Name der Zeitschrift: Semiotica Jahrgang: 2017 Heft: 216 Seiten: 339-361.

In recent years, substructural approaches to paradoxes have become quite popular. But whatever restrictions on structural rules we may want to enforce, it is highly desirable that such restrictions be accompanied by independent philosophical motivation, not directly related to paradoxes. Indeed, while these recent developments have shed new light on a number of issues pertaining to paradoxes, it seems that we now have even more open questions than before, in particular two very pressing ones: what (independent) motivations (...) do we have (if any) for restrictions on structural rules, and what to make of the plurality of new logics emerging from these restrictions, i.e. how to ‘choose’ among the different options. In this paper, we address these two questions from the perspective of a dialogical conception of logic that we've been advocating in recent years. We will argue that dialogical interpretations of structural rules, that is, as rules determining specific properties of the dialogues in question, provide a conveniently neutral framework to adjudicate between the different substructural proposals that have been made in the literature on paradoxes. (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)

This paper aims to present how logic may undermine a parliamentary assault on democratic institutions based on the analysis conducted with reference to the so-called Polish constitutional crisis. I analyse whether a law can be reviewed on the basis of this law itself. The Polish Constitutional Tribunal faced such a problem while passing the verdict of 9th March, 2016, regarding the constitutionality of the amendment to the Statute on the Constitutional Tribunal from 22nd December, 2015. This problem, called a ‘verdict (...) paradox’, was claimed to be a type of the Liar paradox. I argue that, contrary to the common view, the problem of the verdict paradox is not based on the Liar paradox; for this purpose, a logical analysis is applied to four variants of a reasoning with regard to the constitutionality of the said amendment. The distinction between two levels of analysis concerning emerging reasonings, namely an abstract level and a concrete level placed in the context of the legal system, is also introduced. This paper demonstrates that although only two variants of the reasoning concerning a law’s judicial review based on the law itself involve logical contradiction, the possibility of employing reasonings from other variants must be excluded, albeit due to alternative reasons. Therefore, the Constitutional Tribunal’s decision to avoid the verdict paradox by passing over the reviewed provisions in the review process was correct and might be perceived as an example of how logic and reason can defend the institutional guarantees of political freedom. (shrink)

First paragraph: This paper seeks to understand various paradoxes as cases of conflicting rules. In particular, the ambition is to outline a new perspective on and response to the Liar -- though it will take us a while to get that far. We begin in Section 1 with an account of simple rule confliction. Section 2 then brings this account to bear on a paradox, the Secretary Liberation Paradox, which is readily seen to involve conflicting rules. Finally in (...) Section 3 I suggest that the Liar can also be seen as a case of rule confliction, and outline briefly how that perspective provides for Liar arguments to be blocked. (shrink)

In this paper Section 1 distinguishes between two modes of interpreting legal rules: rehearsal and discourse, arguing that the former takes priority over the latter in law, as in many other contexts. Section 2 offers two arguments that following a legal rule in the rehearsing mode presents a riddle. The first argument develops from law, and submits that legal rules do not tell us anything, because they are tautological. The second one develops from philosophy (Wittgenstein's later works), confronting us (...) with the paradox that incompatible courses of action may be derived from any rule. My solution presents a theory of rules as icons (Section 3). I use “icon” rather than “picture,” partly to avoid confusion with what is known among philosophers as “the picture theory of meaning.” Interpretation in the rehearsing mode hinges on imagination: imagining oneself in the space of reasons for action rather than reasoning oneself. In this act of imagination, we project ourselves into the rule in ways that are similar to the way we grasp the sense of paintings, music, stories, or poems. Finally (Section 4) I will defend the position that my view solves the puzzles in the second section, by arguing (a) that it is a better account of what Wittgenstein wrote than two competing theories (intuitionism and conventionalism), and (b) that it provides a more satisfactory account of how lawyers deal with legal rules in actual practice. (shrink)

Two readings of Wittgenstein's rule-following paradox dominate the literature: either his arguments lead to skepticism, and thus to the view that only a deflated account of meaning is available, or they lead to quietism, and thus to the view that no philosophical account of meaning is called for. I argue, against both these positions, that a proper diagnosis of the paradox points the way towards a constructive, non-sceptical account of meaning.

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

In virtue of what does a sign have meaning? This is the question raised by Wittgenstein's rule-following considerations. Semantic dispositionalism is a (type of) theory that purports to answer this question. The present paper argues that semantic dispositionalism faces a heretofore unnoticed problem, one that ultimately comes down to its reliance on unanalyzed notions of repeated types of signs. In the context of responding to the rule-following paradox—and offering a putative solution to it—this amounts to simply assuming a (...) solution to the problem in one domain and using it to solve the same problem in another. Given, moreover, the level at which the rule-following paradox undercuts dispositionalism—the level of the notion of a sign's repetition—the objections made to the view also rule out causal/informational theories of meaning as well as communitarian/assertion-theoretic ones as potential solutions to the rule-following paradox. (shrink)

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)

As it is well known, in the forties of the past century, Curry proved that in any logic S closed under Modus Ponens, uniform substitution of propositional variables and the Contraction Law, the naïve Comprehension axiom trivializes S in the sense that all propositions are derivable in S plus CA. Not less known is the fact that, ever since Curry published his proof, theses and rules weaker than W have been shown to cause the same effect as W causes. Among (...) these, the Contraction rule or the Modus Ponens axiom, for example, are to be noted. But, moreover, as Brady has proved, even the Generalized Modus Ponens axiom or the Generalized Contraction rule give rise to “Curry’s Paradox” under the same circumstances as W does. In some previous work by us, “weak relevant model structures” are defined on “weak relevant matrices” by generalizing Brady’s model structure MCL built upon Meyer’s Crystal matrix CL. We have proved that wr-ms only verify logics with the “depth relevance condition”. The aim of this paper is to show how to falsify gMPa and gRW in certain wr-ms. In particular, it will be shown that gMPa is falisfied in any wr-ms and gRW in any wr-ms verifying Routley and Meyer’s basic positive logic B+. (shrink)

Kripke’s version of Wittgenstein’s rule-following paradox has been influential. My concern is with how it—and Wittgenstein’s views more generally—have been perceived as undercutting the individualistic picture of mathematical practice: the view that individuals— Robinson Crusoes —can, entirely independently of a community, engage in cogent mathematics, and indeed have “private languages.” What has been denied is that phrases like “correctly counting” can be applied to such individuals because these normative notions can only be applied cogently in a context involving community (...) standards. I attempt to show that this shocking corollary doesn’t follow even if Kripke’s Wittgensteinian objections to dispositional approaches to rule-following are largely right. My reason for claiming this is that there is another solution to the rule-following paradox, one that doesn’t favor community standards over individual ones. Furthermore, it doesn’t replace truth conditions with assertability conditions; and this latter maneuver is essential to Kripke’s sceptical solution favoring the community over the individual. (shrink)

Saul Kripke has famously argued that the central question of Wittgenstein's Philosophical Investigations, at least in relation to Wittgenstein's discussion of meaning, is the question: what facts determine that a speaker is following a particular rule? For example, assuming that language-use is a rule-governed activity, what facts determine that the rule a speaker is complying with in her current usage of a word is equivalent to the rule she complied with in her previous usage of the (...) word? According to Kripke, Wittgenstein articulates this problem most perspicuously in the form of a paradox, which may be regarded as a new form of philosophical scepticism. This paper takes another look at Kripke's development of the Wittgensteinian paradox, advancing the thesis that the paradox admits of a very natural straight solution, one that has not been pursued in the scholarly literature, and one that Kripke himself entertains and then quickly disqualifies. Specifically, it is argued that Kripke's hypothetical sceptic errs in his response to the objection that he operates with a faulty model of the instruction one is given regarding a particular term or expression. Once the correct model of instruction is taken into account, the argument loses its plausibility. (shrink)

Redefining god -- The battle between grace and truth -- Qualifying the unqualified -- Breaking cultural rules -- Rejected to redeemed -- Who wants the oil? -- Sweet vindication -- Falling forward -- Pushing boundaries -- The power of again -- The now and the next -- A clean slate.

An apparent paradox proposed by Aharonov and Vaidman in which a single particle can be found with certainty in two (or more) boxes is analyzed by way of a simple thought experiment. It is found that the apparent paradox arises from an invalid counterfactual usage of the Aharonov-Bergmann-Lebowitz (ABL) rule and effectively attributes conflicting properties not to the same particle but no different particles. A connection is made between the present analysis and the consistent histories formulation of Griffiths. Finally, (...) a critique is given of some recent counterarguments by Vaidman against the rejection of the counterfactual usage of the ABL rule. (shrink)

The rule-following paradox of Kripke's Wittgenstein posits that there is no fact of the matter about an individual that can determine whether he means one thing or another by a term, such as "+". The paradox thus renders the existence of meaning illusory. The objective of this thesis is to examine the paradox and try to offer a version of a dispositional account that can counteract Kripke's skeptics. ;Gaining insights from previous dispositionalist accounts of meaning and rule-following, including (...) those of Dretske, Fodor, Millikan, Martin & Heil, Shogenji, and Yallowitz, my project is to put all those insights together to formulate a functional view of human dispositions to rule-following which will resolve the error, finitude, and first-person epistemic problems that Kripke raises against the dispositionalist approach. Specifically, I argue that rule-following or meaning consists in one's possessing a disposition, realistically construed. A rule-following disposition is real in the sense that it is responsible for, and hence not to be equated with, its manifestations under various conditions. A person acquires a real disposition to rule-following through a learning history which is constrained by biologically innate human endowments of learning and cognition. The error problem then becomes the problem of how to identify the disposition without vacuity or circularity. My claim is that identifying a rule-following disposition is a task of scientific hypothesizing, which is epistemically and methodologically sound. The finitude problem is in my view a form of Humean inductive skepticism. My response to it is to adopt a reliabilist theory of justification and its treatment of the induction problem. A distinctive contribution of mine is to offer a functionalist account of dispositions and introspection in the resolution of the first-person epistemic problem. My aim is to do full justice to the phenomenology and epistemology of meaning and rule-following from the first-person point of view. ;My conclusion is that a satisfactory dispositional account such as the one I offer not only vindicates the reality of rule-following and meaning but also increases our understanding of the nature of meaning and human rule-following phenomenon. (shrink)

In §201 of Philosophical Investigations, Ludwig Wittgenstein puts forward his famous "rule-following paradox". The paradox is how can one follow in accord with a rule - the applications of which are potentially infinite - when the instances from which one learns the rule and the instances in which one displays that one has learned the rule are only finite? How can one be certain of rule-following at all? In Wittgenstein: On Rules and Private Language, Saul (...) Kripke concedes the skeptical position that there are no facts that we follow a rule but that there are still conditions under which we are warranted in asserting of others that they are following a rule. In this paper, I explain why Kripke's solution to the rule-following paradox fails. I then offer an alternative. (shrink)

: HIPAA is often described as a privacy rule. It is not. In fact, HIPAA is a disclosure regulation, and it has effectively dismantled the longstanding moral and legal tradition of patient confidentiality. By permitting broad and easy dissemination of patients’ medical information, with no audit trails for most disclosures, it has undermined both medical ethics and the effectiveness of medical care.

We reflect on lessons that the lottery and preface paradoxes provide for the logic of uncertain inference. One of these lessons is the unreliability of the rule of conjunction of conclusions in such contexts, whether the inferences are probabilistic or qualitative; this leads us to an examination of consequence relations without that rule, the study of other rules that may nevertheless be satisfied in its absence, and a partial rehabilitation of conjunction as a ‘lossy’ rule. A (...) second lesson is the possibility of rational inconsistent belief; this leads us to formulate criteria for deciding when an inconsistent set of beliefs may reasonably be retained. (shrink)

This paper focuses on the dynamics of ethical perspectives that embody the Golden Rule of Morality. Based on critical analysis of this rule in various cultural and religious contexts, but also from the perspective of humanism, the author presents its paradoxical character, the essence of which is interpreted here in terms of a pointer to metaphysical reality. It turns out that social conditionality, as well as the self-referential concept as a starting point of any ethical reasoning, are serious (...) epistemological challenges for the application of the Golden Rule in the position of universal normativity that this study addresses. On the other hand, Judeo-Christian cosmology and the related basis for ethical foundations is presented here as an inspirational space of ethical reasoning in which the paradoxical character of the Golden Rule becomes rather an indicator of a deeper metaethical interpretation of one's own particular ethical attitudes and outcomes than a practical guide to the discovery of ethical universals. (shrink)

I consider Lewis’ appeal to naturalness to solve Kripke ’s rule - following paradox. I then present a different interpretation of this paradox and offer reasons for thinking that this is what Kripke had in mind. I argue that Lewis’ proposal cannot provide a solution to this version of paradox.

‘Rule-following’ is a name for a cluster of phenomena where we seem both guided and “normatively” constrained by something general in performing particular actions. Understanding the phenomenon is important because of its connection to meaning, representation, and content. This article gives an overview of the philosophical discussion of rule-following with emphasis on Kripke’s skeptical paradox and recent work on possible solutions. Part I of this two-part contribution is devoted to the basic issues from Wittgenstein to Kripke. Part II (...) will be about recent answers to the skeptical paradox and Boghossian’s and Wright’s new puzzles. (shrink)

The purpose of this note is to examine the claim made by Howard Smokler that “Goodman's paradox should be considered as an independent argument against a conception of inductive logic which makes use of rules of acceptance”.Smokler's claim arises from his treatment of Goodman's paradox in the form given it by Israel Scheffler. Schefflerhas discussed this paradox primarily in the context of a methodology of induction which views inductive rules as rules of acceptance permitting one to assert detached conclusions. The (...) inductive rule considered by Scheffler is described as follows: What leads us to make one particular prediction rather than its opposite is not its deducibility froIII evidence but rather its congruence with a generalization thoroughly in accord with all such evidence, and the correlative disconfirmation of the contrary generalization by the same evidence.. (shrink)

This paper presents two possibility results and one impossibility result about a situation with three voters under a pairwise majoritarian aggregation function voting on a countably infi nite number of candidates. First, from individual orders with no maximal or minimal element, it is possible to generate an aggregate order with a maximal or minimal element. Second, from dense individual orders, it is possible to generate a discrete aggregate order. Finally, I show that, from discrete orders with a particular property, namely (...) the finite-distance property, it is not possible to generate a dense aggregate order. (shrink)

This book develops a framework for analysing strategic rationality, a notion central to contemporary game theory, which is the formal study of the interaction of rational agents and which has proved extremely fruitful in economics, political theory and business management. The author argues that a logical paradox lies at the root of a number of persistent puzzles in game theory, in particular those concerning rational agents who seek to establish some kind of reputation. Building on the work of Parsons, Burge, (...) Gaifman and Barwise and Etchemendy, Robert Koons constructs a context-sensitive solution to the whole family of liar-like paradoxes including, for the first time, a detailed account of how the interpretation of paradoxical statements is fixed by context. This analysis provides an understanding of how the rational agent model can account for the emergence of rules, practices and institutions. (shrink)

The rule-following debate, in its concern with the metaphysics and epistemology of linguistic meaning and mental content, goes to the heart of the most fundamental questions of contemporary philosophy of mind and language. This volume gathers together the most important contributions to the topic, including papers by Simon Blackburn, Paul Boghossian, Graeme Forbes, Warren Goldfarb, Paul Horwich, John McDowell, Colin McGinn, Ruth Millikan, Philip Pettit, George Wilson, and José Zalabardo. This debate has centred on Saul Kripke's reading of the (...) rule-following sections in Wittgenstein and his consequent posing of a "sceptical paradox" that threatens our every day notions of linguistic meaning and mental content. These essays are attempts to respond to this challenge and represent some of the most important work in contemporary theory of meaning. They examine the notion of meaning; whether it is possible to find a suitable meaning-constituting fact from our previous behaviour or mental histories; objections to, and defenses of, dispositional accounts of meaning; the plausibility of non-factualism about meaning; our attempts to develop non-reductionist accounts of meaning; and the sources of the normativity which attaches to meaning, such as the linguistic practice of the community or the dispositions of the individual. With an introductory essay and a comprehensive guide to further reading the book is an excellent resource for courses in philosophy of mind, philosophy of language, Wittgenstein, and metaphysics, as well as for all philosophers, linguists, and cognitive scientists with interests in these areas. Contributors include Simon Blackburn, Paul Boghossian, Graeme Forbes, Warren Goldfarb, Paul Horwich, John McDowell, Colin McGinn, Alexander Miller, Ruth Garrett Millikan, Philip Pettit, George. M. Wilson, Crispin Wright, and José L. Zalabardo. (shrink)

Quine and Kripke's Wittgenstein both present “skeptical” arguments for the conclusion that there are no facts about meaning. In each case the argument for the conclusion is that if there are facts about meaning, then they must be determined by some more fundamental facts, but facts about meaning are not determined by any such facts. Consequently there are no facts about meanings. Within this overall framework, Quine and Kripke's Wittgenstein differ substantially — both in their reasons for thinking that facts (...) about meaning are not determined by other facts, and in their responses to the alleged elimination of these facts. Despite this, I believe that their arguments fail for essentially the same reason; each equivocates about what it means for one set of facts to determine another. Once the equivocation is eliminated, the arguments lose their plausibility. (shrink)

I endorse Kripke's (Wittgenstein's) conclusion that the standard of correct application required by the notion of rule-following can only be made sense of in terms of intersubjective agreement. This is not to be taken, as Kripke does, merely as providing assertibility conditions, but rather as a genuine account of what normativity consists in. As Blackburn has pointed out, this result entails that the notion of objective judgment is dependent, in a sense, on the shared inclinations of the members of (...) the community. But since the sceptical paradox admits of no noncommunal solution, it is the inclination-independence of the notion of objective judgment that has to be given up. (shrink)

Inferential expressivism makes a systematic distinction between inferences that are valid qua preserving commitment and inferences that are valid qua preserving evidence. I argue that the characteristic inferences licensed by the principle of comprehension, from "x is P" to "x is in the extension of P" and vice versa, fail to preserve evidence, but do preserve commitment. Taking this observation into account allows one to phrase inference rules for unrestricted comprehension without running into Russell’s paradox. In the resulting logic, one (...) can derive full second-order arithmetic. Thus, it is possible to derive classical arithmetic in a consistent logic with unrestricted comprehension. (shrink)

The project of this chapter is to explore some relations between the rule-following considerations and radical interpretation. I spell out the sense in which the rule-following considerations are about meaning determination, and investigate whether the principle of meaning determination used in the early Davidson's account of meaning determination - the principle of charity - provides an answer to what I shall call "Wittgenstein's paradox". More precisely, I am interested in one aspect of the paradox: the "problem of objectivity". (...) My question then is whether meaning, as determined by charity, is such that the correctness of the applications of meaningful expressions is an objective matter. After running us through the basics of the radical interpretation account of meaning determination I argue that the principle of charity does seem to fall prey to the problem of objectivity. After unsuccessfully trying to rescue objectivity by means of Lewisian natural properties, this is the verdict I in the end endorse. (shrink)

In The Grasshopper: Games, Life, and Utopia, Suits maintains the following two theses: game-playing is defined as ‘activity directed towards bringing about a specific state of affairs, using only means permitted by rules, where the rules prohibit more efficient in favour of less efficient means, and where such rules are accepted just because they make possible such activity’ and ‘game playing is what makes Utopia intelligible.’ Observing that these two theses cannot be jointly maintained absent paradox, this essay explores the (...) logical possibility that if is true, then must be false. More specifically, in the tradition of conceptual analysis it is argued that Suits’ definition of game-playing is too narrow inasmuch as it excludes really magnificent Utopian games of significance. (shrink)

Famously, Kripke has argued that the central portion of the Philosophical Investigations describes both a skeptical paradox and its skeptical solution. Solving the paradox involves the element of the community, which determines correctness conditions for rule-following behavior. What do such conditions precisely consist of? Is it accurate to say that there is no fact to the matter of rule following? How are the correctness conditions sustained in the community? My answers to these questions revolve around the idea that (...) a rule is followed insofar as a convention is in place. In particular, I consider the game-theoretic definition of convention offered by David Lewis and I show that it illuminates essential aspects of the communitarian understanding of rule-following. Make the following experiment: say “It’s cold here” and mean “It’s warm here”. Can you do it?Ludwig Wittgenstein, Philosophical Investigations, 1953, §510.I can’t say “it’s cold here” and mean “it’s warm here”—at least, not without a little help from my friends.David Lewis, Convention. (shrink)

Logical orthodoxy has it that classical first-order logic, or some extension thereof, provides the right extension of the logical consequence relation. However, together with naïve but intuitive principles about semantic notions such as truth, denotation, satisfaction, and possibly validity and other naïve logical properties, classical logic quickly leads to inconsistency, and indeed triviality. At least since the publication of Kripke’s Outline of a theory of truth , an increasingly popular diagnosis has been to restore consistency, or at least non-triviality, by (...) restricting some classical rules. Our modest aim in this note is to briefly introduce the main strands of the current debate on paradox and logical revision, and point to some of the potential challenges revisionary approaches might face, with reference to the nine contributions to the present volume.For a recent introduction to non-classical theories of truth and other semantic notions, see the excellent Beall a .. (shrink)

Andrew Bacon, John Hawthorne, and Gabriel Uzquiano have recently argued that free logics—logics that reject or restrict Universal Instantiation—are ultimately not promising approaches to resolving a family of intensional paradoxes due to Arthur Prior. These logics encompass ramified and contextualist approaches to paradoxes, and broadly speaking, there are two kinds of criticism they face. First, they fail to address every version of the Priorean paradoxes. Second, the theoretical considerations behind the logics make absolutely general statements about all (...) propositions, properties of propositions, etc., but because this sort of intensional quantification is always restricted in the logics, they cannot even express those considerations. I present a novel sort of free logic, which rejects the standard Universal Instantiation but validates a restricted form of the rule, and which addresses both kinds of criticism by allowing some propositions to be unrestricted in their quantification. (shrink)

There are two paradoxes of satisfaction, and they are of different kinds. The classic satisfaction paradox is a version of Grelling’s: does ‘does not satisfy itself’ satisfy itself? The Unsatisfied paradox finds a predicate, P, such that Px if and only if x does not satisfy that predicate: paradox results for any x. The two are intuitively different as their predicates have different paradoxical extensions. Analysis reduces each paradoxical argument to differing rule sets, wherein their respective pathologies lie. (...) Having different pathologies, they are paradoxes of different kinds. Furthermore, each of these satisfaction paradoxes has an analogue with the same pathology in set theory. Therefore, these analogues are respectively of the same two kinds. This level of abstraction is significant in that it tracks two related but different pathologies. Thus, not all paradoxes of semantics and set theory share the same pathology: there are at least two kinds of paradox cutting across the semantic and set-theoretic distinction. (shrink)

JEL Classification: B41, B53, B31, B2, P48, A12 Abstract: Wittgenstein’s rule-following paradox has important implications for two aspects of Austrian theory. First, it makes it possible to reconcile the Misesian, Rothbardian, and hermeneutical approaches to methodology; second, it provides a way of defending a stateless legal order against the charge that such an order lacks, yet needs, a final arbiter.

In this article, I engage with what relevant literature addresses as the ‘paradox of democracy’ and trace it back to the dialectic between authorization and representation established by social contract theories. To make my argument, I take Rousseau’s Social Contract as a paradigmatic example of the paradox and analyse it in light of Hegel’s critical response. My aim is to show that, although Rousseau rejects the idea of representing the popular will, representation resurfaces in his Republic from top to bottom (...) and engenders a structural opposition between citizens and rulers: drawing on the Hegelian scrutiny of contractarianism, I focus on three key moments in Rousseau’s theory, namely the Lawgiver, the majority rule and the executive power. After illustrating how the social contract undermines democratic participation in deliberative processes, I suggest that Hegel’s philosophy of right overcomes the paradox by positively assuming it as a dialectical contradiction that requires a specific constitutional approach to democracy. In this sense, I argue, the Hegelian perspective on democratic deliberation helps us to better frame Rousseau’s ambition to conceive the Republic as a free community of equals and urges us to elaborate a more coherent understanding of participation in a pluralistic society. (shrink)