Ioannis G. Ntagkas

Traditionally, a justification for believing something is a priori is if, and only if, it is independent of experience. Throughout Western philosophy since Plato, some of the most divisive questions have been whether a priori justification exists, how it is possible, and how far it reaches. This book is structured around these three main questions. The first question has recently been modulated as to concern the significance of a priori justification: given the unclarities and presuppositions attached to standard explications of the notion of a priori justification, is it still a useful notion for epistemology? In a tight dialectic, the chapters in this part either attack or defend the theoretical importance of that notion. The second part concerns the sources of a priori justification: since a priori justification is not grounded in experience--our arguably best understood source of justification--in what can it be grounded? The chapters in this part explore the possibility that a priori justification is grounded either in intuition or in understanding. The third part concerns the extent of a priori justification: beyond core cases like mathematical proof, what methods can yield a priori justification? The chapters in this part investigate to what degree and why methods like introspection, testimony, and others have an import on a priori justification. Overall, the book showcases and furthers some of the latest contemporary trends in thinking about these questions.

In this work we argue that there is no strong demarcation between pure and applied mathematics. We show this first by stressing non-deductive components within pure mathematics, like axiomatization and theory-building in general. We also stress the “purer” components of applied mathematics, like the theory of the models that are concerned with practical purposes. We further show that some mathematical theories can be viewed through either a pure or applied lens. These different lenses are tied to different communities, which endorse different evaluative standards for theories. We evaluate the distinction between pure and applied mathematics from a late Wittgensteinian perspective. We note that the classical exegesis of the later Wittgenstein’s philosophy of mathematics, due to Maddy, leads to a clear-cut but misguided demarcation. We then turn our attention to a more niche interpretation of Wittgenstein by Dawson, which captures aspects of the aforementioned distinction more accurately. Building on this newer, maverick interpretation of the later Wittgenstein’s philosophy of mathematics, and endorsing an extended notion of meaning as use which includes social, mundane uses, we elaborate a fuzzy, but more realistic, demarcation. This demarcation, relying on family resemblance, is based on how direct and intended technical applications are, the kind of evaluative standards featured, and the range of rhetorical purposes at stake.

Members of the field of philosophy have, just as other people, political convictions or, as psychologists call them, ideologies. How are different ideologies distributed and perceived in the field? Using the familiar distinction between the political left and right, we surveyed an international sample of 794 subjects in philosophy. We found that survey participants clearly leaned left (75%), while right-leaning individuals (14%) and moderates (11%) were underrepresented. Moreover, and strikingly, across the political spectrum, from very left-leaning individuals and moderates to very right-leaning individuals, participants reported experiencing ideological hostility in the field, occasionally even from those from their own side of the political spectrum. Finally, while about half of the subjects believed that discrimination against left- or right-leaning individuals in the field is not justified, a significant minority displayed an explicit willingness to discriminate against colleagues with the opposite ideology. Our findings are both surprising and important, because a commitment to tolerance and equality is widespread in philosophy, and there is reason to think that ideological similarity, hostility, and discrimination undermine reliable belief formation in many areas of the discipline.

This special issue aims to explore and investigate a new subfield, namely experimental philosophy of medicine. Whereas experimental philosophy is relatively new on the philosophical block, some of its takes and findings have already shaped central debates in ethics, philosophy of action, philosophy of language, and epistemology. Interestingly, the approach of this program was for a long time almost wholly ignored within bioethics and philosophy of medicine—although this seems to have changed somewhat recently. In this introduction, we briefly sketch the program of experimental philosophy and how it can be used to shed philosophical light on issues in the philosophy of medicine.

Human behavior and thought often exhibit a familiar pattern of within group similarity and between group difference. Many of these patterns are attributed to cultural differences. For much of the history of its investigation into behavior and thought, however, cognitive science has been disproportionately focused on uncovering and explaining the more universal features of human minds—or the universal features of minds in general. This entry charts out the ways in which this has changed over recent decades. It sketches the motivation behind the cultural turn in cognitive science, and situates some of its central findings with respect to the questions that animate it and the debates that it has inspired. Woven throughout the entry are examples of how the cognitive science of culture, and especially its elevated concern with different forms of diversity and variation, continues to influence and be influenced by philosophers. One cluster of philosophical work falls within the traditional subject matter of philosophy of science, in this case of the cognitive and social sciences. Philosophers have analyzed and assessed the methods and evidence central to the scientific study of cognition and culture, and have offered conceptual scrutiny, clarification, and synthesis. Research in a second vein sees philosophers themselves contributing more directly to cognitive scientific projects, (co)constructing theories, helping build computational models, even gathering empirical data. A third kind of work is naturalistic philosophy or philosophy of nature, wherein philosophers seek to use results from the cognitive science of culture to inform or transform debates over long-standing philosophical questions, including questions about the nature of philosophy and philosophical methodology itself.

Maladapting Minds discusses a number of reasons why philosophers of psychiatry should take an interest in evolutionary explanations of mental disorders and, more generally, in evolutionary thinking. First of all, there is the nascent field of evolutionary psychiatry. Unlike other psychiatrists, evolutionary psychiatrists engage with ultimate, rather than proximate, questions about mental illnesses. Being a young and youthful new discipline, evolutionary psychiatry allows for a nice case study in the philosophy of science. Secondly, philosophers of psychiatry have engaged with evolutionary theory because evolutionary considerations are often said to play a role in defining the concept of mental disorder. The basic question here is: Can the concept of mental disorder be given an objective definition, or is it rather a normative concept? Thirdly and finally, evolutionary thinking in psychiatry has often been a source of inspiration for a philosophical view on human nature. Thus evolutionary psychiatrists have suggested, for example, that man's vulnerability to mental disorders may well be one of the defining features of our species. Written by leading authors in philosophy, psychiatry, biology and psychology, this volume illustrates that many debates in contemporary philosophy of psychiatry are profoundly influenced by evolutionary approaches to mental disorders. Conversely, it also reveals how philosophers can help contribute to the burgeoning field of evolutionary psychiatry. It is important reading for a wide range of readers interested in mental health care and philosophy.

This is a companion article to the translation of ‘Zasada sprzeczności a logika symboliczna’, the appendix on symbolic logic of Jan Łukasiewicz's 1910 book O zasadzie sprzeczności u Arytotelesa (On the Principle of Contradiction in Aristotle). While the appendix closely follows Couturat's 1905 book L'algebra de la logique (The Algebra of Logic), footnotes show that Łukasiewicz was aware of the work of Peirce, Huntington and Russell (before Principia Mathematica). This appendix was influential in the development of the Polish school of logic, directly inspiring Stanisław Leśniewski and Leon Chwistek and more widely by serving as a text of the new symbolic logic. This appendix was an important source of the dominant algebraic logic in Poland, but also indicates that Łukasiewicz appreciated Russell's axiomatic approach to logic.

Originally published in 1910, Principia Mathematica led to the development of mathematical logic and computers and thus to information sciences. It became a model for modern analytic philosophy and remains an important work. In the late 1960s the Bertrand Russell Archives at McMaster University in Canada obtained Russell's papers, letters and library. These archives contained the manuscripts for the new Introduction and three Appendices that Russell added to the second edition in 1925. Also included was another manuscript, 'The Hierarchy of Propositions and Functions', which was divided up and re-used to create the final changes for the second edition. These documents provide fascinating insight, including Russell's attempts to work out the theorems in the flawed Appendix B, 'On Induction'. An extensive introduction describes the stages of the manuscript material on the way to print and analyzes the proposed changes in the context of the development of symbolic logic after 1910.

In this paper, we develop an alternative strategy, Platonized Naturalism, for reconciling naturalism and Platonism and to account for our knowledge of mathematical objects and properties. A systematic (Principled) Platonism based on a comprehension principle that asserts the existence of a plenitude of abstract objects is not just consistent with, but required (on transcendental grounds) for naturalism. Such a comprehension principle is synthetic, and it is known a priori. Its synthetic a priori character is grounded in the fact that it is an essential part of the logic in which any scientific theory will be formulated and so underlies (our understanding of) the meaningfulness of any such theory (this is why it is required for naturalism). Moreover, the comprehension principle satisfies naturalist standards of reference, knowledge, and ontological parsimony! As part of our argument, we identify mathematical objects as abstract individuals in the domain governed by the comprehension principle, and we show that our knowledge of mathematical truths is linked to our knowledge of that principle.

This thesis is about the metaphysics of logic. I argue against a view I refer to as ‘logical realism’. This is the view that the logical constants represent a particular kind of metaphysical structure, which I dub ‘logico-metaphysical structure’. I argue instead for a more metaphysically lightweight view of logic which I dub ‘logical expressivism’. In the first part of this thesis (Chapters I and II) I argue against a number of arguments that Theodore Sider has given for logical realism. In Chapter I, I present an argument of his to the effect that logico-metaphysical structure provides the only good explanation of the semantic determinacy of the logical constants. I argue that other explanations are possible. In Chapter II, I present another argument of his to the effect that logico-metaphysical structure is something that comes along with ontological realism: the view that there is a non-language-relative fact of the matter about what exists. I argue that the connection between logical and ontological realism is not as close as Sider makes it out to be. In the second part of this thesis (Chapters III – V) I set out a positive view of the logical constants that can explain both why their meanings are semantically determinate, and why they form part of our vocabulary. On that view, the primary bearers of logical structure are propositional attitudes, and the logical constants are in our language as vehicles for the expression of logically complex propositional attitudes. In Chapter III, I set out an expressivist theory of propositional logic. In Chapter IV, I use this theory to explain how the logical connectives end up having determinate meanings. In Chapter V, I extend the expressivist theory to predicate logic.

An important trend in contemporary metaphysics denies that the structure of natural language is an important datum for investigating fundamental structure. Ted Sider proceeds on this basis to propose a metaphysical semantics for natural language. Within this framework he argues that natural language and a fundamental, ‘jointcarving’, language could be subject to distinct logics. Developing an argument of Hartry Field’s, I show that Sider’s preferred option of fundamental classicality combined with non-fundamental non-classicality trivialises within the framework of Siderian metaphysical semantics. The position can be saved only by revising key claims about truth and metaphysical semantics. This has serious implications for methdology in the metaphysics of logic.

A major disagreement between different views about the foundations of quantum mechanics concerns whether for a theory to be intelligible as a fundamental physical theory it must involve a ‘primitive ontology’ (PO), i.e. variables describing the distribution of matter in four-dimensional space–time. In this article, we illustrate the value of having a PO. We do so by focusing on the role that the PO plays for extracting predictions from a given theory and discuss valid and invalid derivations of predictions. To this end, we investigate a number of examples based on toy models built from the elements of familiar interpretations of quantum theory.

Genetic moderation of experience of reward in response to environmental stimuli is relevant for the study of many psychiatric disorders. Experience of reward, however, is difficult to capture, as it involves small fluctuations in affect in response to small events in the flow of daily life. This study examined a momentary assessment reward phenotype in relation to the catechol-O-methyl transferase (COMT) Val158Met polymorphism. A total of 351 participants from a twin study participated in an Experience Sampling Method procedure to collect daily life experiences concerning events, event appraisals, and affect. Reward experience was operationalized, as the effect of event appraisal on positive affect (PA). Associations between COMT Val 158Met genotype and event appraisal on the one hand and PA on the other were examined using multilevel random regression analysis. Ability to experience reward increased with the number of ‘Met’ alleles of the subject, and this differential effect of genotype was greater for events that were experienced as more pleasant. The effect size of genotypic moderation was quite large: subjects with the Val/Val genotype generated almost similar amounts of PA from a ‘very pleasant event’ as Met/Met subjects did from a ‘bit pleasant event’. Genetic variation with functional impact on cortical dopamine tone has a strong influence on reward experience in the flow of daily life. Genetic moderation of ecological measures of reward experience is hypothesized to be of major relevance to the development of various behavioral disorders, including depression and addiction. Neuropsychopharmacology (2008) 33, 3030–3036; doi:10.1038/sj.npp.1301520; published online 8 August 2007..

Computer models and simulations have provided enormous benefits to researchers in the natural and social sciences, as well as many areas of philosophy. However, to date, there has been little attempt to use computer models in the development and evaluation of metaphysical theories. This is a shame, as there are good reasons for believing that metaphysics could benefit just as much from this practice as other disciplines. In this paper I assess the possibilities and limitations of using computer models in metaphysics. I outline the way in which different kinds of model could be useful for different areas of metaphysics, and I illustrate in more detail how agent-based models specifically could be used to model two well-known theories of laws: David Lewis’s "Best System Account" and David Armstrong's "Nomic Necessitation" view. Some logically possible processes cannot be simulated on a standard computing device. I finish by assessing how much of a threat this is to the prospect of metaphysical modeling in general.

Why microscopic objects exhibit wave properties (are delocalized), but macroscopic do not (are localized)? Traditional quantum mechanics attributes wave properties to all objects. When complemented with a deterministic collapse model (Quantum Stud.: Math. Found. 3, 279 (2016)) quantum mechanics can dissolve the discrepancy. Collapse in this model means contraction and occurs when the object gets in touch with other objects and satisfies a certain criterion. One single collapse usually does not suffice for localization. But the object rapidly gets in touch with other objects in a short time, leading to rapid localization. Decoherence is not involved.

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor (−1)2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required

We expound an alternative to the Copenhagen interpretation of the formalism of nonrelativistic quantum mechanics. The basic difference is that the new interpretation is formulated in the language of epistemological realism. It involves a change in some basic physical concepts. The ψ function is no longer interpreted as a probability amplitude of the observed behaviour of elementary particles but as an objective physical field representing the particles themselves. The particles are thus extended objects whose extension varies in time according to the variation of ψ. They are considered as fundamental regions of space with some kind of nonlocality. Special consideration is given to the Heisenberg relations, the Einstein-Podolsky- Rosen correlations, the reduction process, the problem of measurement, and the quantum-statistical distributions.

‘Quantum Gravity’ does not denote any existing theory: the field of quantum gravity is very much a ‘work in progress’. As you will see in this chapter, there are multiple lines of attack each with the same core goal: to find a theory that unifies, in some sense, general relativity (Einstein’s classical field theory of gravitation) and quantum field theory (the theoretical framework through which we understand the behaviour of particles in non-gravitational fields). Quantum field theory and general relativity seem to be like oil and water, they don’t like to mix—it is fair to say that combining them to produce a theory of quantum gravity constitutes the greatest unresolved puzzle in physics. Our goal in this chapter is to give the reader an impression of what the problem of quantum gravity is; why it is an important problem; the ways that have been suggested to resolve it; and what philosophical issues these approaches, and the problem itself, generate. This review is extremely selective, as it has to be to remain a manageable size: generally, rather than going into great detail in some area, we highlight the key features and the options, in the hope that readers may take up the problem for themselves—however, some of the basic formalism will be introduced so that the reader is able to enter the physics and (what little there is of) the philosophy of physics literature prepared. I have also supplied references for those cases where I have omitted some important facts. Hence, this chapter is intended primarily as a catalyst for future research projects by philosophers of physics, both budding and well-matured.

In the Copenhagen interpretation the Heisenberg inequality ΔQΔP≥ℏ/2 is interpreted as the mathematical expression of the concept of complementarity, quantifying the mutual disturbance necessarily taking place in a simultaneous or joint measurement of incompatible observables. This interpretation was criticized a long time ago and has recently been challenged in an experimental way. These criticisms can be substantiated by using the generalized formalism of positive operator-valued measures, from which an inequality, different from the Heisenberg inequality, can be derived, precisely illustrating the Copenhagen concept of complementarity. The different roles of preparation and measurement in creating uncertainty in quantum mechanics are discussed.

To honor Henry Margenau on the occasion of his 90th birthday, we attempt in this essay to integrate certain aspects of the physics, philosophy, and pedagogy of quantum mechanics in a manner very much inspired by Margenau's idealist scientific epistemology. Over half a century ago, Margenau was perhaps the first philosopher of science to recognize and elaborate upon the essential distinction between thepreparation of a quantum state and themeasurement of an observable associated with a system in that state; yet in contemporary quantum texts that distinction rarely receives adequate emphasis even though, as we demonstrate, it may be explicated through a series of simple illustrations

The main claim of this talk is that mathematical physics and philosophy of physics are not different. This claim, so formulated, is obviously false because it is overstated; however, since no non-tautological statement is likely to be completely true, it is a meaningful question whether the overstated claim expresses some truth. I hope it does, or so I’ll argue. The argument consists of two parts: First I’ll recall some characteristic features of von Neumann’s work on mathematical foundations of quantum mechanics and will claim that von Neumann’s motivation and results are essentially philosophical in their nature; hence, to the extent von Neumann’s work exemplifies what is considered to be mathematical physics, mathematical physics appears as formally explicit philosophy of physics. The second argument is based on a rather trivial interpretation of what mathematical physics is. That interpretation implies that mathematical physics shares some key characteristic features with philosophy of physics which make the two almost indistinguishable.