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.

We determine the consistency strength of determinacy for projective games of length ω^2. Our main theorem is that $\Pi _{n + 1}^1$-determinacy for games of length ω^2 implies the existence of a model of set theory with ω + n Woodin cardinals. In a first step, we show that this hypothesis implies that there is a countable set of reals A such that M_n(A), the canonical inner model for n Woodin cardinals constructed over A, satisfies $A = (...) R$ and the Axiom of Determinacy. Then we argue how to obtain a model with ω + n Woodin cardinal from this. We also show how the proof can be adapted to investigate the consistency strength of determinacy for games of length ω^2 with payoff in $R^R\Pi _1^1$ or with σ-projective payoff. (shrink)

We study the notion of [Formula: see text]-MAD families where [Formula: see text] is a Borel ideal on [Formula: see text]. We show that if [Formula: see text] is any finite or countably iterated Fubini product of the ideal of finite sets [Formula: see text], then there are no analytic infinite [Formula: see text]-MAD families, and assuming Projective Determinacy and Dependent Choice there are no infinite projective [Formula: see text]-MAD families; and under the full Axiom of (...) class='Hi'>Determinacy [Formula: see text][Formula: see text] or under [Formula: see text] there are no infinite [Formula: see text]-mad families. Similar results are obtained in Solovay’s model. These results apply in particular to the ideal [Formula: see text], which corresponds to the classical notion of MAD families, as well as to the ideal [Formula: see text]. The proofs combine ideas from invariant descriptive set theory and forcing. (shrink)

We prove the following result which is due to the third author. Let [Formula: see text]. If [Formula: see text] determinacy and [Formula: see text] determinacy both hold true and there is no [Formula: see text]-definable [Formula: see text]-sequence of pairwise distinct reals, then [Formula: see text] exists and is [Formula: see text]-iterable. The proof yields that [Formula: see text] determinacy implies that [Formula: see text] exists and is [Formula: see text]-iterable for all reals [Formula: see text]. (...) A consequence is the Determinacy Transfer Theorem for arbitrary [Formula: see text], namely the statement that [Formula: see text] determinacy implies [Formula: see text] determinacy. (shrink)

We prove the following result which is due to the third author. Let [Formula: see text]. If [Formula: see text] determinacy and [Formula: see text] determinacy both hold true and there is no [Formula: see text]-definable [Formula: see text]-sequence of pairwise distinct reals, then [Formula: see text] exists and is [Formula: see text]-iterable. The proof yields that [Formula: see text] determinacy implies that [Formula: see text] exists and is [Formula: see text]-iterable for all reals [Formula: see text]. (...) A consequence is the Determinacy Transfer Theorem for arbitrary [Formula: see text], namely the statement that [Formula: see text] determinacy implies [Formula: see text] determinacy. (shrink)

In this paper I shall present a method for proving determinacy from large cardinals which, in many cases, seems to yield optimal results. One of the main applications extends theorems of Martin, Steel and Woodin about determinacy within the projective hierarchy. The method can also be used to give a new proof of Woodin's theorem about determinacy in L.The reason we look for optimal determinacy proofs is not only vanity. Such proofs serve to tighten the (...) connection between large cardinals and descriptive set theory, letting us bring our knowledge of one subject to bear on the other, and thus increasing our understanding of both. A classic example of this is the Harrington-Martin proof that -determinacy implies -determinacy. This is an example of a transfer theorem, which assumes a certain determinacy hypothesis and proves a stronger one. While the statement of the theorem makes no mention of large cardinals, its proof goes through 0#, first proving that-determinacy ⇒ 0# exists,and then that0# exists ⇒ -determinacyMore recent examples of the connection between large cardinals and descriptive set theory include Steel's proof thatADL ⇒ HODL ⊨ GCH,see [9], and several results of Woodin about models of AD+, a strengthening of the axiom of determinacy AD which Woodin has introduced. These proofs not only use large cardinals, but also reveal a deep, structural connection between descriptive set theoretic notions and notions related to large cardinals. (shrink)

We prove a number of results on the determinacy of σ-projective sets of reals, i.e., those belonging to the smallest pointclass containing the open sets and closed under complements, countable unions, and projections. We first prove the equivalence between σ-projective determinacy and the determinacy of certain classes of games of variable length <ω^2 (Theorem 2.4). We then give an elementary proof of the determinacy of σ-projective sets from optimal large-cardinal hypotheses (Theorem 4.4). Finally, (...) we show how to generalize the proof to obtain proofs of the determinacy of σ-projective games of a given countable length and of games with payoff in the smallest σ-algebra containing the projective sets, from corresponding assumptions (Theorem 5.1, Theorem 5.4). (shrink)

Let Mn♯ denote the minimal active iterable extender model which has n Woodin cardinals and contains all reals, if it exists, in which case we denote by Mn the class-sized model obtained by iterating the topmost measure of Mn class-many times. We characterize the sets of reals which are Σ1-definable from R over Mn, under the assumption that projective games on reals are determined:1. for even n, Σ1Mn=⅁RΠn+11;2. for odd n, Σ1Mn=⅁RΣn+11.This generalizes a theorem of Martin and Steel for (...) L, that is, the case n=0. As consequences of the proof, we see that determinacy of all projective games with moves in R is equivalent to the statement that Mn♯ exists for all n∈N, and that determinacy of all projective games of length ω2 with moves in N is equivalent to the statement that Mn♯ exists and satisfies AD for all n∈N. (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)

It is proved that in the absence of proper class inner models with Woodin cardinals, for each n ε {1,…,ω}, ∑3 + n1 absoluteness implies there are n strong cardinals in K (where this denotes a suitably defined global version of the core model for one Woodin cardinal as exposed by Steel. Combined with a forcing argument of Woodin, this establishes that the consistency strength of ∑3 + n1 absoluteness is exactly that of n strong cardinals so that in particular (...) projective absoluteness is equiconsistent with the existence of infinitely many strong cardinals. It is also argued how this theorem is to be construed as the first step in the long range program of showing that projective determinacy is equivalent to its analytical consequences for the projective sets which would settle positively a conjecture of Woodin and thereby solve the last Delfino problem. (shrink)

The Axiom of Projective Determinacy implies the existence of a universal $\utilde{\Pi}^{1}_{n}\setminus\utilde{\Delta}^{1}_{n}$ set for every $n \geq 1$. Assuming $\text{\upshape MA}(\aleph_{1})+\aleph_{1}=\aleph_{1}^{\mathbb{L}}$ there exists a universal $\utilde{\Pi}^{1}_{1}\setminus\utilde{\Delta}^{1}_{1}$ set. In ZFC there is a universal $\utilde{\Pi}^{0}_{\alpha}\setminus\utilde{\Delta}^{0}_{\alpha}$ set for every $\alpha$.

I offer a reconstruction of contemporary medical procedures of sex assignment for infants with intersex conditions. In the perspective adopted, sex assignment to intersexed newborns can be understood as a procedure that imposes determinate sex predicates. The account describes two stages of sex assignment. At the first stage of the process, the sex predicates ‘female’, ‘male’, or ‘intersexed’ are taken to denote genital morphology. Initial genital assessment of newborns imposes clear boundaries upon the extensions of these predicates through diagnostic schemes (...) of precisification. At the second stage, the sex predicates ‘female’ and ‘male’ denote sex of rearing, a therapeutic and pedagogical project aimed at producing stable and psycho-socially well-adjusted gender identity. The multi-dimensional indeterminacy of prognosticating sex of rearing at the second stage is mitigated through the prioritization of some subsets of the medical data. (shrink)

We show that every dominating analytic set in the Baire space has a dominating closed subset. This improves a theorem of Spinas [15] saying that every dominating analytic set contains the branches of a uniform tree, i.e. a superperfect tree with the property that for every splitnode all the successor splitnodes have the same length. In [15], a subset of the Baire space is called u-regular if either it is not dominating or it contains the branches of a uniform tree, (...) and it was proved that Σ21-Kσ-regularity implies Σ21-u-regularity. Here we show that these properties are in fact equivalent. Since the proof of analytic u-regularity uses a game argument it was clear that determinacy implies u-regularity of all sets. Here we show that an inaccessible cardinal is enough to construct a model for projective u-regularity, namely it holds in Solovay's model. Finally we show that forcing with uniform trees is equivalent to Laver forcing. (shrink)

In this paper I examine two theories of democracy that can be found in contemporary French philosophy. Both Cornelius Castoriadis and Jacques Rancière offer a critique of modern democracy with the purpose of refounding it. The ‘refoundation narratives’ they propose are both based on an account of the origins of democracy in ancient Greece. According to Castoriadis, ancient democracy is grounded in a ‘magma’ of ‘social imaginary significations’ in which ‘autonomy’ is considered the correct response to Being defined as an (...) insurmountable ‘Chaos’. On the contrary, modern democracy defines Being as a determinacy and consequently fails to grasp the notion of autonomy. According to Rancière, the origins of democracy are to be found in the invasion of the public space by ‘those without a part’ who consequently have no title to govern. The problem with the ‘domesticated’ modern democracy is that it denies the existence of Otherness; that is, of non-citizens excluded from the public space. Therefore it appears incapable of letting the ‘dis-agreement’ manifest itself and consequently incapable of transforming the ‘police’ order. After examining the meaning of both theories, I attempt to elucidate the difficulties encountered by each author in the attainment of his goal, which is that of refounding modern democracy. (shrink)

Praise for Volume 1: "... a first-rate edition, which supersedes all other portable Peirces.... all the Peirce most people will ever need." —Louis Menand, The New York Review of Books Volume 2 of this convenient two-volume chronological reader’s edition provides the first comprehensive anthology of the brilliant American thinker Charles Sanders Peirce’s mature philosophy. A central focus of Volume 2 is Peirce’s evolving theory of signs and its appplication to his pragmatism.

The Bentham Project is delighted to announce a call for papers for “Bentham and Australia: Convicts, Utility, and Empire”, a conference to be held at University College London on 11-12 April 2019 to mark the forthcoming publication of Writings on Australia, a volume of The Collected Works of Jeremy Bentham. The conference will explore themes such as the influence and impact of Bentham’s ideas on the theory and practice of punishment in convict Australia, on advocates and opponents of co...

Volume 8 of this landmark edition follows Peirce from May 1890 through July 1892—a period of turmoil as his career unraveled at the U.S. Coast and Geodetic Survey. The loss of his principal source of income meant the beginning of permanent penury and a lifelong struggle to find gainful employment. His key achievement during these years is his celebrated Monist metaphysical project, which consists of five classic articles on evolutionary cosmology. Also included are reviews and essays from The Nation in (...) which Peirce critiques Paul Carus, William James, Auguste Comte, Cesare Lombroso, and Karl Pearson, and takes part in a famous dispute between Francis E. Abbot and Josiah Royce. Peirce's short philosophical essays, studies in non-Euclidean geometry and number theory, and his only known experiment in prose fiction complete his production during these years. Peirce's 1883-1909 contributions to the Century Dictionary form the content of volume 7 which is forthcoming. (shrink)

Praise for Volume 1: "... a first-rate edition, which supersedes all other portable Peirces.... all the Peirce most people will ever need." —Louis Menand, The New York Review of Books Volume 2 of this convenient two-volume chronological reader’s edition provides the first comprehensive anthology of the brilliant American thinker Charles Sanders Peirce’s mature philosophy. A central focus of Volume 2 is Peirce’s evolving theory of signs and its appplication to his pragmatism.

We show that, assuming the consistency of a supercompact cardinal, the first inaccessible cardinal can satisfy a strong form of a Löwenheim–Skolem–Tarski theorem for the equicardinality logic L, a logic introduced in [5] strictly between first order logic and second order logic. On the other hand we show that in the light of present day inner model technology, nothing short of a supercompact cardinal suffices for this result. In particular, we show that the Löwenheim–Skolem–Tarski theorem for the equicardinality logic at (...) κ implies the Singular Cardinals Hypothesis above κ as well as Projective Determinacy. (shrink)

All spaces are assumed to be separable and metrizable. Consider the following properties of a space X. X is Polish.For every countable crowded Q⊆X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q \subseteq X}$$\end{document} there exists a crowded Q′⊆Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q'\subseteq Q}$$\end{document} with compact closure.Every closed subspace of X is either scattered or it contains a homeomorphic copy of 2ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${2^\omega}$$\end{document}.Every closed subspace of X (...) is a Baire space. While is the well-known property of being completely Baire, properties and have been recently introduced by Kunen, Medini and Zdomskyy, who named them the Miller property and the Cantor-Bendixson property respectively. It turns out that the implications →→→\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ \rightarrow \rightarrow \rightarrow }$$\end{document} hold for every space X. Furthermore, it follows from a classical result of Hurewicz that all these implications are equivalences if X is coanalytic. Under the axiom of Projective Determinacy, this equivalence result extends to all projective spaces. We will complete the picture by giving a ZFC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf ZFC}$$\end{document} counterexample and a consistent definable counterexample of lowest possible complexity to the implication ←\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ \leftarrow }$$\end{document} for i=1,2,3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${i = 1, 2, 3}$$\end{document}. For one of these counterexamples we will need a classical theorem of Martin and Solovay, of which we give a new proof, based on a result of Baldwin and Beaudoin. Finally, using a method of Fischer and Friedman, we will investigate how changing the value of the continuum affects the definability of these counterexamples. Along the way, we will show that every uncountable completely Baire space has size continuum. (shrink)

For every countable wellordering $\alpha $ greater than $\omega $, it is shown that clopen determinacy for games of length $\alpha $ with moves in $\mathbb {N}$ is equivalent to determinacy for a class of shorter games, but with more complicated payoff. In particular, it is shown that clopen determinacy for games of length $\omega ^2$ is equivalent to $\sigma $ -projective determinacy for games of length $\omega $ and that clopen determinacy for games (...) of length $\omega ^3$ is equivalent to determinacy for games of length $\omega ^2$ in the smallest $\sigma $ -algebra on $\mathbb {R}$ containing all open sets and closed under the real game quantifier. (shrink)

We prove that every analytic set in ω ω × ω ω with σ-bounded sections has a not σ-bounded closed free set. We show that this result is sharp. There exists a closed set with bounded sections which has no dominating analytic free set, and there exists a closed set with non-dominating sections which does not have a not σ-bounded analytic free set. Under projective determinacy analytic can be replaced in the above results by projective.

§0. Preface. There has been an expectation that the endgame of the more tenacious problems raised by the Los Angeles ‘cabal’ school of descriptive set theory in the 1970's should ultimately be played out with the use of inner model theory. Questions phrased in the language of descriptive set theory, where both the conclusions and the assumptions are couched in terms that only mention simply definable sets of reals, and which have proved resistant to purely descriptive set theoretic arguments, may (...) at last find their solution through the connection between determinacy and large cardinals.Perhaps the most striking example was given by [24], where the core model theory was used to analyze the structure of HOD and then show that all regular cardinals below ΘL are measurable. John Steel's analysis also settled a number of structural questions regarding HODL, such as GCH.Another illustration is provided by [21]. There an application of large cardinals and inner model theory is used to generalize the Harrington-Martin theorem that determinacy implies )determinacy.However, it is harder to find examples of theorems regarding the structure of the projective sets whose only known proof from determinacy assumptions uses the link between determinacy and large cardinals. We may equivalently ask whether there are second order statements of number theory that cannot be proved under PD–the axiom of projective determinacy–without appealing to the large cardinal consequences of the PD, such as the existence of certain kinds of inner models that contain given types of large cardinals. (shrink)

We provide partial answers to the following problem: Is the class of Borel linear orders well-quasi-ordered under embeddability? We show that it is indeed the case for those Borel orders which are embeddable in R ω , with the lexicographic ordering. For Borel orders embeddable in R 2 , our proof works in ZFC, but it uses projective determinacy for Borel orders embeddable in some $\mathbf{R}^n, n , and hyperprojective determinacy for the general case.

§0. Preface. There has been an expectation that the endgame of the more tenacious problems raised by the Los Angeles ‘cabal’ school of descriptive set theory in the 1970's should ultimately be played out with the use of inner model theory. Questions phrased in the language of descriptive set theory, where both the conclusions and the assumptions are couched in terms that only mention simply definable sets of reals, and which have proved resistant to purely descriptive set theoretic arguments, may (...) at last find their solution through the connection between determinacy and large cardinals.Perhaps the most striking example was given by [24], where the core model theory was used to analyze the structure of HOD and then show that all regular cardinals below ΘL are measurable. John Steel's analysis also settled a number of structural questions regarding HODL, such as GCH.Another illustration is provided by [21]. There an application of large cardinals and inner model theory is used to generalize the Harrington-Martin theorem that determinacy implies )determinacy.However, it is harder to find examples of theorems regarding the structure of the projective sets whose only known proof from determinacy assumptions uses the link between determinacy and large cardinals. We may equivalently ask whether there are second order statements of number theory that cannot be proved under PD–the axiom of projective determinacy–without appealing to the large cardinal consequences of the PD, such as the existence of certain kinds of inner models that contain given types of large cardinals. (shrink)

Atypical among Heidegger’s numerous discussions of poets is the condemnation of Rilke in the 1942-43 lecture course Parmenides. At stake is the definition of “the open” (das Offene): Rilke reserves the open for animals as freedom from conceptual determinacy, whereas Heidegger reserves it for human beings as the place of Being in which things first appear as what they are. The open, for Heidegger, names the existential conception of place (as distinct from a geographical point) and features in his (...) life-long attempts to articulate the relations between language, human existence, poetry and the everyday. By denying that human beings have access to the open, Rilke runs athwart this project and by denying it in a poem he confounds the expectations that Heidegger harbours with respect to the work of art as a site of the opening up of aesthetic experience, within the everyday, to ontological questioning. (shrink)

Many recent writers in the philosophy of mathematics have put great weight on the relative categoricity of the traditional axiomatizations of our foundational theories of arithmetic and set theory. Another great enterprise in contemporary philosophy of mathematics has been Wright's and Hale's project of founding mathematics on abstraction principles. In earlier work, it was noted that one traditional abstraction principle, namely Hume's Principle, had a certain relative categoricity property, which here we term natural relative categoricity. In this paper, we show (...) that most other abstraction principles are not naturally relatively categorical, so that there is in fact a large amount of incompatibility between these two recent trends in contemporary philosophy of mathematics. To better understand the precise demands of relative categoricity in the context of abstraction principles, we compare and contrast these constraints to stability-like acceptability criteria on abstraction principles, the Tarski-Sher logicality requirements on abstraction principles studied by Antonelli and Fine, and supervaluational ideas coming out of Hodes' work. (shrink)

In his new paper, “Eligibility and Inscrutability,” J. R. G. Williams presents a surprising new challenge to David Lewis’ theory of interpretation. Although Williams frames this challenge primarily as a response to Lewis’ criticisms of Putnam’s model-theoretic argument, the challenge itself goes to the heart of Lewis’ own account of interpretation. Further, and leaving Lewis’ project aside for a moment, Williams’ argument highlights some important—and some fairly general—points concerning the relationship between model theory and semantic determinacy.

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)

Anti-foundationalism is a central topic in recent legal scholarship. The critical legal studies movement (CLS) has mounted a strong challenge to the traditional belief that legal materials (constitutions, statutes, and precedents) determine legal outcomes and constrain judicial decision making. This scholarship has overlooked, however, the degree to which the debate between traditional legal determinacy and anti-foundational indeterminacy is yet another manifestation of a continuous debate in Western thought – one that has its roots in pre-Socratic rhetoric and philosophy.This paper (...) traces the indeterminacy thesis back to the contest of ideas between Protagoras and Plato. I examine two well-known and elated Protagorean notions: first, that two arguments (logoi) are always set in opposition to one another with regard to every matter and, second, that the rhetorician can always ‘make the weaker argument the stronger.’ I contend that taking these Protagorean notions seriously – perhaps even more seriously than self-avowed anti-foundationalists customarily do – leads paradoxically to a modified endorsement of foundationalism that is nevertheless wholly consistent with the Protagorean project. Calling upon texts by Aristotle, Seneca and René Girard, I focus upon how fictionality in representations of Platonically conceived Truth reveals a binarization in thought that is simultaneously untenable and unavoidable. (shrink)

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)

We analyze the degree-structure induced by large reducibilities under the Axiom of Determinacy. This generalizes the analysis of Borel reducibilities given in Alessandro Andretta and Donald A. Martin [1], Luca Motto Ros [6] and Luca Motto Ros. [5] e.g. to the projective levels.

Since 1976 Hilary Putnam has on many occasions proposed an argument, founded on some model-theoretic results, to the effect that any philosophical programme whose purpose is to naturalize semantics would fail to account for an important feature of every natural language, the determinacy of reference. Here, after having presented the argument, I will suggest that it does not work, because it simply assumes what it should prove, that is that we cannot extend the metatheory: Putnam appears to think that (...) all we may determinately say about the relations between words and entities in the world is what the model theory tells us, but he has never offered justifications for that. At the end of the article, I will discuss the apparently reliable intuition that seems to me to be at the root of the argument, that is that, given a formal theory, there is an infinite number of ways of connecting it to, or of projecting it onto, the world. I will suggest that we should resist this intuition, because it rests on a very doubtful notion of world, which assumes that for any class of objects there is a corresponding property. (shrink)

We propose a simple notion of "extender" for coding large elementary embeddings of models of set theory. As an application we present a self-contained proof of the theorem by D. Martin and J. Steel that infinitely many Woodin cardinals imply the determinacy of every projective set.

We work under the assumption of the Axiom of Determinacy and associate a measure to each cardinal $\kappa < \aleph_{\varepsilon_0}$ in a recursive definition of a canonical measure assignment. We give algorithmic applications of the existence of such a canonical measure assignment (computation of cofinalities, computation of the Kleinberg sequences associated to the normal ultrafilters on all projective ordinals).

We extend work of H. Friedman, L. Harrington and P. Welch to the third level of the projective hierarchy. Our main theorems say that (under appropriate background assumptions) the possibility to select definable elements of non-empty sets of reals at the third level of the projective hierarchy is equivalent to the disjunction of determinacy of games at the second level of the projective hierarchy and the existence of a core model (corresponding to this fragment of (...) class='Hi'>determinacy) which must then contain all real numbers. The proofs use Sacks forcing with perfect trees and core model techniques. (shrink)

The purpose of the present article is to propose a research project which will analyse the issue of theoretization of empirical data which takes place in the process of formulating scientific problems. J. Hintikka’s interrogative model of inquiry will serve us as a starting point for our considerations. First, his proposal of viewing the theory-dependence of facts will be characterized. Then, with reference to the results of K. Jodkowski, three interpretations of theory-laden thesis will be given: a radical, a modest (...) and a weak one. This will render it possible to further develop a critique of certain aspects of Hintikka’s conception. Subsequently, the critique will provide a basis for presenting a new way of viewing theory-dependence of empirical data. Some considerations regarding a possible use of the received conceptual scheme for analyzing certain problems of philosophy of science will close the article. A possibility of analyzing such classical problems as falsification and the use of the principle of auto-determinacy in science will also be offered. Lastly, with reference to A. Grobler’s analyses, a possibility of representing a process of rejecting metaphysical presuppositions in science will be considered. (shrink)

In this dissertation, I develop a post-reflexive philosophical account of self-knowing subjectivity. I argue that ambiguity, not clarity, is the hallmark of intersubjective being and knowing, and that ambiguous being is particularly evident precisely where subjectivity occupies a central place: in theory. To illustrate this claim, I turn to the ubiquitous and indispensable technology of the glassy mirror, a material object and discursive trope which I use to enliven the Beauvoirean concept of situation: a lived ambiguity of being both subject (...) and object, both universal and particular, both for-self and for-others. Far from eschewing the historical importance of precision and determinacy in Western views of knowing well, my appeal to mirrors in this project allows me to read such values as sedimented in knowers’ ways of making sense of the world – of themselves and their objects of knowledge, as these are expressed through theoretical engagements. (shrink)

Ms. Neumer and her team began their project with a critical analysis of the various theories of the relationship between language and thought. Their aim was to develop a theoretical position concerning the issue of universalism versus relativism. This issue is closely bound up with one of the main questions of the history of East and Central Europe, namely, the question of the nation, and the possibility of mutual understanding between national cultures. The team attempted to avoid falling into an (...) all-too-common trap, that of allowing a political perspective to obscure the central theoretical issues. In a project whose outcome totalled over 1000 pages of manuscript in German, English and Hungarian, they touched on cognitive psychological, linguistic, semiotic, socio-semiotic, and other such themes. Their experience has convinced them of the fruitful heuristic possibilities of the interaction of scientific and philosophical approaches in this area of research. A preliminary analysis of the history of philosophy and inquiries into conceptual fields revealed that, in order to reach strong relativist conclusions concerning the unity of thought and language, it is required to take as a point of departure the widest possible sense of these concepts. But in fact, such an option ends up refuting itself: pursuing the premises to their final conclusion one arrives at the restriction of relativism. The team outlined a theory of the understanding of the Other which, borrowing from analytical as well as continental-hermeneutic trends, does not underestimate, on the one hand, the difficulties of understanding between various forms of life, cultures, and languages, but, on the other hand, can provide an alternative solution to the theory of incommensurabiltiy. Within the boundary of this problematic the team studied the problems of translatability, the acquisition of the mother and foreign languages, and natural or cultural determinacy of kind terms. The team regards its most original contribution to be the association of the problem of relativism-universalism and the language-thought relation with contemporary investigations into the question of orality, literacy, and secondary orality. Their conclusion was that, although certain connections can be revealed both between forms of communication and the thesis of the unity of language and thought, and between periods in the history of communication and the predominance of relativistic or universalistic tendencies, forms of communication do not unequivocally determine the answers to these questions. (shrink)

In this work I bring a conception of language and meaning as a shared institution to bear upon rule-following scepticism, i.e., upon the sceptical problem concerning the semantic determinacy of expressions involving infinite or indefinitely large and open extensions. Such scepticism proceeds from the observation that the extensions of expressions of this kind are not uniquely determined by epistemically accessible facts, to conclude that the expressions in question are indeterminate in point of extension, and that their meaning must consist (...) in their use. ;In the first chapter of this work, I argue that rule-following considerations by themselves do not suffice to establish these conclusions, and that additional premises are needed. I consider both internalist and extensionalist schemes to supplement the sceptical argument. I find such schemes lacking in persuasive support. Chapter 2, in particular, concentrates on Kripke's well known exegesis of Wittgenstein's argument, and on the internalist requirements upon which it is based. ;In Chapter 3, I offer an externalist account of the normative aspect in rule following. On the account I give, the rule one is projecting is determined extensionally by one's position in a community in which his projections would be corrected and evaluated by other members, and from which one has acquired the rule in the first place through a chain of communication, rather than by one's own projections, taken in isolation, which constitute only a partial understanding of the rule in question. This account is not designed to refute scepticism; rather its aim is to account for the normativity of rule-following in ways which do not invoke the internalist requirement upon which rule following scepticism is based. (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)

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)

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 $\Delta _{1}^{1}-{\rm Det}_{0}={\rm ACA}_{0}+\Delta _{1}^{1}-{\rm Det}$.