Many of the methods commonly used to research mathematical practice, such as analyses of historical episodes or individual cases, are particularly well-suited to generating causal hypotheses, but less well-suited to testing causal hypotheses. In this paper we reflect on the contribution that the so-called hypothetico-deductive method, with a particular focus on experimental studies, can make to our understanding of mathematical practice. By way of illustration, we report an experiment that investigated how mathematicians attribute aesthetic properties to mathematical proofs. We demonstrate (...) that perceptions of the aesthetic properties of mathematical proofs are, in some cases at least, subject to social influence. Specifically, we show that mathematicians’ aesthetic judgements tend to conform to the judgements made by others. Pedagogical implications are discussed. (shrink)
By examining Dainton's account of the temporality of consciousness in the context of long-running debates about the specious present and time consciousness in both the Jamesian and the phenomenological traditions, I raise critical objections to his overlap model. Dainton's interpretations of Broad and Husserl are both insightful and problematic. In addition, there are unresolved problems in Dainton's own analysis of conscious experience. These problems involve ongoing content, lingering content, and a lack of phenomenological clarity concerning the central concept of overlapping (...) experiences. (shrink)
Distinguished researchers from across the globe assess, in a rare example of successful cross-disciplinary engagement, the explanatory power of chaos theory, new evolutionary theory, path dependency, neo-institutional economics, multiple modernities and historical institutionalism. The book provides an exciting panorama of state of the art thinking and new avenues to combining the power of various traditions of thought.
In this review essay of Michelle Montague’s The Given we focus on the central thesis in the book: the awareness of awareness thesis. On that thesis, a state of awareness constitutively involves an awareness of itself. In Section 2, we discuss what the awareness of awareness thesis amounts to, how it contrasts with the transparency of experience, and how it might be motivated. In Section 3, we discuss one of Montague’s two theoretical arguments for the awareness of awareness thesis. A (...) view that accepts the awareness of awareness thesis, Montague argues, is to be preferred over competing views because it outperforms them in accounting for the property attributions one makes in perceptual experience. We suggest that it is not clear that this argument for the awareness of awareness thesis is successful. Finally, in Section 4 we consider the relation between Montague’s view of color experience and what she calls Strawson’s datum, arguing that Montague may not be able to explain this datum as straightforwardly as she supposes. This, we suggest, threatens Montague’s second theoretical argument for the awareness of awareness thesis. (shrink)
This essay questions the meaning of be-ing and non-be-ing in the DDJ with regard to the root-source meaning of dao. I first explore the meaning of dao as the dark non-be-ing, revealing the connotations of the distinction between dao and things by comparison with some forms of Western metaphysics. The meaning of non-be-ing is elaborated in terms of the dynamic meanings of xu 虚 and chong 沖; The play between be-ing and non-be-ing is explored through the lens of yin and (...) yang qi thinking. Qi thinking determines the mutually manifest and mutually interpretive characteristic of be-ing and non-be-ing. Be-ing and non-be-ing thus understood is an ever-flowing and mutually transforming process that penetrates the different levels of dao, things and humans. In the last part I investigate the meaning of “Be-ing comes from non-be-ing”. (shrink)
I develop a challenge for a widely suggested knowledge-first account of belief that turns, primarily, on unknowable propositions. I consider and reject several responses to my challenge and sketch a new knowledge-first account of belief that avoids it.
What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.
We investigated whether mathematicians typically agree about the qualities of mathematical proofs. Between-mathematician consensus in proof appraisals is an implicit assumption of many arguments made by philosophers of mathematics, but to our knowledge the issue has not previously been empirically investigated. We asked a group of mathematicians to assess a specific proof on four dimensions, using the framework identified by Inglis and Aberdein (2015). We found widespread disagreement between our participants about the aesthetics, intricacy, precision and utility of the proof, (...) suggesting that a priori assumptions about the consistency of mathematical proof appraisals are unreasonable. (shrink)
“Thing” and “nothing” are metaphysical themes of thinking for major philosophers both in the West and in East Asia, such as Heidegger, Kant, and Laozi 老子. In light of a discussion of Heidegger’s understanding of thing-ing and no-thing and of his critical interpretation of Kant on the same issue, I shall in this essay reconstruct a Laozian theory of thing and nothing. My conclusion is that thing and nothing are not two “things,” as often assumed by an epistemological approach, but (...) ontologically one thing cut by an absolute limit set up by human rationality which is contained either in our consciousness or in our languages. (shrink)
In this paper we present a logic that determines when implications in a classical logic context express a relevant connection between antecedent and consequent. In contrast with logics in the relevance logic literature, we leave classical negation intact—in the sense that the law of non-contradiction can be used to obtain relevant implications, as long as there is a connection between antecedent and consequent. On the other hand, we give up the requirement that our theory of relevance should be able to (...) define a new standard of deduction. We present and argue for a list of requirements such a logical theory of classical relevance needs to meet and go on to formulate a system that respects each of these requirements. The presented system is a Tarski logic that extends the relevance logic R with a new relevant implication which allows for Disjunctive Syllogism and similar rules. This is achieved by interpreting the logical symbols in the antecedents in a stronger way than the logical symbols in consequents. A proof theory and an algebraic semantics are formulated and interesting metatheorems are proven. Finally we give a philosophical motivation for our non-standard relevant implication and the asymmetric interpretation of antecedents and consequents. (shrink)
Aquinas is often presented as following Aristotle's "Nicomachean Ethics" when treating moral virtue. Less often do philosophers consider that Aquinas's conception of the highest good and its relation to the functional character of human activity led him to break with Aristotle by replicating each of the acquired moral virtues on an infused level. The author suggests that we can discern reasons for this move by examining Aquinas's commentary on the "Sententiae" of Peter the Lombard and the "Summa theologiae" within their (...) historical context. The author's thesis is that Dominican pastoral and intellectual concerns led Aquinas to argue that moral virtue must necessarily be ordered toward the highest good. Understanding this purpose helps to explain his presentation of moral virtue and its implications for standard philosophical interpretations of his work. (shrink)
This essay highlights an alternative tradition of understanding value conflicts in early Confucian thought. In contrast to a prominent position among interpreters that argues for the resolvability or harmonization of conflicting values, I argue that some early Confucians conceptualized value conflicts as irresolvable. In other words, when meaningful aspects of a situation come into tension with each other and values are threatened to be either left unfulfilled or harmed, early Confucians put forth a variety of views. Some believed that all (...) values could be tended to as long as one had the moral imagination of a sage, whereas others saw the world as a place where irreconcilable conflicts between values could occur for even the most profound people. Within this diversity, I take up a view about irresolvable value conflicts where the confrontation with a deep value conflict leaves behind a moral remainder that can mar even the character of a sage. (shrink)
A meadow is a commutative ring with an inverse operator satisfying 0⁻¹ = 0. We determine the initial algebra of the meadows of characteristic 0 and prove a normal form theorem for it. As an immediate consequence we obtain the decidability of the closed term problem for meadows and the computability of their initial object.
Bare particularism is a constituent ontology according to which substances—concrete, particular objects like people, tables, and tomatoes—are complex entities constituted by their properties and their bare particulars. Yet, aside from this description, much about bare particularism is fundamentally unclear. In this paper, I attempt to clarify this muddle by elucidating the key metaphysical commitments underpinning any plausible formulation of the position. So the aim here is primarily catechismal rather than evangelical—I don’t intend to convert anyone to bare particularism, but, by (...) looking at a series of questions, to instead specify what, if one is a bare particularist, one is committed to. Along the way, I address three major objections: a classic objection about whether bare particulars have properties, a new objection raised by Bailey, and an understanding objection that questions some of the position’s resources. (shrink)
Mathematical explanations are poorly understood. Although mathematicians seem to regularly suggest that some proofs are explanatory whereas others are not, none of the philosophical accounts of what such claims mean has become widely accepted. In this paper we explore Wilkenfeld’s suggestion that explanations are those sorts of things that generate understanding. By considering a basic model of human cognitive architecture, we suggest that existing accounts of mathematical explanation are all derivable consequences of Wilkenfeld’s ‘functional explanation’ proposal. We therefore argue that (...) the explanatory criteria offered by earlier accounts can all be thought of as features that make it more likely that a mathematical proof will generate understanding. On the functional account, features such as characterising properties, unification, and salience correlate with explanatoriness, but they do not define explanatoriness. (shrink)
Major paradigms in immigration research, including assimilation theory, multiculturalism, and ethnic studies, take it for granted that dividing society into ethnic groups is analytically and empirically meaningful because each of these groups is characterized by a specific culture, dense networks of solidarity, and shared identity. Three major revisions of this perspective have been proposed in the comparative ethnicity literature over the past decades, leading to a renewed concern with the emergence and transformation of ethnic boundaries. In immigration research, "assimilation" and (...) u integration" have been reconceived as potentially reversible, powerdriven processes of boundary shifting. After a synthetic summary of the major theoretical propositions of this emerging paradigm, I offer suggestions on how to bring it to fruition in future empirical research. First, major mechanisms and factors influencing the dynamics of ethnic boundary -making are specified, emphasizing the need to disentangle them from other dynamics unrelated to ethnicity. I then discuss a series of promising research designs, most based on nonethnic units of observation and analysis, that allow for a better understanding of these mechanisms and factors. (shrink)
The Islamic philosophical tradition was the privileged site for the study and continuation of the Classical philosophical tradition in the Middle Ages. An initial chapter on the history of Islamic philosophy sets the stage for sixteen articles on issues across the Islamic, Jewish and Christian traditions. The goal is to see the Islamic tradition in its own richness and complexity as the context of much Jewish intellectual work. Taken together, these two traditions provide the wider context to which Latin Christian (...) intellectuals would turn. The articles are grouped under six topics relevant both to the period and to current philosophical interest: the Islamic philosophical context, the nature of philosophy in the Middle Ages, Neoplatonism and the activity of the soul, creation, virtue, and the Latin reception. Since the nineteenth century Islamic and Jewish philosophy have been neglected in the standard histories of medieval philosophy. The time is right to begin to write a more balanced history of medieval philosophy. In order to begin to write this history, this book focuses on the Islamic, Jewish, and Christian use of - and reaction to - Classical philosophy during the Middle Ages. (shrink)
Michael Ing's The Dysfunction of Ritual in Early Confucianism is the first monograph in English about the Liji--a text that purports to be the writings of Confucius' immediate disciples, and part of the earliest canon of Confucian texts called ''The Five Classics,'' included in the canon several centuries before the Analects. Ing uses his analysis of the Liji to show how early Confucians coped with situations where their rituals failed to achieve their intended aims. In contrast to most contemporary interpreters (...) of Confucianism, Ing demonstrates that early Confucian texts can be read as arguments for ambiguity in ritual failure. (shrink)
Analysis of the local implementation of paternity establishment and child support policy in four Wisconsin counties suggests that these policies reproduce some aspects of patriarchal gender relations. The counties' information-collecting practices focused on nonmarital mothers' sexual activity and nonmarital fathers' employment and income. Women were questioned far more extensively than men about their sexual practices and partners; women's accounts of their sexual activity were used to evaluate their overall truthfulness, and administrative practices in effect encouraged alleged fathers to state whether (...) they were convinced of the mother's sexual fidelity. By demonstrating the gendered nature of the terms under which public assistance is granted, the findings highlight the significance of the process of policy implementation for understanding the gendered character of state systems of social provision. (shrink)
This introduction to the special issue on ‘Ricoeur and the ethics of care’ is not a standard editorial. It provides not only an explanation of the central questions and a first impression of the articles, but also a critical discussion of them by an expert in the field of care ethics, Joan Tronto. After explaining the reasons to bring Ricoeur into dialogue with the ethics of care, and analyzing how the four articles of this special issue shape this dialogue, the (...) authors give the floor to Tronto. She focuses on the central issue at stake: what may be the value of a more abstract, conceptual approach for the ethics of care as a radically practice-oriented way of thinking? She argues that the four contributions too easily frame this value in terms of Ricoeur’s relational anthropology. Instead she points out that if the ethics of care is a kind of practice, it makes sense to think of such practices as necessarily building upon one another, expanding constantly the context and relationships upon which practices are built. In the final section the authors respond to Tronto’s framing of ‘practices all the way up’ by arguing that this approach need not be at odds with one inspired by Ricoeur’s conceptual thinking. Rather the two can be seen as different movements—upwards and downwards—that both contribute constructively to the shaping of the important intermediary zone between the practices and the abstract ideals. (shrink)
On a widely suggested knowledge-first account of belief, to believe p is to phi as if one knew p. I challenge this view by arguing against various regimentations of it. I conclude by generalizing my argument to alternative knowledge-first views suggested by Williamson and Wimmer.
According to a U.S. court ruling, intelligent design (ID) theory is religious in nature, not scientific, and must not be taught in schools. In opposition, Fuller argues for a closer rapport between science and religion. Here it is emphasized that any allegedly scientific conclusion from design in nature to the existence of God is a hypothesis subject to the same quality norms as empirical hypotheses in general. By quotations from his Iter Lapponicum , Linnæus is summoned in support of a (...) strictly immanent conception of science, against Fuller’s suggestion that Linnæus’ personal piety could be a reason for considering ID scientific. (shrink)
This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. -/- Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, interviews, and data-mining. Distinct themes emerge (...) that reflect recent developments in the field, such as issues concerning the logic of conditionals and the role played by visual elements in some mathematical proofs. -/- Featuring leading figures from experimental philosophy and the fields of philosophy of logic and mathematics, this collection reveals that empirical work in these disciplines has been quietly thriving for some time and stresses the importance of collaboration between philosophers and researchers in mathematics education and mathematical cognition. (shrink)
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