Reviews Wildberger's account of his rational trigonometry project, which argues for a simpler way of doing trigonometry that avoids irrationals.

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Literature 27.2 (2003) 284-303 [Access article in PDF] Accidental Art:Tolstoy's Poetics of Unintentionality Michael A. Denner I ART'S ABILITY TO INFECT another with an emotion, the concept that has come to be probably the most readily identified catchphrase in What Is Art? (though it crops up in his earlier writings on art), derives from L. N. Tolstoy's dynamic identity claim about art: we know an artist has (...) created a genuine work of art when he "hands on to others feelings he has lived through, and that others are infected by these feelings and also experience them." 1 "What is art?" is then a taxonomical question, and, according to Tolstoy, art is identifiable from non-art not by some set of external characteristics—the way, say, Aristotle categorized animals in his natural history—rather art is recognizable by its function, by what it does. In this sense art is like a tool: A given thing is art because it performs a certain task, much as one might claim a screwdriver is anything that sets and removes screws, regardless of its external characteristics. Tolstoy, in fact, repeatedly refers to art as "orudie," "a tool," or even "a weapon."It is worth noting from the outset that this metaphor of contagiousness is one of sublimated violence. For its passive "perceiver" (Tolstoy's characteristic term for the consumer of art), art amounts to irresistible, surreptitious emotional manipulation by an external entity. Tolstoy is ever attentive to the underlying meanings of the words he chooses, and I think he means to emphasize the latent, etymological meaning of the zarazit', to infect, the root of which is razit', to strike, a military term that likely resonated with Tolstoy, a war veteran. 2 Etymological arguments aside, Tolstoy makes explicit the psychological violation that goes hand-in-hand [End Page 284] with the experience of a work of art in a diary entry from a period of work on an earlier variant of What Is Art?: "One must hone the artistic work so that it penetrates. To hone a work means to make it perfect artistically, in which case it will pierce through the indifference...." 3 In an earlier version of the essay, Tolstoy offers "hypnotism" as a synonym for infection (p. 53).With its ability to "penetrate" through indifference and colonize, willy-nilly, the other, art accomplishes directly and immediately what no amount of rational argument could accomplish: "Art is differentiated from the activity of rational activity, which demands preparation and a certain sequence of knowledge (so that one cannot learn trigonometry before knowing geometry), by the fact that it acts on people independently of their state of development and education, that the charm of a picture, of sounds, or of forms, infects any man whatever his plane of development" (p. 178).The effect of art does not depend on some graduated, sequential process as it does for rational activity: art's infectiousness is immediate and irresistible. According to What Is Art?, the summum bonum of art's infectiousness, its best use, but notably not its only, is bringing about the Kingdom of God by effecting a change in the psychology of all the individuals who experience it. "Religious art," Tolstoy's supreme category of art, surmounts the (ultimately illusory for Tolstoy) individuality of the perceiver by inducing in him or her an emotional union with the artist and all others who have experienced the work of art, thereby inducting all perceivers into the universal collective of humankind: "In this freeing of our personality from its separation from other people, from its isolation, in this uniting of personality with others, lies the chief characteristic and the great attractive force of art" (p. 228). Art is a sacrament and the artist a priest of sorts.It is often said, even by those who have read the work, that Tolstoy "rejected" art in the last decades of his life, and What Is Art? is often cited as evidence. Granted, much of the book excoriates much of the art of the ages, but one must not... (shrink)

Recently the geometry of quantum states has been under considerable development. Every good geometry deserves, if possible, an accompanying trigonometry. I will here introduce such a trigonometry to accompany the geometry of quantum states.

This book discusses how rational choice theory grew out of RAND's work for the US Air Force. It concentrates on the work of William J. Riker, Kenneth J. Arrow, James M. Buchanan, Russel Hardin, and John Rawls. It argues that within the context of the US Cold War with its intensive anti-communist and anti-collectivist sentiment, the foundations of capitalist democracy were grounded in the hyper individualist theory of non-cooperative games.

Permissivism about rationality is the view that there is sometimes more than one rational response to a given body of evidence. In this paper I discuss the relationship between permissivism, deference to rationality, and peer disagreement. I begin by arguing that—contrary to popular opinion—permissivism supports at least a moderate version of conciliationism. I then formulate a worry for permissivism. I show that, given a plausible principle of rational deference, permissive rationality seems to become unstable and to collapse into (...) unique rationality. I conclude with a formulation of a way out of this problem on behalf of the permissivist. (shrink)

Mathematical proofs are not sequences of arbitrary deductive steps—each deductive step is, to some extent, rational. This paper aims to identify and characterize the particular form of rationality at play in mathematical proofs. The approach adopted consists in viewing mathematical proofs as reports of proof activities—that is, sequences of deductive inferences—and in characterizing the rationality of the former in terms of that of the latter. It is argued that proof activities are governed by specific norms of rational planning (...) agency, and that a deductive step in a mathematical proof qualifies as rational whenever the corresponding deductive inference in the associated proof activity figures in a plan that has been constructed rationally. It is then shown that mathematical proofs whose associated proof activities violate these norms are likely to be judged as defective by mathematical agents, thereby providing evidence that these norms are indeed present in mathematical practice. We conclude that, if mathematical proofs are not mere sequences of deductive steps, if they possess a rational structure, it is because they are the product of rational planning agents. (shrink)

We propose a framework for including information‐processing bounds in rational analyses. It is an application of bounded optimality (Russell & Subramanian, 1995) to the challenges of developing theories of mechanism and behavior. The framework is based on the idea that behaviors are generated by cognitive mechanisms that are adapted to the structure of not only the environment but also the mind and brain itself. We call the framework computational rationality to emphasize the incorporation of computational mechanism into the definition (...) of rational action. Theories are specified as optimal program problems, defined by an adaptation environment, a bounded machine, and a utility function. Such theories yield different classes of explanation, depending on the extent to which they emphasize adaptation to bounds, and adaptation to some ecology that differs from the immediate local environment. We illustrate this variation with examples from three domains: visual attention in a linguistic task, manual response ordering, and reasoning. We explore the relation of this framework to existing “levels” approaches to explanation, and to other optimality‐based modeling approaches. (shrink)

Rationing is an unavoidable mechanism for reining in healthcare costs. It entails establishing cutoff points that distinguish between what is and is not offered or available to patients. When the resource to be distributed is defined by vague and indeterminate terms such as “beneficial,” “effective,” or even “futile,” the ability to draw meaningful boundary lines that are both ethically and medically sound is problematic. In this article, I draw a parallel between the challenges posed by this problem and the ancient (...) Greek philosophical conundrum known as the “sorites paradox.” I argue, like the paradox, that the dilemma is unsolvable by conventional means of logical analysis. However, I propose another approach that may offer a practical solution that could be applicable to real-life situations in which cutoffs must be decided (such as rationing). (shrink)

Kant was a keen psychological observer and theorist of the forms, mechanisms and sources of self-deception. In this Element, the author discusses the role of rationalizing/Vernünfteln for Kant's moral psychology, normative ethics and philosophical methodology. By drawing on the full breadth of examples of rationalizing Kant discusses, the author shows how rationalizing can extend to general features of morality and corrupt rational agents thoroughly. Furthermore, the author explains the often-overlooked roles common human reason, empirical practical reason and even pure (...) practical reason play for rationalizing. Kant is aware that rationality is a double-edged sword; reason is the source of morality and of our dignity, but it also enables us to seemingly justify moral transgressions to ourselves, and it creates an interest in this justification in the first place. Finally, this Element discusses whether Kant's ethical theory itself can be criticised as a product of rationalizing. (shrink)

The discussion of rationality can only be conducted today against the backdrop of the raging postmodernist and deconstructionist onslaught on the “citadel of reason,” as one writer has put it recently. Although the current postmodernist skirmishes are launched against modernism as represented by Descartes and Kant, it is clear that the proclamation of the bankruptcy of reason or “the end of philosophy,” as both Martin Heidegger and Richard Rorty have put it, goes well beyond the modernism of Descartes and Kant. (...) It is part of the struggle between logos and anti‐logos which is really perennial. (shrink)

Extended Rationality: A Hinge Epistemology provides a novel account of the structure of epistemic justification. Its central claim builds upon Wittgenstein's idea in On Certainty that epistemic justifications hinge on some basic assumptions and that epistemic rationality extends to these very hinges. It exploits these ideas to address major problems in epistemology, such as the nature of perceptual justifications, external world skepticism, epistemic relativism, the epistemic status of basic logical laws, of the Principle of the Uniformity of Nature, of our (...) belief in the existence of the past and of other minds, and the nature of testimonial justification. Along the way, further technical issues, such as the scope of the Principle of Closure of epistemic operators under known entailment, the notion of transmission failure, and the existence of entitlements are addressed in new and illuminating ways. (shrink)

Believing rationally is epistemically valuable, or so we tend to think. It’s something we strive for in our own beliefs, and we criticize others for falling short of it. We theorize about rationality, in part, because we want to be rational. But why? I argue that how we answer this question depends on how permissive our theory of rationality is. Impermissive and extremely permissive views can give good answers; moderately permissive views cannot.

The study of rationality and practical reason, or rationality in action, has been central to Western intellectual culture. In this invigorating book, John Searle lays out six claims of what he calls the Classical Model of rationality and shows why they are false. He then presents an alternative theory of the role of rationality in thought and action. A central point of Searle's theory is that only irrational actions are directly caused by beliefs and desires—for example, the actions of a (...) person in the grip of an obsession or addiction. In most cases of rational action, there is a gap between the motivating desire and the actual decision making. The traditional name for this gap is "freedom of the will." According to Searle, all rational activity presupposes free will. For rationality is possible only where one has a choice among various rational as well as irrational options. Unlike many philosophical tracts, Rationality in Action invites the reader to apply the author's ideas to everyday life. Searle shows, for example, that contrary to the traditional philosophical view, weakness of will is very common. He also points out the absurdity of the claim that rational decision making always starts from a consistent set of desires. Rational decision making, he argues, is often about choosing between conflicting reasons for action. In fact, humans are distinguished by their ability to be rationally motivated by desire-independent reasons for action. Extending his theory of rationality to the self, Searle shows how rational deliberation presupposes an irreducible notion of the self. He also reveals the idea of free will to be essentially a thesis of how the brain works. (shrink)

In Minimal Rationality, Christopher Cherniak boldly challenges the myth of Man the the Rational Animal and the central role that the "perfectly rational...

Topics in Cognitive Science, Volume 14, Issue 3, Page 528-549, July 2022.

In Animal Rationality: Later Medieval Theories 1250-1350, Anselm Oelze offers the first comprehensive and systematic exploration of theories of animal rationality in the later Middle Ages.

Does rationality require logical omniscience? Our best formal theories of rationality imply that it does, but our ordinary evaluations of rationality seem to suggest otherwise. This paper aims to resolve the tension by arguing that our ordinary evaluations of rationality are not only consistent with the thesis that rationality requires logical omniscience, but also provide a compelling rationale for accepting this thesis in the first place. This paper also defends an account of apriori justification for logical beliefs that is designed (...) to explain the rational requirement of logical omniscience. On this account, apriori justification for beliefs about logic has its source in logical facts, rather than psychological facts about experience, reasoning, or understanding. This account has important consequences for the epistemic role of experience in the logical domain. In a slogan, the epistemic role of experience in the apriori domain is not a justifying role, but rather an enabling and disabling role. (shrink)

This article defends the Fixed Point Thesis: that it is always a rational mistake to have false beliefs about the requirements of rationality. The Fixed Point Thesis is inspired by logical omniscience requirements in formal epistemology. It argues to the Fixed Point Thesis from the Akratic Principle: that rationality forbids having an attitude while believing that attitude is rationally forbidden. It then draws out surprising consequences of the Fixed Point Thesis, for instance that certain kinds of a priori justification (...) are indefeasible and that misleading all-things-considered evidence about rational requirements is impossible. Finally, the Fixed Point Thesis is applied to defend the Right Reasons position on peer disagreement, according to which an agent who has drawn the correct conclusion from her evidence should retain belief in that conclusion even in the face of disagreeing peers. (shrink)

Martin Eger's comparison of controversies in science and morals is extended to a consideration of the nature of “rationality” in each. Both theoretical science and moral philosophy are held to be relativist in social and historical terms, but science also has definitive non‐relativist pragmatic criteria of truth. The problem for moral philosophy is to delineate its own appropriate types of social criteria of validity.

Readers interested in this paper will find it is reprinted as chapter nine of my book, Rationality, Relativism and Incommensurability.

Academic writings– writings that take place in academic settings, from undergraduate essays to research monographs – are social practices and methods of knowledge enquiry. In virtue of being social and epistemic, they should be of concern to critical realists because of critical realism's stratified approach to reality. By critiquing approaches to academic writing that can flatten reality, I propose that if academic writings were understood as ontologically stratified social practices, they could afford writers the rational judgement to make textual (...) choices. Specifically, I show there is the possibility to produce discourse that is different from standardized ‘objective' and ‘transparent' academic prose, which, inter alia, also has colonial roots. If academic writings were understood ontologically and epistemologically as practices and methods of enquiry that require writers (i.e. agents) to rationally judge what form their texts should take, this could further academic writing’s educative and emancipatory purpose of advancing knowledge and justice. (shrink)

It is now standard to distinguish between two kinds of rationality: substantive rationality, which consists in holding attitudes that are substantively reasonable or justified, and structural rationality, which consists in holding attitudes that fit together in the right ways. What, if anything, unifies these two kinds of rationality? In this paper, I propose that norms of rationality arise because we are epistemically limited beings who cannot directly ensure the correctness of our attitudes. Substantive and structural rationality represent two different ways (...) of manifesting a fundamental commitment to getting things correct, given our epistemic limitations. Correspondingly, substantive and structural irrationality are distinct rational failures. Substantively irrational attitudes involve a failure to live up to the commitments that constitute those attitudes. Structurally irrational combinations of attitudes are constituted by inconsistent commitments, which guarantees that we will fail to live up to at least some of our commitments in holding these attitudes. (shrink)

Rationality Through Reasoning answers the question of how people are motivated to do what they believe they ought to do, built on a comprehensive account of normativity, rationality and reasoning that differs significantly from much existing philosophical thinking. Develops an original account of normativity, rationality and reasoning significantly different from the majority of existing philosophical thought Includes an account of theoretical and practical reasoning that explains how reasoning is something we ourselves do, rather than something that happens in us Gives (...) an account of what reasons are and argues that the connection between rationality and reasons is much less close than many philosophers have thought Contains rigorous new accounts of oughts including owned oughts, agent-relative reasons, the logic of requirements, instrumental rationality, the role of normativity in reasoning, following a rule, the correctness of reasoning, the connections between intentions and beliefs, and much else. Offers a new answer to the ‘motivation question’ of how a normative belief motivates an action. (shrink)

There are at least two threads in our thought and talk about rationality, both practical and theoretical. In one sense, to be rational is to respond correctly to the reasons one has. Call this substantive rationality. In another sense, to be rational is to be coherent, or to have the right structural relations hold between one’s mental states, independently of whether those attitudes are justified. Call this structural rationality. According to the standard view, structural rationality is associated with (...) a distinctive set of requirements that mandate or prohibit certain combinations of attitudes, and it’s in virtue of violating these requirements that incoherent agents are irrational. I think the standard view is mistaken. The goal of this paper is to explain why, and to motivate an alternative account: rather than corresponding to a set of law-like requirements, structural rationality should be seen as corresponding to a distinctive kind of pro tanto rational pressure—i.e. something that comes in degrees, having both magnitude and direction. Something similar is standardly assumed to be true of substantive rationality. On the resulting picture, each dimension of rational evaluation is associated with a distinct kind of rational pressure—substantive rationality with (what I call) justificatory pressure and structural rationality with attitudinal pressure. The former is generated by one’s reasons while the latter is generated by one’s attitudes. Requirements turn out to be at best a footnote in the theory of rationality. (shrink)

Since it is hard to see how subjective rationality could be normative, a humbler, purely evaluative account of rationality’s importance has been suggested: rationality is a non-moral virtue, and rational action is good so far as it reveals that an agent ‘functions well’. This paper argues, however, that even this fallback position is threatened by ‘eccentric billionaire’ scenarios: sometimes, flouting purported coherence standards of rationality is maximally virtuous. In defense of the virtue account, I argue that a novel view (...) of rational constraints is called for: rationality requires a certain form of higher-order coherence – as considerations about instrumental coherence can show. (shrink)

The article deals with a role of mass culture in term of the theory of the culture industry by M. Horkheimer and T. Adorno and the theory of communicative action by J. Habermas, who continues research of the Frankfurt school. It is known that Habermas says about two types of rationality — communicative and structural. The lifeworld and the system correspond them. Usually, culture correspond to lifeworld because it helps people`s socialization. Also it is a place for communication and finding (...) new meanings. However, a place of mass culture is very controver- sial. In particular, it is necessary to distinguish between popular and mass culture, because these definitions have been used as interchangeable for a long time. Popular culture is still an area of meanings. Moreover, it has the potential for protest. From this point of view, it is clearly part of the life world. But mass culture as a «cultural industry» is not so unambiguous. It is worth considering its characteristics and role in people’s life more detail. Above all, one cannot help paying attention to masses. Already in the last century, H. Arendt characterized them as an atomized and isolated group of people, and they are not united by any common ideas. After all, even in the modern world it is possible to see that they do not have and do not want to search for any ideas or meanings. Masses are a direct consumers of mass culture. It is consumerism that the characteristic feature of modernity. Therefore, mass culture is inseparably connected with the market. On the one hand, it sells entertainments, and on the other hand, it generates new consumers, because it is related to advertising. In the same way, mass culture is connected with agitation and propaganda. Thus, it is possible to speak about its connection with politics. The market and politics correspond to the system and are guided by strategic rationality. This fact gives reason to talk about mass culture as a strategic tool. Such culture with no meanings leads to a crisis in society. (shrink)

En 1676, alors qu'il sejourne encore a Paris, Leibniz entreprend de composer un volumineux traite qui restera sans doute l'un de ses ecrits mathematiques les plus fortement charpentes: La quadrature arithmetique du cercle, de l'ellipse et de l'hyperbole et la trigonometrie sans tables qui en est le corollaire. Ce traite se presente comme un abrege exhaustif de la geometrie infinitesimale, dont Leibniz avait pu esperer qu'elle lui ouvrirait les portes de l'Academie des Sciences. Cependant, contraint de quitter la capitale avant (...) sa publication, il abandonnera derriere lui un ouvrage qui n'allait voir le jour qu'en 1993. Le probleme de la quadrature est pretexte a soulever plusieurs enjeux capitaux tant pour les mathematiques que pour la philosophie. Il permet notamment a Leibniz d'examiner avec une grande precision la question de la methode, des fondements, ainsi que des notions cruciales de rigueur et d'infini, tout en mettant en evidence leurs applications pratiques. Si la presente edition de ce texte foisonnant ne reproduit pas l'integralite des variantes, elle en propose une version corrigee et annotee, qui s'accompagne d'une traduction francaise en regard. (shrink)

This paper is about the connection between rationality and accuracy. I show that one natural picture about how rationality and accuracy are connected emerges if we assume that rational agents are rationally omniscient. I then develop an alternative picture that allows us to relax this assumption, in order to accommodate certain views about higher order evidence.

The paper argues against a widely held synchronic view of emotional rationality. I begin by considering recent philosophical literature on various backward‐looking emotions, such as regret, grief, resentment, and anger. I articulate the general problem these accounts grapple with: a certain diminution in backward‐looking emotions seems fitting while the reasons for these emotions seem to persist. The problem, I argue, rests on the assumption that if the facts that give reason for an emotion remain unchanged, the emotion remains fitting. However, (...) I argue there are rationally self‐consuming attitudes: affective attitudes that become less fitting the longer they endure while the facts that give reason for them persist. A widely held synchronic view of fitting affective attitudes denies that fittingness at a time depends on the agent's attitudes at different times and therefore denies that the fittingness of an affective attitude can depend on its duration. Once we reject the synchronic view, we may see that affective attitudes are often fitting due to the fitting processes of which they are part. These fitting processes explain the fitting diminution of backward‐looking emotions as well as other diachronic aspects of the fittingness of emotions. -/- . (shrink)

Epistemic akrasia arises when one holds a belief even though one judges it to be irrational or unjustified. While there is some debate about whether epistemic akrasia is possible, this paper will assume for the sake of argument that it is in order to consider whether it can be rational. The paper will show that it can. More precisely, cases can arise in which both the belief one judges to be irrational and one’s judgment of it are epistemically (...) class='Hi'>rational in the sense that both are supported by sufficient evidence. (shrink)

John Broome argues that rationality cannot consist in reasons-responsiveness since rationality supervenes on the mind, while reasons-responsiveness does not supervene on the mind. I here defend this conception of rationality by way of defending the assumption that reasons-responsiveness supervenes on the mind. Given the many advantages of an analysis of rationality in terms of reasons-responsiveness, and in light of independent considerations in favour of the view that reasons-responsiveness supervenes on the mind, we should take seriously the backup view, a hypothesis (...) that explains why reasons-responsiveness supervenes on the mind even though paradigmatic reasons are external facts. I argue that Broome’s objections to the backup view, as well as his more general objection to the thesis that reasons-responsiveness supervenes on the mind, do not succeed. (shrink)

The demands of rationality are linked both to our subjective normative perspective (given that rationality is a person-level concept) and to objective reasons or favoring relations (given that rationality is non-contingently authoritative for us). In this paper, I propose a new way of reconciling the tension between these two aspects: roughly, what rationality requires of us is having the attitudes that correspond to our take on reasons in the light of our evidence, but only if it is competent. I show (...) how this view can account for structural rationality on the assumption that intentions and beliefs as such involve competent perceptions of downstream reasons, and explore various implications of the account. (shrink)