I discuss paradoxes of implication in the setting of a proof-conditional theory of meaning for logical constants. I argue that a proper logic of implication should be not only relevant, but also constructive and nonmonotonic. This leads me to select as a plausible candidate LL, a fragment of linear logic that differs from R in that it rejects both contraction and distribution.

This chapter contains sections titled: Paradoxes Stimulate Theory Development An Analogy with Perceptual Illusions Do Logical Paradoxes Exist? Imagination Overflows Logical Possibility Paradoxes Evoke Logical Analogies An Implication about the Nature of Paradox.

There are theoretical limitations to what can be implemented by a computer program. In this paper we are concerned with a limitation on the strength of computer implemented deduction. We use a version of the Curry paradox to arrive at this limitation.

The paradox of material implication has remained unresolved since antiquity because it was believed that the nature of implication was entailment. The article shows that this nature is opposition and therefore the name "implication" should be replaced with the name "competition". A solution to the paradox is provided along with appropriate changes in nomenclature, the addition of connectives and the postulate that the biconditional take over the role of the previous implication. In addition, changes to the nomenclature of logic gates (...) reflecting the competition in electronics are proposed. (shrink)

We argued [Since this argument appeared in other journals, I am reprising it here, almost verbatim.] (Fulda in J Law Info Sci 2:230–232, 1991/AI & Soc 8(4):357–359, 1994) that the paradox of the preface suggests a reason why machines cannot, will not, and should not be allowed to judge criminal cases. The argument merely shows that they cannot now and will not soon or easily be so allowed. The author, in fact, now believes that when—and only when—they are ready they (...) actually should be so allowed, in the interests of justice. Both the original argument applied and this detailed reconsideration applies exclusively to trial courts, and both specifically exclude(d) sentencing. The argument highlights some key relevant differences between minds and machines and attempts, also, to explain why automation is of far greater import for the first-level justice system (trial courts) than for higher courts. A final section discusses why sentencing was, is, and should be excluded. (shrink)

Here I present a new objection to the material or "hook" analysis of indicative conditionals - the thesis that an indicative conditional 'If A then C' has the truth-conditions of the so-called material conditional - based on Liar-like reasoning. This objection seems invulnerable to any Grice-Lewis-Jackson-inspired pragmatic rejoinder.

본 연구는 논리학 및 수리논리학의 토대 개념인 동일성 원리에 대한 역사적인 논쟁들의 교육학적 함의를 도출하는 것이다. 이때 필자가 사용할 중심 방법은 구조-구성주의 인식론이다. 따라서 필자는 구조-구성주의 인식론의 관점에서 동일성 원리에 대한 핵심 논쟁들을 역사-비판적으로 재구성함으로써, 필자가 지속적으로 논변해 온 구조-구성주의 교수학습이론의 확고한 토대를 제공하고자 한다. 이를 위해 본고는 동일성 원리에 대한 역사발생학적 탐구와 정신발생학적 탐구를 종합한다. 구체적인 내용은 피아제의 발생학적 인식론의 관점에서 논리적 개념들 및 공리화에 대한 프레게-러셀의 선험주의적 논리주의와 비트겐슈타인의 회의론적 유명론을 동시에 비판하면서, 구조-구성주의 인식론 및 이것의 교육학적 함의를 (...) 도출하는 것이다. 본고의 최종 결론은 이것이다. 논리적 법칙 또는 공리들은 초인적인 논리학자의 선험적인 직관에 의해서 구성된 것도 아니고, 유명론적 입장의 순수 기호게임으로 환원되는 것도 아니라, 정신 발달과 함께 발달되는 주체와 대상의 상호작용의 결과물, 즉 조작적 구조들의 형식화에 근거한다. 따라서 논리학적 개념들뿐만 아니라, 모든 일반적인 개념을 교육할 때, 교사는 실체와 술어, 개념과 판단, 판단과 추론 사이에 성립되는 미시적 상호의존성과 순환성뿐만 아니라, 이들 전체들 사이에 성립하는 거시적 상호의 존성과 순환성을 동시에 고려해야 한다. (shrink)

This monograph presents Azzouni’s new approach to the rule-following paradox. His solution leaves intact an isolated individual’s capacity to follow rules, and it simultaneously avoids replacing the truth conditions for meaning-talk with mere assertability conditions for that talk. Kripke’s influential version of Wittgenstein’s rule-following paradox—and Wittgenstein’s views more generally—on the contrary, make rule-following practices and assertions about those practices subject to community norms without which they lose their cogency. Azzouni summarizes and develops Kripke’s original version of Wittgenstein’s rule-following paradox to (...) make salient the linchpin assumptions of the paradox. By doing so, Azzouni reveals how compelling Kripke’s earlier work on the paradox was. Objections raised over the years by Fodor, Forbes Ginsborg, Goldfarb, Tait, Wright, and many others, are all shown to fail. No straight solution can be made to work. Azzouni illustrates this in detail by showing that a popular family of straight solutions due to Lewis and refined by Williams, “reference magnetism,” fail as well. And yet an overlooked sceptical solution is still available in logical space. Azzouni describes a series of “disposition-meaning” private languages that he shows can be successfully used by a population of speakers to communicate with one another despite their ideolectical character. The same sorts of languages enable solitary “Robinson Crusoes” to survive and flourish in their island habitats. These languages—sufficiently refined—have the same properties normal human languages have; and this is the key to solving the rule-following paradox without sacrificing the individual’s authority over her self-imposed rules or her ability to follow those rules. Azzouni concludes this unusual monograph by uncovering a striking resemblance between the rule-following paradox and Hume’s problem of induction: he shows the rule-following paradox to be a corollary of Hume’s problem that arises when the problem of induction is applied to an individual’s own abilities to follow rules. (shrink)

Husserlian phenomenology depends upon a particular and limited set of related methodologies, which assume not merely abilities and results on the part of phenomenologists which have been severely criticized, but more profoundly, that mental contents are atomistic and independently manipulable. I will show not only that this assumption is mistaken and that questioning it undermines traditional phenomenological method, but that it leads to a paradox when turned upon itself which forces the rejection of a purely Husserlian phenomenology. More generally, any (...) theory whose data is confined to the results of particular and limited methodologies is by that fact unable to investigate those methodologies, and is thus at best only able to function in a severely restricted realm. (shrink)

In this paper, we aim to devise a logic that can deal with both the paradoxes that motivate dialetheism and the paradoxes related to the irrelevance of material implication. We propose the semantics and the sequent calculus of a relevant logic inspired by difference-making accounts of causation and arguably true to Graham Priest’s Logic of Paradox \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {LP}$$\end{document}: a relevant logic that validates those and only those \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {LP}$$\end{document}-consequences that are not irrelevant. The new logic’s relevant implication is then added to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {LP}$$\end{document} to obtain a logic with the logical vocabulary required to cope with the mentioned paradoxes. (shrink)

The voting paradox occurs when a democratic society seeking to aggregate individual preferences into asocialpreference reaches an intransitive ordering. However it is not widely known that the paradox may also manifest for anindividualaggregating over attributes of risky objects to form a preference over those objects. When this occurs, the relation ‘stochastically greater than’ is not always transitive and so transitivity need not hold between those objects. We discuss the impact of other decision paradoxes to address a series of philosophical (...) and economic arguments against intransitive (cyclical) choice, before concluding that intransitive choices can be justified. (shrink)

Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The (...) view that a statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions. (shrink)

Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The (...) view that a statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions. (shrink)

Does traditional Christianity involve paradoxical doctrines, that is, doctrines that present the appearance (at least) of logical inconsistency? If so, what is the nature of these paradoxes and why do they arise? What is the relationship between "paradox" and "mystery" in theological theorizing? And what are the implications for the rationality, or otherwise, of orthodox Christian beliefs? In Paradox in Christian Theology, James Anderson argues that the doctrines of the Trinity and the incarnation, as derived from Scripture and formulated (...) in the ecumenical creeds, are indeed paradoxical. But this conclusion, he contends, need not imply that Christians who believe these doctrines are irrational in doing so. In support of this claim, Anderson develops and defends a model of understanding paradoxical Christian doctrines according to which the presence of such doctrines is unsurprising and adherence to paradoxical doctrines cannot be considered as a serious intellectual obstacle to belief in Christianity. The case presented in this book has significant implications for the practice of systematic theology, biblical exegesis, and Christian apologetics. (shrink)

Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply (...) troubling epistemic problem. Specifically, if one believes all of the constitutive propositions that make up a paradox, then one is apparently committed to belief in every proposition. This is the result of the principle of classical logical known as ex contradictione (sequitur) quodlibetthat anything and everything follows from a contradiction, and the plausible idea that belief is closed under logical or material implication (i.e. the epistemic closure principle). But, it is manifestly and profoundly irrational to believe every proposition and so the presence of even one contradiction in one’s doxa appears to result in what seems to be total irrationality. This problem is the problem of paradox-induced explosion. In this paper it will be argued that in many cases this problem can plausibly be avoided in a purely epistemic manner, without having either to resort to non-classical logics for belief (e.g. paraconsistent logics) or to the denial of the standard closure principle for beliefs. The manner in which this result can be achieved depends on drawing an important distinction between the propositional attitude of belief and the weaker attitude of acceptance such that paradox constituting propositions are accepted but not believed. Paradox-induced explosion is then avoided by noting that while belief may well be closed under material implication or even under logical implication, these sorts of weaker commitments are not subject to closure principles of those sorts. So, this possibility provides us with a less radical way to deal with the existence of paradoxes and it preserves the idea that intelligent agents can actually entertain paradoxes. (shrink)

Abstract Pavel Florensky solves Lewis Carroll’s ‘Barbershop’ paradox to support his reasoning in a previous chapter. Our discussion includes a) the problem (which we also refer to as the p paradox), b) Carroll’s solution, c) Bertrand Russell’s solution, d) Florensky’s solution and then e) a material example proffered by Florensky. Both Russell and Florensky disagree with Carroll’s solution, yet, (ostensibly) unbeknownst to themselves they offer the same solution, which is ‘p implies not-q’. Given Florensky’s material example, the solution seems to (...) tell us something about the logic of belief. We ask whether Florensky’s example has reverse implications for Russell’s solution. Content Type Journal Article Pages 1-10 DOI 10.1007/s11406-011-9333-6 Authors Michael Rhodes, Philosophy and Religious Studies (NPD), Chicago, IL, USA Journal Philosophia Online ISSN 1574-9274 Print ISSN 0048-3893. (shrink)

Ryan Wasserman explores a range of fascinating puzzles raised by the possibility of time travel, with entertaining examples from physics, science fiction, and popular culture, and he draws out their implications for our understanding of time, tense, freedom, fatalism, causation, counterfactuals, laws of nature, persistence, change, and mereology.

As the title of this paper indicates, I’m going to discuss what we ought to do in situations where our actions affect future generations. More specifically, I shall focus on the moral problems raised by cases where our actions affect who’s going to live, their number and their well being. I’ll start, however, with population axiology. Most discussion in population ethics has concentrated on how to evaluate populations in regard to their goodness, that is, how to order populations by the (...) relations “is better than” and “is as good as”. This field has been riddled with “paradoxes” which purport to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies. Derek Parfit’s Mere Addition Paradox is a case in point. The main question of my paper concerns the implication of such axiological paradoxes for normative theories. Do the axiological paradoxes translate into paradoxes for normative theories or will they, as some believe, disappear if we switch to a normative framework? (shrink)

Aristotle’s solution to Zeno’s arrow paradox differs markedly from the so called at-at solution championed by Russell, which has become the orthodox view in contemporary philosophy. The latter supposes that motion consists in simply being at different places at different times. It can boast parsimony because it eliminates velocity from the ontology. Aristotle, by contrast, solves the paradox by denying that the flight of the arrow is composed of instants; rather, on my reading, he holds that the flight is a (...) unity which is ontologically prior to the temporal parts that may be abstracted from it. I label this position temporal holism; and an entity that is ontological prior to its temporal parts lasting. Lasting, I argue, is the key to Aristotle’s solution to the arrow paradox, but it has received insufficient attention in the relevant literature. I therefore set out here to investigate lasting and highlight its major role in Aristotle’s metaphysics more broadly, and in his solution to other problems of change. I show, too, how lasting within a contemporary context underwrites a parsimonious and intuitive solution to the arrow paradox that retains instantaneous velocity, and hence solves a problem for those who think velocity is required within the ontology to underwrite certain causal roles. (shrink)

Any religion has an ethical component. Thus, the examination of ethical problems is very important for religious studies. Consequentialism is an ethical doctrine according to which a fact is good only if it has good consequences. In order to avoid infinite regression, there is the need for a moral foundation in conformity with the criterion of goodness. The consequentialists proposed various criteria for goodness, such as pleasure, happiness or utility. Any fact will be judged as good only if its consequences (...) belong to the moral basis. The correctness of ethical judgments depends on the analysis of consequence relations. This study takes into account material and strict implication as representations of consequence. Both of them generate ethical paradoxes. If consequence is represented by material implication, according to the Manichean ethics, a fact is either good or bad; there are no neutral ethical facts. If consequence is analyzed by strict implication, the necessary facts will not have a moral value. The present study is to suggest an original solution to these paradoxes. (shrink)

The logic B+ is Routley and Meyer’s basic positive logic. We define the logics BK+ and BK'+ by adding to B+ the K rule and to BK+ the characteristic S4 axiom, respectively. These logics are endowed with a relatively strong non-constructive negation. We prove that all the logics defined lack the K axiom and the standard paradoxes of consistency.

This paper is concerned with the paradox of decrease. Its aim is to defend the answer to this puzzle that was propounded by its originator, namely, the Stoic philosopher Chrysippus. The main trouble with this answer to the paradox is that it has the seemingly problematic implication that a material thing could perish due merely to extrinsic change. It follows that in order to defend Chrysippus’ answer to the paradox, one has to explain how it could be that Theon is (...) destroyed by the amputation without changing intrinsically. In this paper, I shall answer this challenge by appealing to the broadly Aristotelian idea that at least some of the proper parts of a material substance are ontologically dependent on that substance. I will also appeal to this idea in order to offer a new solution to the structurally similar paradox of increase. In this way, we will end up with a unified solution to two structurally similar paradoxes. (shrink)

This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent. $${p\Rightarrow q}$$ p ⇒ q is thus defined as $${\lnot } \Diamond {(p \wedge \lnot q) \wedge } \Diamond {p \wedge } \Diamond {\lnot (...) q}$$ ¬ ◊ ( p ∧ ¬ q ) ∧ ◊ p ∧ ◊ ¬ q. We explore the logical properties of this conditional in a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle’s theses and weak Boethius’ thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut. (shrink)

This paper resolves a paradox concerning colour constancy. On the one hand, our intuitive, pre-theoretical concept holds that colour constancy involves invariance in the perceived colours of surfaces under changes in illumination. On the other, there is a robust scientific consensus that colour constancy can persist in cerebral achromatopsia, a profound impairment in the ability to perceive colours. The first stage of the solution advocates pluralism about our colour constancy capacities. The second details the close relationship between colour constancy and (...) contrast. The third argues that achromatopsics retain a basic type of colour constancy associated with invariants in contrast processing. The fourth suggests that one person-level, conscious upshot of such processing is the visual awareness of chromatic contrasts ‘at’ the edges of surfaces, implicating the ‘colour for form’ perceptual function. This primitive type of constancy sheds new light on our most basic perceptual capacities, which mark the lower borders of representational mind. (shrink)

The last decade has witnessed the emergence of a paradox perspective on corporate sustainability. By explicitly acknowledging tensions between different desirable, yet interdependent and conflicting sustainability objectives, a paradox perspective enables decision makers to achieve competing sustainability objectives simultaneously and creates leeway for superior business contributions to sustainable development. In stark contrast to the business case logic, a paradox perspective does not establish emphasize business considerations over concerns for environmental protection and social well-being at the societal level. In order to (...) contribute to the consolidation of this emergent field of research, we offer a definition of the paradox perspective on corporate sustainability and a framework to delineate its descriptive, instrumental, and normative aspects. This framework clarifies the paradox perspective’s contents and its implications for research and practice. We use the framework to map the contributions to this thematic symposium on paradoxes in sustainability and to propose questions for future research. (shrink)

After an outline of the macrorealistic solutions to the difficulties of the measurement theory, a new paradox is proposed and then discussed in the light of three different interpretations of quantum mechanics.

In representative democracies, referendum voting and parliamentary elections provide two fundamentally different methods for determining the majority opinion. We use three mathematical paradoxes – so-called majority voting paradoxes – to show that referendum voting can reverse the outcome of a parliamentary election, even if the same group of voters have expressed the same preferences on the issues considered in the referendums and the parliamentary election. This insight about the systemic contrarieties between referendum voting and parliamentary elections sheds a (...) new light on the debate about the supplementary value of referendums in representative democracies. Using this insight, we will suggest legal conditions for the implementation of referendums in representative democracies that can pre-empt the conflict between the two methods for determining the majority opinion. (shrink)

Following on theoretical work and studies that assert a relationship between unethical activities and diminished well-being, and a common belief that those more ethically inclined experience greater well-being, the present study examined whether individual differences in ethical orientation may be associated with the experience of well-being. This paper reports the findings of two separate studies showing that individual differences in moral attentiveness, moral identity, idealism, relativism, and integrity were associated with differences in a wide range of well-being measures. Of particular (...) significance is not all ethical orientations were found to contribute to well-being. In fact, some negatively impacted individual levels of well-being. Implications for integrating these new findings into existing ethical theory and considerations for future research are explored. (shrink)

The resolution of the Langevin paradox for an out-and-return journey gives rise to a result which appears to violate the underlying basis of special relativity. The resolution of this second paradox, due to G. Builder, leads to a physically-intelligible interpretation of Einstein's theory and reconciles it with the cosmologically-based fundamental reference frame revealed by modern astronomy.

Many of the psychological studies carried out within virtual environments are motivated by the idea that virtual research findings are generalizable to the non-virtual world. This idea is vulnerable to the paradox of fiction, which questions whether it is possible to express genuine emotion toward a character (or event) known to be fictitious. As many of these virtual studies are designed to elicit, broadly speaking, emotional responses through interactions with fictional characters (avatars) or objects/places, the issue raised by the paradox (...) seems particularly apt. This paper assesses the extent to which the paradox of fiction constitutes a legitimate challenge to psychological research within virtual environments, and argues that any alleged conflict is in fact a product of an overly simplistic view of emotions which a more complete understanding resolves. Moreover, through a more detailed analysis of why the paradox cannot be sustained, one finds justification for the claim that emotions elicited through interactions with virtual (fictitious) objects/events are valid. However, their generalizability to the non-virtual world must still be treated with caution. (shrink)

Social scientists have engaged extensively with the empirical findings of the Easterlin-paradox. However, any statement regarding the meaning and implications of the paradox are derived only through the mediation of normative assumptions. The paper renders these assumptions explicit (and, therefore, open for political discussion), a necessary step in legitimizing the Easterlin paradox as a compass for politics. Based on the analysis of the assumptions lurking behind the common implications of the paradox, the paper opens the door to alternative implications of (...) the paradox. Thus, it refers to other normative assumptions that combine together the assumptions discussed - and is therefore regarded as pluralist in essence - and singles out one particular strong variant - the ‘dual necessity’ variant. This strong assumption, invariably overlooked in the literature, is defined here and its significant political implications for the Easterlin paradox illustrated. (shrink)

This study explored the experiences of the newly-hired faculty in the university to acquire an in-depth and profound understanding of these experiences. It involved eight purposively chosen faculty in a semi-structured interview and focus group discussion documented in voice and video recorders. Using Colaizzi’s seven step-approach to data analysis, results revealed three paradoxical themes: the joys and struggles of teaching, successes and pains of learning, and the privileges and challenges of serving. On the one hand, the joys and struggles of (...) teaching were brought about by their adjustments in instruction. On the other hand, successes and pains of learning centered on professional growth. Finally, the privileges and challenges of serving incorporated the experiences in research, production, and extension. Generally, these teachers have experienced ups and downs in their first two years of teaching at a higher education institution. On the basis of study findings, implications and recommendations are discussed. (shrink)

This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications (...) are connexive logics in that they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the S5-based logic of super-strict implications is equivalent to validity in G. Priest's negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest's logic. (shrink)

It can be shown by means of a paradox that, given the Principle of Sufficient Reason, there is no conjunction of all contingent truths. The question is, or ought to be, how to interpret that result: _Quid sibi velit?_ A celebrated argument against PSR due to Peter van Inwagen and Jonathan Bennett in effect interprets the result to mean that PSR entails that there are no contingent truths. But reflection on parallels in philosophy of mathematics shows it can equally be (...) interpreted either as a proof that there are "too many" contingent truths to combine in a single conjunction or as a proof that the concept _contingent truth_ is indefinitely extensible and there is no such thing as "all contingent truths." Either interpretation would reconcile PSR with contingent truth, but the natural rationales of those interpretations are at odds. This essay argues that the second interpretation is a more satisfactory explanation of why, if PSR is true, there should be no conjunction of all contingent truths. This sheds new light on the nature of the explanatory demand embedded in PSR and uncovers a number of surprising implications for the commitments of rationalism. (shrink)

It is shown that the paradoxes of confirmation are closely linked to the paradoxes of material implication and that they can be avoided by formulating natural laws in terms of a genuine if-Connective rather than the material conditional. However, Natural laws so expressed are not confirmed by simple conjunctions. The question then is whether the common assumption that simple conjunctions do confirm universal generalizations is correct. The answer given is that it is not. In particular, A confirming proposition (...) of the form 'this is a black raven' is not equivalent to 'this is a raven and this is black'. (shrink)

Women are underrepresented in the upper echelons of management in most countries. Despite the effectiveness of identity conscious initiatives for increasing the proportion of women, many organizations have been reluctant to implement such initiatives because potential employees may perceive them negatively. Given the increasing competition for labor, attracting talent is relevant for the long-term success of organizations. In this study, we used an experimental design to examine the effects of identity blind and identity conscious gender diversity initiatives on people’s pursuit (...) intentions toward organizations using them. We used counterfactual thinking, derived from fairness theory, as a guiding framework for our hypothesis development and investigated the moderating influence of a forthcoming government-mandated gender quota as well as individual characteristics. Participants reviewed statements regarding workplace diversity initiatives and rated either the initiatives’ effectiveness or indicated their intentions to pursue employment with organizations using them. Of those rating pursuit intentions, half were informed that the country in which they were conducting their job search was about to implement gender quotas. Results indicated a diversity management paradox such that initiatives perceived as more effective made organizations using them less attractive as employers. However, these negative perceptions were mitigated by a government-mandated quota, and also lower among women. Implications for the study and practice of diversity are discussed. (shrink)

When may someone complain, morally? And what, if any, is the relationship between legitimate moral complaint and one's own behaviour? I point out a perplexity about a certain class of moral complaints. Two very different conceptions of moral complaint seem to be operating, and they often have contrary implications. Moreover, both seem intuitively compelling. This is theoretically and practically troubling, but has not been sufficiently noticed. The Paradox of Moral Complaint seems to point to an inherent difficulty in our reflective (...) moral intuitions. Given the legislative nature of moral agency, the plausible limitations upon reasonable moral complaint seem to contradict the inviolability of central moral constraints and the complaints they allow. In the sort of cases under discussion, morality seems at once both to insist upon the possibility of moral complaint, and to deny it. (Published Online August 21 2006). (shrink)