement of theoretical schemes of optics, electricity and magnetism real unification. Maxwell’s programme surpassed that of Ampére-Weber because it did absorb the ideas of the Ampére-Weber programme, as well as the presuppositions of the programmes of Young-Fresnel and Faraday properly co-ordinating them with each other. But the opposite statement is not true. The Ampére-Weber programme did not assimilate the propositions of the Maxwellian programme. Maxwell’s victory over his rivals became possible because the gist of Maxwell’s unification strategy was formed by Kantian epistemology looked in the light of William Whewell and such representatives of Scottish Enlightenment as Thomas Reid and Sir William Hamilton. Maxwell did put forward as basic synthetic principles the ideas that radically differed from that of Ampére-Weber approach by their open, flexible and contra-ontological, genuinly epistemological, Kantian character. For Maxwell, ether was not the ultimate building block of physical reality, from which all the charges and fields should be constructed. “Action at a distance”, “incompressible fluid”, “molecular vortices”, etc. were contrived analogies for Maxwell, capable only to direct the researcher at the “right” mathematical relations. Key words: J.C. Maxwell, unification of optics and electromagnetism, I. Kant, T. Reid, W. Hamilton . (shrink)