My first aim in this paper is to use time diagrams in the style of Brentano to analyze constructions in Brouwer's separable mathematics more precisely. I argue that constructions must involve not only pairing and projecting as basic operations guaranteed by the intuition of twoity, as sometimes assumed in the literature, but also a recalling operation. My second aim is to argue that Brouwer's views on the intuition of twoity and arithmetic lead to an ontological explosion. (...) Redeveloping the constructions of natural numbers and systems sketched in an appendix to Brouwer's Cambridge lectures, I observe that the only plausible way he can make some elementary arithmetic in his separable mathematics is by allowing for the same canonical number to be determined by multiple separable entities, resulting in an overabundant mathematical ontology. (shrink)

In 'Intuition, iteration, induction', Mark van Atten argues that iteration is an object of intuition for Brouwer and explains the intuitive character of the act of iteration drawing from Husserl’s phenomenology. I find the arguments for this reading of Brouwer unconvincing. In this note I set out some issues with his claim that iteration is an object of intuition and his Husserlian explication of iteration. In particular, I argue that van Atten does not accomplish his goals due (...) to tensions with Brouwer’s comments on second-order mathematics and because Husserl does not understand the experience of succession as Brouwer does. (shrink)

Spatial relations are central to geometrical thinking. With respect to the classical elementary geometry of Euclid’s Elements, a distinction between co-exact, or qualitative, and exact, or metric, spatial relations has recently been advanced as fundamental. We tested the universality of intuitions of these relations in a group of Senegalese and Dutch participants. Participants performed an odd-one-out task with stimuli that in all but one case display a particular spatial relation between geometric objects. As the exact/co-exact distinction is closely related to (...) Kosslyn’s categorical/coordinate distinction, a set of stimuli for testing all four types was used. Results suggest that intuitions of all spatial relations tested are universal. Yet, culture has an important effect on performance: Dutch participants outperformed Senegalese participants and stimulus layouts affect the categorical and coordinate processing in different ways for the two groups. Differences in level of education within the Senegalese participants did not affect performance. (shrink)

In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a necessary, but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework of Cantor’s (...) proof makes, Cantor’s proof invalid. It’s shown that traditional Cantor’s proof has a second necessary, but hidden as well, condition which is teleological by its nature, i.e., is not mathematical. The explication of the second necessary condition makes Cantor’s statement on the uncountability of continuum unprovable from the point of view of classical logic.One of the most dramatic facts in history of science is connected just with the notion of actual infinity and consists in the following. On the one hand, Aristotle, Berkeley, Locke, Descartes, Spinoza, Gauss, Kant, Cauchy, Kronecker, Hermite, Poincaré, Bair, Borel, Brouwer, Quine, Wittgenstein, Weyl, Luzin, and a lot of other outstanding creators of classical logic and classical mathematics, during millenniums, stated categorically and insistently warned about that the actual infinity is a self-contradictory notion and its usage in mathematics is inadmissible (e.g., according to Poincare, “There is no actual infinity. - Cantorians forgot that and fell into contradictions. Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered”). On the other hand, a lot of outstanding scientists of the XX c.c., such as Hilbert, Church, Turing, Gödel, etc., and modern axiomatic set theory as a whole ignored this (intuitive though) opinion of genii and accepted Cantor’s “transfinite paradise”, based on the actual infinity. In the paper some logical, philosophical, and psychological aspects of this historical “favorable opposition” are analyzed, and the fact that the scientific intuition of genii has won the historical battle against the mytho-’logic’ of Cantor’s transfinite ‘paradise’ is explained and logically justified. (shrink)

Gödel has argued that we can cultivate the intuition or perception of abstractconcepts in mathematics and logic. Gödel's ideas about the intuition of conceptsare not incidental to his later philosophical thinking but are related to many otherthemes in his work, and especially to his reflections on the incompleteness theorems.I describe how some of Gödel's claims about the intuition of abstract concepts are related to other themes in his philosophy of mathematics. In most of this paper, however,I focus (...) on a central question that has been raised in the literature on Gödel: what kind of account could be given of the intuition of abstract concepts? I sketch an answer to this question that uses some ideas of a philosopher to whom Gödel also turned in this connection: Edmund Husserl. The answer depends on how we understand the conscious directedness toward objects and the meaning of the term abstract in the context of a theory of the intentionality of cognition. (shrink)

The ArgumentThis article compares the corresponding effects in science and art of a change in the intuition of time at the beginning of this century. McTaggart's distinction between linear time and tense time is applied to the question of whether linear perspective requires a notion of time as succession. It is argued that the problem of self-representation is a basic problem for this kind of uniform space-time because of the contradiction between this model's need for a privileged point of (...) view and its simultaneous denial of such a possibility. (shrink)

Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space (...) that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. (shrink)

Even materialists will admit that mind‐brain identity is counterintuitive. Some materialist philosophers think that this intuition is due to the plausibility of the standard antimaterialist arguments, like Jackson's knowledge argument or Kripke's modal argument. Papineau shows that this cannot be right, since these arguments apply equally in cases in which we feel no intuition of distinctness. Instead, he draws on remarks of Thomas Nagel to argue that the intuition of distinctness is due to an “antipathetic fallacy”: we (...) move from the true premise that phenomenal concepts don’t involve conscious feelings to the false conclusion that they don’t refer to them. (shrink)

Kant's response to ‘Hume's problem’ in his analysis of the a priori structure of causality as law-governed succession in the Second Analogy of Experience has unquestionably overshadowed the account of simultaneity (Zugleichsein), which follows in the Third Analogy. The analysis of simultaneity in the first Critique relies entirely upon that of succession and is ultimately no more than a more complicated variant of the causal dependence of substances: two objects are experienced as simultaneous only when each of those objects grounds (...) some determination of the other, that is when they are reciprocally determined in dynamic community. By investigating Kant's remark in the third Critique that the experience of the sublime “makes simultaneity intuitable” this paper develops a Kantian analysis of simultaneity that is irreducible to the more prominent analysis of causal succession. This more robust account of simultaneity is then seen to play an essential role in the constitution of the objects of perception (and not only the regulation of their relations) as thematized in the Axioms of Intuition in the Critique of Pure Reason. (shrink)

The instant -- The problem of habit and discontinuous time -- The idea of progress and the intuition of discontinuous time -- Conclusion -- Appendix A: "Poetic instant and metaphysical instant" by Gaston Bachelard -- Appendix B: Reading Bachelard reading Siloe: an excerpt from "Introduction to Bachelard's poetics" by Jean Lescure -- Appendix C: A short biography of Gaston Bachelard.

Appearing in English for the first time, _Intuition of the Instant_—Bachelard’s first metaphysical meditation on time and its moral implications—was written in 1932 in the wake of Husserl’s lectures on streaming time-consciousness, Heidegger’s _Being and Time,_ and Henri Bergson’s philosophy of the élan vital. A culmination of Bachelard’s earlier studies in scientific epistemology, this work builds the epistemic framework that would lead theorists of all stripes to advance knowledge by breaking with accepted modes of thought. _Intuition of the Instant _sows (...) the seeds of Bachelard’s future poetics, most notably in the essay “Poetic Instant and Metaphysical Instant” —included in this volume, along with an excerpt from Jean Lescure’s lecture “Introduction to Bachelard’s Poetics”. Eileen Rizo-Patron’s translation offers a key to Bachelard’s subsequent works on science, time, and imagination, which remain epistemological touchstones. (shrink)

Volume 52, Issue 11, October 2020, Page 1120-1125.

How do we determine whether some candidate causal factor is an actual cause of some particular outcome? Many philosophers have wanted a view of actual causation which fits with folk intuitions of actual causation and those who wish to depart from folk intuitions of actual causation are often charged with the task of providing a plausible account of just how and where the folk have gone wrong. In this paper, I provide a range of empirical evidence aimed at showing just (...) how and where the folk go wrong in determining whether an actual causal relation obtains. The evidence suggests that folk intuitions of actual causation are generated by two epistemically defective processes. I situate the empirical evidence within a background discussion of debunking, arguing for a two-pronged debunking explanation of folk intuitions of actual causation. I conclude that those who wish to depart from folk intuitions of actual causation should not be compelled to square their account of actual causation with the verdicts of the folk. In the dispute over actual causation, folk intuitions deserve to be rejected. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

On parity views of mere addition if someone is added to the world at a range of well-being levels – or ‘neutral range’ – leaving existing people unaffected, addition is on a par with the initial situation. Two distinct parity views – ‘rough equality’ and fittingattitudes views – defend the ‘intuition of neutrality’. The first can be interpreted or adjusted so that it can rebut John Broome’s objection that the neutral range is wide. The two views respond in distinct (...) ways to two of Broome’s other objections. Both views can, nonetheless, be plausibly defended against these objections. (shrink)

In “Weighing Lives” (2004) John Broome criticizes a view common to many population axiologists. On that view, population increases with extra people leading decent lives are axiologically neutral: they make the world neither better nor worse, ceteris paribus. Broome argues that this intuition, however, attractive, cannot be sustained, for several independent reasons. I respond to his criticisms and suggest that the neutrality intuition, if correctly interpreted, can after all be defended.On the version I defend,the world with added extra (...) people at wellbeing levels within the neutrality range is incommensurable in value with the world in which these peaople are absent. (shrink)

According to many philosophers, an 'explanatory gap' exists between third-person scientific theories and qualitative firstperson experience of mental states like pain feelings or colour experiences such that the former can't explain the latter. Here it is argued that the thought experiments that are invoked by this position are inconsistent, that the position requires a specific kind of first-person privilege which actually does not exist, and that the underlying argument is circular because it is based on the very 'intuition of (...) distinctness'which it allegedly confirms. The second part of the paper argues that the intuition of distinctness which has seen a significant change during the history of science is itself a product of scientific development. It would follow that future scientific developments can change this intuition and even make the explanatory gap problem disappear. (shrink)

The aim of the paper is to demonstrate that Gilbert Keith Chesterton possessed the genuine intuition of being as defined by the French Thomist, Jacques Maritain, albeit almost without the proper metaphysical habitus. It opens with some explanations of the terms used, and with a short extrapolation of the theory of the intuition of being. Next it proceeds to proving the thesis assumed by the means of demonstrating that Chesterton exhibited the intuition of being as to three (...) most important elements: its proper object, the principle of sufficient reason and the principle of finality. Next it attempts to demonstrate that despite that understanding, he never spoke in a properly metaphysical manner, the fact that points to the lack of metaphysical habitus, and to establish certain consequences of this state of things. The text ends with a list of practical conclusions that could be drawn from an analysis such as this. (shrink)

Les algèbres de dimensions supérieures libèrent les mathématiques de la restriction d'une notation purement linéaire. Elles aident ainsi à la modélisation de la géométrie et procurent une meilleure compréhension et plus de possibilités pour les calculs. Elles nous donnent de nouveaux outils pour l'étude de problèmes non-commutatifs, de dimension supérieure qui assurent le passage du local au global, en utilisant la notion d' «inverse algébrique de subdivision». Nous allons exposer comment ces idées sont venues aux auteurs en prolongeant initialement la (...) notion classique de groupe abstrait à celle de groupoïde abstrait, dont la composition n'est que partiellement définie, et qui ajoute une composante spatiale à la théorie habituelle des groupes. La théorie des noeuds nous fournit un exemple en indiquant comment une telle algèbre peut être utilisée pour décrire la structure d'un espace. Le prolongement à la dimension 2 utilise des compositions de carrés dans deux directions et la richesse de l'algèbre qui en résulte est montrée par certains calculs de dimension 2. La difficulté de la transition de la dimension 1 à la dimension 2 est également illustrée par la comparaison de la notion de carré commutatif à celle de cube commutatif - le traitement de cette dernière nécessitant de nouvelles notions. L'importance de la théorie des catégories est expliquée, de même que les possibilités de l'application d'algèbres de dimensions supérieures. (shrink)

Edmund Husserl has argued that we can intuit essences and, moreover, that it is possible to formulate a method for intuiting essences. Husserl calls this method 'ideation'. In this paper I bring a fresh perspective to bear on these claims by illustrating them in connection with some examples from modern pure geometry. I follow Husserl in describing geometric essences as invariants through different types of free variations and I then link this to the mapping out of geometric invariants in modern (...) mathematics. This view leads naturally to different types of spatial ontologies and it can be used to shed light on Husserl's general claim that there are different ontologies in the eidetic sciences that can be systematically related to one another. The paper is rounded out with a consideration of the role of ideation in the origins of modern geometry, and with a brief discussion of the use of ideation outside of pure geometry. (shrink)

We experience the intuition of distinctness when, for example, we attend introspectively to the phenomenal redness of a current visual sensation and it seems to us that that very property could not literally be a physical property of neural activity in a certain tiny region of our brain. The book begins by arguing that the intuition of distinctness underlies certain otherwise puzzling attitudes manifested in debates both inside and outside philosophy about whether physicalism (or materialism) can accommodate phenomenal (...) properties (or qualia). It then argues systematically against the dualist suggestion that the intuition of distinctness gives us reason to reject the physicalist view that phenomenal properties are physical, and to adopt property dualism instead. In the course of the argument, it defends an unorthodox version of representationalism and offers positive accounts of what makes our introspective knowledge of phenomenal properties special, how introspection could tell us that an introspected property is physical, and what the subjectivity of phenomenal properties could be. Finally, after critically surveying previous attempts to account for the intuition of distinctness consistently with physicalism, it elaborates a novel explanation of the intuition of distinctness. The intuition arises because introspection is, in a certain way, conceptually encapsulated, as a result of which we are unable to do something that we can do in the case of every other kind of identity claim that we believe or entertain, and therefore unable to believe, or even to imagine believing, that an introspected phenomenal property is physical. (shrink)

In recent literature on the metaphysics of consciousness, and in particular on the prospects of physicalism, there are two interesting strands of discussion. One strand concerns the so-called ‘thesis of revelation’, the claim that the essences of phenomenal properties are revealed in experience. The other strand concerns the intuition of dualism, the intuition that consciousness is nonphysical. With a particular focus on the former, this paper advances two main arguments. First, it argues that the thesis of revelation is (...) intuitive; it is part of our ordinary, implicit conception of experience. Second, it brings the two strands of discussion together and puts forward a rational explanation of the intuition of dualism in terms of the intuitiveness of the thesis of revelation. (shrink)

Semantic holism has it that the semantic properties of an individual expression are determined by that expression.

Elijah Chudnoff elaborates and defends a view of intuition according to which intuition purports to, and reveals, how matters stand in abstract reality by making us aware of that reality through the intellect. He explores the experience of having an intuition; justification for beliefs that derives from intuition; and contact with abstract reality.

ABSTRACT ABSTRACT: This paper provides a multifaceted account of intuition. The paper integrates apparently disparate conceptions of intuition, shows how the notion has figured in epistemology as well as in intuitionistic ethics, and clarifies the relation between the intuitive and the self-evident. Ethical intuitionism is characterized in ways that, in phenomenology, epistemology, and ontology, represent an advance over the position of W. D. Ross while preserving its commonsense normative core and intuitionist character. This requires clarifying the sense in (...) which intuitions are non-inferential and explaining how self-evident principles may be maintained without dogmatism, how intuition is significantly analogous to perception, and how rational disagreements can extend even to the self-evident. The paper distinguishes between two orders of normative disagreement, shows how intuition can contribute to resolving normative disagreements, and represents ethical intuitionism as capable of modified forms that depart from its traditional claims in being neutral with respect to both ethical naturalism and metaphysical realism. (shrink)

This article examines whether people share the Gettier intuition (viz. that someone who has a true justified belief that p may nonetheless fail to know that p) in 24 sites, located in 23 countries (counting Hong Kong as a distinct country) and across 17 languages. We also consider the possible influence of gender and personality on this intuition with a very large sample size. Finally, we examine whether the Gettier intuition varies across people as a function of (...) their disposition to engage in “reflective” thinking. (shrink)

��Is moral judgment accomplished by intuition or conscious reasoning? An answer demands a detailed account of the moral principles in question. We investigated three principles that guide moral judgments: (a) Harm caused by action is worse than harm caused by omission, (b) harm intended as the means to a goal is worse than harm foreseen as the side effect of a goal, and (c) harm involving physical contact with the victim is worse than harm involving no physical contact. Asking (...) whether these principles are invoked to explain moral judgments, we found that subjects generally appealed to the first and third principles in their justifications, but not to the second. This finding has significance for methods and theories of moral psychology: The moral principles used in judgment must be directly compared with those articulated in justification, and doing so shows that some moral principles are available to conscious reasoning whereas others are not. (shrink)

In this thesis I seek to advance our understanding of what intuitions are. I argue that intuitions are experiences of a certain kind. In particular, they are experiences with representational content, and with a certain phenomenal character. -/- In Chapter 1 I identify our target and provide some important reliminaries. Intuitions are mental states, but which ones? Giving examples helps: a person has an intuition when it seems to her that torturing the innocent is wrong, or that if something (...) is red it is coloured. We can also provide an initial characterisation of the state by saying that it has representational content, often causes belief, and appears to justify belief. In addition, there is something it is like to have an intuition: intuition has a certain phenomenal character. -/- Some argue that intuition does not explain anything which cannot be explained by other mental states. One version of this view takes intuition to reduce to belief. In Chapter 2 I argue that this entails that agents are rationally criticisable in situations where we know they are not, and that such views are therefore untenable. A parallel argument shows that the corresponding approach to perception fails. This suggests a similarity in nature: both intuition and perception are experiences. -/- Others take intuition to reduce to a disposition to have a belief. In Chapter 3 I consider a line of argument against such views, find it unsuccessful, and present two new arguments. One is likely to be dialectically ineffective. The other suffers no such weakness: it shows that the proposed reduction fails. As before, the argument also applies to perception, and suggests that intuition and perception are both experiences. -/- In the remainder of the thesis I develop an account of intuition as an experience. I distinguish between content-specific and attitude-specific phenomenology, and argue that intuition lacks the former (Chapter 4), but has the latter (Chapter 5). This allows us to say what intuition is: it is is an experience with representational content and with attitude-specific phenomenology of a certain kind. -/- In Chapter 6 I put this account of intuition to use. When a person has a perceptual or intuitional experience, I argue that simply having the experience is what makes the subject justified in believing what the experience represents. Moreover, what explains that intuition and perception can justify belief in this way is precisely their phenomenal character. (shrink)

The intuition of neutrality, as discussed by John Broome, says that the addition of people does not, by itself, produce or subtract value from the world. Such intuition allows us to disregard the effects of climate change policy onto the size of populations, effectively allowing us to make policy recommendations. Broome has argued that the intuition has to go. Orsi responds by urging a normative (rather than Broome's axiological) interpretation of neutrality in terms of an exclusionary permission (...) to disregard the value of adding lives. He explores justifications and limits of such permission by referring to the prospect of human extinction. (shrink)

The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and (...) logarithmic mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education. (shrink)

"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes (...) portrayed as if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book. (shrink)