Context: Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. Problem: First, it is necessary to present a “decent” history of strict finitism (which is now lacking) and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. Method: For the historical part, the historical material is situated in a broader context, and for the argumentative part, (...) an evaluation of arguments and counterarguments is presented. Results: The main result is that strict finitism is indeed a viable option, next to other constructive approaches, in (the foundations of) mathematics. Implications: Arguing for strict finitism is more complex than is usually thought. For future research, strict finitist mathematics itself needs to be written out in more detail to increase its credibility. In as far as strict finitism is a viable option, it will change our views on such “classics” as the platonist-constructivist discussion, the discovery-construction debate and the mysterious applicability problem (why is mathematics so successful in its applications?). Constructivist content: Strict finitism starts from the idea that counting is an act of labeling, hence the mathematician is an active subject right from the start. It differs from other constructivist views in that the finite limitations of the human subject are taken into account. (shrink)

Context: As one of the major approaches within the philosophy of mathematics, constructivism is to be contrasted with realist approaches such as Platonism in that it takes human mental activity as the basis of mathematical content. Problem: Mathematical constructivism is mostly identified as one of the so-called foundationalist accounts internal to mathematics. Other perspectives are possible, however. Results: The notion of “meaning finitism” is exploited to tie together internal and external directions within mathematical constructivism. The various contributions to this issue (...) support our case in different ways. Constructivist content: Further contributions from a multitude of constructivist directions are needed for the puzzle of an integrative, overarching theory of mathematical practice to be solved. (shrink)

Context: Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. Problem: First, it is necessary to present a “decent” history of strict finitism and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. Method: For the historical part, the historical material is situated in a broader context, and for the argumentative part, an evaluation of arguments (...) and counterarguments is presented. Results: The main result is that strict finitism is indeed a viable option, next to other constructive approaches, in mathematics. Implications: Arguing for strict finitism is more complex than is usually thought. For future research, strict finitist mathematics itself needs to be written out in more detail to increase its credibility. In as far as strict finitism is a viable option, it will change our views on such “classics” as the platonist-constructivist discussion, the discovery-construction debate and the mysterious applicability problem . Constructivist content: Strict finitism starts from the idea that counting is an act of labeling, hence the mathematician is an active subject right from the start. It differs from other constructivist views in that the finite limitations of the human subject are taken into account. (shrink)

Open peer commentary on the article “Second-Order Science: Logic, Strategies, Methods” by Stuart A. Umpleby. Upshot: The author makes a strong plea for second-order science but somehow mathematics remains out of focus. The major claim of this commentary is that second-order science requires second-order mathematics.

Everyone is familiar with the measure of beauty that has been proposed by Birkhoff, the famous formula M = O/C. Although I show that the formula in its original form cannot be maintained, I present a reinterpretation that adapts the formula for measuring the beauty of mathematical proofs. However, this type of measure is not the only aesthetic element in mathematics. There exists a 'romantic' side as well, to use the term introduced by François Le Lionnais. Thus, a more complex (...) proposal of mathematical beauty is presented. Finally and as a consequence, I argue against the dichotomy that associates science, including mathematics, with the beauty of simplicity and that associates the arts with the beauty of complexity. As an example, the work of Oulipo, Raymond Queneau in particular, is briefly presented. (shrink)

Open peer commentary on the article “Religion: A Radical-Constructivist Perspective” by Andreas Quale. Upshot: An essential feature of Quale’s point of view is the strict distinction between the cognitive and the non-cognitive. I argue that this position is untenable and hence that a radical constructivist can discuss religious matters.

What is philosophy of mathematics and what is it about? The most popular answer, I suppose, to this question would be that philosophers should provide a justification for our presently most cherished mathematical theories and for the most important tool to develop such theories, namely logico-mathematical proof. In fact, it does cover a large part of the activity of philosophers that think about mathematics. Discussions about the merits and faults of classical logic versus one or other ‘deviant’ logics as the (...) logical basis for mathematical theories, ranging from intuitionist over modal logic to paraconsistent logic, typically belong to this area, as do debates about the natural-number concept, its ‘nature’, its properties, especially its uniqueness, and so on. No doubt sociologists of knowledge could explain why philosophers of mathematics came to select these particular problems and deal with them the way they do. What it does imply, however, is that the question is meaningful whether different kinds of philosophies of mathematics are possible, and—why not?—perhaps even desirable. To a certain extent, the answer is trivial: look at what, e.g., phenomenologists have to say about mathematics and you must notice it does not fit into the scheme sketched above.1 Rather, the question should be whether there are forms that, on the one hand, reinterpret the whole enterprise, and, on the other hand, somehow remain related to the work of ‘mainstream’ philosophers of mathematics today.The book under review here does precisely that. Let me be a bit more precise. The general proposal, present throughout all the contributions, is that even at a first, superficial, glance at what mathematicians do when they do mathematics, it is far more complex than ‘just thinking about and …. (shrink)

According to the cognitive model of psychopathology, maladaptive beliefs about oneself, others, and the world are the main factors contributing to the development and persistence of various forms of mental suffering. Therefore, the key therapeutic process of Cognitive Behavioral Therapy (CBT)—a therapeutic approach rooted in the cognitive model—is cognitive restructuring, i.e., a process of revision of such maladaptive beliefs. In this paper, I examine the philosophical assumptions underlying CBT and offer theoretical reasons to think that the effectiveness of belief revision (...) in psychotherapy is very limited. This is the case, I argue, because the cognitive model wrongly assumes that our body of beliefs is unified, while it is in fact fragmented. (shrink)

Conversational Artificial Intelligence (CAI) systems (also known as AI “chatbots”) are among the most promising examples of the use of technology in mental health care. With already millions of users worldwide, CAI is likely to change the landscape of psychological help. Most researchers agree that existing CAIs are not “digital therapists” and using them is not a substitute for psychotherapy delivered by a human. But if they are not therapists, what are they, and what role can they play in mental (...) health care? To answer these questions, we appeal to two well-established and widely discussed concepts: cognitive and affective artifacts. Cognitive artifacts are artificial devices contributing functionally to the performance of a cognitive task. Affective artifacts are objects which have the capacity to alter subjects’ affective state. We argue that therapeutic CAIs are a kind of cognitive-affective artifacts which contribute to positive therapeutic change by (i) simulating a (quasi-)therapeutic interaction, (ii) supporting the performance of cognitive tasks, and (iii) altering the affective condition of their users. This sheds new light on why virtually all existing mental health CAIs implement principles and techniques of Cognitive Behavioral Therapy — a therapeutic orientation according to which affective change and, ultimately, positive therapeutic change is mediated by cognitive change. Simultaneously, it allows us to conceptualize better the potential and limitations of applying these technologies in therapy. (shrink)

Concerns about censorship have once again reached a fever pitch across the liberal West. In other historical periods, such concerns may have marked reactions to book bans and burnings. Often, they followed prosecutions and subsequent jailtime for things spoken or written. During the Red Scare, they were the hushed response to chilling state-sponsored watch-lists and employer-supported blacklists designed to ensure victory against communism. Against this history, complaints about the new censorship appear differently. With respect to the new censorship, there are (...) no books burnings, no prosecutions, no laws or committees. Indeed, there is no coercive state involvement at all. With a few notable exceptions, complaints about censorship in the 21st-century West are complaints about the behavior of private parties: social groups, employers, media conglomerates, social media platforms, and search engines. -/- To better understand the concerns surrounding nonstate interference with speech, Private Censorship offers an account of censorship, as well as an assessment of the ethical and political issues it raises across contexts. J.P. Messina asks and variously answers questions like: what should we think when employees get fired for things they say and how might patterns of such firings create a climate of fear inimical to free inquiry? When is it appropriate for social media firms to deplatform users, and what does it mean for our democracy that those in charge of such decisions are often wealthy Silicon Valley executives? Do search engines act as massive gatekeepers to information in troubling ways, and how might they be constrained, if they do? Along the way, Messina casts a critical eye on many popular proposals for responding to these complaints. Unlike these popular approaches, Private Censorship foregrounds the importance of rights to property, association, and free expression for thinking well about 21st-century censorship concerns. (shrink)

The act of criminalising conduct has been understood by many theorists as a form of communication. This paper proposes a model, based on speech-act theory, for understanding how that act of communication works. In particular, it focuses on analysing how and where wrongfulness can appear in this speech-act, if one were to argue, as many theorists do, that part of what is being communicated through criminalisation is the wrongfulness of the target conduct. I argue that the act of criminalisation is (...) best understood as an indirect speech-act, which both asserts and declares normative facts, the utterance of which makes it the case that a conduct is now criminalised. Within this speech-act, wrongfulness can appear as an implicit assertion of the wrongness of the conduct, which has to be inferred by hearers from the context of utterance. The paper then briefly discusses the upshots of this model, mainly that it allows a clearer picture of how criminalisation conveys meanings, as well as leaving open the question as to whether it makes sense to think that the wrongfulness being conveyed is specifically of a moral kind. (shrink)

Introduces the applications of repeated measures design processes with the popular IBM® SPSS® software Repeated Measures Design for Empirical Researchers presents comprehensive coverage of the formation of research questions and the analysis of repeated measures using IBM SPSS and also includes the solutions necessary for understanding situations where the designs can be used. In addition to explaining the computation involved in each design, the book presents a unique discussion on how to conceptualize research problems as well as identify appropriate repeated (...) measures designs for research purposes. Featuring practical examples from a multitude of domains including psychology, the social sciences, management, and sports science, the book helps readers better understand the associated theories and methodologies of repeated measures design processes. The book covers various fundamental concepts involved in the design of experiments, basic statistical designs, computational details, differentiating independent and repeated measures designs, and testing assumptions. Along with an introduction to IBM SPSS software, Repeated Measures Design for Empirical Researchers includes: A discussion of the popular repeated measures designs frequently used by researchers, such as one-way repeated measures ANOVA, two-way repeated measures design, two-way mixed design, and mixed design with two-way MANOVA Coverage of sample size determination for the successful implementation of designing and analyzing a repeated measures study A step-by-step guide to analyzing the data obtained with real-world examples throughout to illustrate the underlying advantages and assumptions A companion website with supplementary IBM SPSS data sets and programming solutions as well as additional case studies Repeated Measures Design for Empirical Researchers is a useful textbook for graduate- and PhD-level students majoring in biostatistics, the social sciences, psychology, medicine, management, sports, physical education, and health. The book is also an excellent reference for professionals interested in experimental designs and statistical sciences as well as statistical consultants and practitioners from other fields including biological, medical, agricultural, and horticultural sciences. J. P. Verma, PhD, is Professor of Statistics and Director of the Center for Advanced Studies at Lakshmibai National Institute of Physical Education, India. Professor Verma is an active researcher in sports modeling and data analysis and has conducted many workshops on research methodology, research designs, multivariate analysis, statistical modeling, and data analysis for students of management, physical education, social science, and economics. He is the author of Statistics for Exercise Science and Health with Microsoft® Office Excel®, also published by Wiley. (shrink)

Consciousness is an active area of both philosophical debates and scientific research. Consciousness Quest, rather than covering the broad spectrum of consciousness spread over multiple scientific disciplines, refocuses the quest for consciousness on a specific area where Eastern contemplative traditions, mostly in Hindu and Buddhist theories of mind, meet Western empirical research. This book is an introduction to current scientific thinking and research on consciousness and at the same time acquaints readers with the spectrum of classical and modern philosophical notions (...) on consciousness. (shrink)

The first comprehensive study of Nietzsche's earliest book, The Birth of Tragedy, this important volume by M. S. Silk and J. P. Stern examines the work in detail: its place in Nietzsche's philosophical career; its value as an account of ancient Greek culture; its place in the history of German ideas, and its value as a theory of tragedy and music. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Lesley Chamberlain, illuminating its enduring (...) importance and relevance to philosophical enquiry, this accessible study has been revived for a new generation of readers. (shrink)

Modernism is both a contested aesthetic category and a powerful political statement. Modernist music was condemned as degenerate by the Nazis and forcibly replaced by socialist realism under the Soviets. Sympathetic philosophers and critics have interpreted it as a vital intellectual defence against totalitarianism, yet some American critics consider it elitist, undemocratic, and even unnatural. Drawing extensively on the philosophy of Heidegger and Badiou, Quilting Points proposes a new dialectical theory of faithful, reactive, and obscure subjective responses to musical modernism, (...) which embraces all the music of Western modernity. (shrink)

In the study of expertise, few debates come as big as that between constructivists and realists. This chapter discusses the signal debate between realists and constructivists about expertise. It sets out a view that includes aspects of both the constructivist and realist position to show that insights from what is often considered to be rival camps can be incorporated in a position that does justice to both. The chapter argues that, while expertise is real, there are two distinct social dimensions (...) to the concept of expertise. It attempts to demonstrate two distinct ways in which expertise has a social dimension. First, the chapter develops an account according to which 'is an expert' is a triadic predicate. Second, it considers the fact that attributions of expertise are often done by institutions, i.e. by medical boards certifying doctors, etc. Both dimensions can be acknowledged without undermining the basic case for realism about expertise. (shrink)

Despite Vancil’s (1979) proclamation over twenty years ago that topoi have been abandoned in argument theory, this essay contends that topoi should have a vital role in contemporary argumentation theory. Four key areas are identified where topoi are (or can be) essential tools for argumentation: Locating argument, building argument, development of critical thinking, and argument pedagogy. As a result, teachers and students of argument can both benefit from a (re)discovery of topoi.

The use of tensed language and the metaphor of set ‘formation’ found in informal descriptions of the iterative conception of set are seldom taken at all seriously. Both are eliminated in the nonmodal stage theories that formalise this account. To avoid the paradoxes, such accounts deny the Maximality thesis, the compelling thesis that any sets can form a set. This paper seeks to save the Maximality thesis by taking the tense more seriously than has been customary (although not literally). A (...) modal stage theory, MST, is developed in a bimodal language, governed by a tenselike logic. Such a language permits a very natural axiomatisation of the iterative conception, which upholds the Maximality thesis. It is argued that the modal approach is consonant with mathematical practice and a plausible metaphysics of sets and shown that MST interprets a natural extension of Zermelo set theory less the axiom of Infinity and, when extended with a further axiom concerning the extent of the hierarchy, interprets Zermelo–Fraenkel set theory. (shrink)

This chapter discusses author's view a Thomistic‐like dualism. Next, it lays out the details of his position and he argues that it has certain advantages over physicalist treatments of the human person, and, to a lesser degree, over alternate versions of substance dualism. Then, he responds to some objections against his position. He accepts constituent realism regarding properties (and relations), according to which properties (and relations) are universals that, when exemplified (and they need not be to exist), become constituents of (...) the ordinary particulars that have them. Furthermore, with the Thomistic framework in mind, the chapter offers his view of a human person. Finally, there is the argument that attempts to show that the unity of consciousness cannot be explained if one is a brain, because a brain is just an aggregate of different physical (separable) parts. (shrink)

In The Construction of Social Reality, John Searle develops a theory of institutional facts and objects, of which money, borders and property are presented as prime examples. These objects are the result of us collectively intending certain natural objects to have a certain status, i.e. to ‘count as’ being certain social objects. This view renders such objects irreducible to natural objects. In this paper we propose a radically different approach that is more compatible with standard economic theory. We claim that (...) such institutional objects can be fully understood in terms of actions and incentives, and hence the Searlean apparatus solves a non-existent problem. (shrink)