We prove that various classical tree forcings—for instance Sacks forcing, Mathias forcing, Laver forcing, Miller forcing and Silver forcing—preserve the statement that every real has a sharp and hence analytic determinacy. We then lift this result via methods of inner model theory to obtain level-by-level preservation of projective determinacy (PD). Assuming PD, we further prove that projective generic absoluteness holds and no new equivalence classes are added to thin projective transitive relations by these forcings.

This paper distinguishes between definiteness and determinacy. Definiteness is seen as a morphological category which, in English, marks a uniqueness presupposition, while determinacy consists in denoting an individual. Definite descriptions are argued to be fundamentally predicative, presupposing uniqueness but not existence, and to acquire existential import through general type-shifting operations that apply not only to definites, but also indefinites and possessives. Through these shifts, argumental definite descriptions may become either determinate or indeterminate. The latter option is observed in (...) examples like ‘Anna didn’t give the only invited talk at the conference’, which, on its indeterminate reading, implies that there is nothing in the extension of ‘only invited talk at the conference’. The paper also offers a resolution of the issue of whether possessives are inherently indefinite or definite, suggesting that, like indefinites, they do not mark definiteness lexically, but like definites, they typically yield determinate readings due to a general preference for the shifting operation that produces them. (shrink)

This study is an in-depth examination of the allure of Cartesianism. Its central focus is to uncover the grounds of Cartesianism in the will, and to show how such a grounding accounts for Descartes' immediate popularity and expansive influence. Cartesianism is generally taken to be a species of rationalism or foundationalism. However, it is essential to understanding Cartesianism to see that it has its foundations in an act of pure will. ;This rarely discussed aspect of the grounds of Descartes' method (...) determines every aspect of Cartesianism and is most accessible in the Discourse on Method. However, this is one of the only studies to examine The Rules for the Direction of the Mind from the perspective of Cartesian willfulness. Enumeration operates in The Rules in lieu of prudence and memory, making it appear that the method can be successful without a moment of judgment and concealing the shortcomings of the method which Descartes was not yet ready to admit as clearly as he would later in the Discourse. ;Vico was perhaps the first philosopher to appreciate the foundation of Cartesianism in the will. He was certainly the first to articulate the implications of this facet of Cartesianism in detail. The significance of the primacy of the will at the inception of Cartesianism is that a philosophical comportment to the world, oriented to an apprehension and articulation of the truth of the whole is sacrificed for the possibility of certainty and mastery. Vico defends the traditional project of philosophy against the Cartesian attempt to redefine the paradigm, and he does so in modern terms, in direct response to Descartes. ;Grounded in pure willfulness, Cartesian modernism engendered a myriad of constructivist projects which has polarized the history and field of philosophy. Those who pursue the Cartesian ideal without a sense of irony do so at the expense of a belief to the intelligibility of their experience, for their studies take place in abstract, imaginary, and hypothetical realms. Post-moderns, who have rejected Cartesian method, also abandon the possibility of the intelligibility of their experience for they are unable to fathom non-Cartesian forms of intelligibility. The only philosophical response to Cartesianism in the modern era is to understand it well enough to recognize its influence on our understanding, and try to transcend that influence. (shrink)

In his previous work, the author has introduced the axiom schema of inductive dichotomy, a weak variant of the axiom schema of inductive definition, and used this schema for elementary ) positive operators to separate open and clopen determinacies for those games in which two players make choices from infinitely many alternatives in various circumstances. Among the studies on variants of inductive definitions for bounded ) positive operators, the present article investigates inductive dichotomy for these operators, and applies it to (...) constructive investigations of variants of determinacy statements for those games in which the players make choices from only finitely many alternatives. As a result, three formulations of open determinacy, that are all classically equivalent with each other, are equivalent to three different semi-classical principles, namely Markov’s Principle, Lesser Limited Principle of Omniscience and Limited Principle of Omniscience, over a suitable constructive base theory that proves clopen determinacy. Open and clopen determinacies for these games are thus separated. Some basic results on variants of inductive definitions for \ positive operators will also be given. (shrink)

The supervaluationist approach to branching time (‘SBT-theory’) appears to be threatened by the puzzle of retrospective determinacy: if yesterday I uttered the sentence ‘It will be sunny tomorrow’ and only in some worlds overlapping at the context of utterance it is sunny the next day, my utterance is to be assessed as neither true nor false even if today is indeed a sunny day. John MacFarlane (“Truth in the Garden of Forking Paths” 81) has recently criticized a promising solution (...) to this puzzle for falling short of an adequate account of ‘actually’. In this paper, I aim to rebut MacFarlane's criticism. To this effect, I argue that: (i) ‘actually’ can be construed either as an indexical or as a nonindexical operator; (ii) if ‘actually’ is nonindexical, MacFarlane's criticism is invalid; (iii) there appear to be independent reasons for SBT-theorists to claim that ‘actually’ is a nonindexical expression. (shrink)

Possibility semantics offers an elegant framework for a semantic analysis of modal logic that does not recruit fully determinate entities such as possible worlds. The present papers considers the application of possibility semantics to the modeling of the indeterminacy of the future. Interesting theoretical problems arise in connection to the addition of object-language determinacy operator. We argue that adding a two-dimensional layer to possibility semantics can help solve these problems. The resulting system assigns to the two-dimensional determinacy (...) operator a well-known logic (coinciding with the logic of universal modalities under global consequence). The paper concludes with some preliminary inroads into the question of how to distinguish two-dimensional possibility semantics from the more established branching framework. (shrink)

There are some properties, like being bald, for which it is vague where the boundary between the things that have it and the things that do not lies. A number of arguments threaten to show that such properties can still be associated with determinate and knowable boundaries: not between the things that have it and those that don’t, but between the things such that it is borderline at some order whether they have it and the things for which it is (...) not. I argue that these arguments, if successful, turn on a contentious principle in the logic of determinacy: Brouwer’s Principle, that every truth is determinately not determinately false. Other paradoxes which do not appear to turn on this principle often tacitly make assumptions about assertion, knowledge and higher-order vagueness. In this paper I’ll show how one can avoid sharp higher-order boundaries by rejecting these assumptions. (shrink)

This dissertation explores several illuminating points of intersection between the philosophy of perception and the philosophy of vagueness. Among other things, I argue: (i) that it is entirely unhelpful to theorize about perception or consciousness using Nagelian "what it's like" talk; (ii) that a popular recent account of perceptual phenomenology (representationalism) conflicts with our best theory of vagueness (supervaluationism); (iii) that there are no vague properties, for Evans-esque reasons; (iv) that it is impossible to insert "determinacy" operators into representationalism (...) in a truth-preserving manner; and (v) that strong versions of dualism are unable to accommodate the possibility of borderline consciousness. (shrink)

In this paper I argue that Gareth Evans’ famous proof of the impossibility of de re indeterminate identity fails on a counterpart-theoretic interpretation of the determinacy operators. I attempt to motivate a counterpart-theoretic reading of the determinacy operators and then show that, understood counterpart-theoretically, Evans’ argument is straightforwardly invalid.

Supervaluational accounts of vagueness have come under assault from Timothy Williamson for failing to provide either a sufficiently classical logic or a disquotational notion of truth, and from Crispin Wright and others for incorporating a notion of higher-order vagueness, via the determinacy operator, which leads to contradiction when combined with intuitively appealing ‘gap principles’. We argue that these criticisms of supervaluation theory depend on giving supertruth an unnecessarily central role in that theory as the sole notion of truth, (...) rather than as one mode of truth. Allowing for the co-existence of supertruth and local truth, we define a notion of local entailment in supervaluation theory, and show that the resulting logic is fully classical and allows for the truth of the gap principles. Finally, we argue that both supertruth and local truth are disquotational, when disquotational principles are properly understood. (shrink)

Todd (2016) proposes an analysis of future-directed sentences, in particular sentences of the form 'will(φ)', that is based on the classic Russellian analysis of definite descriptions. Todd's analysis is supposed to vindicate the claim that the future is metaphysically open while retaining a simple Ockhamist semantics of future contingents and the principles of classical logic, i.e. bivalence and the law of excluded middle. Consequently, an open futurist can straightforwardly retain classical logic without appeal to supervaluations, determinacy operators, or any (...) further controversial semantical or metaphysical complication. In this paper, we will show that this quasi-Russellian analysis of 'will' both lacks linguistic motivation and faces a variety of significant problems. In particular, we show that the standard arguments for Russell's treatment of definite descriptions fail to apply to statements of the form 'will(φ)'. (shrink)

How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This paper proposes a model-theoretic framework for investigating the logic and semantics of that interaction. The framework is put forward in an ecumenical spirit: it is intended to be applicable to all theories of vagueness that express vagueness using a definiteness (or: determinacy) operator. We will (...) show how epistemicists, supervaluationists, and theorists of metaphysical vagueness like Barnes and Williams (2010) can interpret the framework.  We will also present a complete axiomatization of the logic we recommend to both epistemicists and local supervaluationists. . (shrink)

Most work on the semantic paradoxes within classical logic has centered around what this essay calls “linguistic” accounts of the paradoxes: they attribute to sentences or utterances of sentences some property that is supposed to explain their paradoxical or nonparadoxical status. “No proposition” views are paradigm examples of linguistic theories, although practically all accounts of the paradoxes subscribe to some kind of linguistic theory. This essay shows that linguistic accounts of the paradoxes endorsing classical logic are subject to a particularly (...) acute form of the revenge paradox: that there is no exhaustive classification of sentences into “good” and “bad” such that the T-schema holds when restricted to the “good” sentences unless it is also possible to prove some “bad” sentences. The foundations for an alternative classical nonlinguistic approach is outlined that is not subject to the same kinds of problems. Although revenge paradoxes of different strengths can be formulated, they are found to be indeterminate at higher orders and not inconsistent. (shrink)

Short abstract: this is a reply to Schoubye and Rabern's 2017 paper, in Mind, to my own 2016 paper, also in Mind, "Future Contingents are All False! On Behalf of a Russellian Open Future." -/- Long abstract: There is a familiar philosophical position – sometimes called the doctrine of the open future ­– according to which future contingents (claims about underdetermined aspects of the future) systematically fail to be true. For well over 2000 years, however, open futurists have been accused (...) of denying certain logical laws – bivalence, excluded middle, or both – for entirely ad hoc reasons, most notably, that their denials are required for the preservation of something we hold dear. In a recent paper, however, I sought to argue that this deeply entrenched narrative ought to be overturned. My thought was this: given a popular, plausible approach to the semantics of future contingents, we can reduce the question of their status to the Russell/Strawson debate concerning presupposition failure, definite descriptions, and bivalence. In that case, we will see that open futurists in fact needn’t deny bivalence (Russell), or, if they do, they will do so for perfectly general (Strawsonian) reasons – reasons for which we all must deny bivalence. Of course, the metaphysical objections to the open futurist’s model of the future will remain just as they were. However, the millennia-old “semantic” or “logical” objections to the doctrine would be answered. In developing this approach, however, I came in fact to see the deep attractions of what I saw as the Russellian approach to these questions, and in my paper, I sought to articulate and display those attractions. The principal advantage of the view I wished to defend is that it is simple (no determinacy operators, no supervaluations, no third truth values) and it is classical. The view I developed, however, has recently come in for criticism in a paper by Anders Schoubye and Brian Rabern. The aim of this paper is to defend this view against their criticisms. The result, I believe, is an improved version of the theory, and a renewed defense of a radical claim: future contingents are systematically false. (shrink)

To accommodate vague statements and predicates, I propose an infinite-valued, non-truth-functional interpretation of logic on which the tautologies are exactly the tautologies of classical two-valued logic. iI introduce a determinacy operator, analogous to the necessity operator in alethic modal logic, to allow the definition of first-order and higher-order borderline cases. On the interpretation proposed for determinacy, every statement corresponding to a theorem of modal system T is a logical truth, and I conjecture that every logical truth (...) on the interpretation corresponds to a theorem of T. the interpretation is extended to predicate logic. A borderline case of a predicate 'F’ is neither determinately F nor determinately not-F. Traditional sorites arguments are seen to fall apart early in their gradual stepwise passage from truth to falsity. (shrink)

In “Proof-Theoretic Justification of Logic”, building on work by Dummett and Prawitz, I show how to construct use-based meaning-theories for the logical constants. The assertability-conditional meaning-theory takes the meaning of the logical constants to be given by their introduction rules; the consequence-conditional meaning-theory takes the meaning of the logical constants to be given by their elimination rules. I then consider the question: given a set of introduction rules \, what are the strongest elimination rules that are validated by an assertability (...) conditional meaning-theory based on \? I prove that the intuitionistic introduction rules are the strongest rules that are validated by the intuitionistic elimination rules. I then prove that intuitionistic logic is the strongest logic that can be given either an assertability-conditional or consequence-conditional meaning-theory. In “Grounding Grounding” I discuss the notion of grounding. My discussion revolves around the problem of iterated grounding-claims. Suppose that \ grounds \; what grounds that \ grounds that \? I argue that unless we can get a satisfactory answer to this question the notion of grounding will be useless. I discuss and reject some proposed accounts of iterated grounding claims. I then develop a new way of expressing grounding, propose an account of iterated grounding-claims and show how we can develop logics for grounding. In “Is the Vagueness Argument Valid?” I argue that the Vagueness Argument in favor of unrestricted composition isn’t valid. However, if the premisses of the argument are true and the conclusion false, mereological facts fail to supervene on non-mereological facts. I argue that this failure of supervenience is an artifact of the interplay between the necessity and determinacy operators and that it does not mean that mereological facts fail to depend on non-mereological facts. I sketch a deflationary view of ontology to establish this. (shrink)

If there are vague numbers, it would be easier to use numbers as semantic values in a treatment of vagueness while avoiding precise cut-off points. When we assign a particular statement a range of values (less than 1 and greater than 0) there is no precise sharp cut-off point that locates the greatest lower bound or the least upper bound of the interval, I should like to say. Is this possible? “Vague Numbers” stands for awareness of the problem. I do (...) not present a serious theory of vague numbers. I sketch some reasons for using a many-value semantics. These reasons refer to my earlier treatments of determinacy and definitions of higher-order borderline cases. I also sketch how definitions of independence use the determinacy operator. The distinction between actually assigned values and values whose assignments are acceptable helps avoid unwanted precise cut-off points. (shrink)

Inspired by the supervenience-determined consequence relation and the semantics of agreement operator, we introduce a modal logic of supervenience, which has a dyadic operator of supervenience as a sole modality. The semantics of supervenience modality very naturally correspond to the supervenience-determined consequence relation, in a quite similar way that the strict implication corresponds to the inference-determined consequence relation. We show that this new logic is more expressive than the modal logic of agreement, by proposing a notion of bisimulation (...) for the latter. We provide a sound proof system for the new logic. We lift onto more general logics of supervenience. Related to this, we address an interesting open research direction listed in the literature, by comparing propositional logic of determinacy and noncontingency logic in expressive powers and axiomatizing propositional logic of determinacy over various classes of frames. We also obtain an alternative axiomatization for propositional logic of determinacy over universal models. (shrink)

The first part of this book is of an epistemological nature and develops an original theory of scientific objectivity, understood in a weak sense (as intersubjective agreement among the specialists) and a strong sense (as having precise concrete referents). In both cases it relies upon the adoption of operational criteria designed within the particular perspective under which any single science considers reality. The "object" so attained has a proper ontological status, dependent on the specific character of the criteria of reference (...) (regional ontologies). This justifies a form of scientific realism. Such perspectives are also the result of a complex cultural-historical situation. The awareness of such a "historical determinacy" of science justifies including in the philosophy of science the problems of ethics of science, relations of science with metaphysics, and social dimensions of science that overstep the traditional restriction of the philosophy of science to an epistemology of science. It is to this "context" that the second part of the book is devoted. (shrink)

We perceive a world of mind-independent macroscopic material objects such as stones, tables, trees, and animals. Our experience is the joint upshot of the way these things are and our route through them, along with the various relevant circumstances of perception; and it depends on the normal operation of our perceptual systems. How should we characterise our perceptual experience so as to respect its basis and explain its role in grounding empirical thought and knowledge? I offered an answer to this (...) question in Perception and its objects. Here I aim to clarify some of my central arguments and to develop and defend the position further in the light of subsequent critical discussion. (shrink)

Using a quantified propositional logic involving the operators it is known that and it is possible to know that, we formalize various interesting philosophical claims involved in the realism debate. We set out inferential rules for the epistemic modalities, ranging from ones that are obviously analytic, to ones that are epistemologically more substantive or even controversial. Then we investigate various aporias for the realism debate. These are constructively inconsistent triads of claims from our list: a claim expressing some sort of (...) common ground in the debate; a characteristically anti-realist thesis about truth and knowability; and a characteristically realist thesis about determinacy of truth value. Various patterns of reductio proof for these inconsistent triads are generated, so as to display their variety. The reductio proofs use only the inferential rules set out earlier. The philosophical utility of each aporia for the anti-realist is then assessed. This involves consideration of the acceptability of the premiss expressing common ground; the strength and plausibility of the anti-realist premiss; the strength of the realist premiss that is the ultimate target of the reductio; and the analytic status of the inferential rules applied within the proof. (shrink)

Logicians interested in naive theories of truth or set have proposed logical frameworks in which classical operational rules are retained but structural rules are restricted. One increasingly popular way to do this is by restricting transitivity of entailment. This paper discusses a series of logics in this tradition, in which the transitivity restrictions are effected by a determinacy constraint on assumptions occurring in both the major and minor premises of certain rules. Semantics and proof theory for 3-valued, continuum-valued and (...) surreal-valued semantics are given and the proof theory for the systems outlined. The framework is robust in the sense that no conditional, defined or primitive, which sustains the contraction principles underlying Curry paradoxes can be expressed. Classical recapture is smoothly achievable in the system which however is expressively limited and not semantically closed. The conclusion considers the issue of how to extend the system to capture full naive set theory. (shrink)

We consider fixed point logics, i.e., extensions of first order predicate logic with operators defining fixed points. A number of such operators, generalizing inductive definitions, have been studied in the context of finite model theory, including nondeterministic and alternating operators. We review results established in finite model theory, and also consider the expressive power of the resulting logics on infinite structures. In particular, we establish the relationship between inflationary and nondeterministic fixed point logics and second order logic, and we consider (...) questions related to the determinacy of games associated with alternating fixed points. (shrink)

In Metaphysics Delta 29 Aristotle distinguishes three classes of falsity and three corresponding senses of the ‘false’. The paper examines Aristotle’s arguments from a close-reading perspective, and analyses the meaning of false ‘as a thing’ , the significance of Aristotle’s dispute with Antisthenes on the subject of contradiction and verbal falsehood, and Aristotle’s conception of the false person. By paying attention to the precise order of Aristotle’s presentation, the paper raises the question about the manner in which the three classes (...) of falsity are related to one another and provides a tentative answer that could explain why the ‘false’ is included in the philosophical dictionary of the Metaphysics. On the proposed interpretation, Aristotle assumes that a fundamental difference operates in all cases of falsity , and that this difference is the outcome of the ontological determinacy of substance. Keywords: Aristotle; Metaphysics; falsity; factual falsity; propositional falsity; ethical falsity; Antisthenes; contradiction; substance; ontology; logic. (shrink)

We show that, assuming the Axiom of Determinacy, every non-selfdual Wadge class can be constructed by starting with those of level $\omega _1$ and iteratively applying the operations of expansion and separated differences. The proof is essentially due to Louveau, and it yields at the same time a new proof of a theorem of Van Wesep. The exposition is self-contained, except for facts from classical descriptive set theory.

It is shown that the determinacy of $G_{\delta \sigma }$ games of length $\omega ^2$ is equivalent to the existence of a transitive model of ${\mathsf {KP}} + {\mathsf {AD}} + \Pi _1\textrm {-MI}_{\mathbb {R}}$ containing $\mathbb {R}$. Here, $\Pi _1\textrm {-MI}_{\mathbb {R}}$ is the axiom asserting that every monotone $\Pi _1$ operator on the real numbers has an inductive fixpoint.

In lieu of an abstract, here is a brief excerpt of the content:Nāgārjuna's Affective Account of MisknowingRoshni PatelIt is maintained that all beings and (their) qualitiesAre the fuel for the fire of awareness.Having been incinerated by brilliantTrue analysis, they are (all) pacified.—Ratnāvalī (RV)1.971In Nāgārjuna's formulation, ignorance about the nature of existents is scorching and thereby needs the alleviation that true analysis offers. This article explores what ignorance feels like from the subjective side of a knower in the Madhyamaka Buddhist tradition (...) through an analysis of epistemic affect. I borrow two affective concepts—"epistemic emotion" and "epistemic feeling"—from theorists in Anglo-American analytic epistemology to discuss affectively charged misknowing.2 In this literature, epistemic emotions are affective experiences that participate in a knower's epistemic activity in positive or negative ways, but are not necessary for that activity to proceed. In contrast, epistemic feelings are affectively qualitative experiences that are integral to a knower's activity. With a focus on texts by Nāgārjuna, I present fear as a paradoxical epistemic emotion that correlates with a similarly pathogenic and instigative function in Buddhist moral psychology. I then present determinacy as a more subtly operating epistemic feeling in reificatory ignorance. In addition to expanding epistemologically oriented discussions within Buddhist philosophy, this article also contributes to scholarly discussion of epistemic affect by introducing determinacy as a new epistemic feeling. [End Page 44]Diffuse and Complex IgnoranceThe central role of ignorance in formulating the problem of suffering and its cessation implies that in many ways all of Buddhism is interested in how we know and understand. This centrality is evident in the Avijja Sutta when the Buddha states:Bhikkhus, ignorance is the forerunner in the entry upon unwholesome states, with shamelessness and fearlessness of wrongdoing following along. For an unwise person immersed in ignorance, wrong view springs up. For one of wrong view, wrong intention springs up. For one of wrong intention, wrong speech springs up. For one of wrong speech, wrong action springs up. For one of wrong action, wrong livelihood springs up. For one of wrong livelihood, wrong effort springs up. For one of wrong effort, wrong mindfulness springs up. For one of wrong mindfulness, wrong concentration springs up.(Saṃyutta Nikāya (SN) 45.1)Here we see that avijjā, or ignorance, impedes the path of removing suffering. Similarly, in the twelve links of dependent origination, ignorance is at the start of the chain conditioning the other links that culminate in suffering (SN 12.2). Nāgārjuna also positions ignorance as a potential gatekeeper when he says that ignorance (ajñāna) causes some people to be intolerant of the wisdom of the Mahāyāna path taught by the Buddhas (RV 4.83).3 While we have ample exposition on the role of ignorance in various causal chains, what remains elusive is how to recognize our own ignorance as such in the experiential folds of seeing, feeling, and knowing. This is especially the case in the early works of the critical project of Madhyamaka ("Middle Way") philosophy by Nāgārjuna. The bulk of these works presents arguments against any ignorant metaphysics that essentializes existents in efforts to claim epistemic access to an objective ultimate reality. This article argues that through a certain way of reading Madhyamaka philosophical texts, we find helpful information for recognizing what ignorance feels like. I develop the phenomenology of epistemic emotions and feelings that coincide with the ignorant practices centrally targeted by Madhyamaka critical analysis.The encompassing scope of ignorance motivates us to conceive of it as entangled with a range of elements, including the affective components of knowing. While the terms avijjā or avidyā, are most often translated as "ignorance" this term can be problematically imprecise in philosophical contexts. In the subfield of ignorance studies within current Western philosophy, ignorance is often classified according to the object of which a subject lacks knowledge. By this paradigm, ignorance can be (1) factual in [End Page 45] the case of not knowing a particular fact, (2) erotetic when a subject does not know the answer to a question, or (3) practical when a subject does... (shrink)

The intersectionality argument originating in Black feminism challenges the preponderance of “single-axis thinking” (Crenshaw), and the decolonial critique of Eurocentrism challenges the assumption of neutral universality or “zero-point hubris” (Castro-Gómez) on the part of colonial thinking. Inspired by these challenges, this paper brings decolonial, intersectional, and phenomenological thought into conversation to consider how philosophical thinking can operate in light of these risks. The first section distinguishes between the inevitable, existential condition by which we inhabit determinate forms of life, and the (...) pernicious way in which some forms come to masquerade as universal and dominate others. The second section aids in opposing the pernicious by working *through* the existential, showing that it is our very determinacy that fosters the possibility of understanding others and working toward universality on the basis of two arguments. First, we all experience ourselves as one among many, developing inside of an interpersonal reality in which interaction guides us to sense, and this shared structure of perspective renders us different and opens us to the possibility of further transformation through exposure. Second, thinking and determinacy are inevitably linked, as each of us draws on local mechanisms available to us to give expression to meanings we experience as non-local, and the possibility of universality lies on the horizon, in answerability to other pairings of determinacy and meaning. In the course of making these conceptual arguments, the paper flags both the mechanisms by which practical reality could be structured to encourage exposure to the determinacy that supports thinking, and the challenges and hubristic risks we face in doing so. (shrink)

We implement a recent characterization of metaphysical indeterminacy in the context of orthodox quantum theory, developing the syntax and semantics of two propositional logics equipped with determinacy and indeterminacy operators. These logics, which extend a novel semantics for standard quantum logic that accounts for Hilbert spaces with superselection sectors, preserve different desirable features of quantum logic and logics of indeterminacy. In addition to comparing the relative advantages of the two, we also explain how each logic answers Williamson’s challenge to (...) any substantive account of determinacy: For any proposition p, what could the difference between “p” and “it’s determinate that p” ever amount to? (shrink)

This paper adopts an economic interpretation of the legal process, explaining legal change as the outcome of the complex interplay of entrepreneurial forces operating inside, as well as outside the legal system. The question of concern is whether the concept of entrepreneur as elaborated by Kirzner in a theory of the market process can be extended to understand the legal process as well. The focus on the alertness of legal decision-makers, their capacity to learn from experience and the multitude of (...) legal and nonlegal sources they are referring to, seems to provide a possible methodology for an economic approach to law that avoids the exaggerated belief in the objectivity, determinacy and cogency of legal reasoning typical for mainstream law-and-economics, and at the same time the opposite exaggeration of law’s radical subjectivity and indeterminacy characterizing most of contemporary critical legal literature.Cet article adopte une interprétation économique du processus juridique en expliquant l’évolution du droit comme le résultat de l’interaction complexe de forces entrepreneuriales opérant à l’ intérieur et à l’extérieur du système juridique. Il s’agit de montrer que le concept d’entrepreneur élaboré par Kirzner pour expliquer le fonctionnement du processus de marché peut offrir une méthodologie également pour comprendre les processus de production du droit. En mettant l’accent sur la vigilance des décideurs, leur capacité d’apprendre par l’expérience, ainsi que la multitude des sources juridiques et extrajuridiques auxquelles ils se réfèrent, une approche économique du droit qui renvoie à cette théorie de l’entrepreneur, peut éviter d’un côté l’hypothèse irréaliste d’omniscience de l’autorité juridique qui sous-tend l’analyse économique traditionnelle du droit et de l’autre côté, l’hypothèse opposée non moins exagérée de la subjectivité et de l’indétermination radicales de l’évolution juridique qui caractérise une partie dominante de la littérature juridique critique contemporaine. (shrink)

This dissertation argues for a position called "legal pluralism". According to legal pluralism, most legal decision-making, especially decision-making by judges in "hard cases", is best analyzed as the application of a plurality of legal values which often conflict. Moreover, legal pluralism claims that these conflicts often cannot be resolved, and therefore decision-making in law is genuinely indeterministic in many cases. The position contrasts with two common accounts of judicial decision-making in hard cases: the claim that judicial decision-making is significantly determinate (...) and the claim that it is radically indeterminate . ;The first chapter argues for the first part of pluralism, namely that there is a plurality of legal values which typically conflict in hard cases of legal interpretation. It also argues against the doctrine of "intentionalism" which claims that determinacy can be achieved in legal interpretation by identifying the correct legal answer with the author's intended answer. The second chapter provides an extended analysis of Dworkin's doctrine of "law as integrity". It argues that Dworkin's theory of law is "monistic" in two senses. First, his theory attempts to provide a method for achieving deterministic decision-making; and secondly, his theory is committed to treating a single legal value--the value of "integrity"--as overriding. I claim that neither form of monism can plausibly be maintained. The third chapter argues that pluralism provides the best account of the special features of legal disagreement in hard cases and attempts to rebut counter-arguments suggesting that disagreement is epistemic disagreement only. The fourth and final chapter focuses on the nature of the values over which judges disagree. It proposes that the conflicts between values in some cases are genuine legal dilemmas because legal conflicts are often conflicts between "generically different" values or "incommensurable" values. In particular, "institutional" values--values which enhance the operation of law conceived as an institution having a certain function in society--are incommensurable with the values of substantive justice. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Diacritics 30.3 (2000) 90-104 [Access article in PDF] After Death Jonathan Strauss According to Philippe Ariès, the nineteenth century was a turning point in the history of death. On the one hand there emerged a new sense of the irreplaceability of individual people, of the finality of death and the immeasurable preciousness of a single life. On the other hand death, that which followed one's demise, became conceptually more (...) austere. For the first time since antiquity, perhaps ever, the belief that death is pure negativity or nothingness asserted itself with enough success to become a generally accepted cultural attitude. 1 This image of sheer nonexistence, this death stripped down to its ontological minimum, is the most extreme form of mortality that has arisen in the history of the West, the hardest perhaps to take, the most naked. In ways that could not have occurred before, these two developments in the history of death have worked with and against each other to create a new understanding of subjectivity, a set of theorizations about human individuality that, for all their diversity of detail, are bound together by a certain historical determinacy. Hegel's views on the relation between mortality and subjectivity, for instance, like Heidegger's or Blanchot's, have no precedent, but they do have endless repercussions. Whatever their causes, the newness and the effectiveness of these theories indicate that during the nineteenth century a unique cultural formation arose in relation to mortality. The moment still has not passed, since the basic elements of the new death continue to operate on contemporary imaginations and theorizations. What follows is an attempt to draw the portrait of the death that emerged for the first time in the nineteenth century: to critically and analytically examine formulations of the relation between death and identity in order to determine the value of absolute mortality as an individualizing principle. Often these formulations are most clearly articulated by post-nineteenth-century thinkers, but they are the products, and indeed the expressions, of that historical transformation that occurred sometime after the Revolution. When we read these texts and arguments, we are asking not merely whether they are valid as arguments, but about the value of the general attitude they reflect—the value not only of a specific kind of death, but of a kind of subjectivity that is unique to the last two hundred years. And since that subjectivity is probably the most significant product of those centuries, the most pervasive and the most intimately affecting, we are also, intentionally or not, asking about the value of a whole period.To read this relation between mortality and subjectivity, we must come to some understanding about the terms at issue, especially what death is or is not when considered in its most extreme form as simple nothingness. It may seem odd that this is an issue at all, but nonexistence has proven a difficult concept to integrate into theorizations [End Page 90] of human life. The first question to raise in this context is whether death can be considered a state, a divisive proposition on which much hangs. In the introduction to a recent collection of essays on metaphysics and death, John Martin Fischer baldly asserted that "being dead is a condition or a state" [4]. The philosopher Paul Edwards, however, has pointed to some of the "absurdities," as he puts it, of considering death as an ontological condition. To imagine death as a state is, he argues, to attribute to it some sort of being, but death, understood as the permanent loss of consciousness and experience, has no being and is simply absence. To imagine otherwise leads to attempts (made by such existentialist philosophers as Ferrater Mora [175-203] and Tillich) to understand death "from the inside"—that is, to imagine what it would be like to experience the absence of experience. 2 Edwards's approach does not deny the possibility or value of investigations into the psychological significance of that absolute privation (that is, the meaning of death for the living), but it does preclude any understanding of death as such. This is, undoubtedly, part of the... (shrink)

Thinkers have never been able to deny the centrality of negation and contradiction in everything human, despite all their efforts to banish both from the domains of truth, right, and beauty. Unless we properly understand the fundamental significance of negation and contradiction, we cannot free ourselves from bondage to opinion, arbitrary convention, and subjective taste. Of all philosophers, Hegel has most resolutely confronted the role of negation and contradiction in the most essential strivings of humanity, and it is high time (...) to put his comprehension to work. The essay does just this, showing how negation and contradiction operate in the different levels of logical determinacy and how their role in self-determination allows for truth, right, and beauty to be and to be conceived. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume's Natural History: Religion and "Explanation" M. JAMIE FERREIRA HUME'S BOLDLYSIMPLESTATEMENTof the genesis of religion--that "the anxious concern for happiness, the dread of future misery, the terror of death, the thirst for revenge, the appetite for food and other necessaries" led humankind to see "the first obscure traces of divinity"--is supported by appeals to what he considers plain common sense.' For example, given that at "the first origin of (...) society" (e4) our ancestors were obviously "ignorant and barbarous" (23), anxiously helpless in the face of threatening natural events--hence, obviously with neither the leisure nor the impulse nor the aptitude for serious reflection--it was obviously passionate fears and hopes, not reason, which motivated their beliefs. Given that the mind obviously "rises from inferior to superior," and that humankind obviouslyhasn't "inhabited palaces before huts and cottages or studied geometry before agriculture" (~4), polytheism obviously antedated monotheism. In the course of detailing his commonsensical account of the origin and development of religion, Hume highlights a wide variety of natural tendencies, principles, and propensities which are operative. Keith Yandell offers a recent reading of one such propensity at work in the origin of religion--namely, what Hume calls the "propensity of human nature, which leads into a system, that gives them some satisfaction" (29)--and Yandell explicitly takes it to be a propensity to an "explanatory" system.2 I want to argue in what follows that any reading of Hume's account of religion which highlights an explanatory motivation can be significantly misleading insofar as it obscures the way in which Hume's account differs markedly from other classical genetic accounts which emphasize explanation. ' The Natural History ofReligion, ed. H. E. Root (Stanford, CA, 1956), 28. Further parenthetical page references in the text will be to this work. His later formulation--"The primary religion of mankind arises chiefly from an anxious fear of future events" (65)--recalls Philo's pithy version, namely, "terror is the primary principle of religion" (Dialoguesconcerning Natural Religion, XII). ~Hume's "Inexplicable Mystery": His Views on Religion (Philadelphia, 199o), 9. Hereafter HIM. [5931 594 JOURNAL OF THE HISTORY OF PHILOSOPHY 33:4 OCTOBER 1995 In his account of the "propensity of human nature, which leads into a system, that gives them some satisfaction," Yandell admits that "no explanation is given of exactly what sort of satisfaction is in question," yet he goes on without a pause to speak of how "people accept different and various explanatory systems"; referring to a natural "propensity to understand," he concludes that "for Hume, we need not accept a religious system of explanation, but most of us in fact do so."s I suggest that Yandell's shift from "system" to "explanatory system," which is unheralded, is of crucial significance because the emphasis on explanation tends to call to a reader's mind just the sort of appeal which Hume decisively rejects. I shall argue that Hume draws our attention to and decisively excludes from his account a concept of explanation which actually does play an important role in other parallel accounts--namely, a concept which focuses on the integrity of a broad picture and an ultimate accounting; Hume points to such a concept in his references to the "frame of the universe," "final causes," and the "first rise of the visible system." Such a role might seem to elaborate Hume's appeal to common sense--after all, isn't the natural response to "unknown causes" to try to understand them, and isn't the attempt to understand them the same as looking for an "ultimate" explanation, however crude it might be at the outset? Although this might seem commonsensical to others (as we shall see), I want to argue that what Hume sees at work in the origin of religion is not a search for such an explanation, even a crude one. Rather, on Hume's view the only curiosity at work is a curiosity about how to cope: the propensity to a system is the propensity to the kind of determinacy which is expedient for control, and the only satisfaction the system provides is one in terms of a coping which is independent of truth-seeking... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume's Natural History: Religion and "Explanation" M. JAMIE FERREIRA HUME'S BOLDLYSIMPLESTATEMENTof the genesis of religion--that "the anxious concern for happiness, the dread of future misery, the terror of death, the thirst for revenge, the appetite for food and other necessaries" led humankind to see "the first obscure traces of divinity"--is supported by appeals to what he considers plain common sense.' For example, given that at "the first origin of (...) society" (e4) our ancestors were obviously "ignorant and barbarous" (23), anxiously helpless in the face of threatening natural events--hence, obviously with neither the leisure nor the impulse nor the aptitude for serious reflection--it was obviously passionate fears and hopes, not reason, which motivated their beliefs. Given that the mind obviously "rises from inferior to superior," and that humankind obviouslyhasn't "inhabited palaces before huts and cottages or studied geometry before agriculture" (~4), polytheism obviously antedated monotheism. In the course of detailing his commonsensical account of the origin and development of religion, Hume highlights a wide variety of natural tendencies, principles, and propensities which are operative. Keith Yandell offers a recent reading of one such propensity at work in the origin of religion--namely, what Hume calls the "propensity of human nature, which leads into a system, that gives them some satisfaction" (29)--and Yandell explicitly takes it to be a propensity to an "explanatory" system.2 I want to argue in what follows that any reading of Hume's account of religion which highlights an explanatory motivation can be significantly misleading insofar as it obscures the way in which Hume's account differs markedly from other classical genetic accounts which emphasize explanation. ' The Natural History ofReligion, ed. H. E. Root (Stanford, CA, 1956), 28. Further parenthetical page references in the text will be to this work. His later formulation--"The primary religion of mankind arises chiefly from an anxious fear of future events" (65)--recalls Philo's pithy version, namely, "terror is the primary principle of religion" (Dialoguesconcerning Natural Religion, XII). ~Hume's "Inexplicable Mystery": His Views on Religion (Philadelphia, 199o), 9. Hereafter HIM. [5931 594 JOURNAL OF THE HISTORY OF PHILOSOPHY 33:4 OCTOBER 1995 In his account of the "propensity of human nature, which leads into a system, that gives them some satisfaction," Yandell admits that "no explanation is given of exactly what sort of satisfaction is in question," yet he goes on without a pause to speak of how "people accept different and various explanatory systems"; referring to a natural "propensity to understand," he concludes that "for Hume, we need not accept a religious system of explanation, but most of us in fact do so."s I suggest that Yandell's shift from "system" to "explanatory system," which is unheralded, is of crucial significance because the emphasis on explanation tends to call to a reader's mind just the sort of appeal which Hume decisively rejects. I shall argue that Hume draws our attention to and decisively excludes from his account a concept of explanation which actually does play an important role in other parallel accounts--namely, a concept which focuses on the integrity of a broad picture and an ultimate accounting; Hume points to such a concept in his references to the "frame of the universe," "final causes," and the "first rise of the visible system." Such a role might seem to elaborate Hume's appeal to common sense--after all, isn't the natural response to "unknown causes" to try to understand them, and isn't the attempt to understand them the same as looking for an "ultimate" explanation, however crude it might be at the outset? Although this might seem commonsensical to others (as we shall see), I want to argue that what Hume sees at work in the origin of religion is not a search for such an explanation, even a crude one. Rather, on Hume's view the only curiosity at work is a curiosity about how to cope: the propensity to a system is the propensity to the kind of determinacy which is expedient for control, and the only satisfaction the system provides is one in terms of a coping which is independent of truth-seeking... (shrink)

In this paper we study the logical strength of the determinacy of infinite binary games in terms of second order arithmetic. We define new determinacy schemata inspired by the Wadge classes of Polish spaces and show the following equivalences over the system RCA0*, which consists of the axioms of discrete ordered semi‐rings with exponentiation, Δ10 comprehension and Π00 induction, and which is known as a weaker system than the popularbase theory RCA0: 1. Bisep(Δ10, Σ10)‐Det* ↔ WKL0, 2. Bisep(Δ10, (...) Σ20)‐Det* ↔ ATR0 + Σ11 induction, 3. Bisep(Σ10, Σ20)‐Det* ↔ Sep(Σ10, Σ20)‐Det* ↔ Π11‐CA0, 4. Bisep(Δ20, Σ20)‐Det* ↔ Π11‐TR0, where Det* stands for the determinacy of infinite games in the Cantor space (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

Schmidt’s game and other similar intersection games have played an important role in recent years in applications to number theory, dynamics, and Diophantine approximation theory. These games are real games, that is, games in which the players make moves from a complete separable metric space. The determinacy of these games trivially follows from the axiom of determinacy for real games, $\mathsf {AD}_{\mathbb R}$, which is a much stronger axiom than that asserting all integer games are determined, $\mathsf {AD}$. (...) One of our main results is a general theorem which under the hypothesis $\mathsf {AD}$ implies the determinacy of intersection games which have a property allowing strategies to be simplified. In particular, we show that Schmidt’s $(\alpha,\beta,\rho )$ game on $\mathbb R$ is determined from $\mathsf {AD}$ alone, but on $\mathbb R^n$ for $n \geq 3$ we show that $\mathsf {AD}$ does not imply the determinacy of this game. We then give an application of simple strategies and prove that the winning player in Schmidt’s $(\alpha, \beta, \rho )$ game on $\mathbb {R}$ has a winning positional strategy, without appealing to the axiom of choice. We also prove several other results specifically related to the determinacy of Schmidt’s game. These results highlight the obstacles in obtaining the determinacy of Schmidt’s game from $\mathsf {AD}$. (shrink)

This paper addresses debates in German idealism that arise in response to the modal shift in logic, proposed by Kant, from a logic of thinking to a logic of experience. With the Kantian logic of experience arises a problem of radical contingency or 'rhapsodic determination' for logic. While Fichte and Hegel attempt to resolve the problem of contingency by constructing rational systems aimed at established the grounds for logic, I show how Schelling brings into view, in a proto-existentialist movement, the (...) way in which the indeterminacy of the will undergirds rational system construction and, thereby, presents a limiting problem for the question of the value of system-building itself. (shrink)

This chapter analyzes the different ways to describe brain behaviour with the goal to provide a basis for an informed discussion of the nature of decisions and actions that humans perform in their lives. The chapter is organized as follows. Section 2 outlines a number of concepts exhibiting how many subtle details and distinctions lie behind the broad notions of determinacy and stochasticity. These details are necessary for a discussion, in Section 3, of particular aspects relevant for the characterization (...) of brain states and their dynamics. The descriptions of brain behaviour currently provided by neuroscience depend on the level and context of the descriptions. There is no clear-cut evidence for ultimately determinate or ultimately stochastic brain behaviour. As a consequence, there is no solid neurobiological basis to argue either in favour of or against any fundamental determination or openness of human decisions and actions. (shrink)

We show that each of $\Delta _{3}^{1}-{\rm CA}_{0}+\Sigma _{3}^{1}-{\rm IND}$ and $\Pi _{2}^{1}-{\rm CA}_{0}+\Pi _{3}^{1}-{\rm TI}$ proves $\Delta _{3}^{0}-{\rm Det}$ and that neither $\Sigma _{3}^{1}-{\rm IND}$ nor $\Pi _{3}^{1}-{\rm TI}$ can be dropped. We also show that neither $\Delta _{3}^{1}-{\rm CA}_{0}+\Sigma _{\infty}^{1}-{\rm IND}$ nor $\Pi _{2}^{1}-{\rm CA}_{0}+\Pi _{\infty}^{1}-{\rm TI}$ proves $\Sigma _{3}^{0}-{\rm Det}$. Moreover, we prove that none of $\Delta _{2}^{1}-{\rm CA}_{0}$, $\Sigma _{3}^{1}-{\rm IND}$ and $\Pi _{2}^{1}-{\rm TI}$ is provable in $\Delta _{1}^{1}-{\rm Det}_{0}={\rm ACA}_{0}+\Delta _{1}^{1}-{\rm Det}$.

We analyze the set-theoretic strength of determinacy for levels of the Borel hierarchy of the form$\Sigma _{1 + \alpha + 3}^0 $, forα<ω1. Well-known results of H. Friedman and D.A. Martin have shown this determinacy to requireα+ 1 iterations of the Power Set Axiom, but we ask what additional ambient set theory is strictly necessary. To this end, we isolate a family of weak reflection principles, Π1-RAPα, whose consistency strength corresponds exactly to the logical strength of${\rm{\Sigma }}_{1 + (...) \alpha + 3}^0 $determinacy, for$\alpha < \omega _1^{CK} $. This yields a characterization of the levels ofLby or at which winning strategies in these games must be constructed. Whenα= 0, we have the following concise result: The leastθso that all winning strategies in${\rm{\Sigma }}_4^0 $games belong toLθ+1is the least so that$L_\theta \models {\rm{``}}{\cal P}\left$exists, and all wellfounded trees are ranked”. (shrink)

Many theorists understand human rights as only aiming to secure a minimally decent existence, rather than a positively good or flourishing life. Some of the theoretical considerations that support this minimalist view have been mapped out in the philosophical literature. The aim of this paper is to explain how a relatively neglected theoretical desideratum – namely, determinacy – can be invoked in arguing for human rights minimalism. Most of us want a theory of human rights whose demands can be (...) realized, and which is acceptable to a range of worldviews. But we might also expect our theory to provide determinate answers to questions of scope (i.e. which putative rights are bona fide human rights?) and practical implementation (i.e. what concrete duties are generated by which rights?). A minimalist view of human rights makes it is easier to jointly fulfil all of these desiderata. (shrink)

A skeptical worry known as ‘the indeterminacy of computation’ animates much recent philosophical reflection on the computational identity of physical systems. On the one hand, computational explanation seems to require that physical computing systems fall under a single, unique computational description at a time. On the other, if a physical system falls under any computational description, it seems to fall under many simultaneously. Absent some principled reason to take just one of these descriptions in particular as relevant for computational explanation, (...) widespread failure of computational explanation would appear to follow. This paper advances a new solution to the indeterminacy of computation. Very roughly, I argue that the computational identity of a physical system is determinate relative to a contextually specified way of regarding that system computationally—known as a labelling scheme. When a system simultaneously implements multiple computations, it does so relative to different labelling schemes. But relative to a fixed labelling scheme, a physical system has a unique computational identity. I argue that this relativistic conception of computational identity vindicates computational explanation in the face of simultaneous implementation. (shrink)

We show, assuming weak large cardinals, that in the context of games of length \ with moves coming from a proper class, clopen determinacy is strictly weaker than open determinacy. The proof amounts to an analysis of a certain level of L that exists under large cardinal assumptions weaker than an inaccessible. Our argument is sufficiently general to give a family of determinacy separation results applying in any setting where the universal class is sufficiently closed; e.g., in (...) third, seventh, or \\)th order arithmetic. We also prove bounds on the strength of Borel determinacy for proper class games. These results answer questions of Gitman and Hamkins. (shrink)

DuBose, D.A., Determinacy and the sharp function on the reals, Annals of Pure and Applied Logic 55 237–263. We characterize in terms of determinacy, the existence of the least inner model of “every real has a sharp”. We let 1 be the sharp function on the reals and define two classes of sets, * and *+, which lie strictly between β<ω2 an d Δ. We show that the determinacy of * follows from L[#1] xvR; “every real has (...) a sharp”; and we show that the existence of indiscernibles for L[#1] is equivalent to a slightly determinacy hypothesis, the determinacy of *+. (shrink)