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We propose a model of physics that blends Rovelli’s relational quantum mechanics (RQM) interpretation with the language of finite information quantities (FIQs), defined by Gisin and Del Santo in the spirit of intuitionistic mathematics. We discuss deficiencies of using real numbers to model physical systems in general, and particularly under the RQM interpretation. With this motivation for an alternative mathematical language, we propose the use of FIQs to model the world under the RQM interpretation, wherein we view the propensities that make up a FIQ as quantifications of potential interaction. Under this model, the stable facts, relative facts, and shifting perspectives that make up the relational interpretation correspond to shifting digits and propensities of the FIQs. The model’s predictions agree with those of both classical and quantum physics, and it is indeterministic. We also propose explanations, with examples, for how the propensities of a FIQ are distributed, and how its digits become actualized. This is equivalent to the notion of the measurement problem, and the question of what causes wave function collapse. In short, by stepping through the “new door” opened by the language of FIQs, we attempt to describe the world under the relational interpretation. [ABSTRACT FROM AUTHOR]

In 2017, Michael Nair-Collins formulated his Transitivity Argument which claimed that brain-dead patients are alive according to a concept that defines death in terms of the loss of moral status. This article challenges Nair-Collins' view in three steps. First, I elaborate on the concept of moral status, claiming that to understand this notion appropriately, one must grasp the distinction between direct and indirect duties. Second, I argue that his understanding of moral status implicit in the Transitivity Argument is faulty since it is not based on a distinction between direct and indirect duties. Third, I show how this flaw in Nair-Collins' argument is grounded in the more general problems between preference utilitarianism and desire fulfillment theory. Finally, I present the constructivist theory of moral status and the associated moral concept of death and explain how this concept challenges the Transitivity Argument. According to my view, brain death constitutes a valid criterion of death since brain death is incompatible with the preserved capacity to have affective attitudes and to value anything. [ABSTRACT FROM AUTHOR]

This paper extends the axiomatic treatment of intuitionistic mereology introduced in Maffezioli and Varzi (Synthese, 198(S18), 4277–4302 2021) by examining the behavior of constructive notions of overlap and disjointness. We consider both (i) various ways of defining such notions in terms of other intuitionistic mereological primitives, and (ii) the possibility of treating them as mereological primitives of their own. [ABSTRACT FROM AUTHOR]

In one of his meetings with members of the Vienna Circle, Wittgenstein discusses Hermann Weyl’s brief conversion to intuitionism and criticizes his arguments against applying the law of the excluded middle to generalizations over the natural numbers. Like Weyl, however, Wittgenstein rejects the classical model theoretic conception of generality when it comes to infinite domains. Nonetheless, he disagrees with him about the reasons for doing so. This paper provides an account of Wittgenstein’s criticism of Weyl that is based on his differing understanding of what a general statement over infinite domains consists in. This difference in their conception of generality is argued to be central to the middle Wittgenstein’s overall stance on intuitionism as well. While Weyl (and other intuitionists) reject the law of the excluded middle on grounds of constructivity, Wittgenstein argues that general statements over infinite domains do not express propositions in the first place. The origin of this position as well as its consequences for contemporary debates on generality are further assessed. [ABSTRACT FROM AUTHOR]

Brouwer’s intuitionistic program was an intriguing attempt to reform the foundations of mathematics that eventually did not prevail. The current paper offers a new perspective on the scientific community’s lack of reception to Brouwer’s intuitionism by considering it in light of Michael Friedman’s model of parallel transitions in philosophy and science, specifically focusing on Friedman’s story of Einstein’s theory of relativity. Such a juxtaposition raises onto the surface the differences between Brouwer’s and Einstein’s stories and suggests that contrary to Einstein’s story, the philosophical roots of Brouwer’s intuitionism cannot be traced to any previously established philosophical traditions. The paper concludes by showing how the intuitionistic inclinations of Hermann Weyl and Abraham Fraenkel serve as telling cases of how individuals are involved in setting in motion, adopting, and resisting framework transitions during periods of disagreement within a discipline. [ABSTRACT FROM AUTHOR]

Most people believe some moral propositions are true. Most people would say that they know that rape is wrong, torturing people is wrong, and so on. But despite decades of intense epistemological study, philosophers cannot even provide a rudimentary sketch of moral knowledge. In my view, the fact that we have very strong epistemic confidence in some fundamental moral propositions and the fact that it is extremely difficult for us to provide even the basics of an account of moral knowledge gives us an important clue. Both of these facts stem from the very nature of moral knowledge. In this paper I provide an intuitionist account of moral knowledge. I try to remove misunderstanding and add to our understanding of the contemporary account of self-evident moral propositions. For a theory of moral knowledge to be acceptable it must explain both the moral knowledge we have and why it is so very difficult for us to explain. My theory meets both requirements. [ABSTRACT FROM AUTHOR]

Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to "speak" of indeterminism, its inability to present us a worldview in which new information is created as time passes. In such a case, scientific determinism would only be an illusion due to the timeless mathematical language scientists use. To investigate this possibility it is necessary to develop an alternative mathematical language that is both powerful enough to allow scientists to compute predictions and compatible with indeterminism and the passage of time. We suggest that intuitionistic mathematics provides such a language and we illustrate it in simple terms. [ABSTRACT FROM AUTHOR]

Two mereological theories are presented based on a primitive apartness relation along with binary relations of mereological excess and weak excess, respectively. It is shown that both theories are acceptable from the standpoint of constructive reasoning while remaining faithful to the spirit of classical mereology. The two theories are then compared and assessed with regard to their extensional import. [ABSTRACT FROM AUTHOR]

We begin with the idea that lines of reasoning are continuous mental processes and develop a notion of continuity in proof. This requires abstracting the notion of a proof as a set of sentences ordered by provability. We can then distinguish between discrete steps of a proof and possibly continuous stages, defining indexing functions to pick these out. Proof stages can be associated with the application of continuously variable rules, connecting continuity in lines of reasoning with continuously variable reasons. Some examples of continuous proofs are provided. We conclude by presenting some fundamental facts about continuous proofs, analogous to continuous structural rules and composition. We take this to be a development on its own, as well as lending support to non-finitistic constructionism. [ABSTRACT FROM AUTHOR]

To make evaluations about the morally relevant impacts of algorithms, transparency is needed. This paper lays out discussion of algorithms and transparency in an explicitly moral analysis with a special focus on the domain of justice and security. The paper provides an account of the moral import of transparency, defined itself as an instrumental value denoting a state of affairs conducive to acquisition of knowledge about some X. A normative account of transparency is outlined relying on an intuitionist framework rooted in the works of Ross and Robert Audi. It will be argued that transparency can be derived as a subsidiary (prima facie) principle from other duties including beneficence and justice and that it is groundable in the value of knowledge. Building on this foundation, the paper examines transparency and duty conflict with a special focus on algorithms in justice and security, recognising that complete transparency can be impossible where duties conflict. It is argued that as a subsidiary (prima facie) principle, transparency is overridable but ineradicable, which is to say that sufficiently justifiable reasons for secrecy or opacity can licence limiting transparency, that is, there may be occasion where full transparency is not our final duty. [ABSTRACT FROM AUTHOR]

In this paper, I develop a view on set-theoretic ontology I call Universe-Indeterminism, according to which there is a unique but indeterminate universe of sets. I argue that Solomon Feferman's work on semi-constructive set theories can be adapted to this project, and develop a philosophical motivation for a semi-constructive set theory closely based on Feferman's but tailored to the Universe-Indeterminist's viewpoint. I also compare the emergent Universe-Indeterminist view to some more familiar views on set-theoretic ontology. [ABSTRACT FROM AUTHOR]

We may try to explain proofs as chains of valid inference, but the concept of validity needed in such an explanation cannot be the traditional one. For an inference to be legitimate in a proof it must have sufficient epistemic power, so that the proof really justifies its final conclusion. However, the epistemic concepts used to account for this power are in their turn usually explained in terms of the concept of proof. To get out of this circle we may consider an idea within intuitionism about what it is to justify the assertion of a proposition. It depends on Heyting's view of the meaning of a proposition, but does not presuppose the concept of inference or of proof as chains of inferences. I discuss this idea and what is required in order to use it for an adequate notion of valid inference. [ABSTRACT FROM AUTHOR]

In his paper "Explaining Deductive Inference" Prawitz states what he calls «a fundamental problem of logic and the philosophy of logic»: the problem of explaining «Why do certain inferences have the epistemic power to confer evidence on the conclusion when applied to premisses for which there is evidence already?». In this paper I suggest a way of articulating, and partly modifying, the intuitionistic answer to this problem in such a way as to both answer Prawitz's problem and satisfy a requirement I argue to be crucial for any epistemic theory of the meaning of the logical constants: the requirement that evidence is epistemically transparent. [ABSTRACT FROM AUTHOR]

I see the question what it is that makes an inference valid and thereby gives a proof its epistemic power as the most fundamental problem of general proof theory. It has been surprisingly neglected in logic and philosophy of mathematics with two exceptions: Gentzen's remarks about what justifies the rules of his system of natural deduction and proposals in the intuitionistic tradition about what a proof is. They are reviewed in the paper and I discuss to what extent they succeed in answering what a proof is. Gentzen's ideas are shown to give rise to a new notion of valid argument. At the end of the paper I summarize and briefly discuss an approach to the problem that I have proposed earlier. [ABSTRACT FROM AUTHOR]

The field of sociology has long been subject to critique for alleged ideological bias and left-wing groupthink linked to its social justice mission. Critics contend that the construction of “sacred victims” by progressive intellectuals hinders their ability to objectively appraise the circumstances of such vulnerable groups. To address this criticism, we survey 479 sociologists in national universities and colleges in the U.S. regarding three sensitive controversies: urban poverty in the black community; gendered differences in occupational choices; and immigration. We find significant patterns in the data. Commitment to the field’s “moral mission,” preferred research paradigm, gender, and especially political orientation are all significant predictors of sociologists’ views. The results, we suggest, can be understood by conceptualizing the field of sociology as an “emotive community.” In doing so, we draw upon current social psychological research on moral foundations theory developed by Jonathan Haidt and colleagues. [ABSTRACT FROM AUTHOR]

Husserl claims that his phenomenological-epistemological system amounts to a “universal” form of empiricism. The present paper shows that this universal moment of Husserl’s empiricism is why his empiricism qualifies as a rationalism. What is empiricist about Husserl’s phenomenological-epistemological system is that he takes experiences to be an autonomous source of immediate justification. On top of that, Husserl takes experiences to be the ultimate source of justification. For Husserl, every justified belief ultimately depends epistemically on the subject’s experiences. These are paradigms of empiricist claims and thus Husserl seems to subscribe to empiricism. However, what is universal about Husserl’s “empiricism” is that he does not limit the concept of (justification-conferring) experiences to sensory experiences or sensory experiences plus introspective intuitions but broadens the concept of experience such that also a priori intuitions are included. Husserl insists that logical, mathematical, and phenomenological intuitions such as ~ (p ∧  ~ p), 2 + 2 = 4, and “Experiences necessarily bear the mark of intentionality” provide non-inferential justification analogous to how sensory experiences can non-inferentially justify beliefs such as “There is a table in front of me.” Importantly, Husserl makes clear that such a priori intuitions are not about our concepts but about reality. This is why Husserl’s universal empiricism is a rationalism. Husserl differs from traditional rationalism as he allows that a priori intuitions can be fallible and empirically underminable. This distinguishes Husserl’s rationalism from Descartes’ and makes him a proponent of moderate rationalism as currently championed by Laurence BonJour. [ABSTRACT FROM AUTHOR]

In The Boundary Stones of Thought (2015), Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Motivated by the definition of semi-Nelson algebras, a propositional calculus called semi-intuitionistic logic with strong negation is introduced and proved to be complete with respect to that class of algebras. An axiomatic extension is proved to have as algebraic semantics the class of Nelson algebras. [ABSTRACT FROM AUTHOR]

Uncertainty measure can supply a new viewpoint for analyzing knowledge conveyed by an Atanassov's intuitionistic fuzzy set (AIFS). So uncertainty measurement is a key topic in AIFS theory, analogous to the role of entropy in probability theory. After reviewing the existing measures of uncertainty (entropy) for AIFSs, we argue that the existing measures of uncertainty cannot capture all facets of uncertainty associated with an AIFS. Then we point out and justify that there are at least three kinds of uncertainty for an AIFS, namely non-specificity, fuzziness, and intuitionism. We provide formal measures of non-specificity, fuzziness, and intuitionism, together with their properties and proofs. Properties of the proposed non-specificity measure are especially investigated. Finally, a general uncertainty measure consisting of these three uncertainties is presented. Illustrative examples show that the proposed uncertainty measure is consistent with intuitive cognize, and it is more sensitive to changes of AIFSs. Moreover, the proposed uncertainty measure can also discriminate uncertainty hiding in classical sets. Thus, it provides an alternative way to construct unified uncertainty measures. [ABSTRACT FROM AUTHOR]

This article shows that an apparent puzzle in finance and accounting is resolved by changing from classical to constructive (more specifically, intuitionistic) mathematics. Our position is that it is unproblematic if real-world actors behave inconsistently with nonconstructive mathematical results. Thus the solution to our puzzle lies in a deeper challenge to the standard view of how rational agents reason. The alternative we propose gives refutable predictions that find support in the empirical capital markets literature. Our main tool, intuitionistic mathematics, plays a similar role in the mathematical philosophy literature to that of ambiguity in decision theoretic work. [ABSTRACT FROM AUTHOR]

Moral intuitionism, once an apparently moribund metaethical position, has seen a resurgence of interest of late. Robert Audi, a leading moral intuitionist, has argued that in order for a moral belief to qualify as intuitional, it must fulfill four criteria: it must be non-inferential, firmly held, comprehended, and pre-theoretical. This paper centers on the fourth and seemingly most problematic criterion: pre-theoreticality. The paper begins by stipulating the defensibility of the moral cognitivism upon which moral intuitionism turns. Next, the paper develops the distinction between semantic and epistemic pre-theoreticality, and goes on to explore and reject the putative ubiquity of the theoreticality of first-order moral discourse: it argues that on a defensible understanding of theoryhood, both semantic and epistemic pre-theoretical moral belief is not only possible, but in fact frequently realized. The paper then briefly explores and rebuts objections to (epistemic) pre-theoreticality issuing from (i) the 'Cornell Realists' and (ii) considerations of the epistemic relevance of the epistemic/valuational background of moral belief. The paper concludes that, so far as the pre-theoreticality criterion is concerned, moral intuitionism remains in the running as a viable thesis regarding foundationally justified first-order moral belief and knowledge. [ABSTRACT FROM AUTHOR]

I propose a new semantics for intuitionistic logic, which is a cross between the construction-oriented semantics of Brouwer-Heyting-Kolmogorov and the condition-oriented semantics of Kripke. The new semantics shows how there might be a common semantical underpinning for intuitionistic and classical logic and how intuitionistic logic might thereby be tied to a realist conception of the relationship between language and the world. [ABSTRACT FROM AUTHOR]

In moral epistemology, the method of reflective equilibrium is often characterized in terms of intuitions or understood as a method for justifying intuitions. An analysis of reflective equilibrium and current theories of moral intuitions reveals that this picture is problematic. Reflective equilibrium cannot be adequately characterized in terms of intuitions. Although the method presupposes that we have initially credible commitments, it does not presuppose that they are intuitions. Nonetheless, intuitions can enter the process of developing a reflective equilibrium and, if the process is successful, be justified. Since the method of reflective equilibrium does not essentially involve intuitions, it does not constitute a form of intuitionism in any substantial sense. It may be classified as intuitionist only in the minimal sense of not reducing justification to a matter of inference relations alone. [ABSTRACT FROM AUTHOR]

In this paper, we provide a semantic analysis of the well-known knowability paradox stemming from the Church–Fitch observation that the meaningful knowability principle all truths are knowable, when expressed as a bi-modal principle $${\diamondsuit}$$ , yields an unacceptable omniscience property all truths are known. We offer an alternative semantic proof of this fact independent of the Church–Fitch argument. This shows that the knowability paradox is not intrinsically related to the Church–Fitch proof, nor to the Moore sentence upon which it relies, but rather to the knowability principle itself. Further, we show that, from a verifiability perspective, the knowability principle fails in the classical logic setting because it is missing the explicit incorporation of a hidden assumption of stability: ‘the proposition in question does not change from true to false in the process of discovery.’ Once stability is taken into account, the resulting stable knowability principle and its nuanced versions more accurately represent verification-based knowability and do not yield omniscience. [ABSTRACT FROM AUTHOR]

Most empirical accounts of design suggest that designing is an activity where objects and representations are progressively constructed. Despite this fact, whether design is a constructive process or not is not a question directly addressed in the current design research. By contrast, in other fields such as Mathematics or Psychology, the notion of constructivism is seen as a foundational issue. The present paper defends the point of view that forms of constructivism in design need to be identified and integrated as a foundational element in design research as well. In fact, a look at the literature reveals at least two types of constructive processes that are well embedded in design research: first, an interactive constructivism, where a designer engages a conversation with media, that allows changing the course of the activity as a result of this interaction; second, a social constructivism, where designers need to handle communication and negotiation aspects, that allows integrating individuals' expertise into the global design process. A key feature lacking these well-established paradigms is the explicit consideration of creativity as a central issue of design. To explore how creative and constructivist aspects of design can be taken into account conjointly, the present paper pursues a theoretical approach. We consider the roots of constructivism in mathematics, namely the Intuitionist Mathematics, in order to shed light on the original insights that led to the development of a notion of constructivism. Intuitionists describe mathematics as the process of mental mathematical constructions realized by a creative subject over time. One of the most original features of intuitionist constructivism is the introduction of incomplete objects into the heart of mathematics by means of lawless sequences and free choices. This allows the possibility to formulate undecided propositions and the consideration of creative acts within a formal constructive process. We provide an in-depth analysis of intuitionism from a design standpoint showing that the original notion is more than a pure constructivism where new objects are a mere bottom-up combination of already known objects. Rather, intuitionism describes an imaginative constructivist process that allows combining bottom-up and top-down processes and the expansion of both propositions and objects with free choices of a creative subject. We suggest that this new form of constructivism we identify is also relevant in interpreting conventional design processes and discuss its status with respect to other forms of constructivism in design. [ABSTRACT FROM AUTHOR]

We describe a variety of sets internal to models of intuitionistic set theory that (1) manifest some of the crucial behaviors of potentially infinite sets as described in the foundational literature going back to Aristotle, and (2) provide models for systems of predicative arithmetic. We close with a brief discussion of Church's Thesis for predicative arithmetic. [ABSTRACT FROM AUTHOR]

Call an argument a 'happy sorites' if it is a sorites argument with true premises and a false conclusion. It is a striking fact that although most philosophers working on the sorites paradox find it at prima facie highly compelling that the premises of the sorites paradox are true and its conclusion false, few (if any) of the standard theories on the issue ultimately allow for happy sorites arguments. There is one philosophical view, however, that appears to allow for at least some happy sorites arguments: strict finitism in the philosophy of mathematics. My aim in this paper is to explore to what extent this appearance is accurate. As we shall see, this question is far from trivial. In particular, I will discuss two arguments that threaten to show that strict finitism cannot consistently accept happy sorites arguments, but I will argue that (given reasonable assumptions on strict finitistic logic) these arguments can ultimately be avoided, and the view can indeed allow for happy sorites arguments. [ABSTRACT FROM AUTHOR]

I will be concerned with the following question: are there compelling arguments for postulating a distinction between the truth of a statement and the recognition of its truth, when truth is conceived along the lines of a suitable generalization of the intuitionistic idea that it should be characterized as the existence of a proof? I will argue that the distinction is not necessary within the conceptual framework of intuitionism by replying to two arguments to the contrary, one based on the paradox of inference, the other on considerations concerning the content of a statement. [ABSTRACT FROM AUTHOR]

What is the appropriate notion of truth for sentences whose meanings are understood in epistemic terms such as proof or ground for an assertion? It seems that the truth of such sentences has to be identified with the existence of proofs or grounds, and the main issue is whether this existence is to be understood in a temporal sense as meaning that we have actually found a proof or a ground, or if it could be taken in an abstract, tenseless sense. Would the latter alternative amount to realism with respect to proofs or grounds in a way that would be contrary to the supposedly anti-realistic standpoint underlying the epistemic understanding of linguistic expressions? Before discussing this question, I shall consider reasons for construing linguistic meaning epistemically and relations between such reasons and reasons for taking an anti-realist point of view towards the discourse in question. [ABSTRACT FROM AUTHOR]

In a series of recent papers, Walter Sinnott-Armstrong has developed a novel argument against moral intuitionism. I suggest a defense on behalf of the intuitionist against Sinnott-Armstrong's objections. Rather than focus on the main premises of his argument, I instead examine the way in which Sinnott-Armstrong construes the intuitionistic position. I claim that Sinnott-Armstrong's understanding of intuitionism is mistaken. In particular, I argue that Sinnott-Armstrong mischaracterizes non-inferentiality as it figures in intuitionism. To the extent that Sinnott-Armstrong's account of intuitionism has been adopted by others uncritically, intuitionists have cause for concern. I develop an alternative, and more accurate, reading of what is non-inferential about intuitionistic moral knowledge. In light of this alternative reading, certain elements of Sinnott-Armstrong's case against intuitionism are significantly weakened. But perhaps more importantly, this paper helps clarify what circumspect intuitionists mean when they claim that some moral knowledge is non-inferential. [ABSTRACT FROM AUTHOR]

Given a reasonable coherentist view of justification in ethics, applied ethics, as here conceived of, cannot only guide us, in our practical decisions, but also provide moral understanding through explanation of our moral obligations. Furthermore, applied ethics can contribute to the growth of knowledge in ethics as such. We put moral hypotheses to crucial test in individual cases. This claim is defended against the challenges from moral intuitionism and particularism. [ABSTRACT FROM AUTHOR]

G. A. Cohen's Rescuing Justice and Equality proposes that both concepts need rescuing from the work of John Rawls. Especially, it is concerned with Rawls' famous second principle of justice according to which social primary goods should be distributed equally unless an unequal distribution is to the benefit of the worst off. The question is why this would ever be necessary if all parties are just. Cohen and I agree that Rawls cannot really justify inequalities on the basis given. But he also thinks equality is the correct analysis of justice, though he provides no actual direct arguments for this. He does, however, provide a striking analytical argument claiming that fundamental principles of justice must be fact insensitive, and that Rawls's view of justice violates this requirement. I argue that the requirement is itself misconceived and that principles of justice cannot possibly be fact insensitive in the sense developed by Cohen. Few philosophers share this view of Cohen's-which I argue is due to several conceptual mistakes. With these ironed out, the contractarian view, broadly speaking, is seen to be plausible and powerful. Meanwhile Cohen appears to embrace intuitionism, a stance that cannot possibly be acceptable in social philosophy. In the end, Cohen is successful in arguing that Rawls cannot have what he wants, but neither is Cohen successful in claiming that justice is equality. [ABSTRACT FROM AUTHOR]

In this essay, Perraudin sets out to contrast the competing philosophies of time and imagination of two major French thinkers of the twentieth century: Henri Bergson (1859–1941) and Gaston Bachelard (1884–1962). Despite Bachelard’s polemical approach vis-à-vis philosophical tradition in his works on epistemology and poetics, his accounts of time and imagination have been shown by several critics to be significantly influenced and inspired by his predecessor. Perraudin nonetheless argues that Bachelard’s critique of Bergson’s theory of continuous temporality opens the way—through the subtle dialectics of his “philosophy of no”—to more prolific, and as yet untapped, therapeutic possibilities in our understanding of time and imagination than Bergson’s accounts of continuum of the élan vital had managed to reveal. [ABSTRACT FROM AUTHOR]

Radical experimentalists argue that we should give up using intuitions as evidence in philosophy. In this paper, I first argue that the studies presented by the radical experimentalists in fact suggest that some intuitions are reliable. I next consider and reject a different way of handling the radical experimentalists’ challenge, what I call the Argument from Robust Intuitions. I then propose a way of understanding why some intuitions can be unreliable and how intuitions can conflict, and I argue that on this understanding, both moderate experimentalism and the standard philosophical practice of using intuitions as evidence can help resolve these conflicts. [ABSTRACT FROM AUTHOR]

The ethical matrix approach was developed by Prof Ben Mepham and his colleagues at the University of Nottingham in the early 1990s. Since then the approach has received increasing attention and has been used by several researchers in different projects related to assessing ethical impacts of different food production technologies and other policy options of societal concern. The ethical matrix is sometimes understood simply as a checklist of ethical concerns, but might also be seen as a guide to coming to conclusions on moral questions. The problem I discuss in this paper relates to how using the ethical matrix method as a decision guide can be combined with respecting pluralism. The aim of the paper is to suggest a framework making it possible to -- at the same time -- enhance public justification of judgments and respect pluralism. I argue that pluralism is fundamental to the ethical matrix approach; I distinguish between intuitionist principled pluralism and societal value pluralism; and I show how both kinds of pluralism imply restrictions on how conclusions can be made. No substantive moral decision principles can be allowed. Still, I argue, decision principles of a more epistemological or procedural character can be acceptable even within pluralism. The pragmatist principle of inquiry is defended as an account of moral problem solving compatible with both principled pluralism and value pluralism. When an ethical matrix is used within such a participatory inquiry process substantive conclusions can be drawn. [ABSTRACT FROM AUTHOR]

In this article (1) I extract from Brentano’s works (three) formal arguments against “genealogical explanations” of ethical claims. Such explanation can also be designated as “naturalism” (not his appellation); (2) I counter these arguments, by showing how genealogical explanations of even apodictic moral claims are logically possible (albeit only if certain unlikely, stringent conditions are met); (3) I show how Nietzsche’s ethics meets these stringent conditions, but evolutionary ethics does not. My more general thesis is that naturalism and intuitionism in ethics need not be mutually incompatible. [ABSTRACT FROM AUTHOR]

We analyse the proposition that the spacetime structure is modified at short distances or at high energies due to weakening of classical logic. The logic assigned to the regions of spacetime is intuitionistic logic of some topoi. Several cases of special topoi are considered. The quantum mechanical effects can be generated by such semi-classical spacetimes. The issues of: background independence and general relativity covariance, field theoretic renormalization of divergent expressions, the existence and definition of path integral measures, are briefly discussed in the proposal. The connection with some problems in foundations of mathematics and differential topology are also discussed. [ABSTRACT FROM AUTHOR]

Champions of virtue ethics frequently appeal to moral perception: the notion that virtuous people can “see” what to do. According to a traditional account of virtue, the cultivation of proper feeling through imitation and habituation issues in a sensitivity to reasons to act. Thus, we learn to see what to do by coming to feel the demands of courage, kindness, and the like. But virtue ethics also claims superiority over other theories that adopt a perceptual moral epistemology, such as intuitionism – which John McDowell criticizes for illicitly “borrow[ing] the epistemological credentials” of perception. In this paper, I suggest that the most promising way for virtue ethics to use perceptual metaphors innocuously is by adopting a skill model of virtue, on which the virtues are modeled on forms of practical know-how. Yet I contend that this model is double-edged for virtue ethics. The skill model belies some central ambitions and dogmas of the traditional view, especially its most idealized claims about virtue and the virtuous. While this may be a cost that its champions are unprepared to pay, I suggest that virtue ethics would do well to embrace a more realistic moral psychology and a correspondingly less sublime conception of virtue. [ABSTRACT FROM AUTHOR]

This work is a sequel to our [16]. It is shown how Theorem 4 of [16], dealing with the translatability of HA(Heyting's arithmetic) into negationless arithmetic NA, can be extended to the case of intuitionistic arithmetic in higher types. [ABSTRACT FROM AUTHOR]

The original Brouwerian counter examples were algorithmic in nature; after the introduction of choice sequences, Brouwer devised a version which did not depend on algorithms. This is the origin of the ‘creating subject’ technique. The method allowed stronger refutations of classical principles. Here it is used to show that ‘negative dense’ subsets of the continuum are indecomposable. [ABSTRACT FROM AUTHOR]

The most important distinction in value theory is the subjective-objective distinction which determines the epistemological status of value judgments about medical intervention. Ethical decisions in medical intervention presuppose one of three structures of justification - namely, an inductive approach, a deductive approach which can be either consequentialist or non-consequentialist, and a uniquely ethical approach. Inductivism and deductivism have been discussed extensively in the literature and are only briefly described here. The uniquely ethical approach which presupposes value objectivism is analyzed in detail. This method involves a purely ethical inference which moves from facts to values directly with an emphasis on reason which involves a non-logical justification (as opposed to illogical). It involves the use of natural practical arguments which have an imperative conclusion but no imperative premise and exhibit a value-requiredness between two states of affairs. [ABSTRACT FROM AUTHOR]

This paper explores the classical idea of complementarity in mathematics concerning the relationship of intuition and axiomatic proof. Section I illustrates the basic concepts of the paper, while Section II presents opposing accounts of intuitionist and axiomatic approaches to mathematics. Section III analyzes one of Einstein's lecture on the topic and Section IV examines an application of the issues in mathematics and science education. Section V discusses the idea of complementarity by examining one of Zeno's paradoxes. This is followed by presenting a few more programmatic suggestions and a brief summary. [ABSTRACT FROM AUTHOR]

For quite some time, the research in artificial intelligence has focused on expert systems, because here are to be found practical applications at the experimental stage which may soon become widespread. This focus makes more pressing the need to link the debate about the fundamental efficiency of artificial intelligence with those activities that aim at the application of specialized expert systems. In this paper, I begin by considering the stages and the development of human expertise. As a frame of reference I propose a polar dialectic model of the development of human acting and thinking that explicitly deals with the interplay of calculating rationality and intuition. This suggests the use of expert systems as decision aids particularly in the field of maintenance work on the shop-floor. With regard to this case, some theses concerning the human-centred shaping of technology and work are presented. [ABSTRACT FROM AUTHOR]

In this paper we address the problem of combining a logic Λ with nonmonotonic modal logic. In particular we study the intuitionistic case. We start from a formal analysis of the notion of intuitionistic consistency via the sequent calculus. The epistemic operator M is interpreted as the consistency operator of intuitionistic logic by introducing intuitionistic stable sets. On the basis of a bimodal structure we also provide a semantics for intuitionistic stable sets. [ABSTRACT FROM AUTHOR]