A controversial claim in recent dual process accounts of reasoning is that intuitive processes not only lead to bias but are also sensitive to the logical status of an argument. The intuitive logic hypothesis draws upon evidence that reasoners take longer and are less confident on belief–logic conflict problems, irrespective of whether they give the correct logical response. In this paper, we examine conflict detection under conditions in which participants are asked to either judge the logical (...) validity or believability of a presented conclusion, accompanied by measures of eye movement and pupil dilation. The findings show an effect of conflict, under both types of instruction, on accuracy, latency, gaze shifts, and pupil dilation. Importantly, these effects extend to conflict trials in which participants give a belief‐based response (incorrectly under logic instructions or correctly under belief instructions) demonstrating both behavioral and physiological evidence in support of the logical intuition hypothesis. (shrink)

It is well established that beliefs provide powerful cues that influence reasoning. Over the last decade research has revealed that judgments based upon logical structure may also pre-empt deliberative reasoning. Evidence for ‘intuitive logic’ has been claimed using a range of measures (i.e. confidence ratings or latency of response on conflict problems). However, it is unclear how well such measures genuinely reflect logical intuition. In this paper we introduce a new method designed to test for evidence of (...) class='Hi'>intuitive logic. In two experiments participants were asked to make random judgments about the logical validity of a series of simple and complex syllogistic arguments. For simple arguments there was an effect of logical validity on random responding, which was absent for complex arguments. These findings provide a novel demonstration that people are intuitively sensitive to logical structure. (shrink)

Claims concerning what is or is not possible abound in contemporary philosophy. The epistemology of such claims, however, remains largely unexplored. Anything imaginable is possible, we are told, with the proviso that imagination be governed by logic. Many who defend this methodology argue that logic frees us from recourse to some mysterious a priori faculty of intuition. Anything is possible so long as it does not contain a contradiction—and we don’t need intuition to tell us what is contradictory, (...) just logic. Logic is thus supposed to provide us with a non-mysterious, intuition-free, modal epistemology. The purpose of this paper is to argue that logic does not deliver on this promise. The argument proceeds along two fronts. First, I argue that logic is not sufficient for the task. Not only are there consistent but impossible propositions, there are even inconsistent propositions that are possible. Second, and more fundamentally, I question the epistemic independence of appeals to logical consistency. I will argue that in judging a proposition to be consistent we rely upon our intuitions concerning what is possible. In other words, our modal beliefs undergird our judgments about consistency and not vice-versa. (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)

This collection of new essays offers a 'state-of-the-art' conspectus of major trends in the philosophy of logic and philosophy of mathematics. A distinguished group of philosophers addresses issues at the centre of contemporary debate: semantic and set-theoretic paradoxes, the set/class distinction, foundations of set theory, mathematical intuition and many others. The volume includes Hilary Putnam's 1995 Alfred Tarski lectures, published here for the first time.

Intuitions play a significant role in debates about logic. In this paper, I analyze how legitimate is that practice. In the first part of the paper, I distinguish between theoretical and pretheoretical intuitions, and argue that some pretheoretical intuitions are not to be taken into account in logic. Particularly, our pretheoretical intuitions about the concept of validity are not of much importance, since we don’t have a uniform or clear concept of validity in the natural language to be (...) elucidated. Nevertheless, I argue that, since logical connectives are more homogeneously used in our ordinary speech, we can appeal to pretheoretical intuitions to establish their meaning in a logical theory. In the second part of the paper, I consider and reply to four objections to this moderate proposal. Two of them try to show that, if this position is adopted, then the pretheoretical intuitions about the connectives are completely unreliable and useless. One of them argues that this mixed position is unstable: pretheoretical intuitions about the connectives are also pretheoretical intuitions about validity. The last problem is related to the definition of validity and the possibility of revising it. (shrink)

Anti-exceptionalists about logic claim that logical methodology is not different from scientific methodology when it comes to theory choice. Two anti-exceptionalist accounts of theory choice in logic are abductivism and predictivism. These accounts have in common reliance on pre-theoretical logical intuitions for the assessment of candidate logical theories. In this paper, I investigate whether intuitions can provide what abductivism and predictivism want from them and conclude that they do not. As an alternative to these approaches, I propose a (...) Carnapian view on logical theorizing according to which logical theories do not simply account for pre-theoretical intuitions, but rather improve on them. In this account, logical theories are ameliorative, rather than representational. (shrink)

Four known three-valued logics are formulated axiomatically and several completeness theorems with respect to nonstandard intuitive semantics, connected with the notions of information, contrariety and subcontrariety is given.

The split in our thinking between "masculine" and "feminine" is probably as old as language itself. Human beings seem to have a natural tendency to divide things into pairs: good/bad, light/dark, subject/object and so on. It is not surprising, then, that the male/female or masculine/feminine dichotomy is used to classify things other than men and women. Many languages actually classify all nouns as "masculine" or "feminine" (although not very consistently: for example, the Spanish masculine noun pollo means "hen", while the (...) feminine polla is slang for "penis"). This is perfectly natural; it is part of the way categorisation works in language. This does not, however, mean that it is right. It is probably unimportant whether a table or a chair is thought of as masculine or feminine. It may not even be very important these days whether we think of the sun as male and the moon as female (like the ancient Greeks) or vice versa (like most of the German tribes). However, when we start associating abstract concepts like Reason or Nature with men and women, we run into serious difficulties. (shrink)

Some children seem blessed, almost from birth, with a capacity for critical thinking. They won't let a fallacious argument pass unnoticed or unscathed. And some are fortunate enough to be exposed at an early age to fine examples of good reasoning. In their listening and their reading they learn, by intellectual osmosis as it were, to think logically. Yet even these fortunate ones, like the rest of us, can benefit by having their logical intuitions and reasoning skills sharpened by precept (...) and practice. (shrink)

Recent reasoning accounts suggest that people can process elementary logical principles intuitively. These controversial “logical intuitions” are believed to result from a learning process in which developing reasoners automatize their application. To verify this automatization hypothesis, we contrasted the reasoning performance of younger (7th grade) and older (12th grade) reasoners with a two-response paradigm. Participants initially responded with the first intuitive response that came to mind and subsequently were allowed to deliberate on classic “bias” problems (base-rate problems and syllogisms). (...) Results showed that in addition to showing less deliberate correction of an initial erroneous response, younger reasoners were specifically less likely to generate the correct response from the outset. The findings lend credence to the role of a developmental automatization process and indicate that developmental improvements in reasoning accuracy are at least partially driven by an improvement in the accuracy of our intuitions. (shrink)

In this work I study the main tenets of the logicist philosophy of mathematics. I deal, basically, with two problems: (1) To what extent can one dispense with intuition in mathematics? (2) What is the appropriate logic for the purposes of logicism? By means of my considerations I try to determine the pros and cons of logicism. My standpoint favors the logicist line of thought. -/- .

The essay addresses the well‐known idea that there has to be a place for intuition, thought of as a kind of non‐inferential rational insight, in the epistemology of basic logic if our knowledge of its principles is non‐empirical and is to allow of any finite, non‐circular reconstruction. It is argued that the error in this idea consists in its overlooking the possibility that there is, properly speaking, no knowledge of the validity of principles of basic logic. When certain (...) important distinctions are observed, for instance that between recognising that Modus Ponenes is sound and recognising that it is proof against the competent discovery of basic counterexamples, the case for thinking that there is indeed no space for genuine recognition of the validity of Modus Ponens becomes increasingly impressive. It is argued however that, the impossibility of knowledge notwithstanding, we are, in an important sense, entitled to take it that Modus Ponens is sound and that this notion of entitlement can help break the trichotomy ‐ intuition, inference, experience ‐ which imprisons our ordinary thinking about logical knowledge. (shrink)

We use formal semantic analysis based on new constructions to study abstract realizability, introduced by Läuchli in 1970, and expose its algebraic content. We claim realizability so conceived generates semantics-based intuitive confidence that the Heyting Calculus is an appropriate system of deduction for constructive reasoning.Well-known semantic formalisms have been defined by Kripke and Beth, but these have no formal concepts corresponding to constructions, and shed little intuitive light on the meanings of formulae. In particular, the completeness proofs for (...) these semantics do not generate confidence in the sufficiency of the Heyting Calculus, since we have no reason to believe that every intuitively constructive truth is valid in the formal semantics.Läuchli has proved completeness for a realizability semantics with formal concepts analogous to constructions. We argue in some detail that, in spite of a certain inherent inexactness of the analogy, every intuitively constructive truth is valid in Läuchli semantics, and therefore the Heyting Calculus is powerful enough to prove all constructive truths. Our argument is based on the postulate that a uniformly constructible object must be communicable in spite of imprecision in our language, and that the permutations in Läuchli's semantics represent conceivable imprecision in a language, while allowing a certain amount of freedom in choosing the particular structure of the language.We give a detailed generalization of Läuchli's proof of completeness for the propositional part of the Heyting Calculus, in order to make explicit constructive and algebraic content.In our treatment, we establish several new results about Läuchli models. We show how to extend the sconing and gluing constructions familiar from Kripke and Frame semantics and Topos theory, to Läuchli models, and use them to give an algebraic approach to countermodel construction. In particular, the Läuchli arguments are given without the restriction to the integers, Z, as a group of permutations, which makes much of the coding scheme used in Läuchli's original paper transparent.We also make use of a new propositions-as-types syntax for the Heyting calculus, with limited nondeterminism, in which validity of formulae can be decided without loop-detection. (shrink)

This Book Is The Result Of Intensive And Critical Study Of The Different Aspects Of Indian Epistemology Viz. The Nyaya Theory Of Perception, Some Problems Of Meaning In Purva-Mimamsa And Vedanta, Problem Of Vyapti According To Jaina-Logicians And Vallabhacarya Etc.

ABSTRACTThe general assumption that people fail to notice discrepancy between their answer and the normative answer in the conjunction fallacy task has been challenged by the theory of Logical Intuition. This theory suggests that people can detect the conflict between the heuristic and normative answers even if they do not always manage to inhibit their intuitive choice. This theory gained support from the finding that people report lower levels of confidence in their choice after they commit the conjunction fallacy (...) compared to when their answer is not in conflict with logic. In four experiments we asked the participants to give probability estimations to the options of the conflict and no-conflict versions of the tasks in the original set-up of the experiment or in a three-option design. We found that participants perceive probabilities for the options of the conflict version less similar than for the no-conflict version. As people are less confident when choosing between more similar options, this simil.. (shrink)

In an attempt to be rational and objective, and, possibly, to avoid the charge of moral relativism, ethicists seek to categorise and characterise ethical dilemmas. This approach is intended to minimise the effect of the confusing individuality of the context within which ethically challenging problems exist. Despite and I argue partly as a result of this attempt to be rational and objective, even when the logic of the argument is accepted—for example, by healthcare professionals—those same professionals might well respond (...) by stating that the conclusions are unacceptable to them. In this paper, I argue that an interpretative approach to ethical analysis, involving an examination of the ways in which ethical arguments are constructed and shared, can help ethicists to understand the origins of this gap between logic and intuition. I suggest that an argument will be persuasive either if the values underpinning the proposed argument accord with the reader’s values and worldview, or if the argument succeeds in persuading the reader to alter these. A failure either to appreciate or to acknowledge those things that give meaning to the lives of all the interested parties will make this objective far harder, if not impossible, to achieve. If, as a consequence, the narratives ethicists use to make their arguments seem to be about people living in different circumstances, and faced with different choices and challenges, from those the readers or listeners consider important or have to face in their own lives, then the argument is unlikely to seem either relevant or applicable to those people. The conclusion offered by the ethicist will be, for that individual, counterintuitive. Abortion, euthanasia and cadaveric organ donation are used as examples to support my argument. (shrink)

This essay attempts to approach the dispute over the conceptualist or non-conceptualist interpretation of Husserl’s conception of intentional experience from a specific question: Is the intuitive act essentially a carrier of meaning? In the sixth Investigation, Husserl apparently tries to show that intuition is no carrier of meaning and therefore must be unified with a meaning-conferring act in order to be meaningful. But it seems to me that the brief arguments given by Husserl here are far from conclusive and (...) that there are passages in the Logical Investigations which suggest otherwise. I will try to demonstrate that the sense conferred by the interpretation in perception is not different from linguistic meaning, and therefore perception is actually a synthetic act of fulfillment and is always meaningful. The conceptualist reading is no less convincing and no less susceptible to objections than the non-conceptualist one. (shrink)

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This essay aims to provide a modal logic for rational intuition. Similarly to treatments of the property of knowledge in epistemic logic, I argue that rational intuition can be codified by a modal operator governed by the modal $\mu$-calculus. Via correspondence results between fixed point modal propositional logic and the bisimulation-invariant fragment of monadic second-order logic, a precise translation can then be provided between the notion of 'intuition-of', i.e., the cognitive phenomenal properties of thoughts, and the (...) modal operators regimenting the notion of 'intuition-that'. I argue that intuition-that can further be shown to entrain conceptual elucidation, by way of figuring as a dynamic-interpretational modality which induces the reinterpretation of both domains of quantification and the intensions and hyperintensions of mathematical concepts that are formalizable in monadic first- and second-order formal languages. Hyperintensionality is countenanced via a topic-sensitive epistemic two-dimensional truthmaker semantics. (shrink)

This paper is addressed to the problem of how is applied mathematics possible?

often insisted existence in mathematics means logical consistency, and formal logic is the sole guarantor of rigor. The paper joins this to his view of intuition and his own mathematics. It looks at predicativity and the infinite, Poincaré's early endorsement of the axiom of choice, and Cantor's set theory versus Zermelo's axioms. Poincaré discussed constructivism sympathetically only once, a few months before his death, and conspicuously avoided committing himself. We end with Poincaré on Couturat, Russell, and Hilbert.

All along, many commentators stressed the differences of Chinese and Western philosophy and method of Qi, that philosophy and approach to the Western emphasis on analysis, argumentation and logic, and China's philosophical method is longer than intuition, and permits will be realized. Different methods by which they believe will give different results: the knowledge of the outside world through Western methods may be, can be obtained through the French inner truth. The former purpose we got outside, after all is (...) also in the contented. The authors believe that this orthodoxy and popular opinion is a great problem. One problem is: with or without the so-called intrinsic truth, they say, intuitive method of physical certificates but not feasible. In addition to resorting to a very small number of believers of the first-person authority, they can not explain the methods and procedures, they can not prove its effectiveness. In addition, they oppose the West, although on the surface of the speculative method, which emphasizes the importance of reflexivity within the card, but when their faith in order to convince the people off the outer ring of authenticity Wuzhen Dao, in fact, they unwittingly use on the Western speculative methods, but not the logic of Western speculative, but now the speculative. The purpose of this article, first through a thought experiment of the anti-theory, went on to argue that the orthodox view of the popular errors and false. The authors believe that: this say just false, but logically self-denial. (shrink)

According to a widely held view, a Kantian intuition functions like a singular term. I argue that this view is false. Its apparent plausibility, both textual and philosophical, rests on attributing to Kant a Fregean conception of judgment. I show that Kant does not hold a Fregean conception of judgment and argue that, as a consequence, intuition cannot be understood on analogy with singular terms.

El trabajo que se presenta constituye un análisis epistemológico del aprendizaje intuitivo como dimensión humana. Su objetivo es caracterizar el marco referencial para una epistemología de lo intuitivo, a partir de la revisión bibliográfica y con la utilización del método hermenéutico, el histórico- lógico, la inducción- deducción y el análisis - síntesis. Sus principales resultados son los fundamentos epistemológicos del aprendizaje intuitivo, la definición pedagógica del aprendizaje intuitivo y la caracterización de las experiencias intuitivas. This article constitutes an epistemological analysis (...) of the intuitive learning as a human dimension. Its objective is to characterize the referential sitting for an epistemology about the intuitive beginning myth the cheering of the bibliography and the Hermeneutical method, Historical- logical, Induction- deduction, and analysis and synthesis. Its main results are: the epistemological foundation of the intuitive learning, the pedagogical definition of the intuitive learning and the characterization of the intuitive experiences. (shrink)

Why we get the world wrong -- Intuitive theories of the physical world -- Matter : what is the world made of? How do those components interact? -- Energy : what makes something hot? What makes something loud? -- Gravity : what makes something heavy? What makes something fall? -- Motion : what makes objects move? What paths do moving objects take? -- Cosmos : what is the shape of our world? What is its place in the cosmos? -- (...) Earth : why do continents drift? Why do climates change? -- Intuitive theories of the biological world -- Life : what makes us alive? What causes us to die? -- Growth : why do we grow bigger? Why do we grow older? -- Inheritance : why do we resemble our parents? Where did we get our traits? -- Illness : what makes us ill? How does illness spread? -- Adaptation : why are there so many lifeforms? How do they change over time? -- Ancestry : where do species come from? How are they related? -- How to get the world right. (shrink)

Logic and Knowledge -/- Editor: Carlo Cellucci, Emily Grosholz and Emiliano Ippoliti Date Of Publication: Aug 2011 Isbn13: 978-1-4438-3008-9 Isbn: 1-4438-3008-9 -/- The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VI–VII of Plato’s Republic and Aristotle’s Prior and Posterior Analytics, to Kant’s Critique of Pure Reason and Mill’s A System of Logic, Ratiocinative and Inductive. It provides the title of an important (...) collection of papers by Bertrand Russell (Logic and Knowledge. Essays, 1901–1950). However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate from knowledge. -/- This book does not hope to make up for a century-long absence of discussion. Rather, its ambition is to call attention to the theme and stimulating renewed reflection upon it. The book collects essays of leading figures in the field and it addresses the theme as a topic of current debate, or as a historical case study, or when appropriate as both. Each essay is followed by the comments of a younger discussant, in an attempt to transform what might otherwise appear as a monologue into an ongoing dialogue; each section begins with an historical essay and ends with an essay by one of the editors. -/- Carlo Cellucci is Emeritus Professor of Philosophy at the University of Rome ‘La Sapienza,’ Italy. He is currently completing a book entitled, Remaking Logic: What is Logic Really? -/- Emily Grosholz is Professor of Philosophy at the Pennsylvania State University, USA. She is the author of Representation and Productive Ambiguity in Mathematics and the Sciences (Oxford University Press, 2007). -/- Emiliano Ippoliti is a Research Fellow at the University of Rome ‘La Sapienza,’ Italy. His main interests are heuristics, the logic of discovery, and problem-solving. He is currently working on a book, Ampliating Knowledge: Data, Hypotheses and Novelty. -/- TABLE OF CONTENTS -/- Foreword .................................................................................................... ix Acknowledgements ................................................................................. xxv -/- Section I: Logic and Knowledge -/- Chapter One................................................................................................. 3 The Cognitive Importance of Sight and Hearing in Seventeenthand Eighteenth-Century Logic (Mirella Capozzi) Discussion .............................................................................................. 26 (Chiara Fabbrizi) Chapter Two .............................................................................................. 33 Nominalistic Content (Jody Azzouni) Discussion ............................................................................................... 52 (Silvia De Bianchi) Chapter Three ............................................................................................ 57 A Garden of Grounding Trees (Göran Sundholm) Discussion.......................................................................................... .. 75 (Luca Incurvati) Chapter Four .............................................................................................. 81 Logics and Metalogics (Timothy Williamson) Discussion.......................................................................................... 101 (Cesare Cozzo) Chapter Five ............................................................................................ 109 Is Knowledge the Most General Factive Stative Attitude? (Cesare Cozzo) Discussion.......................................................................................... 117 (Timothy Williamson) Chapter Six .............................................................................................. 123 Classifying and Justifying Inference Rules (Carlo Cellucci) Discussion.......................................................................................... 143 (Norma B. Goethe) -/- Section II: Logic and Science -/- Chapter Seven.......................................................................................... 151 The Universal Generalization Problem and the Epistemic Status of Ancient Medicine: Aristotle and Galen (Riccardo Chiaradonna) Discussion.......................................................................................... 168 (Diana Quarantotto) Chapter Eight........................................................................................... 175 The Empiricist View of Logic (Donald Gillies) Discussion.......................................................................................... 191 (Paolo Pecere) Chapter Nine............................................................................................ 197 Artificial Intelligence and Evolutionary Theory: Herbert Simon’s Unifying Framework (Roberto Cordeschi) Discussion.......................................................................................... 216 (Francesca Ervas) Chapter Ten ............................................................................................. 221 Evolutionary Psychology and Morality: The Renaissance of Emotivism? (Mario De Caro) Discussion.......................................................................................... 232 (Annalisa Paese) Chapter Eleven ........................................................................................ 237 Between Data and Hypotheses (Emiliano Ippoliti) Discussion.......................................................................................... 262 (Fabio Sterpetti) -/- Section III: Logic and Mathematics -/- Chapter Twelve ....................................................................................... 273 Dedekind Against Intuition: Rigor, Scope and the Motives of his Logicism (Michael Detlefsen) Discussion.......................................................................................... 290 (Marianna Antonutti) Chapter Thirteen...................................................................................... 297 Mathematical Intuition: Poincaré, Polya, Dewey (Reuben Hersh) Discussion.......................................................................................... 324 (Claudio Bernardi) Chapter Fourteen ..................................................................................... 329 On the Finite: Kant and the Paradoxes of Knowledge (Carl Posy) Discussion.......................................................................................... 358 (Silvia Di Paolo) Chapter Fifteen ........................................................................................ 363 Assimilation: Not Only Indiscernibles are Identified (Robert Thomas) Discussion.......................................................................................... 380 (Diego De Simone) Chapter Sixteen ....................................................................................... 385 Proofs and Perfect Syllogisms (Dag Prawitz) Discussion.......................................................................................... 403 (Julien Murzi) Chapter Seventeen ................................................................................... 411 Logic, Mathematics, Heterogeneity (Emily Grosholz) Discussion.......................................................................................... 427 (Valeria Giardino) -/- Contributors........................................................................................ ..... 433 Index............................................................................................... ......... 437 -/- Price Uk Gbp: 49.99 Price Us Usd: 74.99. 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The intuition guiding the de…nition of computation has shifted over time, a process that is re‡ected in the changing formulations of the Church-Turing thesis. The theory of computation began with logic and gradually moved to the capacity of …nite automata. Consequently, modern computer models rely on general physical principles, with quantum computers representing the extreme case. The paper discusses this development, and the challenges to the Church-Turing thesis in its physical form, in particular, Kieu’s quantum computer and relativistic hyper-computation. (...) Finally, the robustness of the boundary between polynomial and exponential time complexity is considered in connection with quantum computers and quantum information theory. (shrink)

In a Socratic spirit of coming to a better understanding of man who finds himself in the midst of a "crisis about knowledge," this dissertation proposes to examine the human subject as a cognitive animal by turning to the long and rich tradition of Aristotelian philosophy, largely ignored today, to focus on and gain inspiration from one of its principal currents of reflection: nous inasmuch as this refers to the human intellectual operation intuiting the substantial level of reality, which can (...) then anchor scientific knowledge of it. ;The examination of nous is based on the text Posterior Analytics II.19, in which Aristotle briefly presents the "habit of nous" as the culmination of a non-rational-discursive process by which the principles of demonstration are acquired. By looking at each of the stages mentioned in the text, there is offered the opportunity to study in detail the different human cognitive capacities and the cognition they provide. This also allows for a comparison and contrast of the capacities and the relationships that can be established between them, which is helpful in understanding man as a cognitive animal, in general, and in determining, in particular, the place and role of intuition in human cognition. ;Starting with Aristotle's views on logic and science, it is established that the rational-discursive operations of the intellect presuppose other non-rational-discursive operations of the intellect, which opens the door to another intellectual operation that can complement the first-mentioned. This other intellectual operation is seen to be closely related to sense cognition and its powers, the means through which the intellect makes contact with external reality. The most important of the different levels of cognition provided by the senses is its highest level, experience; and since human experience involves the activity of the intellect, induction of the principles of science is seen to be an act of the intellect starting from the intelligibility of sense experience. It is concluded, finally, that this act of the intellect is essentially intuitive, consisting mainly in an intellectual grasp of a substance, an insight into its essence. (shrink)

The progress in computer programming leads to the shift in traditional correlation between intuitive and formal components of mathematical knowledge. From epistemological point of view the role of intuition decreases in compare with formal representation of mathematical structures. The relevant explanation is to be found in D. Hilbert’s formalism and corresponding Kantian’s motives in it. The notion of sign belongs to both areas under consideration: on the one hand it is object of intuition in Kantian de re sense, on (...) the other hand, it is part of formal structure. Intuitive mathematical knowledge is expressed by primitive recursive reasoning. The W. Tait’s thesis, namely, that finitism as methodology of mathematics is equivalent to primitive recursive reasoning is discussed in connection with some explications of Kantian notion of intuition. The requirements of finitism are compared with normative role of logic. (shrink)

The pretheoretical notions of logical consequence and of a logical expression are linked in vague and complex ways to modal and pragmatic intuitions. I offer an introduction to the difficulties that these intuitions create when one attempts to give precise characterizations of those notions. Special attention is given to Tarski’s theories of logical consequence and logical constancy. I note that the Tarskian theory of logical consequence has fared better in the face of the difficulties than the Tarskian theory of logical (...) constancy. Other theories of these notions are explained and criticized. (shrink)