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.

In this article, we survey intuitionism as a philosophy of mathematics, with emphasis on the philosophical views endorsed by Brouwer, Heyting, and Dummett. Before we proceed, however, a few general remark are in order. We must stress that intuitionism is not to be regarded as synonymous with constructivism, an umbrella term that roughly refers to any particular form of mathematics that adopts "we can construct" as the appropriate interpretation of the phrase "there exists". However, intuitionism remains one (...) of the most prominent varieties of constructive mathematics in existence. The curious reader can see our related entry constructive mathematics for complementary background. For more on the intuitionistic rejection of actual infinities, see also the entry on the infinite. Finally, because intuitionism advocates a revision of classical mathematics, a certain amount of mathematical knowledge is required to fully appreciate some parts of this article, most importantly Section 1.2 on intuitionistic analysis. Readers can check any introductory textbook on classical real analysis or topology if they are not familiar with our terminology. Some familiarity with basic set theory will also be presupposed in Section 1.1, in particular regarding transfinite ordinals and uncountable cardinalities. Since our focus is intuitionistic mathematics, intuitionistic logic is not presented in this article. But we include a list of notable theorems and non-theorems of intuitionistic logic in the appendix for reference. (shrink)

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.

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)

The aims of this paper are twofold: firstly, to say something about that philosophy of mathematics known as 'intuitionism' and, secondly, to fit these remarks into a more general message for the philosophy of mathematics as a whole. What I have to say on the first score can, without too much inaccuracy, be compressed into two theses. The first is that the intuitionistic critique of classical mathematics can be seen as based primarily on epistemological rather than on meaning-theoretic considerations. (...) The second is that the intuitionist's chief objection to the classical mathematician's use of logic does not center on the use of particular logical principles (in particular, the law of excluded middle and its ilk). Rather on the role the classical mathematician assigns (or at least extends) generally (i.e. regardless of the particular principles used) to the use of logic in the production mathematical proofs. Thus, the intuitionist critique of logic that we shall be presenting is far more radical than that which has commonly been presented. Concerning the second, more general, theme, my claim is this: some restriction of the role of logical inference in mathematical proof such as that mentioned above is necessary if one is to account for the seeming difference in the epistemic conditions of provers whose reasoning is based on genuine insight into the subject-matter being investigated, and would-be provers whose reasoning is based not on such insight, but rather on principles of inference which hold of every subject-matter indifferently. (shrink)

Thinking about morality -- Story of contemporary intuitionism -- Moral knowledge -- New challenges to intuitionism -- Grounds of morality -- Right and the good reconsidered -- Intuitionism's rivals -- Being moral: how and why.

Ethical Intuitionism was the dominant moral theory in Britain for much of the 18th, 19th and the first third of the twentieth century. However, during the middle decades of the twentieth century ethical intuitionism came to be regarded as utterly untenable. It was thought to be either empty, or metaphysically and epistemologically extravagant, or both. This hostility led to a neglect of the central intuitionist texts, and encouraged the growth of a caricature of intuitionism that could easily (...) be rejected before moving on to 'more serious' philosophical theories. More recently, however, this hostility towards ethical intuitionism has subsided. A wide range of moral philosophers, from Aristotelians, to rule-consequentialists, to expressivists, Kantians and deontologists, are beginning to look to the ethical intuitionists's work as a positive resource. It is, therefore, a good time to get clear on what it was that intuitionists said, and re-evaluate their contribution to our understanding of morality. This volume is the first serious engagement with ethical intuitionism in the light of contemporary developments in ethical theory. It contains essays by eminent moral philosophers working in very different traditions whose aim is to clarify and assess ethical intuitionism. Issues addressed include whether the plurality of basic principles intuitionists adhere to can be grounded in some more fundamental principle; the autonomy of ethics and self-evidence; moral realism and internalism; and the open question argument and naturalism. (shrink)

Recently, a novel intuitionistic reconstruction of the foundations of physics has been primarily developed by Nicolas Gisin and Flavio Del Santo drawing on naturalism. Our goal in this paper is to examine and develop the philosophical background of their naturalistic intuitionism for physics in contrast with Brouwer's defense of his intuitionistic mathematics. To be exact, we propose a systematic rearticulation of Brouwer's so-called two acts of intuitionism to serve as the self-contained philosophical framework justifying naturalistic intuitionism in (...) physics. This revision is accompanied by an investigation of the distinctive naturalistic treatment of some central intuitionistic topics, including logic, language, time, ontology, meaning, and truth. (shrink)

I define ethical intuitionism as the view that it is appropriate to appeal to inferentially unsupported moral beliefs in the course of moral reasoning. I mention four common objections to this view, including the view that all such appeals to intuition make ethical theory politically and noetically conservative. I defend intuitionism from versions of this criticism expressed by R.B. Brandt, R.M. Hare and Richard Miller.

Intuitionism and nihilism, according to nihilists, have key features in common: the same semantics and the same phenomenology. Intuitionism is the object of nihilism’s attack. The central charge nihilism lodges against intuitionism is that its nonnatural moral properties are queer. Here I’ll examine what ‘queer’ might mean in relation to the doctrines nihilism uses to support this charge. My investigation reveals that nihilism’s queerness charge lacks substance and resembles a tautology served with a frown. There’s really nothing (...) to it. After I show that, I’ll offer an explanation for why nihilism has gotten intuitionism wrong. It makes a central mistaken methodological assumption and doesn’t target any identifiable intuitionism in the last hundred or so years. (shrink)

Attributions of moral knowledge are common in everyday life. We say that we know that some actions are morally right or wrong, permitted or required. Yet, how do we know such moral claims? Moral intuitionism is a family of theories in moral epistemology that tries to answer this question. Intuitionists are not skeptics about moral knowledge. They think that there are moral truths for us to know, and further, that knowledge of these truths is possible. What distinguishes intuitionism (...) from other anti-skeptical moral epistemologies is the idea that we can know some moral truths directly, without inferring them from premises. According to many intuitionists, it is possible for us to know that keeping promises is morally right even if we do not hold this belief on the basis of further evidence or proof. While intuitionism was popular in the early twentieth century, it was since dismissed as implausible. Recently, there has been renewed interest in intuitionism. Philosophers have defended updated versions of the theory and argue that the view has been misunderstood. This chapter considers the merits of intuitionism in moral epistemology. In what follows, I examine different ways of being an intuitionist and indicate the relative strengths and weaknesses of various approaches within intuitionism. (shrink)

This chapter criticizes moral intuitionism, which claims that some moral beliefs are justified independently of any ability to infer them from other beliefs. It defines moral intuitionism, and argues that beliefs need confirmation when they are partial, controversial, emotional, or formed in circumstances that are conducive to illusion or unreliability. Empirical research is cited to show that moral beliefs are subject to these problems and, hence, need confirmation by some inference, so moral intuitionism cannot solve the skeptical (...) regress problem. (shrink)

L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism – from elementary number theory through to Brouwer's uniform continuity theorem – and to the two central topics of 'formalized intuitionism': formal intuitionistic logic, and formal systems for intuitionistic analysis. Building on that, the book proposes a (...) systematic, philosophical foundation for intuitionism that weaves together doctrines about human grasp, mathematical objects and mathematical truth. (shrink)

I define ethical intuitionism as the view that it is appropriate to appeal to inferentially unsupported moral beliefs in the course of moral reasoning. I mention four common objections to this view, including the view that all such appeals to intuitionism collapse into “subjectivism”, i.e., that they make truth in ethical theory depend on what people believe. I defend intuitionism from versions of this criticism expressed by R.M. Hare and Peter Singer.

An opinionated encyclopedia entry detailing and evaluating the utilitarian engagement with intuitionism.

In the recent metaethical literature there has been significant interest in the prospects for what I am denoting ‘Perceptual Intuitionism’: the view that normal ethical agents can and do have non-inferential justification for first-order ethical beliefs by having ethical perceptual experiences, e.g., Cullison 2010, McBrayer 2010, Vayrynen 2008. If true, it promises to constitute an independent a posteriori intuitionist epistemology, providing an alternative to intuitionist accounts which posit a priori intuition and/or emotion as sources of non-inferentially justified ethical beliefs. (...) As it is formulated, it is plausible that a necessary con- dition for the view is the truth of Ethical Perception: normal ethical agents can and do have perceptual experiences (at least some of which are veridical) as of the instantiation of ethical properties. In this paper a sophisticated and promising account of Ethical Perception is offered. Extant objections are shown to fail. However, it will be argued that it is far from obvious that the account of Perceptual Intuitionism which emerges constitutes an independent alternative to other intuitionist accounts. This is because we have reason to think that ethical perceptual experience may be epistemically dependent on other epistemic sources, e.g. a priori intuition or emotion. (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)

It is a central tenet of ethical intuitionism as defended by W. D. Ross and others that moral theory should reflect the convictions of mature moral agents. Hence, intuitionism is plausible to the extent that it corresponds to our well-considered moral judgments. After arguing for this claim, I discuss whether intuitionists offer an empirically adequate account of our moral obligations. I do this by applying recent empirical research by John Mikhail that is based on the idea of a (...) universal moral grammar to a number of claims implicit in W. D. Ross’s normative theory. I argue that the results at least partly vindicate intuitionism. (shrink)

According to pluralistic intuitionist theories, some of our moral beliefs are non-inferentially justified, and these beliefs come in both an a priori and an a posteriori variety. In this paper I present new support for this pluralistic form of intuitionism by examining the deeply social nature of moral inquiry. This is something that intuitionists have tended to neglect. It does play an important role in an intuitionist theory offered by Bengson, Cuneo, and Shafer-Landau (forth), but whilst they invoke the (...) social nature of moral inquiry in order to argue that ordinary moral intuitions are trustworthy, my argument focuses on what I will call the ‘frontiers’ of moral inquiry. I will show that inclusive and cooperative dialogue is necessary at moral inquiry’s frontiers, and that intuitionists can expect such dialogue to result in both a priori and a posteriori moral beliefs. (shrink)

The aim of this paper is to establish a phenomenological mathematical intuitionism that is based on fundamental phenomenological-epistemological principles. According to this intuitionism, mathematical intuitions are sui generis mental states, namely experiences that exhibit a distinctive phenomenal character. The focus is on two questions: what does it mean to undergo a mathematical intuition and what role do mathematical intuitions play in mathematical reasoning? While I crucially draw on Husserlian principles and adopt ideas we find in phenomenologically minded mathematicians (...) such as Hermann Weyl and Kurt Gödel, the overall objective is systematic in nature: to offer a plausible approach towards mathematics. (shrink)

The first phase of the recent intuitionist revival left untouched Ross’s claim that fundamental moral truths are self-evident. In a recent article, Robert Cowan attempts to explain, in a plausible way, how we know moral truths. The result is that, while the broad framework of Ross’s theory appears to remain in place, the self-evidence of moral truths is thrown into doubt. In this paper, I examine Cowan’s Conceptual Intuitionism. I use his own proposal to show how he arrives at (...) a skeptical position on self-evidence. First, he completely ignores the kind of epistemic appraisal intuitionism has always rested on; second, he is committed to the Reasons View of prima facie duty, rather than to Ross’s Properties View; third, he holds that a commitment to self-evidence often comes with a commitment to metaphysically extravagant entities, which he calls Perceptualism; fourth, he scrutinizes only a part of the contemporary theory of self-evidence, overlooking the strengths of the theory when considered as a whole. Revealing these several points supports the conclusion that Cowan has not provided a viable variety of Rossian Intuitionism. (shrink)

Ethical intuitionists regard moral knowledge as deriving from moral intuition, moral observation, moral emotion and inference. However, moral intuitions, observations and emotions are cultural artefacts which often differ starkly between cultures. Intuitionists attribute uncongenial moral intuitions, observations or emotions to bias or to intellectual or moral failings; but that leads to sectarian ad hominen attacks. Intuitionists try to avoid that by restricting epistemically genuine intuitions, observations or emotions to those which are widely agreed. That does not avoid the problem. It (...) also limits epistemically genuine intuitions, observations or emotions to those with meagre content, and the intuitionists offer no plausible explanation for how inference from such insubstantial propositions can engender substantial moral knowledge. Instead of moral knowledge, intuitionism offers the prospect of mutual name-calling between intellectually stagnant groups. I criticise and reject the principle of phenomenal conservatism, to which intuitionists sometimes appeal. (shrink)

Sensibility theorists such as John McDowell have argued that once we appreciate certain similarities between moral values and secondary qualities, a new meta-ethical position might emerge, one that avoids the alleged difficulties with moral intuitionism and non-cognitivism. The aim of this paper is to examine the meta-ethical prospects of this secondary-quality analogy. Of particular concern will be the extent to which McDowell’s comparison of values to secondary qualities supports a viewpoint unique from that of the moral intuitionist. Once we (...) disentangle the various metaphysical and epistemological strands of McDowell’s analogy, McDowell’s position might appear closer to moral intuitionism than initially supposed. This discussion will also help clarify the intended meaning of the secondary-quality analogy, as well as its significance for ethics more generally. (shrink)

This paper outlines and defends a moderate intuitionism. The point of departure is the intuitionism of W. D. Ross (1930) in The Right and the Good, conceived as ethically pluralist and epistemologically rationalist. The paper articulates a conception of self-evidence – including mediate as well as immediate kinds – appropriate to a moderate intuitionism, explores some of the resources and varieties of that position, and considers some problems and prospects for a rationalist version of intuitionism. The (...) final section addresses the issue of how best to conceive the nature and grounds of prima facie duty, the problem of whether intuitionism can adequately deal with conflicts of prima facie duties, and the question of how satisfactorily a moderate intuitionism can account for the epistemic status of moral judgments of overall duty and their connection with rational action. (shrink)

Recent empirical work suggests that intuitions may be less reliable than previously assumed. However, given the ubiquity of intuition in philosophical reasoning, it is tempting to give intuitions some evidential weight. This chapter develops an account called ‘moderate intuitionism’, a view whereby intuitions are generally reliable, but nonetheless capable of substantial degrees of error. Believing that the general reliability of intuition emerges from the nature of language, the chapter develops an outline for a disposition-based metasemantic theory which can ground (...) the link between intuition and truth: terms refer to whatever a speaker would be disposed to apply them to when in possession of all relevant information. Well-constructed thought experiments can elicit intuitions and generally reflect the semantic facts but this account can also explain why intuitions occasionally err — i.e. when a thought experiment fails to specify information that would influence the speaker’s dispositions. (shrink)

This chapter extends and clarifies the Kantian intuitionist view that a qualified Rossian intuitionism can be integrated with a version of Kant's humanity formula. In doing this, it briefly sketches Kantian intuitionism; it explicates the notion of treatment of persons — whether merely as means or as ends in themselves — as kinds of _conduct_ in a sense the chapter explicates; and it introduces a distinction between thick and thin ethical questions. Thin ethical questions concern act-types, understood one-dimensionally; (...) thick ethical questions concern conduct-types, which are three-dimensional. The theoretical framework provided by the chapter clarifies the way in which an understanding of the obligations expressed in the humanity formula bear on interpreting Rossian principles and on resolving conflicts of obligation that constitute a challenge to the adequacy of intuitionist ethics as developed by Ross. The final section of the chapter formulates a set of weighting principles that enhance the scope, concreteness, and practical applicability of Kantian intuitionism as an ethical theory. (shrink)

Begins the third part of the book, in which the author discusses two important alternatives to naturalism. The alternative that is discussed is intuitionism, a research programme that takes the methods of natural science and rational intuition, but nothing else, as basic sources of evidence. Argues that, unless one has intuitions that support the view that our world is the product of intelligent design, intuitionism is self‐defeating. Also argues that, though there might be empirical reason for thinking that (...) intuition is reliable in some domains, this fact does not save intuitionism from self‐defeat, nor is it of any use to a naturalist in trying to avoid the ontological consequences described in earlier chapters of the book. (shrink)

Walter Sinnott-Armstrong has developed and progressively refined an argument against moral intuitionism—the view on which some moral beliefs enjoy non-inferential justification. He has stated his argument in a few different forms, but the basic idea is straightforward. To start with, Sinnott-Armstrong highlights facts relevant to the truth of moral beliefs: such beliefs are sometimes biased, influenced by various irrelevant factors, and often subject to disagreement. Given these facts, Sinnott-Armstrong infers that many moral beliefs are false. What then shall we (...) think of our own moral beliefs? Either we have reason to think some of our moral beliefs are reliably formed or we have no such reason. If the latter, our moral beliefs are unjustified. If we have reason to think some moral beliefs are reliably formed, then those beliefs are not non-inferentially justified, because then we’ll have reason to accept something—namely, that they are reliably formed—that entails or supports those beliefs. But then, either way, our moral beliefs are not non-inferentially justified, and so moral intuitionism is false. This paper takes issue with Sinnott-Armstrong’s interesting and widely discussed argument, which we here call the Empirical Defeat Argument (EDA). According to us, the EDA does not defeat moral intuitionism. In section 1, we will set out the argument, briefly reviewing the rationale Sinnott-Armstrong offers for the premises. Then, in section 2, we identify a critical but dubious epistemological assumption concerning the nature of defeat that undergirds the argument. Finally, in section 3, we will defend our challenge to the EDA by answering two objections. (shrink)

In recent work, Bengson, Cuneo, and Shafer‐Landau (2020) develop a new social version of moral intuitionism that promises to explain why our moral intuitions are trustworthy. In this paper, we raise several worries for their account and present some general challenges for the broader class of views we call Social Moral Intuitionism. We close by reflecting on Bengson, Cuneo, and Shafer‐Landau's comparison between what they call the “perceptual practice” and the “moral intuition practice”, which we take to raise (...) some difficult normative and meta‐normative questions for theorists of all stripes. (shrink)

Intuitionism in the philosophy of mathematics is attributed to the Dutch mathematician Luitzen Brouwer (1881–1966) and is to this day inextricably linked with his work. We therefore begin this chapter with a brief biography.

In this paper, I defend a non-skeptical intuitionist approach to moral epistemology from recent criticisms. Starting with Sinnott-Armstrong's skeptical attacks, I argue that a familiar sort of skeptical argument rests on a problematic conception of the evidential grounds of our moral judgments. The success of his argument turns on whether we conceive of the evidential grounds of our moral judgments as consisting entirely of non-normative considerations. While we cannot avoid skepticism if we accept this conception of our evidential grounds, that's (...) because accepting this conception of our evidential grounds is tantamount to accepting the skeptic's conclusion. We have nothing to fear from arguments for skepticism from skepticism. (shrink)

This chapter presents and illustrates fundamental principles of the intuitionistic mathematics devised by L.E.J. Brouwer and then describes in largely nontechnical terms metamathematical results that shed light on the logical character of that mathematics. The fundamental principles, such as Uniformity and Brouwer’s Theorem, are drawn from the intuitionistic studies of logic and topology. The metamathematical results include Gödel’s negative and modal translations and Kleene’s realizability interpretation. The chapter closes with an assessment of anti-realism as a philosophy of intuitionism.

The period in the foundations of mathematics that started in 1879 with the publication of Frege's Begriffsschrift and ended in 1931 with Gödel's Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I can reasonably be called the classical period. It saw the development of three major foundational programmes: the logicism of Frege, Russell and Whitehead, the intuitionism of Brouwer, and Hilbert's formalist and proof-theoretic programme. In this period, there were also lively exchanges between the various schools culminating (...) in the famous Hilbert-Brouwer controversy in the 1920s. -/- The purpose of this anthology is to review the programmes in the foundations of mathematics from the classical period and to assess their possible relevance for contemporary philosophy of mathematics. What can we say, in retrospect, about the various foundational programmes of the classical period and the disputes that took place between them? To what extent do the classical programmes of logicism, intuitionism and formalism represent options that are still alive today? These questions are addressed in this volume by leading mathematical logicians and philosophers of mathematics. (shrink)

Intuitionism is occasionally advanced on the grounds that a classical understanding of mathematical discourse could not be acquired, given limitations of the experience available to the language learner. In this note, focusing on the acquisition of the universal quantifier, I argue that this route of attack against a classical construal results, at best, in a Pyrrhic victory. The conditions under which it is successful are such as to redound upon the tenability of intuitionism itself. Adjudication will not follow (...) merely from attending to the learner''s experience. The nature of the agent''s ability to engage in conceptual extrapolation from that experience must be considered as well. (And divergent views regarding this are likely to recapitulate the original disagreement.). (shrink)

Intuitionism, the second type of descriptivism, is the theory that the truth conditions of moral statements depend on irreducible moral properties, which must be defined in moral terms. The intuitionist claims that we have knowledge of moral truths derived from moral intuition. However, because it is a subjective experience, one person's intuition may differ from another's, and the theory offers no way to decide between them. Intuitionism, Hare argues, is really a kind of Subjectivist Naturalism, or Subjectivism; and, (...) as with Naturalism, it also leads to relativism. Therefore, because it is exhausted by these two theories, descriptivism in general must be abandoned if we are to attain the sort of objectivity that will allow us to avoid relativism. (shrink)

According to moral intuitionism, moral properties are objective, but our cognitions of them are not always based on premises. In this paper, I develop a novel version of moral intuitionism and argue that this new intuitionism is worthy of closer attention. The intuitionistic theory I propose, while inspired by the early twentieth-century intuitionism of W. D. Ross, avoids the alleged errors of his view. Furthermore, unlike Robert Audi's contemporary formulation of intuitionism, my theory has the (...) resources to account for the noninferential character of particular, as opposed to merely general, moral beliefs. I achieve this result by avoiding the appeal to self-evidence to explain the possibility of noninferential moral knowledge. (shrink)

Brouwer’s intuitionism is based on quite different philosophical ideas about the nature of mathematical objects than classical mathematics. This intuitionistic point of view results in a different use of language and in a corresponding different intuitionistic logic which is far more subtle than the classical use of language and corresponding classical logic. Nevertheless an intuitionistic deduction system and a notion of intuitionistic deducibility was developed by A. Heyting and it is amazing to see that a small change in the (...) logical axioms, replacing the logical axiom ГГA → A by ГA → (A → B), may have such far reaching consequences. Since finding (intuitionistic) formal deductions may be difficult, an intuitionistic tableaux based formal deduction system is presented in which the construction of intuitionistic deductions is rather straightforward. The semantics of intuitionistic logic and the notion of (intuitionistic) valid consequence are given in terms of (intuitionistic) Kripke models and it is shown that the three notions of intuitionistic valid consequence, intuitionistic deducibility and intuitionistic tableau-deducibility are equivalent. Intuitionistic sets are either finite constructions or otherwise, they are (subsets of) construction projects. Spreads are a particular kind of construction project, inducing specific principles which typically do not hold for other sets. (shrink)

Hume bequeathed to rational intuitionists a problem concerning moral judgment and the will – a problem of sufficient severity that it is still cited as one of the major reasons why intuitionism is untenable.1 Stated in general terms, the problem concerns how an intuitionist moral theory can account for the intimate connection between moral judgment and moral motivation. One reason that this is still considered to be a problem for intuitionists is that it is widely assumed that the early (...) intuitionists made little progress towards solving it. In this essay, I wish to challenge this assumption by examining one of the more subtle intuitionist responses to Hume, viz., that offered by Thomas Reid. For reasons that remain unclear to me, Reid's response to Hume on this issue has been almost entirely neglected. I shall argue that it is nonetheless one that merits our attention, for at least two reasons. In the first place, Reid's response to Hume's challenge to rational intuitionism bears a close affinity to the type of response that he offers to Hume's broadly skeptical challenge to realist views regarding our perception of the external world. Since Reid's strategy in the latter case is widely regarded as exhibiting significant promise, it is natural to wonder whether, when applied to the moral domain, this type of strategy displays similar promise.2 I will suggest that it does. That is, I will suggest that since Reid's broadly nativist position in perception is one well worth considering, then so also is his broadly nativist account of moral motivation. Second, Reid's position regarding moral motivation represents an intriguing attempt to blend a broadly intuitionist view with important insights from the sentimentalist tradition. In this respect, Reid's view is a genuine hybrid position unlike that offered by other intuitionists such as Richard Price. The synthetic character of Reid's position, I claim, gives it a unique type of theoretical richness, since it incorporates some very attractive features of both rational intuitionism and sentimentalism. (shrink)

This chapter contains sections titled: Logic: The Proof Interpretation Analysis: Choice Sequences Further Semantics.

This chapter deals with intuitionism. According to L.E.J. Brouwer, it is possible to have a mathematics with an austere ontological basis of mental acts, and nevertheless accept undefinable real numbers. That is allegedly made possible by freely-proceeding choice sequences, i.e., sequences created through repeated random choices of elements by a creating subject, in a potentially infinite process. The author argues that we are not as fortunate as Brouwer thought.This chapter can be read in isolation from the rest of the (...) book. (shrink)

Since the 2004 publication of his book The Good in the Right, Robert Audi has been at the forefront of the current resurgence of interest in intuitionism – the idea that human beings have an intuitive sense of right and wrong – in ethics. The New Intuitionism brings together some of the world’s most important contemporary writers from such diverse fields as metaethics, epistemology and moral psychology to explore the latest implications of, and challenges to, Audi’s work. The (...) book also includes an opening chapter that surveys the development of contemporary intuitionism and a conclusion that lays the ground for future developments and debates both written by Audi himself, making this an essential survey of this important school of ethical thought for anyone working in the field. (shrink)

In this work the social intuitionism defended by Jonathan Haidt is explored and compared with the dual reasoning theory (TDR), this theory belongs to a family of proposals that maintain that there is a duality in the field of the mental. On the one hand, social intuitionism has argued that it receives support from TDR, on the other hand, TDR has pointed out similarities with social intuitionism; despite the mutual references mentioned, an analysis of what the precise (...) relationship between these projects could be has not been carried out. This work is an attempt to carry out such analysis, in which it is argued that a) it is not clear that the division of social intuitionism between reasoning, intuition, and emotion is equivalent to that of the defenders of TDR; b) social intuitionism has certain differences both with the default-interventionist version and with the parallel version of the TDR; and, finally, c) it is not evident that social intuitionism is an extension of a TDR to the field of moral judgment. It is necessary to carry out more studies that delve into the different elements of social intuitionism and TDR, in order to understand how human beings make judgments and decisions, either within the scope of morality or outside it. (shrink)

The basic tenets of intuitionism are the rejection of the law of excluded middle and the view that a judgement is correct if it is knowable, indicating a reversal in priority between the objective and the subjective. Intuitionism revived the age-old problem of universals, and the controversy between nominalism, conceptualism, and realism, now represented by formalism (nominalism), intuitionism (conceptualism), and set-theoretical Platonism (realism). In the old controversy, moderate realism, i.e., the Aristotelic-Thomistic school, came out on top, with (...) its simultaneous rejection of conceptualism and exaggerated realism, on the grounds that the former leads to subjectivism, and the latter is epistemologically untenable. This paper takes a similar stance in the modern foundational debate: set-theoretical Platonism, is rejected on epistemological grounds, and pure conceptualism is rejected on the grounds that if fails to account for the objective nature of mathematics. (shrink)

The article discusses the metaethical views of the philosophers associated with the Lvov-Warsaw School, namely Tadeusz Czeżowski, Tadeusz Kotarbiński, Marian Przełęcki, and Władysław Tatarkiewicz. The common feature of their views is the presence of axiological intuition, understood as direct cognition of values. The similarities as well as the differences between the views of the mentioned authors are listed. These analyses are preceded by conceptual distinctions between types of intuition and kinds of intuitionism.

In this article, we will consider the application of intuitionistic tense logics to construct logical systems in which the thesis of logical determinism cannot be expressed.

It seems impossible that organisms selected to maximize their genetic legacy could also be moral agents in a world in which taking risks for strangers is sometimes morally laudable. Brian Zamulinski argues that it is possible if morality is an evolutionary by-product rather than an adaptation.Evolutionary Intuitionism presents a new evolutionary theory of human morality. Zamulinski explains the evolution of foundational attitudes, whose relationships to acts constitute moral facts. With foundational attitudes and the resulting moral facts in place, he (...) shows how they ground a plausible normative morality, give answers to meta-ethical questions, and provide an account of moral motivation. He explains the nature of moral intuitions and, thus, of our access to the moral facts. He shows that the theory makes confirmed empirical predictions, including the observable variation in moral views. The combination of intuitionism and evolutionary ethics enables Zamulinski to overcome the standard objections to both.Evolutionary Intuitionism is a unified theory of human morality that explains how an objective morality could develop naturally in a physical world like ours, among organisms like us. (shrink)

A. W. Moore; II*—A Problem for Intuitionism: The Apparent Possibility of Performing Infinitely Many Tasks in a Finite Time, Proceedings of the Aristotelian Soci.