This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. (...) Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method. (shrink)

Dans cet article je présente une analyse critique de l’approche habituelle de l’identité mathématique qui a son origine dans les travaux de Frege et Russell, en faisant un contraste avec les approches alternatives de Platon et Geach. Je pose ensuite ce problème dans un cadre de la théorie des catégories et montre que la notion d’identité ne peut pas être « internalisée » par les moyens catégoriques standards. Enfin, je présente deux approches de l’identité mathématique plus spécifiques: une avec la (...) fibration catégorielle et l’autre avec des catégories supérieures faibles. (shrink)

Dans cet article je présente une analyse critique de l’approche habituelle de l’identité mathématique qui a son origine dans les travaux de Frege et Russell, en faisant un contraste avec les approches alternatives de Platon et Geach. Je pose ensuite ce problème dans un cadre de la théorie des catégories et montre que la notion d’identité ne peut pas être « internalisée » par les moyens catégoriques standards. Enfin, je présente deux approches de l’identité mathématique plus spécifiques: une avec la (...) fibration catégorielle et l’autre avec des catégories supérieures faibles. (shrink)

The popular view according to which category theory provides a support for mathematical structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics studies ‘invariant form’ (Awodey) categorical mathematics studies covariant and contravariant transformations which, generally, have no invariants. In this paper I develop a non-structuralist interpretation of categorical mathematics.

When the traditional distinction between a mathematical concept and a mathematical intuition is tested against examples taken from the real history of mathematics one can observe the following interesting phenomena. First, there are multiple examples where concepts and intuitions do not well fit together; some of these examples can be described as “poorly conceptualised intuitions” while some others can be described as “poorly intuited concepts”. Second, the historical development of mathematics involves two kinds of corresponding processes: poorly conceptualised intuitions are (...) further conceptualised while poorly intuited concepts are further intuited. In this paper I study this latter process in mathematics during the twentieth century and, more specifically, show the role of set theory and category theory in this process. I use this material for defending the following claims: (1) mathematical intuitions are subject to historical development just like mathematical concepts; (2) mathematical intuitions continue to play their traditional role in today's mathematics and will plausibly do so in the foreseeable future. This second claim implies that the popular view, according to which modern mathematical concepts, unlike their more traditional predecessors, cannot be directly intuited, is not justified. (shrink)

This article asks whether a country that suffers from serious environmental problems caused by another country could have a just cause for a defensive war? Danish philosopher Kasper Lippert-Rasmussen has argued that under certain conditions extreme poverty may give a just cause for a country to defensive war, if that poverty is caused by other countries. This raises the question whether the victims of environmental damages could also have a similar right to self-defense. Although the article concerns justice of war, (...) we will concentrate only on the issue of what can be just causes of war, instead of evaluating the entire justification of war. This is to say that we will limit our discussion to the question concerning just cause and leave aside more general questions concerning justness and moral permissibility of war. Our aim is to list the questions that must be made and settled if defensive war in the case of serious environmental problems is said to have (or not to have) a just cause. We will argue that there are three questions that are most important in this context. They are the question concerning liability, the question of collective responsibility, and the question whether environmental harms may create a “sufficient reason” for raising a war. (shrink)

Category theory doesn't support Mathematical Structuralism but suggests a new philosophical view on mathematics, which differs both from Structuralism and from traditional Substantialism about mathematical objects. While Structuralism implies thinking of mathematical objects up to isomorphism the new categorical view implies thinking up to general morphism.

In addition to the “universal glue,” which is the local mechanical causation, the standard explanatory scheme of classical science presumes two “universal vessels,” which are global space and time. I call this outdated metaphysical setting “black-and-white” because it allows for only two principal scales. A prospective metaphysics able to bind existing sciences together needs to be “colored,” that is, allow for scale relativity and diversification by domain.

In 1900 David Hilbert announced his famous list of then-opened mathematical problems; the problem number 6 in this list is axiomatization of physical theories. Since then a lot of systematic efforts have been invested into solving this problem. However the results of these efforts turned to be less successful than the early enthusiasts of axiomatic method expected. The existing axiomatizations of physical and biological theories provide a valuable logical analysis of these theories but they do not constitute anything like their (...) standard presentation,which can be used for transmission, evaluation, and justification of physical and biological knowledge. This state of theart in the axiomatization of physics is strong evidence that the standard notion of axiomatic theory stemming from Hilbert and Tarski is not appropriate for thet ask. However in the recent years in mathematics there emerged a new axiomatic approach best represented by the Homotopy Type theory (HoTT). We argue that the constructive axiomatic architecture used in HoTT has better chances to be successfully applied in physics as well as in computer science and engineering. (shrink)

I take it that the following is a desideratum of our theories in the philosophy of mind. A theory in the philosophy of mind should help us better understand ourselves as agents and aid in our theorizing about the nature of action and agency. In this paper I discuss a strategy adopted by some defenders of nonreductive physicalism in response to the problem of causal exclusion. The strategy, which I refer to as “intralevelism,” relies on treating mental causation as intra (...) level mental to mental causation, rather than as involving any inter level mental to physical causation. I raise problems for intralevelist theories of mental causation that stem from action-theoretic considerations. Specifically, I focus on the failure of intralevelist proposals to account for the problem of basic causal deviance in the etiology of action. To the extent that intralevelism fails to make room for basic causal deviance, the strategy fails to satisfy the aforementioned desideratum, viz ., that our theories in the philosophy of mind should be of use in theorizing about action and agency. The upshot is that intralevelism is a less promising strategy for nonreductive physicalists than it appears at first glance. (shrink)

This essay attempts to develop a new theoretical model for business ethics distinct from the two canonical business‐ethics theories, the stakeholder theory and the shareholder value theory. Milton Friedman argued that because managers are agents of the company's owners, their sole moral responsibility is to maximize owner returns. Thomas Pogge has recently suggested that such a view involves a kind of moral incoherence and that we should reject the efficacy of social arrangements like the principal‐agent relationship in altering moral obligations. (...) Both views fail to give proper account of the dispersal of moral responsibilities in business contexts. We must distinguish “minimal moral obligations” (stemming from justice and rights) from “maximal moral obligations” (stemming from all other moral considerations, including duties of aid, beneficence, and the virtues). Minimal obligations apply to all persons, but maximal obligations can be effected by social arrangements like the owner‐manager relationship. There may be moral obligations incumbent on owners that do not apply to managers. Understanding this distribution of responsibilities enables us to develop a new and attractive model of business ethics––“the ownership model”––which places greater emphasis on the rights and responsibilities of the owners of business than has been traditional in business ethics. (shrink)

This book, the third in a series on the life course, has significance in today's world of research, professional practice, and public policy because it symbolizes the gradual reemergence of power in the social sciences. Focusing on "self-directedness and efficacy" over the life course, this text addresses the following issues: * the causes of change * how changes affect the individual, the family system, social groups, and society at large * how various disciplines--anthropology, sociology, psychology, epidemiology--approach this field of study, (...) with consideration given to common themes and differences Finally, an effort is made to develop a multidisciplinary perspective unique to the study of self-directedness and efficacy. (shrink)

Cultural schemas are a central cognitive mechanism through which culture affects action. In this article, we develop a theoretical model of cultural schemas that is better able to support empirical work, including inferential, sensitizing, and operational uses. We propose a multilevel framework centered on a high-level definition of cultural schemas that is sufficiently broad to capture its major sociological applications but still sufficiently narrow to identify a set of cognitive phenomena with key functional properties in common: cultural schemas are socially (...) shared representations deployable in automatic cognition. We use this conception to elaborate the main theoretical properties of cultural schemas, and to provide clear criteria that distinguish them from other cultural or cognitive elements. We then propose a series of concrete tests empirical scholarship can use to determine if these properties apply. We also demonstrate how this approach can identify potentially faulty theoretical inferences present in existing work. Moving to a lower level of analysis, we elaborate how cultural schemas can be algorithmically conceptualized in terms of their building blocks. This leads us to recommend improvements to methods for measuring cultural schemas. We conclude by outlining questions for a broader research program. (shrink)

Generic statements (e.g., “Birds lay eggs”) express generalizations about categories. In this paper, we hypothesized that there is a paradoxical asymmetry at the core of generic meaning, such that these sentences have extremely strong implications but require little evidence to be judged true. Four experiments confirmed the hypothesized asymmetry: Participants interpreted novel generics such as “Lorches have purple feathers” as referring to nearly all lorches, but they judged the same novel generics to be true given a wide range of prevalence (...) levels (e.g., even when only 10% or 30% of lorches had purple feathers). A second hypothesis, also confirmed by the results, was that novel generic sentences about dangerous or distinctive properties would be more acceptable than generic sentences that were similar but did not have these connotations. In addition to clarifying important aspects of generics’ meaning, these findings are applicable to a range of real-world processes such as stereotyping and political discourse. (shrink)

We propose that human reasoning relies on an inherence heuristic, an implicit cognitive process that leads people to explain observed patterns (e.g., girls wear pink) in terms of the inherent features of their constituents (e.g., pink is an inherently feminine color). We then demonstrate how this proposed heuristic can provide a unified account for a broad set of findings spanning areas of research that might at first appear unrelated (e.g., system justification, nominal realism, is–ought errors in moral reasoning). By revealing (...) the deep commonalities among the diverse phenomena that fall under its scope, our account is able to generate new insights into these phenomena, as well as new empirical predictions. A second main goal of this paper, aside from introducing the inherence heuristic, is to articulate the proposal that the heuristic serves as a foundation for the development of psychological essentialism. More specifically, we propose that essentialism—which is the common belief that natural and social categories are underlain by hidden, causally powerful “essences”—emerges over the first few years of life as an elaboration of the earlier, and more open-ended, intuitions supplied by the inherence heuristic. In the final part of the paper, we distinguish our proposal from competing accounts (e.g., Strevens' K-laws) and clarify the relationship between the inherence heuristic and related cognitive tendencies (e.g., the correspondence bias). In sum, this paper illuminates a basic cognitive process that emerges early in life and is likely to have profound effects on many aspects of human psychology. (shrink)

According to traditional Judeo-Christian-Islamic theism, God is an omniscient, omnipotent, and morally perfect agent. This volume shows that philosophy of religion needs to take seriously alternative concepts of the divine, and demonstrates the considerable philosophical interest that they hold.

Mainstream political liberals hold that state coercion is legitimate only if it is justified on the grounds of reasons that all may reasonably be expected to accept. Critics argue that this public justification principle is self-defeating, because it depends on moral justifications that not all may reasonably be expected to accept. To rebut the self-defeat objection, I elaborate on the following disjunction: one either agrees or disagrees that it is wrong to impose one’s morality on others by the coercive power (...) of the state. Those who disagree reject PJP, they understand politics as war. Those who agree accept PJP, they understand politics as competition. Political competitors abide by PJP to avoid politics as war, by enforcing PJP on political combatants they engage in a war that is unavoidable. In both cases their exercise of political power has a justification that is reasonably acceptable to all. (shrink)

Some philosophers working on the metaphysics of agency argue that if agency is understood in terms of settling the truth of some matters, then the power required for the exercise of intentional agency is an irreducible two-way power to either make it true that p or not-p. In this paper, the focus is on two-way powers in decision-making. Two problems are raised for theories of decision-making that are ontologically committed to irreducible two-way powers. First, recent accounts lack an adequate framework (...) for explaining decisions by the reasons of agents. Second, accepting ontologically irreducible two-way powers into one’s metaphysic of agency implies an ontological commitment to substance dualism. An ontologically less-costly alternative to irreducible two-way powers is offered. It is argued that a reductive account of two-way powers in terms of what George Molnar called “derivative powers” should be accepted. The reductive account can provide us with the truthmakers for talk about two-way powers. Moreover, the reductive account does not share the liabilities of accepting irreducible two-way powers. (shrink)

This book, a history of a religious category of ancient philosophy, is the first synthesis on the notion of daimōn in the Platonic tradition. It focuses on the relationship between demonology and, respectively, cosmology, the philosophical hermeneutics of religion and theories of the soul. Histoire d’une catégorie religieuse de la philosophie ancienne, ce livre représente la première synthèse sur la notion de daimōn dans la tradition platonicienne. Il étudie les relations de la démonologie avec la cosmologie, l’herméneutique philosophique de la (...) religion et les théories de l’âme. (shrink)

This Element focuses on some core conceptual and ontological issues related to pantheistic conceptions of God by engaging with recent work in analytic philosophy of religion on this topic. The conceptual and ontological commitments of pantheism are contrasted with those of other conceptions of God. The concept of God assumed by pantheism is clarified and the question about what type of unity the universe must exhibit in order to be identical with God receives the most attention. It is argued that (...) the sort of unity the universe must display is the sort of unity characteristic of conscious cognitive systems. Some alternative ontological frameworks for grounding such cognitive unity are considered. Further, the question of whether God can be understood as personal on pantheism is explored. (shrink)

The standard liberal egalitarian approach to religious exemptions from generally applicable laws implies that such exemptions may be necessary in the name of equal respect for each citizen’s conscience. In each particular case this approach requires balancing the claims of devout believers against the countervailing claims of other citizens. I contend, firstly, that under the conditions of deep moral and ideological disagreement the balancing procedure proves to be extremely inconclusive. It does not provide an unequivocal solution even in the imaginary (...) case based on the biblical story of Abraham’s sacrifice, not to speak of real-life cases that are far less suggestive. Secondly, I argue that it is possible to consider demands for religious exemptions respectfully, without even challenging the way they are justified, but still reject them for principled reasons—namely, because these demands cannot be met without arbitrarily bending popular sovereignty to the dictate of religious doctrines. (shrink)

It has become increasingly popular to argue that legal positivism is actually a normative theory, and that it cannot be purely descriptive and morally neutral as H.L.A. Hart has suggested. This article purports to disprove this line of thought. It argues that legal positivism is best understood as a descriptive, morally neutral, theory about the nature of law. The article distinguishes between five possible views about the relations between normative claims and legal positivism, arguing that some of them are not (...) at odds with Hart’s thesis about the nature of jurisprudence, while the others are wrong, both as expositions of legal positivism or as critiques of it. Legal positivism does not necessarily purport to justify any aspect of its subject matter, nor is it committed to any particular moral or political evaluations. (shrink)

In her recent paper, “A Defense of Substance Causation,” Ann Whittle makes a case for substance causation. In this paper, assuming that causation is a generative or productive relation, I argue that Whittle’s argument is not successful. While substances are causally relevant in causal processes owing to outcomes being counterfactually dependent upon their role in such occurrences, the real productive work in causal processes is accomplished by the causal powers of substances.

This paper examines the ability of countries in Central and Eastern Europe to ensure appropriate protection of research participants in the field of increasingly globalizing biomedical research. By applying an analytical framework for identifying gaps in policies and programs for human subjects protection to four countries of CEE—Belarus, Latvia, Lithuania, and Poland, substantial gaps in the scope and content of relevant policies and major impediments to program performance have been revealed. In these countries, public policies on the protection of research (...) participants lack consistency and reliable mechanisms for their implementation. Impediments to program performance most often relate to inadequacies in the national research ethics systems with regard to organizational structure, budgetary support, supervision, and training. The level of research ethics capacity varies from country to country and depends on socio-economic and political factors of post-communist transition. The breadth and depth of the problems identified suggest that the current level of protection for research participants in CEE might be inadequate to the challenges posed by the globalization of biomedical research. In CEE countries, there is a need for strengthening research ethics capacity through modification of relevant policies and improvement of program management. The differences among the countries call for further research on identifying the best approaches for filling the gaps in the policies and programs aimed at ensuring effective protection of research participants. (shrink)

ABSTRACT: Defending the distinction between believing and accepting a proposition, I argue that cases where agents allegedly exercise direct voluntary control over their beliefs are instances of agents exercising direct voluntary control over accepting a proposition. The upshot is that any decision to believe a proposition cannot result directly in one’s acquiring the belief. Accepting is an instrumental mental action the agent performs that may trigger belief. A model of the relationship between acceptance and belief is sketched and defended. The (...) consequences of the distinction between belief and acceptance, and the model of belief control sketched are then applied to the recent case made by Carl Ginet in defense of the conceptual and psychological possibility of agents exercising direct voluntary control over their beliefs. n. (shrink)

The article analyzes the possibilities and limitations of artificial intelligence. The article considers the subjectivity of artificial intelligence, determines its necessity for solving intellectual problems depending on the possibility of representing the real world as a deterministic system. Methodological limitations of artificial intelligence, which is based on the use of big data technologies, are stated. These limitations cause the impossibility of forming a holistic representation of the objects of cognition and the world as a whole. As a tool for deterministic (...) description of the universe it is proposed to use empirical-metaphysical general theory of systems, which is an extension of existing general theories of systems due to ontological justification of the phenomenon of isomorphism and definition of a limited set of laws, rules, patterns and primitives of forms and relations of objects in the universe. The distinction of natural (human) and artificial intelligence is considered, including the realization of multisystem integration of intelligence in physical, biological, social and spiritual systems. A philosophically grounded approach to ensuring the evolutionary properties of artificial intelligence is formulated, based on the inclusion of non-equilibrium mechanisms through which stability is realized. (shrink)

The ways in which we exercise intentional agency are varied. I take the domain of intentional agency to include all that we intentionally do versus what merely happens to us. So the scope of our intentional agency is not limited to intentional action. One can also exercise some intentional agency in omitting to act and, importantly, in producing the intentional outcome of an intentional action. So, for instance, when an agent is dieting, there is an exercise of agency both with (...) respect to the agent’s actions and omissions that constitute her dieting behavior and in achieving the intended outcome of losing weight. In our mental lives we exercise intentional agency both in performing mental actions and when we intentionally produce certain outcomes at which our mental actions are aimed. The nature and scope of our intentional agency in our mental lives with respect to controlling the acquisition of mental states such as belief, desire, and intention is a topic that is of interest in its own right. In this essay, I will focus solely on our control over coming to believe. Understanding what sort of control we have our beliefs has far-reaching implications. For instance, theorizing about self-deception and wishful thinking is aided by theorizing about what if any intentional agency we can exercise with respect to acquiring beliefs. Another often mentioned concern that motivates thinking about doxastic agency comes from religion (when conversion requires a change of belief). We also hold persons morally and epistemically responsible for beliefs they have or fail to have. Finally, some deontological theories of epistemic justification require that agents be able to exercise a robust form of doxastic control. Fruitful work on any of these problems requires that we have an account of our intentional agency in acquiring beliefs. There are at least three loci of doxastic control. The first is over acquiring beliefs. The second is over maintaining beliefs. The third is over how we use our beliefs. I am chiefly concerned with the first locus of doxastic control in this essay, but I will say something about the second locus along the way. Also, I will only consider one way we might exercise control over acquiring beliefs. Specifically, I will present an argument against direct doxastic voluntarism (DDV). By “DDV” I mean to refer to the thesis that it is conceptually possible for agents to consciously exercise the same sort of direct voluntary control over coming to acquire a doxastic attitude—such as belief, suspension of belief, and disbelief—that they exercise over uncontroversial basic actions. If DDV is correct, then coming to believe can be a basic action-type. DDV, or something very close to it, was Bernard Williams’ target in his 1973 paper, “Deciding to Believe.” Williams’s argument is widely regarded as having been a failure. But I think that Williams was on to something in his paper. Hence, in this paper, while I do not attempt to resurrect Williams’s argument, I develop and defend a revised argument for a thesis that is quite close to Williams’s. I will proceed as follows. First, I will discuss Bernard Williams’ (1973) failed attempt at showing that DDV is conceptually impossible. This will be followed by a discussion of some constraints on our belief-forming activities. I will then clarify my target a bit more than Williams does in his original paper. Finally, I will present my own argument against the conceptual possibility of DDV. (shrink)