Problems are defined as abstract procedures. An explication of procedures as used in Transparent Intensional Logic and called constructions is presented and the subclass of constructions called concepts is defined. Concepts as closed constructions modulo α- and η-conversion can be associated with meaningful expressions of a natural or professional language in harmony with Church’s conception. Thus every meaningful expression expresses a concept. Since every problem can be unambiguously determined by a concept we can state that every problem is a concept (...) and every concept can be viewed as a problem.Kolmogorov’s idea of a connection between problems and Heyting’s calculus is examined and the non-classical features of the latter are shown to be compatible with realistic logic using partial functions. (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.

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)

Any "classical" theory of truth will satisfy tarski's criterion ("p" is true if and only if p), And the principle of bivalence (every proposition is either true or false). A non-Classical theory may be obtained by rejecting these principles: - in fact it is shown that rejection of the second entails rejection of the first. If the resulting non-Classical theory is formalized, A system structurally isomorphic to either s4 or s5 is obtained. An attempt is made to show that the (...) essential insights of intuitionist logic may be preserved if we replace their complex and in many respects "unintuitive" propositional logic by a theory of truth which is non-Classical in the sense described above. (shrink)

In this paper, I argue against the view, most eloquently advocated by Dieter Schönecker, that Kant is what I call a “sensualist intuitionist.” Kant’s text does not accommodate a sensualist intuitionist reading; the fact of reason is cognized by reason, not intuition. I agree with Schönecker that the feeling of respect for the moral law makes us feel its obligatory character, but I disagree that this feeling constitutes cognition of the normative content of the moral law. We do not cognize (...) the validity of the moral law through feeling. I argue instead for what I take to be the standard view: We feel through respect for the moral law the limiting and humiliating effect that rational cognition of the moral law has on our sensibility. (shrink)

ABSTRACT:Most medical learned societies have endorsed both "equivalence" between all forms of withholding or withdrawing treatment and the "discontinuity" between euthanasia and practices to withhold or withdraw treatment. While the latter are morally acceptable insofar as they consist in letting the patient die, the former constitutes an illegitimate act of actively interfering with a patient's life. The moral distinction between killing and letting die has been hotly debated both conceptually and empirically, most notably by experimental philosophers, with inconclusive results. This (...) article employs a "revisionary" intuititionist perspective to discuss the results of a clinical ethics study about intensivists' perceptions of withhold or withdraw decisions. The results show that practitioners' moral experience is at odds with both the discontinuity and equivalence theses. This outcome allows us to revisit certain concepts, such as intention and causal relationship, that are prominent in the conceptual debate. Intensivists also regard end-of-life decisions as being on a scale from least to most active, and whether they regard active forms of end-of-life decisions as ethically acceptable depends on the overarching professional values they endorse: the patient's best chances of survival, or the patient's quality of life. (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)

Philosophers have in the past had difficulty in determining how to define ethical terms. here they are defined as open-context terms with a loosely limited range of substitution instances, in conformity with actual language usage. ethical terms are in themselves meaningless. it is a misuse to say, "x is wrong in itself." ethical terms then reduce to empirical terms concerning wants, likes, knowledge of cause and effect and consequences, knowledge of how ethical terms themselves work. ethical commands reduce to if-then (...) statements. blame may possibly never make sense. (shrink)

The history of ethics often presupposes rationalist thinking on moral issues. An alternative to rationalism has been proposed by the social intuitionist model. This model suggests the bulk of our moral decisions are ‘gut reactions’ or intuitions. Unlike the rationalists, which support reasons and deliberation to draw moral conclusions, intuitionists argue such reasoning is used to support preconceived ethical decisions. This paper provides the first investigation to determine if intuitionism has any validity within business ethics. Using data from the (...) Defining Issues Test and individual journal entries, results indicate discussion-based pedagogy improved the moral reasoning of participants but had very little influence over their beliefs. In short, the social intuitionist model is supported by this study. Most importantly, ethics education that focuses on peer-to-peer discussion can change how students’ reason about moral problems and should be heavily incorporated into classrooms. (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.

This paper provides a novel critique of Walter Sinnott-Armstrong’s influential argument against epistemological moral intuitionism, the view that some people are non-inferentially justified in believing some moral propositions. At the beginning of the twenty-first century, this view experienced a revival, which coincided with an increasing interest in empirical research on intuitions. The results of that research are seen by some as casting serious doubt on the reliability of our moral intuitions. According to Sinnott-Armstrong, empirical evidence shows that our moral (...) beliefs have a high error rate in general, which creates a need for inferential confirmation for every single moral belief. His argument involves the problematic assumption that it is reasonable for informed moral believers to ascribe a high probability of error to every particular moral belief unless the believer has some special evidence that this particular moral belief belongs to a class that has a lower probability of error than the class of moral beliefs. Focussing on the non-moral example that Sinnott-Armstrong uses in the latest reformulation of his argument, the “Californian wine example”, I argue that apart from exceptional circumstances, the description of moral agents as ascribing correctness probabilities to their moral beliefs is odd, ERROR reveals an awkward picture of how agents relate to their moral beliefs and ERROR is problematic from the perspective of moral competence. This critique goes deeper than the worries raised by other critics to earlier versions of the argument, and part of it applies to moral intuitionism as well. (shrink)

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)

Alexander George; Discussions: ‘Goldbach's Conjecture Can Be Decided in One Minute’: On an Alleged Problem for Intuitionism, Proceedings of the Aristotelian Soc.

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)

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)

The interplay of introduction and elimination rules for propositional connectives is often seen as suggesting a distinguished role for intuitionistic logic. We prove three formal results about intuitionistic propositional logic that bear on that perspective, and discuss their significance.

The constructive mathematics developed by Bishop in Foundations of Constructive Analysis succeeded in gaining the attention of mathematicians, but discussions of its underlying philosophy are still rare in the literature. Commentators seem to conclude, from Bishop’s rejection of choice sequences and his severe criticism of Brouwerian intuitionism, that he is not an intuitionist–broadly understood as someone who maintains that mathematics is a mental creation, mathematics is meaningful and eludes formalization, mathematical objects are mind-dependent constructions given in intuition, and mathematical (...) truths are experienceable. This paper develops and defends an intuitionistic interpretation of Bishop’s philosophical views. (shrink)