This work is intended as an introduction to the study of Soviet psy chology. In it we have tried to present the main lines of Soviet psycho logical theory, in particular, the philosophical principles on which that theory is founded. There are surprisingly few books in English on Soviet psychology, or, indeed, in any Western European language. The works that exist usually take the form of symposia or are collections of articles translated from Soviet periodicals. The most important of these (...) are Psychology in the Soviet Union (ed. by Brian Simon), Recent Soviet Psychology (ed. by Neil O'Connor) and Soviet Psychology, A Symposium (ed. by Ralf Winn). Raymond Bauer has also edited an interesting symposium entitled Some Views on Soviet Psychology. Only two systematic studies of Soviet psychology have been published to date: Joseph Wortis' Soviet Psychiatry and Raymond Bauer's The New Man in Soviet Psychology. Both are valuable introductions to Soviet psychology; Bauer's book, in particular, gives a good account of the debates on psychological theory in the Soviet Union in the nineteen twenties and -thirties. Both, however, are somewhat out of date. There are also a number of interesting articles written by Ivan D. London and Gregory Razran, which give general surveys of particular periods or aspects of Soviet psychology. These have been listed in the bibliography. (shrink)

We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems (...) to necessitate the addition of subsets to V. We argue that despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We analyse extant interpretations of such talk, and analyse various tradeoffs in naturality that might be made. We conclude that the Universist has promising options for interpreting different forcing constructions. (shrink)

It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and that (...) the continuum is a proper class. We examine several principles based on maximality considerations in this framework, and show how some (namely Ordinal Inner Model Hypotheses) enable us to incorporate standard set theories (including ZFC with large cardinals added). We conclude that the systems considered raise questions concerning the foundational purposes of set theory. (shrink)

Let's suppose you think that there are no uncountable sets. Have you adopted a restrictive position? It is certainly tempting to say yes---you've prohibited the existence of certain kinds of large set. This paper argues that this intuition can be challenged. Instead, I argue that there are some considerations based on a formal notion of restrictiveness which suggest that it is restrictive to hold that there are uncountable sets.

The Continuum Hypothesis featured top of Hilbert's list of 23 problems in 1900. Today, we still consider the question, with various programmes pulling in different directions. This conceptual diversity raises a puzzle: In what sense do we disagree when we talk about it? A standard assumption takes it that the content of our thought about classes and the Continuum Hypothesis has not changed. Assuming a moderate view of how content is determined, I reject this assumption but also argue that whilst (...) the Continuum Hypothesis can have different content for different agents, it can also be determinate for certain programmes. In particular, I suggest that there is a fault line between those who think there are uncountable sets and recent countabilist programmes. (shrink)

Addiction is almost universally held to be characterized by a loss of control over drug-seeking and consuming behavior. But the actions of addicts, even of those who seem to want to abstain from drugs, seem to be guided by reasons. In this paper, I argue that we can explain this fact, consistent with continuing to maintain that addiction involves a loss of control, by understanding addiction as involving an oscillation between conflicting judgments. I argue that the dysfunction of the mesolimbic (...) dopamine system that typifies addictions causes the generation of a mismatch between the top-down model of the world that reflects the judgment that the addict ought to refrain from drugs, and bottom-up input caused by cues predictive of drug availability. This constitutes a powerful pressure toward revising the judgment and thereby attenuating the prediction error. But the new model is not stable, and shifts under the pressure of bottom-up inputs in different contexts; hence the oscillation of all-things-considered judgment. Evidence from social psychology is adduced, to suggest that a similar process may be involved in ordinary cases of weakness of will. (shrink)

Multiverse Views in set theory advocate the claim that there are many universes of sets, no-one of which is canonical, and have risen to prominence over the last few years. One motivating factor is that such positions are often argued to account very elegantly for technical practice. While there is much discussion of the technical aspects of these views, in this paper I analyse a radical form of Multiversism on largely philosophical grounds. Of particular importance will be an account of (...) reference on the Multiversist conception, and the relativism that it implies. I argue that analysis of this central issue in the Philosophy of Mathematics indicates that Radical Multiversism must be algebraic, and cannot be viewed as an attempt to provide an account of reference without a softening of the position. (shrink)

In the contemporary philosophy of set theory, discussion of new axioms that purport to resolve independence necessitates an explanation of how they come to be justified. Ordinarily, justification is divided into two broad kinds: intrinsic justification relates to how `intuitively plausible' an axiom is, whereas extrinsic justification supports an axiom by identifying certain `desirable' consequences. This paper puts pressure on how this distinction is formulated and construed. In particular, we argue that the distinction as often presented is neither well-demarcated nor (...) sufficiently precise. Instead, we suggest that the process of justification in set theory should not be thought of as neatly divisible in this way, but should rather be understood as a conceptually indivisible notion linked to the goal of explanation. (shrink)

Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...) work in numerical cognition and ontogenetic studies. (shrink)

A pervasive thought in contemporary philosophy of mathematics is that in order to justify reflection principles, one must hold universism: the view that there is a single universe of pure sets. I challenge this kind of reasoning by contrasting universism with a Zermelian form of multiversism. I argue that if extant justifications of reflection principles using notions of richness are acceptable for the universist, then the Zermelian can use similar justifications. However, I note that for some forms of richness argument, (...) the status of reflection principles as axioms is left open for the Zermelian. (shrink)

Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power (...) and meta-theoretic properties when comparing first-order and second-order logic. (shrink)

The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper I question this claim. I show that there is a kind of maximality (namely absoluteness) on which large cardinal axioms come out as restrictive relative to a formal notion of restrictiveness. Within this framework, I argue that large cardinal axioms can still play many of (...) their usual foundational roles. (shrink)

Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance different underlying logics (intermediate between first- and second-order) for formulating set theory. By bringing considerations of (...) perturbations in modal space to bear on the debate, we will suggest that a promising option for representing current set-theoretic thought is given by formulating set theory using quasi-weak second-order logic. These observations indicate that the usual division of structures into \particular (e.g. the natural number structure) and general (e.g. the group structure) is perhaps too coarse grained; we should also make a distinction between intentionally and unintentionally general structures. (shrink)

We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width (...) reflection in contrast to the usual height reflection of the Lévy–Montague reflection theorem. They are each equiconsistent with ZFC and indeed \Pi_2-conservative over ZFC, being forceable by class forcing while preserving any desired rank-initial segment of the universe. Furthermore, the inner-model reflection principle is a consequence of the existence of sufficient large cardinals, and lightface formulations of the reflection principles follow from the maximality principle MP and from the inner-model hypothesis IMH. We also consider some questions concerning the expressibility of the principles. (shrink)

This article articulates and assesses an imperatival approach to the foundations of mathematics. The core idea for the program is that mathematical domains of interest can fruitfully be viewed as the outputs of construction procedures. We apply this idea to provide a novel formalisation of arithmetic and set theory in terms of such procedures, and discuss the significance of this perspective for the philosophy of mathematics.

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' perspective (...) to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

I provide an examination and comparison of modal theories for underwriting different non-modal theories of sets. I argue that there is a respect in which the `standard' modal theory for set construction---on which sets are formed via the successive individuation of powersets---raises a significant challenge for some recently proposed `countabilist' modal theories (i.e. ones that imply that every set is countable). I examine how the countabilist can respond to this issue via the use of regularity axioms and raise some questions (...) about this approach. I argue that by comparing them with the `standard' uncountabilist theory, a new approach that brings in arbitrariness rather than the strict controls of forcing is desirable. (shrink)

Let mathematical justification be the kind of justification obtained when a mathematician provides a proof of a theorem. Are Gettier cases possible for this kind of justification? At first sight we might think not: The standard for mathematical justification is proof and, since proof is bound at the hip with truth, there is no possibility of having an epistemically lucky justification of a true mathematical proposition. In this paper, I argue that Gettier cases are possible (and indeed actual) in mathematical (...) reasoning. By analysing these cases, I suggest that the Gettier phenomenon indicates some upshots for actual mathematical practice. (shrink)

To date, philosophical discussions of animal ethics and Critical Animal Studies have been dominated by Western perspectives and Western thinkers. This book makes a novel contribution to animal ethics in showing the range and richness of ideas offered to these fields by diverse Asian traditions. Asian Perspectives on Animal Ethics is the first of its kind to include the intersection of Asian and European traditions with respect to human and nonhuman relations. Presenting a series of studies focusing on specific Asian (...) traditions, as well as studies that put those traditions in dialogue with Western thinkers, this book looks at Asian philosophical doctrines concerning compassion and nonviolence as these apply to nonhuman animals, as well as the moral rights and status of nonhuman animals in Asian traditions. Using Asian perspectives to explore ontological, ethical and political questions, contributors analyze humanism and post-humanism in Asian and comparative traditions and offer insight into the special ethical relations between humans and other particular species of animals. This book will be of interest to students and scholars of Asian religion and philosophy, as well as to those interested in animal ethics and Critical Animal Studies. (shrink)

Much of the discussion of set-theoretic independence, and whether or not we could legitimately expand our foundational theory, concerns how we could possibly come to know the truth value of independent sentences. This paper pursues a slightly different tack, examining how we are ignorant of issues surrounding their truth. We argue that a study of how we are ignorant reveals a need for an understanding of set-theoretic explanation and motivates a pluralism concerning the adoption of foundational theory.

In this article, I survey some philosophical attitudes to talk concerning `the' universe of sets. I separate out four different strands of the debate, namely: (i) Universism, (ii) Multiversism, (iii) Potentialism, and (iv) Pluralism. I discuss standard arguments and counterarguments concerning the positions and some of the natural mathematical programmes that are suggested by the various views.

How does our language relate to reality? This is a question that is especially pertinent in set theory, where we seem to talk of large infinite entities. Based on an analogy with the use of models in the natural sciences, we argue for a threefold correspondence between our language, models, and reality. We argue that so conceived, the existence of models can be underwritten by a weak notion of existence, where weak existence is to be understood as existing in virtue (...) of language. (shrink)

Alexander Anievas and Kerem Nişancıoğlu’sHow the West Came to Ruleis an important intervention within Marxist historical debates which seeks to use the theory of uneven and combined development to explain the origin and rise to dominance of capitalism. The argument is shaped by a critique of Political Marxist ‘internalist’ explanations of the process, to which the authors counterpose an account which emphasises its inescapably ‘inter-societal’ nature. While recognising the many contributions that the book makes to our historical understanding, this article (...) argues that these insights do not depend onUCD, and could have been arrived at without reference to it. In particular, it will try to show thatUCDis inapplicable in periods before the consolidation of capitalism, but might be more usefully extended spatially rather than chronologically. (shrink)

The prevailing view of Advaita Vedānta as world negating and disengaged with worldly activity provides little space for an ethic of environmental care, or a psychology for eco-resilience beyond passive indifference. However, many sources for environmentalism within the Advaita Vedānta tradition and its canon of texts remain untapped. In this paper, I explore the ritual ecology found in chapter three of the Bhagavadgītā as the ground to construct an Advaitin ecotheology and ecopsychology. This all-encompassing ritual ecology, described as a sacrificial (...) wheel, provides meaning to the world and views individuals as essential causative participants within it. Individuals have the religious and moral responsibility to perpetuate the wheel through a relationship of mutual reciprocity with the gods based on an economy of food. I extend this ritual ecology to include moral responsibility to the environment and explain how it provides a religious psychology and practice for handling our anxiety of imminent ecological catastrophe. (shrink)

Should we be Roschians about the concept of disease, rather than taking a classical approach? A classical concept of disease defines disease in terms of necessary and sufficient conditions; any things and only things which meet this definition are members of the class. In Roschian concepts of disease, it is supposed that degree of similarity to a prototype determines membership in the class of diseases. In this paper, the two approaches are pitched against one another in a series of tests (...) which appear on first sight to favor Roschian accounts.These tests are 1) the capacity to accommodate the variety of the class of disease, 2) the capacity to explain controversies about disease attribution, and 3) the capacity to... (shrink)

The opening of the fourth session of The Neutral — the course given by Roland Barthes at the Collège de France in 1977–8 — is marked by a dramatic spillage of ink. Rather than take this as an incidental, trivial moment, I read it as one of the many ‘ink blots’ that colour the work of Barthes. Tracing his ‘almost obsessive relation to writing instruments’ and the material act of inscription, this essay relates the ‘ink blots’ to the development of (...) a ‘non-arrogant’, non-expressive, non-idealistic theory of language in The Neutral and other texts by Barthes. (shrink)

In the light of the publication of Roland Barthes's Mourning Diary, this essay examines how the influential theory of the photographic punctum has cinematic roots which are repressed in Barthes's Camera Lucida. My aim is not to repeat familiar arguments about how Barthes's ‘The Third Meaning’ anticipates the photographic punctum in a cinematic context; it is, rather, to attend specifically to Mourning Diary as a much closer, more precise precursor which has been visible only since 2009, and which casts new (...) light upon the work of Roland Barthes. (shrink)

LandryElaine, * ed. Categories for the Working Philosopher. Oxford University Press, 2017. ISBN 978-0-19-874899-1 ; 978-0-19-106582-8. Pp. xiv + 471.

In his collection of essays titled Journeying (originally published as L’infinito viaggiare in 2005 and translated by Anne Milano Appel, 2018), Claudio Magris describes the way in which certain pla...