In this article I assess Rossian Intuitionism, which is the view that the Rossian Principles of Duty are self-evident. I begin by motivating and clarifying a version of the view—Rossian Conceptual Intuitionism—that hasn’t been adequately considered by Rossians. After defending it against a series of significant objections, I show that enthusiasm for Rossian Conceptual Intuitionism should be muted. Specifically, I argue that we lack sufficient reason for thinking that the Rossian Principles are self-evident, and that (...) insisting that they are self-evident may commit Rossians to radically expanding the scope of self-evidence. (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)

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.

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)

Robert Audi's ethical intuitionism (Audi, 1997, 1998) deals effectively with standard epistemological problems facing the intuitionist. This is primarily because the notion of self-evidence employed by Audi commits to very little. Importantly, according to Audi we might understand a self-evident moral proposition and yet not believe it, and we might accept a self-evident proposition because it is self-evident, and yet fail to see that it is self-evident. I argue that these and similar features give rise to certain challenges to (...) Audi's intuitionism. It becomes harder to argue that there are any self-evident propositions at all, or more than just a few such propositions. It is questionable whether all moral propositions that we take an interest in are evidentially connected to self-evident propositions. It is difficult to understand what could guide the sort conceptual revision that is likely to take place in our moral theorising. It is hard to account for the epistemic value of the sort of systematicity usually praised in moral theorising. Finally, it is difficult to see what difference the truth of Audi's ethical intuitionism would make to the way in which we (fail to) handle moral disagreement. (shrink)

We consider a “polarized” version of bi-intuitionistic logic [5, 2, 6, 4] as a logic of assertions and hypotheses and show that it supports a “rich proof theory” and an interesting categorical interpretation, unlike the standard approach of C. Rauszer’s Heyting-Brouwer logic [28, 29], whose categorical models are all partial orders by Crolard’s theorem [8]. We show that P.A. Melliès notion of chirality [21, 22] appears as the right mathematical representation of the mirror symmetry between the intuitionistic and co-intuitionistc sides (...) of polarized bi-intuitionism. Philosophically, we extend Dalla Pozza and Garola’s pragmatic interpretation of intuitionism as a logic of assertions [10] to bi-intuitionism as a logic of assertions and hypotheses. We focus on the logical role of illocutionary forces and justification conditions in order to provide “intended interpretations” of logical systems that classify inferential uses in natural language and remain acceptable from an intuitionistic point of view. Although Dalla Pozza and Garola originally provide a constructive interpretation of intuitionism in a classical setting, we claim that some conceptual refinements suffice to make their “pragmatic interpretation” a bona fide representation of intuitionism. We sketch a meaning-asuse interpretation of co-intuitionism that seems to fulfil the requirements of Dummett and Prawitz’s justificationist approach. We extend the Brouwer-Heyting-Kolmogorov interpretation to bi-intuitionism by regarding co-intuitionistic formulas as types of the evidence for them: if conclusive evidence is needed to justify assertions, only a scintilla of evidence suffices to justify hypotheses. (shrink)

The article approaches cut elimination from a new angle. On the basis of an arbitrary inference relation among logically atomic formulae, an inference relation on a language possessing logical operators is defined by means of inductive clauses similar to the operator-introducing rules of a cut-free intuitionistic sequent calculus. The logical terminology of the richer language is not uniquely specified, but assumed to satisfy certain conditions of a general nature, allowing for, but not requiring, the existence of infinite conjunctions and disjunctions. (...) We investigate to what extent structural properties of the given atomic relation are preserved through the extension to the full language. While closure under the Cut rule narrowly construed is not in general thus preserved, two properties jointly amounting to closure under the ordinary structural rules, including Cut, are. -/- Attention is then narrowed down to the special case of a standard first-order language, where a similar result is obtained also for closure under substitution of terms for individual parameters. Taken together, the three preservation results imply the familiar cut-elimination theorem for pure first-order intuitionistic sequent calculus. -/- In the interest of conceptual economy, all deducibility relations are specified purely inductively, rather than in terms of the existence of formal proofs of any kind. (shrink)

The paper pores over the recent conceptions of normative judgement developed against the background of advances in psychology and neuroscience. It begins by analyzing what normative claim of morality and law consists of before presenting and criticizing the Social Intuitionist Model of normative judgement developed by Jonathan Haidt. The model poses serious challenges for well-established normative concepts, and the concept of normativity as objective reason for action in particular. A question is asked of what the relationship between philosophical conceptions and (...) the findings of neuroscience should be. The conclusion is that, in the face of new scientific facts, philosophers have no choice but to carefully revise their conceptual schemes. (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)

Liberal egalitarians argue that the state is justified in taxing members of a political community to achieve distributive justice and ensure political equality and regime stability. This involves an uneasy compromise between equality and efficiency, a compromise that many argue has recently been undermined by the growth of unchecked wealth and income inequality. This essay argues that there is also a trade-off between selecting fair processes for taxation and aiming for particular distributive outcomes. The way people accumulate wealth, and the (...) way states tax often matters more than distributive outcomes. Policymakers must allow for the fair assessment of tax liabilities, avoid excessive enforcement costs and prevent political actors from using tax systems to achieve their partial ends. Recognizing these considerations justifies a systematic scheme of taxation while constraining the mechanisms for collecting revenue. I justify this position using comparative analysis, which I contrast with the conceptual intuitionistic approach associated with egalitarianism. (shrink)

This dissertation is a contribution to the field of empirically informed metaethics, which combines the rigorous conceptual clarity of traditional metaethics with a careful review of empirical evidence. More specifically, this work stands at the intersection of moral psychology, moral epistemology, and philosophy of action. The study comprises six chapters on three distinct (although related) topics. Each chapter is structured as an independent paper and addresses a specific open question in the literature. The first part concerns the psychological features (...) and cognitive function of moral intuition. Chapter 1 (“Moral intuition, strength, and metacognition”) is focused on the concept of intuitive strength, which is one of the defining features of moral intuition. I provide a metacognitive account of intuitive strength and show why such a view is preferable to emotional or quasi-perceptual accounts. Then, in Chapter 2 (“Dual process reflective equilibrium”), I will discuss the interplay between intuition and reflection in moral reasoning. I will contend that the influential “default-interventionist” model of reasoning, theorized by Greene, is insufficiently supported by the evidence. In light of some recent studies, I outline an account of moral reasoning in which intuition and reflection are not in conflict but cooperate to reach a reflective goal. I call this model dual process reflective equilibrium. The aim of the first part is descriptive, i.e., it argues for an accurate understanding of moral intuition and reasoning in light of the available empirical evidence. In contrast, the second part addresses a normative question: is a subject epistemically justified in forming a belief on the basis of a moral intuition? Skeptics of moral intuition argue that accepting moral intuitions should be the exception rather than the rule to the extent that epistemically defective processes determine the content of moral intuitions. Chapter 3 (“Moral intuitionism and the reliability challenge”) introduces the recent empirical challenges to the reliability of moral intuitions and elaborates a promising strategy for defending intuitionism. In short, I consider whether subjects can track the reliability of their intuitions with their confidence. In Chapter 4 (“The argument from limited cognitive resources”), I evaluate a different strategy to defend moral intuitionism. Specifically, I develop an argument according to which accepting moral intuitions is legitimate because it is the most rational option that a subject has, given her limited resources. The third and final part of the dissertation concerns the role of moral intuitions in action. The influence of automatic processes on moral conduct raises different challenges to moral philosophy. The first challenge is to explain how a subject can be motivated by certain values without the mental effort of deliberation. Chapter 5 (“Caring, moral motivation, and automatic conduct”) tackles this issue. Chapter 6 (“Moral sensitivity as skillful automaticity”) aims to explain how moral agents can be sensitive to good reasons through automatic mental processes. (shrink)

The intuitionistic conception of truth defended by Dummett, Martin Löf and Prawitz, according to which the notion of proof is conceptually prior1 to the notion of truth, is a particular version of the epistemic conception of truth. The paradox of knowability (first published by Frederic Fitch in 1963) has been described by many authors2 as an argument which threatens the epistemic, and the intuitionistic, conception of truth. In order to establish whether this is really so, one has to understand what (...) the epistemic conception of truth really is. So I shall start inpart I with a description of the matter at issue between theepistemic conception of truth and the opposite position, therealistic conception of truth. Inpart II I shall very briefly describe the paradox. Inpart III I shall try to answer the question which appears in the title of this paper: What can we learn from the paradox of knowability?. My conclusion will be that the paradox of knowability is not a refutation of the epistemic conception of truth, but helps us to better formulate (and understand) such a view. (shrink)

Intuitionism—in some form or another—is the most widely recognized and thoroughly discussed method of justification for moral theories. It rests on the claim that a moral theory must not deviate too much from our pre-theoretical moral convictions. In some form or another, this methodology goes back at least as far as Aristotle, and has been discussed, refined, and defended by such contemporary philosophers as John Rawls and Norman Daniels.There is, however, another methodology for constructing and defending moral theories. It (...) draws on premises about human nature or the nature of persons to support conclusions about the nature and structure of morality. This method—which I will call thenature to morality methodology—evaluates a moral claim or moral theory on the basis of its relation to some facts about the kind of beings we are. For brevity, I will use the term ‘nature-claims’ to refer to claims about human nature or the nature of persons, and the term ‘nature-facts’ to refer to true nature-claims. The nature-claims that have been used to support or criticize various moral theories include claims about human motivation, personal identity, the human soul, and the conceptual features of personhood or rational agency. (shrink)

We study a range of issues connected with the idea of replacing one formula by another in a fixed context. The replacement core of a consequence relation ⊢ is the relation holding between a set of formulas {A1,..., Am,...} and a formula B when for every context C, we have C,..., C,... ⊢ C. Section 1 looks at some differences between which inferences are lost on passing to the replacement cores of the classical and intuitionistic consequence relations. For example, we (...) find that while the inference from A and B to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A \land B$\end{document}, sanctioned by both these initial consequence relations, is retained on passage to the replacement core in the classical case, it is lost in the intuitionistic case. Further discussion of these two logics occupies Sections 3 and 4. Section 2 looks at the m = 1 case, describing A as replaceable by B according to ⊢ when B is a consequence of A by the replacement core of ⊢, and inquiring as to which choices of ⊢ render this induced replaceability relation symmetric. Section 5 investigates further conceptual refinements— such as a contrast between horizontal and vertical replaceability—suggested by some work of R. B. Angell and R. Harrop in the 1950s and 1960s. Appendix 1 examines a related aspect of term-for-term replacement in connection with identity in predicate logic. Appendix 2 is a repository for proofs which would otherwise clutter up Section 3. (shrink)

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. (shrink)

It is well-established that topos theory is inherently connected with intuitionistic logic. In recent times several works appeared concerning so-called complement-toposes, which are allegedly connected to the dual to intuitionistic logic. In this paper I present this new notion, some of the motivations for it, and some of its consequences. Then, I argue that, assuming equivalence of certain two definitions of a topos, the concept of a complement-classifier is, at least in general and within the conceptual framework of category (...) theory, not appropriately defined. For this purpose, I first analyze the standard notion of a subobject classifier, show its connection with the representability of the functor Sub via the Yoneda lemma, recall some other properties of the internal structure of a topos and, based on these, I critically comment on the notion of a complement-classifier. (shrink)

According to the “paradox of knowability”, the moderate thesis that all truths are knowable – ... – implies the seemingly preposterous claim that all truths are actually known – ... –, i.e. that we are omniscient. If Fitch’s argument were successful, it would amount to a knockdown rebuttal of anti-realism by reductio. In the paper I defend the nowadays rather neglected strategy of intuitionistic revisionism. Employing only intuitionistically acceptable rules of inference, the conclusion of the argument is, firstly, not ..., (...) but .... Secondly, even if there were an intuitionistically acceptable proof of ..., i.e. an argument based on a different set of premises, the conclusion would have to be interpreted in accordance with Heyting semantics, and read in this way, the apparently preposterous conclusion would be true on conceptual grounds and acceptable even from a realist point of view. Fitch’s argument, understood as an immanent critique of verificationism, fails because in a debate dealing with the justification of deduction there can be no interpreted formal language on which realists and anti-realists could agree. Thus, the underlying problem is that a satisfactory solution to the “problem of shared content” is not available. I conclude with some remarks on the proposals by J. Salerno and N. Tennant to reconstruct certain arguments in the debate on anti-realism by establishing aporias. (shrink)

Intuitionism—in some form or another—is the most widely recognized and thoroughly discussed method of justification for moral theories. It rests on the claim that a moral theory must not deviate too much from our pre-theoretical moral convictions. In some form or another, this methodology goes back at least as far as Aristotle, and has been discussed, refined, and defended by such contemporary philosophers as John Rawls and Norman Daniels.There is, however, another methodology for constructing and defending moral theories. It (...) draws on premises about human nature or the nature of persons to support conclusions about the nature and structure of morality. This method—which I will call thenature to morality methodology—evaluates a moral claim or moral theory on the basis of its relation to some facts about the kind of beings we are. For brevity, I will use the term ‘nature-claims’ to refer to claims about human nature or the nature of persons, and the term ‘nature-facts’ to refer to true nature-claims. The nature-claims that have been used to support or criticize various moral theories include claims about human motivation, personal identity, the human soul, and the conceptual features of personhood or rational agency. (shrink)

This PhD thesis provides an extended evaluation of evolutionary debunking arguments in meta-ethics. Such arguments attempt to show that evolutionary theory, together with a commitment to robust moral objectivity, lead to moral scepticism: the implausible view that we lack moral knowledge or that our moral beliefs are never justified (e.g. Joyce 2006, Street 2005, Kahane 2011). To establish that, these arguments rely on certain epistemic principles. But most of the epistemic principles appealed to in the literature on evolutionary debunking arguments (...) are imprecise, confused or simply implausible. My PhD aims to rectify that. Informed by debates in cutting-edge contemporary epistemology, Chapter 1 distinguishes three general, independently motivated principles that, combined with evolution, seem to render knowledge of robustly objective moral facts problematic. These epistemic principles state that (i.) our getting facts often right in a given domain requires explanation – and if we cannot provide one, our beliefs about that domain are unjustified; (ii.) higher-order evidence of error undermines justification; and (iii.) for our beliefs to be justified, our having them must be best explained by the facts they are about. Chapters 2-4 develop and critically assess evolutionary debunking arguments based on those principles, showing that only the one inspired by (iii.) succeeds. Chapter 2 investigates the argument that evolution makes explaining why we get moral facts often right impossible. I argue that Justin Clarke-Doane’s recent response (2014, 2015, 2016, 2017) works, yet neglects an issue about epistemic luck that spells trouble for robust moral objectivity. Chapter 3 discusses the argument that evolution provides higher-order evidence of error regarding belief in robustly objective moral facts. I show that such an argument falls prey to Katia Vavova’s (2014) self-defeat objection, even if evolutionary debunkers tweak their background view on the epistemic significance of higher-order evidence. Chapter 4 develops the argument that evolution, rather than robustly objective moral facts, best explains why we hold our moral beliefs. I offer a systematic, comprehensive defence of that argument against Andreas Mogensen’s (2015) charge of explanatory levels confusion, Terrence Cuneo’s (2007) companion in guilt strategy, and David Enoch’s (2012, 2016) appeal to deliberative indispensability. Chapter 5 brings everything together. It investigates whether robust moral objectivity survives the worry about epistemic luck raised in Chapter 2 and the explanatory challenge developed in Chapter 4. Making progress, however, requires a better idea of how we form true, justified beliefs about and acquire knowledge of robustly objective moral facts. Since it offers the most popular and best-developed epistemology of robustly objective morality, my inquiry in Chapter 5 focuses on contemporary moral intuitionism: the view that moral intuitions can be the source of basic moral knowledge. I argue that its success is mixed. While moral intuitionism has the conceptual tools to tackle the problem of epistemic luck from Chapter 2, it cannot insulate knowledge of robustly objective moral facts against the sceptical worry raised by the evolutionary debunking argument developed in Chapter 4. Thus, evolutionary theory, together with a commitment to robust moral objectivity, does lead to a form of unacceptable moral scepticism. (shrink)

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. (shrink)

The thirty-three essays in <I>Relativism: A Contemporary Anthology</I> grapple with one of the most intriguing, enduring, and far-reaching philosophical problems of our age. Relativism comes in many varieties. It is often defined as the belief that truth, goodness, or beauty is relative to some context or reference frame, and that no absolute standards can adjudicate between competing reference frames. Michael Krausz's anthology captures the significance and range of relativistic doctrines, rehearsing their virtues and vices and reflecting on a spectrum of (...) attitudes. Invoking diverse philosophical orientations, these doctrines concern conceptions of relativism in relation to facts and conceptual schemes, realism and objectivity, universalism and foundationalism, solidarity and rationality, pluralism and moral relativism, and feminism and poststructuralism. Featuring nine original essays, the volume also includes many classic articles, making it a standard resource for students, scholars, and researchers. <B>Table of Contents:</B> Foreword by Alan Ryan Preface Introduction Michael Krausz <B>Part I. Orienting Relativism</B> 1. Mapping Relativisms Michael Krausz 2. A Brief History of Relativism Maria Baghramian <B>Part II. Relativism, Truth, and Knowledge</B> 3. Subjective, Objective, and Conceptual Relativisms Maurice Mandelbaum 4. “Just the Facts, Ma’am!” Nelson Goodman 5. Relativism in Philosophy of Science Nancy Cartwright 6. The Truth About Relativism Joseph Margolis 7. Making Sense of Relative Truth John MacFarlane 8. On the Very Idea of a Conceptual Scheme Donald Davidson 9. Truth and Convention: On Davidson’s Refutation of Conceptual Relativism Hilary Putnam 10. Conceptual Schemes Simon Blackburn 11. Relativizing the Facts Paul A. Boghossian 12. Targets of Anti-Relativist Arguments Harvey Siegel 13. Realism and Relativism Akeel Bilgrami <B>Part III. Moral Relativism, Objectivity, and Reasons</B> 14. Moral Relativism Defended Gilbert Harman 15. The Truth in Relativism Bernard Williams 16. Pluralism and Ambivalence David B. Wong 17. The Relativity of Fact and the Objectivity of Value Catherine Z. Elgin 18. Senses of Moral Relativity David Wiggins 19. Ethical Relativism and the Problem of Incoherence David Lyons 20. Understanding Alien Morals Gopal Sreenivasan 21. Value: Realism and Objectivity Thomas Nagel 22. Intuitionism, Realism, Relativism, and Rhubarb Crispin Wright 23. Moral Relativism and Moral Realism Russ Schafer-Landau <B>Part IV. Relativism, Culture, and Understanding</B> 24. Anti Anti-Relativism Clifford Geertz 25. Solidarity or Objectivity? Richard Rorty 26. Relativism, Power, and Philosophy Alasdair MacIntyre 27. Internal Criticism and Indian Rationalist Traditions Martha C. Nussbaum and Amartya Sen 28. Phenomenological Rationality and the Overcoming of Relativism Jitendra N. Mohanty 29. Understanding and Ethnocentricity Charles Taylor 30. Relativism and Cross-Cultural Understanding Kwame Anthony Appiah 31. Relativism, Persons, and Practices Amélie Oksenberg Rorty 32. One What? Relativism and Poststructuralism David Couzens Hoy 33. Must a Feminist Be a Relativist After All? Lorraine Code List of Contributors Index. (shrink)

According to semantic antirealism, intuitionistic logic satisfies the requirement that truth should be constrained by provability in principle. Some philosophers have argued that semantic antirealism must be committed to effective provability and that the commitment leads to a stronger kind of logical revisionism exemplified by substructural logics. I shall take into account two different kinds of reply. The first is concerned with meaning per se and grasp or fixing of meaning. It rests on the idea that if we have a (...) method which may be used over some surveyable range, we have determined a way of applying the method everywhere in principle, and that this is enough as far as fixing or grasping meaning is concerned. The second concerns two radical antirealist principles disqualifying structural rules: Token Preservation and Preservation of Local Feasibility. Against criticisms, I shall argue that conceptual support may be provided for both. The main point in this debate is that there is a decisive difference between the rejection of classical logic via the curbing of the epistemic idealizations embedded in structural rules and the rejection of classical logic via the intuitionistic criticism of invalid introduction and elimination rules. It will be explained why the second rejection is stronger than the former. (shrink)

The young Hegel was entranced by the notion of intellectual intuition, and this notion continues to entrance many of Hegel’ commentators. I argue that Kant provided three distinct conceptions of an intuitive intellect, that none of these involve aconceptual intuitionism, and that they differ markedly from Fichte’s and Schelling’s conceptions of intellectual intuition. I further argue that by 1804 Hegel recognized that appealing to an aconceptual model, or to Schelling’s model, or to his own early model of intellectual intuition (...) generates inevitable and insoluble problems of question-begging. By incorporating several important points from Kant’s Transcendental Ideal into his reinterpretation of Kant’s Transcendental Deduction and Refutation of Idealism, Hegel’s mature discursive and conceptual account of ‘absolute knowing’ performs some of the functions Kant assigned to the intuitive intellect, though without invoking any such intuitive intellect. I discuss several of these functions. (shrink)

Of the various accounts of negation that have been offered by logicians in the history of Western logic, that of negation as cancellation is a very distinctive one, quite different from the explosive accounts of modern "classical" and intuitionist logics, and from the accounts offered in standard relevant and paraconsistent logics. Despite its ancient origin, however, a precise understanding of the notion is still wanting. The first half of this paper offers one. Both conceptually and historically, the account of negation (...) as cancellation is intimately connected with connexivist principles such as ¬( ¬). Despite this, standard connexivist logics incorporate quite different accounts of negation. The second half of the paper shows how the cancellation account of negation of the first part gives rise to a semantics for a simple connexivist logic. (shrink)

Are moral standards relative to cultures? Are there any moral facts? What is goodness? If there are moral facts how do we learn about them?_ _These are all questions in metaethics, the branch of ethics that investigates the status of morality, the nature of ethical facts, and the meaning of ethical statements. To the uninitiated it can appear abstract and far removed from its two more concrete cousins, ethical theory and applied ethics, yet it is one of the fastest-growing and (...) most exciting areas of ethics. _What is this thing called Metaethics?_ demystifies this important subject and is ideal for students coming to it for the first time. Beginning with a brief historical overview of metaethics and the development of a "conceptual toolkit," Matthew Chrisman introduces and assesses the following key topics: • ethical reality: including questions about naturalism and non-naturalism, moral facts, and the distinction between realism and antirealism • ethical language: does language represent reality? What mental states are expressed by moral statements? • ethical psychology: the Humean theory of motivation and the connection between moral judgement and motivation • ethical knowledge: intuitionist and coherentist moral epistemologies, and theories of objectivity and relativism in metaethics • new directions in metaethics, including non-traditional theories and extensions to metaepistemology and metanormative theory. Additional features such as chapter summaries, questions of understanding, and a glossary make this an ideal introduction to metaethics. (shrink)

A number of general points behind the story of this paper may be worth setting out separately, now that we have come to the end.There is perhaps one obvious omission to be addressed right away. Although the word “information” has occurred throughout this paper, it must have struck the reader that we have had nothing to say on what information is. In this respect, our theories may be like those in physics: which do not explain what “energy” is (a notion (...) which seems quite similar to “information” in several ways), but only give some basic laws about its behaviour and transmission.The eventual recommendation made here has been to use a broad type-theoretic framework for studying various more classical and more dynamic notions of proposition in their interaction. This is not quite the viewpoint advocated by many current authors in the area, who argue for a whole-sale switch from a ‘static’ to a ‘dynamic’ perspective on propositions. This is not the place, however, to survey the conceptual arguments for and against such a more radical move.This still leaves many questions about possible reductions from one perspective to another. For instance, it would seem that classical systems ought to serve as a ‘limiting case’, which should still be valid after procedural details of some cognitive process have been forgotten. There are various ways of implementing the desired correspondence: e.g. by considering extreme cases with ⫅ equal to identity, or, in the pure relational algebra framework by considering only pairs (x, x). What we shall want then are reductions of dynamic logics, in those special cases, to classical logic. But perhaps also, more sophisticated views are possible. How do we take a piece of ‘dynamic’ prose, remove control instructions and the like, and obtain a piece of ‘classical’ text, suitable for inference ‘in the light of eternity’?There is also a more technical side to the matter of ‘reduction’. By now, Logic has reached such a state of ‘inter-translatability’ that almost all known variant logics can be embedded into each other, via suitable translations. In particular, once an adequate semantic has been given for a new system, this usually induces an embedding into standard logic: as we know, e.g., for the case of Modal Logic. Like-wise, all systems of dynamic interpretation or inference proposed so far admit of direct embedding into an ordinary ‘static’ predicate logic having explicit transition predicates (cf. van Benthem 1988b). Thus, our moral is this. The issue is not whether the new systems of information structure or processing are essentially beyond the expressive resources of traditional logical systems: for, they are not. The issue is rather which interesting phenomena and questions will be put into the right focus by them.The next broad issue concerns the specific use of the perspective proposed here, vis-à-vis concrete proposals for information-oriented or dynamic semantics. The general strategy advocated here is to locate some suitable base calculus and then consider which ‘extras’ are peculiar to the proposal. For instance, this is the spirit in which modal S4 would be a base logic of information models, and intuitionistic logicthe special theory devoting itself to upward persistent propositions. Or, with the examples in Section 4.1, the underlying base logic is our relational algebra, whereas, say, ordinary updates then impose special properties, such as ‘idempotence’: $$xRy \Rightarrow yRy$$ Does this kind of application presuppose the existence of one distinguished base logic, of which all others are extensions? This would be attractive-and some form of relational algebra or linear logic might be a reasonable candidate. Nevertheless, the enterprise does not rest on this outcome. What matters is an increased sensitivity to the ‘landscape’ of dynamic logics, just as with the ‘Categorial Hierarchy’ in Categorial Grammar (cf. van Benthem 1989a, 1991) where the family of logics with their interconnections seems more important than any specific patriarch.Finally, perhaps the most important issue in the new framework is the possibility of new kinds of questions arising precisely because of its differences from standard logic. Notably, given the option of regarding propositions as programs, it will be of interest to consider systematically which major questions about programming languages now make sense inside logic too.EXAMPLE. Correctness. When do we have $$\left[\kern-0.15em\left[ \pi \right]\kern-0.15em\right](\left[\kern-0.15em\left[ A \right]\kern-0.15em\right]) \subseteq \left[\kern-0.15em\left[ B \right]\kern-0.15em\right]$$ for (s, t) propositions A, B and a dynamic (s, (s, t)) proposition π?Program Synthesis. Which dynamic proposition will take us from an information state satisfying A to one satisfying B? (This question needs refinement, lest there be trivial answers.)Determinism. Which propositions as programs are deterministic, in the sense of defining single-valued functions from states to states?Querying. What does it mean to ask for information in the present setting? (Again, individual types referring to e will be crucial here.)This is not merely an agenda for wishful thinking. Within Logic, there are various ways of introducing such concerns into semantics, especially, using tools from Automata Theory. (See van Benthem 1989c for further discussion of such computational perspectives in ‘cognitive programming’.)At least if one believes that ‘dynamics’ is of the essence in cognition (rather than a mere interfacing problem between the halls of eternal truth and the noisy streets of reality), the true test for the present enterprise is the development of a significant new research program not merely copying the questions of old. (shrink)

The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...) and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski's work on truth. (shrink)

Semantic justifications of the classical rules of logical inference typically make use of a notion of bivalent truth, understood as a property guaranteed to attach to a sentence or its negation regardless of the prospects for speakers to determine it as so doing. For want of a convincing alternative account of classical logic, some philosophers suspicious of such recognition-transcending bivalence have seen no choice but to declare classical deduction unwarranted and settle for a weaker system; intuitionistic logic in particular, buttressed (...) by assertion-conditional semantics, is often considered to enjoy a degree of meaning-theoretical respectability unattainable by classical logic.The decision to forgo the classical inference rules is not always made lightly. Thus, Dummett: " In the resolution of the conflict between [the view that generally accepted classical modes of inference ought to be theoretically accommodated, and the demand that any such accommodation be achieved without recourse to bivalence] lies, as I see it, one of the most fundamental and intractable problems in the theory of meaning; indeed, in all philosophy. "The present article ventures to suggest that the conflict need not be irresoluble. Helping ourselves only to such conceptual resources as are standardly invoked by proponents of intuitionistic logic, we shall formulate a rudimentary meaning theory for a selection of logical constants, define a relation of valid inferability, and prove that the latter includes all of classical first-order logic. The result is essentially that reported in Sandqvist as Theorem 2.20.2. TheoryWe will be considering a standard-syntax first-order language with ⊃, ⊥ and ∀ as its only primitive logical constants. We assume countable supplies of individual constants, individual functors , and predicates , as well as a denumerably infinite set of individual variables. By a basic 1 formula we will mean one that …[Full Text of this Article]. (shrink)

The general framework of this paper is a reformulation of Hilbert’s program using the theory of locales, also known as formal or point-free topology [P.T. Johnstone, Stone Spaces, in: Cambridge Studies in Advanced Mathematics, vol. 3, 1982; Th. Coquand, G. Sambin, J. Smith, S. Valentini, Inductively generated formal topologies, Ann. Pure Appl. Logic 124 71–106; G. Sambin, Intuitionistic formal spaces–a first communication, in: D. Skordev , Mathematical Logic and its Applications, Plenum, New York, 1987, pp. 187–204]. Formal topology presents a (...) topological space, not as a set of points, but as a logical theory which describes the lattice of open sets. The application to Hilbert’s program is then the following. Hilbert’s ideal objects are represented by points of such a formal space. There are general methods to “eliminate” the use of points, close to the notion of forcing and to the “elimination of choice sequences” in intuitionist mathematics, which correspond to Hilbert’s required elimination of ideal objects. This paper illustrates further this general program on the notion of valuations. They were introduced by Dedekind and Weber [R. Dedekind, H. Weber, Theorie des algebraischen Funktionen einer Veränderlichen, J. de Crelle t. XCII 181–290] to give a rigorous presentation of Riemann surfaces. It can be argued that it is one of the first example in mathematics of point-free representation of spaces [N. Bourbaki, Eléments de Mathématique. Algèbre commutative, Hermann, Paris, 1965, Chapitre 7]. It is thus of historical and conceptual interest to be able to represent this notion in formal topology. (shrink)

There are two principles that lend Brouwer's mathematics the extra power beyond arithmetic. Both are presented in Brouwer's writings with little or no argument. One, the principle of bar induction, will not concern us here. The other, the continuity principle for numbers, occurs for the first time in print in [4]. It is formulated and immediately applied to show that the set of numerical choice sequences is not enumerable. In fact, the idea of the continuity property can be dated fairly (...) precisely, it is to be found in the margin of Brouwer's notes for his course on Pointset Theory of 1915/16. The course was repeated in 1916/17 and he must have inserted his first formulation of the continuity principle in the fall of 1916 as new material right at the beginning of the course.In modern language, the principle readswhere α and β range over choice sequences of natural numbers, m and x over natural numbers, and stands for ⟨α, α, …, α⟩, the initial segment of α of length m.An immediate consequence of WC-N is that all full functions are continuous, and, as a corollary, that the continuum is unsplittable [28]. Note that WC-N is incompatible with Church's thesis, [22], section 4.6.After Brouwer asserted WC-N, Troelstra was the first to ask in print for a conceptual motivation, but he remained an exception; most authors followed Brouwer by simply asserting it, cf. [18].Let us note first that in one particular case the principle is obvious indeed, namely in the case of the lawless sequences. The notion of lawless sequence surfaced fairly late in the history of intuitionism. Kreisel introduced it in [17] for metamathematical purposes. There is a letter from Brouwer to Heyting in which the phenomenon also occurs [7]. This is an important and interesting fact since it is the only time that Brouwer made use of a possibility expressly stipulated in, e.g., [5], see below. (shrink)

Moral properties would supervene upon non-moral properties and be conceptually autonomous. That, according to Simon Blackburn, would make them if not impossible at least mysterious, and evidence for them best explained by theorists who say they are not real. In fact moral properties would not challenge in ways Blackburn has contended. There is, however, something new that can be gathered from his arguments. What would the supervenience of moral properties and their conceptual autonomy from at least total non-moral properties (...) entail not only for Intuitionists, who ‘knew this all along,’ but for all moral realists, that there are synthetic necessary moral principles? There is for all moral realists the problem of explaining ‘what in the world’ makes possible these necessities. (shrink)

The topic of this paper is the question whether there is a logic which could be justly called the logic of inference. It may seem that at least since Prawitz, Dummett and others demonstrated the proof-theoretical prominency of intuitionistic logic, the forthcoming answer is that it is this logic that is the obvious choice for the accolade. Though there is little doubt that this choice is correct (provided that inference is construed as inherently single-conclusion and complying with the Gentzenian structural (...) rules), I do not think that the usual justification of it is satisfactory. Therefore, I will first try to clarify what exactly is meant by the question, and then sketch a conceptual framework in which it can be reasonably handled. I will introduce the concept of 'inferentially native' logical operators (those which explicate inferential properties) and I will show that the axiomatization of these operators leads to the axiomatic system of intuitionistic logic. Finally, I will discuss what modifications of this answer enter the picture when more general notions of inference are considered. (shrink)

Moral properties would supervene upon non‐moral properties and be conceptually autonomous. That, according to Simon Blackburn, would make them if not impossible at least mysterious, and evidence for them best explained by theorists who say they are not real. In fact moral properties would not challenge in ways Blackburn has contended. There is, however, something new that can be gathered from his arguments. What would the supervenience of moral properties and their conceptual autonomy from at least total non‐moral properties (...) entail not only for Intuitionists, who ‘knew this all along,’ but for all moral realists, that there are synthetic necessary moral principles? There is for all moral realists the problem of explaining ‘what in the world’makes possible these necessities. (shrink)

In an article dating back in 1992, Kosta Došen initiated a project of modal translations in substructural logics, aiming at generalising the well-known Gödel–McKinsey–Tarski translation of intuitionistic logic into S4. Došen's translation worked well for (variants of) BCI and stronger systems (BCW, BCK), but not for systems below BCI. Dropping structural rules results in logic systems without distribution. In this article, we show, via translation, that every substructural (indeed, every non-distributive) logic is a fragment of a corresponding sorted, residuated (multi) (...) modal logic. At the conceptual and philosophical level, the translation provides a classical interpretation of the meaning of the logical operators of various non-distributive propositional calculi. Technically, it allows for an effortless transfer of results, such as compactness and the Löwenheim-Skolem property and it opens up new directions for deducing properties of substructural logic systems by establishing appropriate transfer theorems. (shrink)

Preface -- Part I: Philosophical logic and philosophy of language -- Rules versus theorems : a new approach for mediation -- Between intuitionistic and two-valued logic -- On the relation between the partition of a whole into parts and the attribution of properties to an object -- Basic objectives of dialogic logic in historical perspective -- Pragmatic and semiotic prerequisites for predication : a dialogue model -- Pragmatics and semiotics : the peircean version of ontology and epistemology -- Intentionality and (...) its language-dependency -- Meaning postulates and rules of argumentation : remarks concerning the pragmatic tie between meaning (of terms) and truth (of propositions) -- What do language games measure? -- Features of Indian logic -- Part II: Methods in philosophy, in art, and in science -- The concept of science : some remarks on the methodological issue construction versus description in the philosophy of science -- Is and ought revisited -- Competition and cooperation : are they antagonistic or complementary? -- Another version of methodological dualism -- The pre-established harmony between the two Adams -- On the way to conceptual and perceptual knowledge -- Self and other : remarks on human nature and human culture -- On the concept of symmetry -- Procedural principles of the Eerlangen School : on the interrelation between the principles of method, of dialogue, and of reason. (shrink)

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and (...) in theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (2nd Edition), Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects, J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2. (shrink)

Moral properties would supervene upon non‐moral properties and be conceptually autonomous. That, according to Simon Blackburn, would make them if not impossible at least mysterious, and evidence for them best explained by theorists who say they are not real. In fact moral properties would not challenge in ways Blackburn has contended. There is, however, something new that can be gathered from his arguments. What would the supervenience of moral properties and their conceptual autonomy from at least total non‐moral properties (...) entail not only for Intuitionists, who ‘knew this all along,’ but for all moral realists, that there are synthetic necessary moral principles? There is for all moral realists the problem of explaining ‘what in the world’makes possible these necessities. (shrink)