This book presents a paragraph-by-paragraph analysis of all of the major arguments and explanations in the "aesthetic" of Kant's Critique of Pure Reason. The first part of the book aims to provide a clear analysis of the meanings of the terms Kant uses to name faculties and types of representation, the second offers a thorough account of the reasoning behind the "metaphysical" and "transcendental" expositions, and the third investigates the basis for Kant's major conclusions about space, time, appearances, things in (...) themselves, and the cognitive constitution of the subject. A major goal of the work is to establish that Kant takes spatiotemporal form to be originally given through the constitution of the subject's receptive faculty, not generated through synthetic procedures of the imagination or understanding. (shrink)

The core doctrine of ethical intuitionism is that some of our ethical knowledge is non-inferential. Against this, Sturgeon has recently objected that if ethical intuitionists accept a certain plausible rationale for the autonomy of ethics, then their foundationalism commits them to an implausible epistemology outside ethics. I show that irrespective of whether ethical intuitionists take non-inferential ethical knowledge to be a priori or a posteriori, their commitment to the autonomy of ethics and foundationalism does not entail any implausible non-inferential (...) knowledge in areas outside ethics (such as the past, the future, or the unobservable). However, each form of intuitionism does require a controversial stand on certain unresolved issues outside ethics. (shrink)

Walter Sinnott-Armstrong has argued against moral intuitionism, according to which some of our moral beliefs are justified without needing to be inferred from any other beliefs. He claims that any prima facie justification some non-inferred moral beliefs might have enjoyed is removed because many of our moral beliefs are formed in circumstances where either (1) we are partial, (2) others disagree with us and there is no reason to prefer our moral judgement to theirs, (3) we are emotional in (...) a way that clouds our judgement, (4) the circumstances are conducive to illusion, or (5) the source of our moral beliefs is unreliable or disreputable. I take issue with the elements of Sinnott-Armstrong’s argument that centre on (1) to (3) and (5), concluding that his case against moral intuitionism is unpersuasive. (shrink)

Over the course of human history there appears to have been a global shift in moral values towards a broadly ‘liberal’ orientation. Huemer argues that this shift better accords with a realist than an antirealist metaethics: it is best explained by the discovery of mind-independent truths through intuition. In this article I argue, contra Huemer, that the historical data are better explained assuming the truth of moral antirealism. Realism does not fit the data as well as Huemer suggests, whereas antirealists (...) have underappreciated resources to explain the relevant historical dynamics. These resources include an appeal to socialization, to technological and economical convergences, to lessons learned from history, to changes induced by consistency reasoning and to the social function of moral norms in overcoming some of the cooperation problems that globalizing societies face. I point out that the realist’s explanans has multiple shortcomings, that the antirealist’s explanans has several explanatory virtues, and conclude that the latter provides a superior account of the historical shift towards liberal values. (shrink)

It is argued that Brouwer’s philosophy of mathematics makes perfect sense if viewed from an Eastern philosophical perspective, as a mathematics in what Erich Fromm called “the being mode of existence.” The difficulty Western philosophers have accepting its validity under Brouwer’s own justifications is that mathematics is one of the highest prized treasures of Western philosophy (those footnotes to Plato’s dialogues).

According to Plato’s Apology of Socrates, a humanly wise person is distinguished by her ability to correctly assess the epistemic status and value of her beliefs. She knows when she has knowledge or has mere belief or is ignorant. She makes no unjustified knowledge claims and considers her knowledge to be limited in scope and value. This means: A humanly wise person is intellectually modest. However, when interpreted classically, Socratic wisdom cannot be modest. For in classical epistemic logic, modelling second-order (...) knowledge of knowing something or not, i.e. positive and negative introspection, requires a degree of self-transparency that would at most be attributed to an omniscient and infallible agent. If intellectual modesty is part of Socratic wisdom, we have to look for another epistemic model. I will offer three proposals and argue that an intuitionist reading of the classical concept of knowledge is best suited for this purpose. (shrink)

This book publishes for the first time notes from two notebooks of Gödel which formed the basis of a course on intuitionism Gödel delivered at Princeton in the.

The aim of this paper is to defend moral intuitionism, in its new formulations, against the criticism that there is something objectionably non-natural about its conception of moral properties. The force of this complaint depends crucially on what it means to be a non-natural property. I consider a number of ways of drawing the natural/non-natural distinction and argue that, once the notion of 'non-natural property' is sufficiently clarified, it fails to figure in a compelling argument against moral intuitionism.

Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer’s main interest, however, was in the foundation of (...) mathematics which led him to introduce, and then consolidate, constructive methods under the name ‘intuitionism’. This made him one of the main protagonists in the ‘foundation crisis’ of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict. It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century. (shrink)

The lives of few mathematicians offer the drama that is presented by the life of L. E. J. Brouwer, correctly identified on the cover of this book as a topologist, intuitionist, and philosopher, and before we go any further, it will be worth indicating why.It is not just that Brouwer would rank high among mathematicians for his work in topology alone: he set standards for rigour and created a theory of dimension for topological spaces, and his fixed-point theorem is of (...) great importance. Nor is it just that his philosophy of intuitionism created a new and vibrant branch of logic, that is, arguably, the only viable alternative to naïve, classical logic outside the enclave of professional logicians. Rather, it is that there is a tension, popularly taken to amount to a contradiction, in the fundamental ideas behind his topology and his intuitionism. Added to that, he took a highly principled stand on mathematical issues that led him into confrontations with major figures and a certain degre .. (shrink)

The present paper is a response to Hugh Lehman’s “Intuitionism and Platonism on Infinite Totalities,” which appeared in this journal in 1983. I think that Lehman has attributed to the intuitionist a position which is not that of intuitionism, and hence that his criticisms of what he takes to be the intuitionist’s objections to the classical notion of infinity carry no weight against the intuitionist position.

This is a response by the author of Ethical Intuitionism to criticisms raised by Fred Seddon (Jars, Spring 2007). Among other things, Huemer observes that his attack on ethical reductionism does not depend upon excluding relational properties from consideration at the start; that he does not claim that all philosophers are intuitionists; and that Objectivism is susceptible to the general arguments he discusses against the possibility of deriving an "ought" from an "is".

In Chapter 7 of The Taming of the True, Neil Tennant provides a new argument from Michael Dummett's ``manifestation requirement'' to the incorrectness of classical logic and the correctness of intuitionistic logic. I show that Tennant's new argument is only valid if one interprets crucial existence claims occurring in the proof in the manner of intuitionists. If one interprets the existence claims as a classical logician would, then one can accept Tennant's premises while rejecting his conclusion of logical revision. Thus, (...) Tennant has provided no evidence that should convince anyone who is not already an intuitionist. Since his proof is a proof for the correctness of intuitionism, it begs the question. (shrink)

(2005). Being and Time and Brouwer's Intuitionism. Angelaki: Vol. 10, continental philosophy and the sciences the german traditionissue editor: damian veal, pp. 181-186.

This paper aims to extend the dialogue between social intuitionism and the genetic perspectives of moral psychology, pointing out the contributions and limitations of each one to advance in the understanding of the formulation and transformation of moral judgments. An examination of how the relations between the subject and the object of knowledge have been approached in the light of the contributions of constructivist psychological tradition has been proposed. The relations between emotions, reasoning, and the specific social situation in (...) which such cognitive processes take place it will be examined, taking up particularly the contributions of cultural psychology. By critically examining the three theoretical perspectives, it was possible to point out their contributions and limitations, as well as to appreciate the undoubted contribution of social intuitionism to moral psychology, its limitations and to elucidate the theses that shape this theory. It is precisely by examining the relationships, convergences and profound differences between social intuitionism, constructivism, and cultural psychology in their approaches to moral judgment that it is possible to contribute to promoting their revision and elucidation. (shrink)

This book defends a form of ethical intuitionism, according to which (i) there are objective moral truths; (ii) we know some of these truths through a kind of immediate, intellectual awareness, or "intuition"; and (iii) our knowledge of moral truths gives us reasons for action independent of our desires. The author rebuts all the major objections to this theory and shows that the alternative theories about the nature of ethics all face grave difficulties.

Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations (...) arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of _weak implicative semilattices_, whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana’s strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus. (shrink)

Christian Ethics and Commonsense Morality goes against the grain of various postmodern approaches to morality in contemporary religious ethics. In this book, Jung seeks to provide a new framework in which the nature of common Christian moral beliefs and practices can be given a new meaning. He suggests that, once major philosophical assumptions behind postmodern theories of morality are called into question, we may look at Christian morality in quite a different light. On his account, Christian morality is a historical (...) morality insofar as it is rooted in the rich historical traditions of the Christian church. Yet this kind of historical dependence does not entail the evidential dependence of all moral beliefs on historical traditions. It is possible to argue for the epistemic autonomy of moral beliefs, according to which Christian and other moral beliefs can be justified independently of their historical sources. The particularity of Christian morality lies not in its particular historical sources that also function as the grounds of justification, but rather in its explanatory and motivational capacity to further articulate the kind of moral knowledge that is readily available to most human beings and to enable people to act upon their moral knowledge. (shrink)

Crispin Wright joins the ranks of those who have sought to refute mechanist theories of mind by invoking Gödel's Incompleteness Theorems. His predecessors include Gödel himself, J. R. Lucas and, most recently, Roger Penrose. The aim of this essay is to show that, like his predecessors, Wright, too, fails to make his case, and that, indeed, he fails to do so even when judged by standards of success which he himself lays down.

I argue that, given evidence of the factors that tend to distort our intuitions, ethical intuitionists should disown a wide range of common moral intuitions, and that they should typically give preference to abstract, formal intuitions over more substantive ethical intuitions. In place of the common sense morality with which intuitionism has traditionally allied, the suggested approach may lead to a highly revisionary normative ethics.

We develop intuitionistic public announcement logic over intuitionistic \({\textbf{K}}\), \({{\textbf{K}}}{{\textbf{T}}}\), \({{\textbf{K}}}{{\textbf{4}}}\), and \({{\textbf{S}}}{{\textbf{4}}}\) with distributed knowledge. We reveal that a recursion axiom for the distributed knowledge is _not_ valid for a frame class discussed in [ 12 ] but valid for the restricted frame class introduced in [ 20, 26 ]. The semantic completeness of the static logics for this restricted frame class is established via the concept of pseudo-model.

According to moral intuitionism, at least some moral seeming states are justification-conferring. The primary defense of this view currently comes from advocates of the standard account, who take the justification-conferring power of a moral seeming to be determined by its phenomenological credentials alone. However, the standard account is vulnerable to a problem. In brief, the standard account implies that moral knowledge is seriously undermined by those commonplace moral disagreements in which both agents have equally good phenomenological credentials supporting their (...) disputed moral beliefs. However, it is implausible to think that commonplace disagreement seriously undermines moral knowledge, and thus it is implausible to think that the standard account of moral intuitionism is true. (shrink)

Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with (...) the so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist’s characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ‘it is clearly the case that’. S4M opens the way to an account of higher-order vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson’s objections to intuitionistic treatments of vagueness. (shrink)

This paper explores the generally overlooked relevance of an important contemporary debate in mainstream epistemology to philosophers working within ethics on questions concerning moral knowledge. It is argued that this debate, between internalists and externalists about the accessibility of epistemic justification, has the potential to be both significantly influenced by, and have a significant impact upon, the study of moral knowledge. The moral sphere provides a particular type of strong evidence in favour of externalism, and mainstream epistemologists might benefit from (...) paying attention to this fact. At the same time, the terrain of moral epistemology (approached as a sub-field of metaethics) needs to be reshaped by the realisation that externalists can steal the thunder of intuitionists when it comes to knowledge constituted by seemingly self-evident beliefs.1. (shrink)

Vers 1918 Hermann Weyl abandonnait le logicisme et donc la tentative de réduire les mathématiques à la logique et la théorie des ensembles. Au niveau philosophique, ses points de référence furent ensuite Husserl et Fichte. Dans les années 1920 il distingua leurs positions, entre une direction intuitionniste-phénoménologique d’un côté, et formaliste-constructiviste de l’autre. Peu après Weyl, Oskar Becker adopta une distinction similaire. Mais à la différence du phénoménologue Becker, Weyl considérait l’approche active du constructivisme de Fichte comme supérieure à la (...) vision d’essences passive de Husserl. Dans cet essai, je montre ce développement dans la pensée de Weyl. Bien que certains points dans sa réception de Husserl et Fichte ne soient pas soutenables, je vais argumenter en faveur de la distinction fondamentale mentionnée ci-dessus. (shrink)

Vers 1918 Hermann Weyl abandonnait le logicisme et donc la tentative de réduire les mathématiques à la logique et la théorie des ensembles. Au niveau philosophique, ses points de référence furent ensuite Husserl et Fichte. Dans les années 1920 il distingua leurs positions, entre une direction intuitionniste-phénoménologique d’un côté, et formaliste-constructiviste de l’autre. Peu après Weyl, Oskar Becker adopta une distinction similaire. Mais à la différence du phénoménologue Becker, Weyl considérait l’approche active du constructivisme de Fichte comme supérieure à la (...) vision d’essences passive de Husserl. Dans cet essai, je montre ce développement dans la pensée de Weyl. Bien que certains points dans sa réception de Husserl et Fichte ne soient pas soutenables, je vais argumenter en faveur de la distinction fondamentale mentionnée ci-dessus. (shrink)

When Heidegger insists that each of us is distinctive because “the most radical individuation” is both possible and necessary for us, he might mean: it is possible and necessary to be an individual in the most radical way; or it is possible and necessary to engage in the project of becoming a distinct individual in the most radical way; or it is possible and necessary to see the distinct individual that I am, and to do so in the most radical (...) way. Although all three readings are possible and defensible, I’d like to explore in this paper a -type reading of Heidegger’s claim. What would it mean to see the distinct individual that I am in the most radical way? (shrink)

In ``Revising the Logic of LogicalRevision'' J. Salerno attempts to undermineCrispin Wright 's recent arguments forintuitionism, and to replace Wright andDummett's arguments with a revisionary argumentof his own. I show that Salerno's criticismsof Wright involve both attributing an inferenceto Wright that no intuitionist would make andfallaciously treating a negative universal asan existential negative. Then I show how verygeneral considerations about the nature ofwarrant undermine both Wright and Salerno'sarguments, when these arguments are applied todiscourses with defeasible warrants. WhileSalerno explicitly restricts his (...) discussion tomathematics, Wright and Dummett intend theirrevisionary arguments to have much widerscope. (shrink)