In this paper, I argue that Dual Process Theories of cognition offer a useful framework to understand the nature and role of concepts in cognitive science and intuitions in epistemology.

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 foundation of Mathematics is both a logico-formal issue and an epistemological one. By the first, we mean the explicitation and analysis of formal proof principles, which, largely a posteriori, ground proof on general deduction rules and schemata. By the second, we mean the investigation of the constitutive genesis of concepts and structures, the aim of this paper. This “genealogy of concepts”, so dear to Riemann, Poincaré and Enriques among others, is necessary both in order to enrich the (...) foundational analysis with an often disregarded aspect (the cognitive and historical constitution of mathematical structures) and because of the provable incompleteness of proof principles also in the analysis of deduction. For the purposes of our investigation, we will hint here to a philosophical frame as well as to some recent experimental studies on numerical cognition that support our claim on the cognitive origin and the constitutive role of mathematical intuition. (shrink)

I start with a brief look at what the classic British intuitionists (Ewing, Broad, Ross) had to say about the relation between judgment and emotion. I then look at some more recent work in the intuitionist tradition and try to develop a conception of moral emotion as a form of practical seeming, suggesting that some moral intuitions are exactly that sort of emotion. My general theme is that the standard contrast between intuition and emotion is a mistake and that (...) intuitionism can happily accommodate the results of recent work in empirical moral psychology. (shrink)

This paper engages with Kant‘s account of space as a continuum. The stage is set by looking at how the question of spatial continuity comes up in a debate from the 1920s between Ernst Cassirer and logical empiricist thinkers about Kant‘s conception of spatial representation as a pure intuition. While granting that concrete features of space can only be known empirically, Cassirer attempted to save Kant‘s conception by restricting it to the core commitment of space as a continuous coexistent (...) manifold. Cassirer did not however come up with a transcendental argument for spatial continuity. The paper presents such an argument by providing a reading of Kant‘s from which it transpires that Kant does not simply rely on supposed into the continuity of space. It is by way ofinstead that we can know space to be continuous and Kant’s distinction between intuitions and concepts does hinge on such knowledge. (shrink)

Gerald Harrison has argued that the readiness with which we have and agree to moral intuitions about the value of disembodied persons shows that persons are essentially non-material, for if we were essentially material we would not so easily be able to ascribe moral value to an impossible non-material person. To support this point, he advances a somewhat novel metaphor of intuitions as a "call" to a help desk which can answer our queries about counter-factual scenarios. I first point out (...) that the help desk metaphor is not only compatible with, but actually suggestive of, the possibility of systematic error on the part of our intuitions. But more crucially, rapid acquisition of and widespread agreement on even plausible intuitions about counter-factual scenarios does nothing to show that the counter-factual scenarios are possible, let alone true, giving several other counter-examples to this idea. I conclude with the suggestion that imagining such counter-factual scenarios should not be seen as a mode of accessing a fixed source of truths in a "help desk" manual, but as a constructive way of understanding the relationship between concepts, and hence ultimately as a mode of writing small parts of this heretofore unwritten text. (shrink)

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)

A popular argument supporting functionalism has been what is commonly called the “multiple realizability” argument. One version of this argument uses thought experiments designed to show that minds could be composed of different types of material. This article offers a metaphilosophical analysis of this argument and shows that it fails to provide a strong case for functionalism. The multiple realizability argument is best understood as an inference‐to‐the‐best‐explanation argument, whereby a functionalist account of our mental concepts serves to explain our (...) multiple realizability intuitions. I show that the argument is inadequate because alternative accounts of our mental concepts exist that provide equally plausible explanations for these intuitions. Moreover, in the case of our qualia concepts, a nonfunctionalist account explains several other intuitions that functionalism cannot explain. Thus, despite its popularity, the intuition‐based version of the multiple realizability argument is a poor reason for accepting functionalism. (shrink)

Humans have two kinds of beliefs, intuitive beliefs and reflective beliefs. Intuitive beliefs are a fundamental category of cognition, defined in the architecture of the mind. They are formulated in an intuitive mental lexicon. Humans are also capable of entertaining an indefinite variety of higher‐order or‘reflective’propositional attitudes, many of which are of a credat sort. Reasons to hold reflective beliefs are provided by other beliefs that describe the source of the reflective belief as reliable, or that provide an explicit argument (...) in favour of the reflective belief. The mental lexicon of reflective beliefs includes not only intuitive, but also reflective concepts. (shrink)

One of the reasons for Carnap’s (1922) analysis of space was the confounding status of many arguments around the state of the art on that topic at that time. The unsatisfactory views supplied by mathematicians, physicists and philosophers led Carnap to propose a new conception of space. His proposal, which employs the notion of intuition as a fundamental tool, fared better, but clashed with his conventionalists intentions derived from an allegedly tolerant attitude. The notion of intuition here examined (...) allows us to claim that Carnap’s target was also an objectivist epistemological program dependent on certain realistic reminiscences embodied in the notion of evidence or matter of fact (Tatbestand). (shrink)

My dissertation examines prominent arguments for and against the use of intuition in philosophical theorizing. Many of the concerns I raise involve areas of oversimplification - particularly concerning the relationship between the reliability of our intuitions and their evidential status. Specifically, I argue that there are two primary barriers to framing the intuition debate as a simple question about whether intuitions are either unreliable and therefore wholly unsuitable for use in philosophy, or reliable and therefore always suitable for (...) philosophical use. The first of these barriers involves the widespread assumption that intuition forms a fairly cohesive, fairly natural mental kind which can be usefully evaluated for reliability. The second involves the assumption that anyone who questions the suitability of intuitions as evidence must deny that intuitions are reliable enough to constitute knowledge. A further theme of my dissertation involves the relationship between the categories delineated by our intuitive classifications and the categories which serve as the targets of philosophical investigation. I examine two major approaches to this relationship - the ‘mentalist’ view, according to which the targets of philosophical analysis are our own concepts, and the ‘extramentalist’ view, according to which the targets of philosophy are external phenomena ‘in the world’. I conclude that both projects are legitimate, but that only the former justifies the commonly held view that there exists a sort of ‘constitutive’ relationship between intuitions and truth. Ultimately, I advocate a position according to which use of intuition in philosophy should be restricted, but not eliminated. (shrink)

The failure of current bootstrapping accounts to explain the emergence of the concept of natural numbers does not entail that no link exists between intuitive and formal number concepts. The epidemiology of representations allows us to explain similarities between intuitive and formal number concepts without requiring that the latter are directly constructed from the former.

Pascal is well known to be an early modern disciple of Augustine, but it has not always been sufficiently emphasized that Pascal’s Augustinianism differs profoundly from its source in many ways. The following essay examines his re-ordering of Augustine’s psychology and its implications for philosophy and religion in the modern period. For Augustine, intellect and will are equal moments in the activity of mens, but Pascal is radically voluntarist. For him, the will’s relation to the good radically transcends intellect’s relation (...) to being. This moves Pascal to a position closer in some respects to neo-Platonism. It also prevents him from appropriating Augustine’s claim that the triadic human mens is a created analogue of the Trinity. Pascal drops Augustine’s teaching on this point, with profound consequences for his conception of humanity’s relation to God. (shrink)

This dissertation is a contribution to the field of empirically informed metaethics, which combines the rigorous conceptual clarity of traditional metaethics with a careful review of empirical evidence. More specifically, this work stands at the intersection of moral psychology, moral epistemology, and philosophy of action. The study comprises six chapters on three distinct (although related) topics. Each chapter is structured as an independent paper and addresses a specific open question in the literature. The first part concerns the psychological features and (...) cognitive function of moral intuition. Chapter 1 (“Moral intuition, strength, and metacognition”) is focused on the concept of intuitive strength, which is one of the defining features of moral intuition. I provide a metacognitive account of intuitive strength and show why such a view is preferable to emotional or quasi-perceptual accounts. Then, in Chapter 2 (“Dual process reflective equilibrium”), I will discuss the interplay between intuition and reflection in moral reasoning. I will contend that the influential “default-interventionist” model of reasoning, theorized by Greene, is insufficiently supported by the evidence. In light of some recent studies, I outline an account of moral reasoning in which intuition and reflection are not in conflict but cooperate to reach a reflective goal. I call this model dual process reflective equilibrium. The aim of the first part is descriptive, i.e., it argues for an accurate understanding of moral intuition and reasoning in light of the available empirical evidence. In contrast, the second part addresses a normative question: is a subject epistemically justified in forming a belief on the basis of a moral intuition? Skeptics of moral intuition argue that accepting moral intuitions should be the exception rather than the rule to the extent that epistemically defective processes determine the content of moral intuitions. Chapter 3 (“Moral intuitionism and the reliability challenge”) introduces the recent empirical challenges to the reliability of moral intuitions and elaborates a promising strategy for defending intuitionism. In short, I consider whether subjects can track the reliability of their intuitions with their confidence. In Chapter 4 (“The argument from limited cognitive resources”), I evaluate a different strategy to defend moral intuitionism. Specifically, I develop an argument according to which accepting moral intuitions is legitimate because it is the most rational option that a subject has, given her limited resources. The third and final part of the dissertation concerns the role of moral intuitions in action. The influence of automatic processes on moral conduct raises different challenges to moral philosophy. The first challenge is to explain how a subject can be motivated by certain values without the mental effort of deliberation. Chapter 5 (“Caring, moral motivation, and automatic conduct”) tackles this issue. Chapter 6 (“Moral sensitivity as skillful automaticity”) aims to explain how moral agents can be sensitive to good reasons through automatic mental processes. (shrink)

In this paper I explicate the notion of “presence” [Gegenwart] as it pertains to intuition. Specifically, I examine two central problems for the position that an empirical intuition is an immediate relation to an existing particular in one’s environment. The first stems from Kant’s description of the faculty of imagination, while the second stems from Kant’s discussion of hallucination. I shall suggest that Kant’s writings indicate at least one possible means of reconciling our two problems with a conception (...) of “presence” such that perceptual and hallucinatory states might be understood as different kinds of intuition. This may not be sufficient to secure the relationalist’s claim that intuition is an immediate relation to an existing particular in one’s environment, but it does show that opposition to this claim will require further argument. (shrink)

While engaged in the analysis of topics such as the nature of knowledge, meaning, or justice, analytic philosophers have traditionally relied extensively on their own intuitions about when the relevant terms can, and can't, be correctly applied. Consequently, if intuitions about possible cases turned out not to be a reliable tool for the proper analysis of philosophically central concepts, then a radical reworking of philosophy's (or at least analytic philosophy's) methodology would seem to be in order. It is thus (...) not surprising that the increasingly critical scrutiny that intuitions have received of late has produced what has been referred to as a "crisis" in analytic philosophy. This paper will argue, however, that at least those criticisms that stem from recent work on semantic externalism are not as serious as their proponents have claimed. Indeed, this paper will argue while the conceptual intuitions (and the analyses that result from them) will have to be recognized as fallible, they still have a prima facie claim to correctness. A naturalistic and externalistic account of concepts thus merely requires that the methodology of conceptual analysis be reinterpreted (from a 'Platonic' to a 'constructive' model) rather than given up. (shrink)

The problem of ‘collective unity’ in the transcendental philosophies of Kant and Husserl is investigated on the basis of number’s exemplary ‘collective unity’. To this end, the investigation reconstructs the historical context of the conceptuality of the mathematics that informs Kant’s and Husserl’s accounts of manifold, intuition, and synthesis. On the basis of this reconstruction, the argument is advanced that the unity of number – not the unity of the ‘concept’ of number – is presupposed by each transcendental philosopher (...) in their accounts of the transcendental foundation of manifold, intuition, and synthesis. This presupposition is ultimately traced to Kant’s and Husserl’s responses to Hume’s philosophy of human understanding and the critical limits of what Kant calls the ‘qualitative’ unity of transcendental consciousness. These critical limits are exposed in both philosophers’ attempts to account for that ‘qualitative’ unity on the basis of the ‘quantitative’ unity of number. (shrink)

To gain insight into human nature philosophers often discuss the inferior performance that results from deficits such as blindsight or amnesia. Less often do they look at superior abilities. A notable exception is Herbert Dreyfus who has developed a theory of expertise according to which expert action generally proceeds automatically and unreflectively. We address one of Dreyfus’s primary examples of expertise: chess. At first glance, chess would seem an obvious counterexample to Dreyfus’s view since, clearly, chess experts are engaged in (...) deep strategic thought. However, Dreyfus’s argument is subtle. He accepts that analysis and deliberation play a role in chess, yet he thinks that all such thought is predicated on intuitive, arational expert perception, and action. We argue that even the so-called intuitive aspect of chess is rational through and through. (shrink)

Mathematicians often describe the importance of well-developed intuition to productive research and successful learning. But neither education researchers nor philosophers interested in epistemic dimensions of mathematical practice have yet given the topic the sustained attention it deserves. The trouble is partly that intuition in the relevant sense lacks a usefully clear characterization, so we begin by offering one: mature intuition, we say, is the capacity for fast, fluent, reliable and insightful inference with respect to some subject matter. (...) We illustrate the role of mature intuition in mathematical practice with an assortment of examples, including data from a sequence of clinical interviews in which a student improves upon initially misleading covariational intuitions. Finally, we show how the study of intuition can yield insights for philosophers and education theorists. First, it contributes to a longstanding debate in epistemology by undermining epistemicism, the view that an agent’s degree of objectual understanding is determined exclusively by their knowledge, beliefs and credences. We argue on the contrary that intuition can contribute directly and independently to understanding. Second, we identify potential pedagogical avenues towards the development of mature intuition, highlighting strategies including adding imagery, developing associations, establishing confidence and generalizing concepts. (shrink)

The conception of a ‘law of nature’ is a human product. It was created to play a role in natural philosophy, in the Cartesian tradition. In light of this, philosophers and scientists must sort out what they mean by a law of nature before evaluating rival theories and approaches. If one’s conception of the laws of nature is yoked to metaphysical notions of truth and explanation, that connection must be made explicit and defended. If, on the other hand, one’s aim (...) is to disentangle laws from truth or from explanation, that must be stated and defended as well. If philosophers do not make such assumptions, intuitions, and methodological commitments clear, then it will be impossible to identify the source of disagreement in debates about the laws of nature. Are the conflicts rooted in disagreement about the conclusions reached, or do the background commitments of the combatants block any resolution to the dispute in principle or in practice? (shrink)

Intuitive judgments elicited by verbal case-descriptions play key roles in philosophical problem-setting and argument. Experimental philosophy's ‘sources project’ seeks to develop psychological explanations of philosophically relevant intuitions which help us assess our warrant for accepting them. This article develops a psycholinguistic explanation of intuitions prompted by philosophical case-descriptions. For proof of concept, we target intuitions underlying a classic paradox about perception, trace them to stereotype-driven inferences automatically executed in verb comprehension, and employ a forced-choice plausibility-ranking task to elicit the relevant (...) stereotypical associations of perception- and appearance-verbs. We obtain a debunking explanation that resolves the philosophical paradox. (shrink)

Modal intuitions are not only the primary source of modal knowledge but also the primary source of modal error. An explanation of how modal error arises — and, in particular, how erroneous modal intuitions arise — is an essential part of a comprehensive theory of knowledge and evidence. This chapter begins with a summary of certain preliminaries: the phenomenology of intuitions, their fallibility, the nature of concept-understanding and its relationship to the reliability of intuitions, and so forth. It then identifies (...) two sources of modal error: the first has to do with the failure to distinguish between metaphysical possibility and various kinds of epistemic possibility; the second, with the local misunderstanding of one's concepts. The first source of error is widely misunderstood; the second source has not been discussed in philosophical literature. This source of modal error, and the potential to overcome it, has wide-ranging implications for philosophical method. The failure to understand these sources of modal error has recently led to sceptical accounts of intuition and modal error, which are, ultimately self-defeating. (shrink)

1. What are called ‘intuitions’ in philosophy are just applications of our ordinary capacities for judgement. We think of them as intuitions when a special kind of scepticism about those capacities is salient. 2. Like scepticism about perception, scepticism about judgement pressures us into conceiving our evidence as facts about our internal psychological states: here, facts about our conscious inclinations to make judgements about some topic rather than facts about the topic itself. But the pressure should be resisted, for it (...) rests on bad epistemology: specifically, on an impossible ideal of unproblematically identifiable evidence. 3. Our resistance to scepticism about judgement is not simply epistemic conservativism, for we resist it on behalf of others as well as ourselves. A reason is needed for thinking that beliefs tend to be true. 4. Evolutionary explanations of the tendency assume what they should explain. Explanations that appeal to constraints on the determination of reference are more promising. Davidson’s truth-maximizing principle of charity is examined but rejected. 5. An alternative principle is defended on which the nature of reference is to maximize knowledge rather than truth. It is related to an externalist conception of mind on which knowing is the central mental state. 6. The knowledge-maximizing principle of charity explains why scenarios for scepticism about judgement do not warrant such scepticism, although it does not explain how we know in any particular case. We should face the fact that evidence is always liable to be contested in philosophy, and stop using talk of intuition to disguise this unpleasant truth from ourselves. (shrink)

Content externalism, as defended by Hilary Putnam, Tyler Burge and several others, is the thesis that the content of our thoughts at a given moment is not uniquely determined by our internal states at that moment. In its causalist version, it has often been presented as a deep revolution in philosophy of mind. Yet a number of medievalists (e.g. Peter King, Calvin Normore, Gyula Klima, and myself) have recently stressed the presence of significant externalist tendencies in late-medieval nominalism, especially in (...) William of Ockham. Now this interpretation has been cleverly challenged in the case of Ockham by Susan Brower-Toland in 2007, with arguments focusing upon Ockham’s theory of intuitive cognition (precisely where the externalist reading had seemed to be the most secured). The present paper is a reply to this challenge. I first summarize the case for seeing Ockham’s theory of intuitive cognition as a causal and externalist approach, and then critically review Brower-Toland’s arguments against it. The whole discussion, as it turns out, sheds new light upon Ockham’s conception of causality and natural order. (shrink)

Using a prototype approach, we assessed people’s lay conceptions of intuition and analysis. Open-ended descriptions of intuition and analysis were generated by participants (Study 1) and resulting exemplars were sorted into features subsequently rated in centrality by independent participants (Study 2). Feature centrality was validated by showing that participants were quicker and more accurate in classifying central (as compared to peripheral) features (Study 3). Centrality ratings suggested a single-factor structure describing analysis but revealed that participants held lay conceptions (...) of intuition as involving two different types of processes: (1) as an automatic, affective, and non-logical processing, and (2) as a holistic processing that can assist in problem-solving. Additional analyses showed that the centrality ratings of intuition’s facets were predicted by participants’ self-reported intuitive style, suggesting intuition is differently perceived by intuitive and non-intuitive people. We discuss the implications of these results for the study of intuition and analysis. (shrink)

The debate on the value of Boyer's minimally counter-intuitive theory continues to generate considerable theoretical and empirical attention. Although the theory offers an explanation as to why certain cultural texts and narratives are particularly well conveyed and transmitted, amidst society and over time, conflicting evidence remains for any mnemonic advantage of minimally counter-intuitive concepts. In an effort to reconcile these conflicting results, Barrett has made a comprehensive attempt in presenting a formal system for quantifying counter – intuitiveness including a (...) distinction between counter-intuitive and counter-schematic concepts. The present article uses this system to generate sentences containing different levels of counter-intuitiveness, and tests whether minimally counter-intuitive items show a mnemonic advantage over concepts which are more counter-intuitive or counter-schematic. Results indicate that MCI concepts hold a mnemonic advantage over counter-schematic and maximally counter-intuitive concepts but only for one-week delayed recall. Interference effects may have masked immediate recall effects. Yes-no recognition after one week delay showed almost 100% accuracy suggesting that availability of retrieval cues is the factor which determines the mnemonic advantage of MCI concepts. (shrink)

There are a number of well-established concepts explaining decision-making. The sociology of wise practice suggests that thinking preferences like the use of intuition form a cornerstone of administrators’ virtuous practice and phronesis is a likely candidate to explain this behaviour. This contribution uses conceptual and theoretical resources from the behavioural sciences, management science as well as philosophy to account for individual level differences of employees regarding thinking preferences in administrative professions. The analysis empirically investigates the behavioural dimension of (...) the preference for intuition vs the preference for deliberation to cast light on three different intuitive markers present among individuals who also prefer to use deliberation. We explore possible explanations for the differences and similarities of our global sample of 2227 workplace respondents who conceptually represent phronetic practitioners. The results show that many phronetic practitioners prefer the intuitive marker of unconscious thought, besides using deliberation. (shrink)

Traditionally, intuitions about cases have been taken as strong evidence for a philosophical position. I argue that intuitions about concept deployment have epistemic value while intuitions about matters of fact have none. I argue this by use of the explanationist criterion which contends that S is justified in believing only those propositions which are part of the best explanation of S’s making the judgements she makes. This criterion accords with scientific practice. Bealer suggests, as a defence of intuition, that (...) naturalists rely on intuition in their arguments against intuition and thus that their arguments are self-undermining. But beliefs based on intuitions about the application of concepts, like ‘justification’ and ‘theory,’ are epistemically justified by the explanationist criterion. It is only intuitions about matters of fact which are rejected. Thus, epistemically-respectable intuitions about concepts are used to undermine intuitions about metaphysics. There is nothing self-undermining about this. (shrink)

It has been argued within the new cognitive science of religion that people's actual religious concepts and inferences differ from their explicitly held religious concepts and beliefs; the latter are too complex to be used in fast online reasoning. Natural intuitions thus tend to overwrite theological doctrine and to drive behavior. The cognitive science of religion has focused on this intuitive aspect of religion, ignoring theological thought. Here I try to outline a theoretical model on the basis of (...) which it should be possible to explain the interaction of the intuitive and explicit processes in religious cognition. (shrink)

I address a criticism of the use of thought experiments in conceptual analysis advanced on the basis of the survey method of so-called experimental philosophy. The criticism holds that surveys show that intuitions are relative to cultures in a way that undermines the claim that intuition-based investigation yields any objective answer to philosophical questions. The crucial question is what intuitions are as philosophers have been interested in them. To answer this question we look at the role of intuitions in (...) philosophical inquiry. When we have done this, we can see that it is impossible for intuitions properly understood to be relative in the way that has been suggested as they are conceived of as expressions of competence in the concepts deployed in their contents. The remaining methodological issues, though not to be dismissed, present no in principle objection to the method of thought experiments. (shrink)

In this paper, I discuss Gaston Bachelard’s criticism of Henri Bergson’s employment of intuition as the specific method of philosophy, and as a reliable means of acquiring knowledge. I locate Bachelard’s criticism within the reception of Bergsonian intuition by rationalist philosophers who subscribed to the Third Republic’s ethos. I argue that the reasons of Bachelard’s rejection of Bergsonian intuition were not only epistemological, but also ethical and pedagogical. His view of knowledge as mediated, social, and historical, cannot (...) be separated from his conceptions of society, education, and the human being. (shrink)

The article is devoted to philosophy of mathematics. Mathematical heuristics, being a complex of methods for solving the non-standard problems of mathematics (such problems which have no known algorithms to be solved), is the main subject of the research. As a specific mechanism for thinking, generating elements of guesswork needed as the basis of mathematical heuristics, the author considers intuition. In the work, the author uses Descartes’s, Poincaré’s, Hadamard’s and Piaget’s findings. Based on Descartes’s concept of rational intuition, (...) the author develops the concept of heuristic intuition. As a result, the author turns to the question of possibility of a complete translation of the user-derived mathematical statements in a discourse, in fact, that means a maximum depth of mathematical proof, i.e. its maximum rationalization. For this purpose, it is necessary to re-attract the intuition since it is able to transform the intuitive elements into the discourse ones. Therefore, from this point of view, the rationale is intuitively derived mathematical proof should be no more than a ‘multilayer‘ creative process. In general, the author, based on Poincaré’s research, proves that the essence of mathematical creativity is not to «sort out» and «choose». Referring to examples for illustration, the author reveals moments of «interference» of intuition, even in the process of solving school problems. Therefore, it is currently impossible to ignore the phenomenon of intuition and the results that have been historically derived a theory of knowledge in the study of creative mechanisms. (shrink)

Mathematical apriorists sometimes hold that our non-derived mathematical beliefs are warranted by mathematical intuition. Against this, Philip Kitcher has argued that if we had the experience of encountering mathematical experts who insisted that an intuition-produced belief was mistaken, this would undermine that belief. Since this would be a case of experience undermining the warrant provided by intuition, such warrant cannot be a priori.I argue that this leaves untouched a conception of intuition as merely an aspect of (...) our ordinary ability to reason. Thus the apriorist may still hold that some mathematical beliefs are warranted by intuition. (shrink)

This paper considers one of the most controversial aspects of Friedrich Schelling’s philosophy, his notion of intellectual intuition and its place within his philosophy of nature. I argue that Schelling developed his account of intellectual intuition through an encounter with--and ultimate critique of--Spinoza’s third kind of knowledge. Thus, Schelling’s notion of intuition was not an appropriation of Fichte’s conception of intuition as an act of consciousness. Nonetheless, and in spite of his sympathy with Spinoza, Schelling contended (...) that intellectual intuition must be “productive” or “constructive.” I explicate how Schelling justified his use of intellectual intuition in his Naturphilosophie, and detail its relation to his notion of the philosophical “construction” of nature. (shrink)

Despite his unreserved appreciation of Turing’s analysis for being a “precise and unquestionably adequate definition” of formal system or mechanical computability, Gödel nevertheless published a short note in 1972 claiming to have found a “philosophical error” in Turing’s argument with regard to the finite nature of mental states and memory. A natural question arises: how could Gödel enjoy the generality conferred on his results by Turing’s work, despite the error of its ways? Previous interpretative strategies by Feferman, Shagrir and others (...) have mainly tried to resolve the disparity by distinguishing different types of arguments in Turing and taking Gödel to approve only some of them. By a more integral examination of their ideas, especially Turing’s response to the “mathematical objection” based on Gödel’s incompleteness theorem and Gödel’s own conception of finite yet non-mechanical procedures, and taking some of the main ideas of current developments in machine learning into consideration, I will try to present a new explanation for the apparent disparity, arguing that there is no “error” on Turing’s side and the seemingly conflicting views held by Turing and Gödel should best be seen as complementary, keeping intuition and ingenuity together. (shrink)

Manifest reality is easily one of the best books in a long time on Kant’s transcendental idealism. So there is a great deal in Allais’s discussion to celebrate. But I want to focus here on two aspects of her views that I am not yet sure about: First, Allais’s understanding of the relationship between concepts and intuitions. And second, her characterization of the manner in which intuitions are object-dependent. I’ll close by making some general remarks about the significance of (...) this for Allais’s understanding of the metaphysics of transcendental idealism. (shrink)

In his first philosophy book, Science and Hypothesis, Poincare provides a picture in which the different sciences are arranged in a hierarchy. Arithmetic is the most general of all the sciences because it is presupposed by all the others. Next comes mathematical magnitude, or the analysis of the continuum, which presupposes arithmetic; and so on. Poincare's basic view was that experiment in science depends on fixing other concepts first. More generally, certain concepts must be fixed before others: hence (...) the hierarchy. This paper attempts to dissolve some potential problems regarding Poincare's hierarchy. One is an apparent epistemological circularity in the hierarchy. A more serious problem regarding the epistemology of analysis is also addressed. (shrink)

Intuition is a concept of western philosophy, and phenomenology holds that under the influence of intuition, the concept of things and thing-in-itself can be well distinguished. Intuition as a method is feasible, and consciousness obtains content through intuition, especially in event analysis, where the phenomenon is the essence. However, phenomena have a dual nature, intuition stimulates intuition and is the exclusive of the mind, which is called mind view in Buddhism, both of which are (...) different from the way of “I think”, but emphasize “I see”, the object of intuition can be the phenomenal world, or consciousness itself, intuition dispels language, accompanied by the spontaneous receptivity of the heart. Buddhism believes that it is impossible for people to strictly distinguish between subject and object in the process of cognition, which is bound to be the blending of mood, even illusory. The phenomenal world is the manifestation of life consciousness. In the face of perceptual experience such as color, sound, fragrance, taste and touch, people can go deep into their hearts and see the consciousness itself frankly. The ancient sages and sages of China found that “view” is closely related to understanding, such as Nagarjuna’s “middle view”. Tiantai’s “one mind and three views”, even in the Western context, cannot escape the metaphysical and transcendental color. Mou Zongsan thought that it was the biggest and most essential difference between Chinese and Western philosophy (Mou, 2001). Buddhism attaches great importance to the body and function of “view”. To some extent, the view of mind is the same as intuition. This paper focuses on the analysis of the possibility of intuitive reduction from the perspective of Buddhist “view of mind”, and advocates that before rational judgment, intuition should be given enough priority, and after rational judgment, mind should be given enough repetition. It further distinguishes the transcendental illusion brought about by intuition, and reveals the efforts of Buddhism to touch transcendental philosophy through the way of mind. (shrink)