In this dissertation I examine the sceptical problem of rule following presented by Saul Kripke in his interpretation of Ludwig Wittgenstein's later works: Do any facts determine what rule we were following in our apparently rule-following activities such as the use of language? I distinguish three ways of understanding this question--modest scepticism, radical scepticism, and metascepticism--and address them in Parts 1, 2 and 3 of the dissertation, respectively. ;Part 1 discusses modest scepticism, which asserts that no finite facts about humans (...) can determine rules which have infinitely many possible applications. I resolve this apparent conflict between the finite and the infinite by incorporating the recursiveness of rule applications into the theory of rules. ;Part 2 discusses radical scepticism, which asserts that no facts determine what normative rules we were following. I show first that this challenge has a wider scope than the Humean Thesis of the underivability of ought from is, and that as a result, the radical sceptic can refute attitudinal theories of norms, which have been considered a possible response to the Humean challenge. I then propose a solution to radical scepticism which explains our practice and beliefs about normative rules without assuming the existence of rule-determining facts. Unlike the solution Kripke ascribes to Wittgenstein, it offers no justification of our practice and beliefs about normative rules. Some methodological implications of the solution are also explored. ;Part 3 discusses metascepticism about rule following, whose challenge extends to the rules used for the very discussion of rule following. I examine first whether such a challenge is self-undermining in that it makes the sceptical argument itself impossible. I propose an extended form of reductio ad absurdum argument by which the metasceptic can challenge rules in general, including those used in the sceptical argument. Then I argue that the solution to radical scepticism given in Part 2 survives metascepticism as well. (shrink)

The author believes that large‐scale rationality on the part of the interpretant is essential to his interpretability, and therefore, in his view, to her having a mind. How, then are cases of irrationality, such as akrasia or self‐deception, judged by the interpretant's own standards, possible? He proposes that, in order to resolve the apparent paradoxes, one must distinguish between accepting a contradictory proposition and accepting separately each of two contradictory propositions, which are held apart, which in turn requires to (...) conceive of the mind as containing a number of semi‐independent structures of interlocking beliefs, desires, emotions, memories, and other mental states. (shrink)

Benardete paradoxes involve infinite collections of Grim Reapers, assassins, demons, deafening peals, or even sentences. These paradoxes have recently been used in arguments for finitist metaphysical theses such as temporal finitism, causal finitism, and discrete views of time. Here we develop a new finite Benardete-like paradox. We then use this paradox to defend a companions in guilt argument that challenges recent applications of patchwork principles on behalf of the aforementioned finitist arguments. Finally, we develop another problem for those (...) applications by examining the notion of exact duplication. (shrink)

THE PARADOXES OF CONFIRMATION ARE CONSTITUTED BY THE CONTRADICTIONS ARISING FROM THE CONJUNCTION OF THREE PRINCIPLES OF CONFIRMATION - NICOD’S CRITERION, THE EQUIVALENCE CONDITION, AND WHAT THE PAPER CALLS THE SCIENTIFIC LAWS CONDITION. THE PAPER DISCUSSES IN DETAIL THE VARIOUS SOLUTIONS PROVIDED BY ABANDONING ONE OF THE PRINCIPLES. IN THE END IT FINDS NICOD’S CRITERION FALSE, BUT FINDS THE EXPLANATIONS GIVEN BY H.G. ALEXANDER AND OTHERS OF WHY NICOD’S CRITERION IS FALSE THEMSELVES UNSATISFACTORY. IT THEN PROVIDES A MORE ADEQUATE (...) ACCOUNT OF THE CIRCUMSTANCES IN WHICH "RA.BA" CONFIRMS "ALL R’S ARE B". (shrink)

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.

Understandably absorbed in technical details, discussion of the semantic paradoxes risks losing sight of broad methodological principles. This chapter sketches a general approach to the comparison of rival logics, and applies it to argue that revision of classical propositional logic has much higher costs than its proponents typically recognize.

Graham Priest (1994) has argued that the following paradoxes all have the same structure: Russell’s Paradox, Burali-Forti’s Paradox, Mirimanoff’s Paradox, König’s Paradox, Berry’s Paradox, Richard’s Paradox, the Liar and Liar Chain Paradoxes, the Knower and Knower Chain Paradoxes, and the Heterological Paradox. Their common structure is given by Russell’s Schema: there is a property φ and function δ such that..

Parties are back, and many are cheering. Party polarization has voters seeing stark differences between Democrats and Republicans and demonstrating more ideological constraint than previous generations. But these signs of a more “responsible” electorate are an illusion, because the public is no more knowledgeable than ever about the type of “information” it needs if it is to exercise effective control over the public‐policy outcomes it cares the most about. Indeed, polarization has produced a political environment where both voters and policy (...) makers may be less likely to learn about the potential consequences of their governing choices. The result is that holding elected politicians to account for policies treated as divisive ends in themselves has become easier—but that holding them accountable for policies intended as means to the achievement of consensual ends has become harder. (shrink)

The coordinated attack scenario and the electronic mail game are two paradoxes of common knowledge. In simple mathematical models of these scenarios, the agents represented by the models can coordinate only if they have common knowledge that they will. As a result, the models predict that the agents will not coordinate in situations where it would be rational to coordinate. I argue that we should resolve this conflict between the models and facts about what it would be rational to (...) do by rejecting common knowledge assumptions implicit in the models. I focus on the assumption that the agents have common knowledge that they are rational, and provide models to show that denying this assumption suffices for a resolution of the paradoxes. I describe how my resolution of the paradoxes fits into a general story about the relationship between rationality in situations involving a single agent and rationality in situations involving many agents. (shrink)

In The Enterprise of Knowledge, I proposed a general theory of rational choice which I intended as a characterization of a prescriptive theory of ideal rationality. A cardinal tenet of this theory is that assessments of expected value or expected utility in the Bayesian sense may not be representable by a numerical indicator or indeed induce an ordering of feasible options in a context of deliberation. My reasons for taking this position are related to my commitment to the inquiry-oriented approach (...) to human knowledge and valuation favored by the American pragmatists, Charles Peirce and John Dewey. A feature of any acceptable view of inquiry ought to be that during an inquiry points under dispute ought to be kept in suspense pending resolution through inquiry. (shrink)

‘A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science’.How many paradoxes are there? By 1920, Bertrand Russell's star student had concluded that there are few or zero paradoxes in philosophy. Most philosophical propositions ‘are not false but nonsensical’.

Hans G. Herzberger; VII*—New Paradoxes for Old, Proceedings of the Aristotelian Society, Volume 81, Issue 1, 1 June 1981, Pages 109–124, https://doi.org/10.1093.

This volume brings together Terence Horgan's essays on paradoxes, both published and new. A common theme unifying these essays is that philosophically interesting paradoxes typically resist either easy solutions or solutions that are formally/mathematically highly technical. Another unifying theme is that such paradoxes often have deep-sometimes disturbing-philosophical morals.

It is “the received wisdom” that any intuitively natural and consistent resolution of a class of semantic paradoxes immediately leads to other paradoxes just as bad as the first. This is often called the “revenge problem”. Some proponents of the received wisdom draw the conclusion that there is no hope of any natural treatment that puts all the paradoxes to rest: we must either live with the existence of paradoxes that we are unable to treat, or (...) adopt artificial and ad hoc means to avoid them. Others (“dialetheists”) argue that we can put the paradoxes to rest, but only by licensing the acceptance of some contradictions (presumably in a paraconsistent logic that prevents the contradictions from spreading everywhere). (shrink)

This paper explores how fair trade social enterprises manage paradoxes in stakeholder-oriented governance models. We use narrative accounts from board members, at governance events and board documents to report an exploratory study of paradoxes in three FTSEs which are partly farmer-owned. Having synthesized the key social enterprise governance literature and framed it alongside the broader paradox theory, we used narratives to explore how tensions are articulated, how they can be applied within an adapted paradox framework, and how governance (...) actors seek to mitigate paradoxes. The paper contributes to current debates in social enterprise scholarship concerning hybridity :455–476, 2010; in Institutional logics in action, Part B, 2012), hybrid organizing :397–441, 2014) and operational tensions :407–442, 2013) by illustrating empirically how the central social/enterprise paradox manifests in FTSEs governance arrangements. We build on the paradox categories proposed by Lüscher and Lewis :221–240, 2008) and adapted in Smith et al. :407–442, 2013) by developing a recursive model of legitimacy-seeking governance processes, conceptualizing how boards seek to mitigate, but not necessarily resolve, paradoxes. (shrink)

Both sustainability and identity are said to be paradoxical issues in organizations. In this study we look at the paradoxes of corporate sustainability at the individual level by studying the identity work of those managers who hold sustainability-dedicated roles in organizations. Analysing 26 interviews with sustainability managers, we identify three main tensions affecting their identity construction process: the business versus values oriented, the organizational insider versus outsider and the short-term versus long-term focused identity work tensions. When dealing with these (...) tensions, some interviewees express a paradoxical perspective in attempting to accept and maintain the two poles of each of them simultaneously. It emerges in particular that metaphorical reasoning can be used by sustainability managers in varied ways to cope with the tensions of identity work. We read these findings in light of the existing literature on the relation between paradoxes and identity work, highlighting and discussing their implications for both research and practice. (shrink)

This article focuses on the construction of two types of non-logical paradoxes in news discourse: 1) inconsistencies of positions and acts; 2) conflicts between reality and expectations or common sense. I will argue that these paradoxes are constructed by various discursive devices and will demonstrate the key role played by conventional and conversational implicatures in this regard. The discussion will focus on 23 items covering disputes between ultra-Orthodox and secular Jews, broadcast on mainstream Israeli television news in 2009. (...) I will show that the journalists consistently attribute paradoxicality to Haredim, and that this corresponds with the common public bitterness towards them because they enjoy financial support from the government, while sharing little of the economic and security burden. Moreover, I will argue that the paradoxical representations of Haredim rely on the secular ‘we’ group view and serve to base its common sense and norms. (shrink)

We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources (...) are tightly related, and can be cleared up by adopting a particular substructural logic in place of classical logic. We then argue that our perspective can be justified via an informational semantics of contraction-free substructural logics. (shrink)

A solution of the zeno paradoxes in terms of a discrete space is usually rejected on the basis of an argument formulated by hermann weyl, The so-Called tile argument. This note shows that, Given a set of reasonable assumptions for a discrete geometry, The weyl argument does not apply. The crucial step is to stress the importance of the nonzero width of a line. The pythagorean theorem is shown to hold for arbitrary right triangles.

1 Background for the Uninitiated RICHMOND CAMPBELL Paradoxes are intrinsically fascinating. They are also distinctively ...

The notion of grounding is usually conceived as an objective and explanatory relation. It connects two relata if one—the ground—determines or explains the other—the consequence. In the contemporary literature on grounding, much effort has been devoted to logically characterize the formal aspects of grounding, but a major hard problem remains: defining suitable grounding principles for universal and existential formulae. Indeed, several grounding principles for quantified formulae have been proposed, but all of them are exposed to paradoxes in some very (...) natural contexts of application. We introduce in this paper a first-order formal system that captures the notion of grounding and avoids the paradoxes in a novel and non-trivial way. The system we present formally develops Bolzano’s ideas on grounding by employing Hilbert’s ε-terms and an adapted version of Fine’s theory of arbitrary objects. (shrink)

This chapter contains sections titled: The concept of phenomenal character is closely related to that of a phenomenal quality. If phenomenal characters are just maximally specific phenomenal qualities, it would follow that there are no phenomenal characters either. The first section gives reasons for fearing that observational predicates are susceptible to sorites paradoxes, but denies that predicates such as “painful” are perfectly observational. They are instead phenomenal, in a sense developed in the second section. The third section considers and (...) rejects a final attempt to revive a sorites paradox for painful. The fourth section tentatively places these thoughts against a background of a general account of sorites paradoxes, on which they may reflect either speakers' ignorance or semantic indeterminacy or both, depending on the facts of the particular case. The arguments of this chapter therefore have parallels for the paradox of small numbers. (shrink)

In the Western philosophical tradition, the earliest recognized paradoxes are attributed to Zeno of Elea (ca. 490–430 B.C.E.) and to Eubulides of Miletus (fl. 4th century B.C.E.). In the Chinese tradition, the earliest and most well-known paradoxes are ascribed to figures associated with the “School of Names” (ming jia 名家), a diverse group of Warring States (479–221 B.C.E.) thinkers who shared an interest in language, logic, and metaphysics. Their investigations led some of these thinkers to propound puzzling, paradoxical (...) statements such as “Today go to Yue but arrive yesterday,” “White horses are not horses,” and “Mountains and gorges are level.” Such paradoxes seem to have been intended to highlight fundamental features of reality or subtleties in semantic relations between words and things. Why were thinkers who advanced paradoxes categorized as a school of “names”? In ancient China, philosophical inquiry concerning language and logic focused on the use of “names” (ming 名, also terms, labels, or reputation) and their semantic relations to “stuff” (shi 實, also objects, features, events, or situations). Hence for classificatory purposes, second-century B.C.E. Han-dynasty archivists grouped together assorted pre-Han figures whose most prominent ideas seemed to concern the relation between names and stuff—or at least strange, unorthodox uses of names—and dubbed them a school or lineage (jia 家) devoted to the study of names. Unfortunately, both the label and the grouping are misleading. Historically, the school was a retrospective, taxonomical fiction. The figures classified under the “School of Names” never formed a distinct circle, movement, tradition, or line of influence devoted to any particular doctrine, theme, method, or way of life. Their intellectual interests overlapped at most only partly, while also overlapping extensively with those of texts associated with other schools or traditions, such as the Mohist “Dialectics” 墨辯, the Zhuangzi 莊子, the Xunzi 荀子, and the Annals of Lü Buwei 呂氏春秋. What perhaps does set the School of Names apart is that some (though not all) of the figures associated with it apparently delighted in propounding paradoxical or preposterous sayings, while the other texts just mentioned generally (though not exclusively) seek to explain and debunk such utterances. (shrink)

Smith argues that, unlike other forms of evidence, naked statistical evidence fails to satisfy normic support. This is his solution to the puzzles of statistical evidence in legal proof. This paper focuses on Smith’s claim that DNA evidence in cold-hit cases does not satisfy normic support. I argue that if this claim is correct, virtually no other form of evidence used at trial can satisfy normic support. This is troublesome. I discuss a few ways in which Smith can respond.

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)

Mechanisms to engage lay citizens in science and technology are currently in vogue worldwide. While some engagement exercises aim to influence policy making, research suggests that they have had little discernable impacts in this regard. We explore the potentials and challenges of facilitating citizen engagement in nanotechnology from the “topdown,” addressing the following questions: Can academics and others within institutions initiate meaningful engagement with unorganized lay citizens from the top-down? Can they facilitate effective engagement among citizens, scientists, and policy makers (...) while building citizen engagement capacities? Is it possible to create independent bottom-up citizen engagement in scientific and technological issues from the top-down, and what are the challenges in doing so? Our experiences show that although academics can build citizens' individual, collective, and political capacities to engage with each other, scientists, and policy makers, this work is enormously time and energy intensive, and institutional support is needed to sustain it. (shrink)

Philosophical Issues, Volume 31, Issue 1, Page 355-373, October 2021.

Supererogatory acts—good deeds “beyond the call of duty”—are a part of moral common sense, but conceptually puzzling. I propose a unified solution to three of the most infamous puzzles: the classic Paradox of Supererogation (if it’s so good, why isn’t it just obligatory?), Horton’s All or Nothing Problem, and Kamm’s Intransitivity Paradox. I conclude that supererogation makes sense if, and only if, the grounds of rightness are multi-dimensional and comparative.

Aharon Aviram; The Paradoxes of Education for Democracy, or the Tragic Dilemmas of the Modern Liberal Educator, Journal of Philosophy of Education, Volume 20, I.

The starting point of Joseph Margolis' last philosophical effort is represented by the problem of the human "gap" in animal continuity: "There appear to be no comparable variants of animal evolution [...] effected by anything like the culturally enabled creation". While we share with other animals more or less refined forms of societal life, acquiring a natural language remains a distinctively human character: although it is grounded in the completely natural favourable changes in the human vocal apparatus and brain, the (...) merely causal emergence of language in humans reacts back into human primates by transforming them into persons or selves. The artifactuality of persons appears to be at the same time a natural and emergent phenomenon, constituting the other side of the process of language acquisition both by early hominids and by human infants. In this perspective the largely informal, mongrel and approximate functionality of ordinary language is interpreted as a good tool for the cultural animal to cope with the world, while the collective dimension of human forms of life appears as the shared context of external and internal constitution of the human selves. (shrink)