Operators in the paradox of the knower

Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom.A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities neednot raise the Paradox of the Knower. This paper attempts to challenge the current wisdom in another way as well: to show that mere appeal to modal operators in the sense of sentence-to-sentence devices is insufficient toescape the Paradox of the Knower. A family of systems is outlined in which closed formulae can encode other formulae and in which the diagonal lemma and Paradox of the Knower are thereby demonstrable for operators in this sense.I am deeply indebted to Robert F. Barnes and Evan W. Conyers, without whom these ideas might not have germinated and certainly would not have grown. Many of the results offered here evolved in the course of mutual discussion and correspondence. I am also grateful to an anonymous reviewer forSynthese for many very helpful suggestions.The current paper contains the technical results promised in Footnote 25 of Grim (1988) and Footnote 26, Chapter 3, of Grim (1991).     

On the Propositional Treatment of Anatmavāda in Early Buddhism and Ātmavāda in Hinduism

As propositions, Anatmavāda and ātmavāda are simply negations of one another. Thus whatever serves as a criterion for truth of the one must serve as a criterion for the other. When we treat them both as a priori propositions, I claim that we are unable to determine their truth value. But if we treat them both as a posteriori propositions, I argue, we are only able to determine their truth value if we attain unqualified omniscience. Because the Hindu account of knowing is far more conducive to the idea of unqualified omniscience, we might be tempted to assert that the empirical verification of these doctrines taken as propositions is far more likely in the Hindu tradition than the early Buddhist one. However, 'empirical omniscience' carries us very far from received views, thus I conclude that it makes no sense to treat these doctrines as truth-valued propositions.     

Truth and Scientific Change

The paper seeks to answer two new questions about truth and scientific change: (a) What lessons does the phenomenon of scientific change teach us about the nature of truth? (b) What light do recent developments in the theory of truth, incorporating these lessons, throw on problems arising from the prevalence of scientific change, specifically, the problem of pessimistic meta-induction?     

More Than Just a Ticklish Subject: History, Postmodernity and God

The paper begins by tracing the development of the understanding of truth as adjunct to the self in postmodernity. It then proceeds to ask what history is in postmodernity in the light of the reconfiguration of truth, and what kinds of response Christianity, and especially Catholic Christianity might develop to the postmodern situation. Using a critique of Habermas' speech "Modernity – an incomplete project" it develops a notion of postmodernity as an extreme interpretation of modernity, solely through reference to the self. By analysing the concept of the universal horizon in Habermas and in Hegel it shows how postmodernity both produces and deflects the notion of modernity, so that prior to the postmodern, neither modernity nor postmodernity can really be said to be thought at all.
The paper suggests that postmodernity is not really 'thought' at all, but rather thinks for us, so that we take it for granted. It then takes a sketch of Nietzsche's critique of the death of God as a springboard to ask what arenas a thoughtless theological response might be tempted into – especially that of conceiving the world purely and baldly as "sacramental" in structure. Finally it concludes by asking what possibilities postmodernity opens up through a thoughtful discernment of how it constitutes us at all     

塔斯基定理的一种推广

当把塔斯基对真概念提出的T-模式拓展到有向图上,塔斯基定理成立与否取决于归谬过程中使用的悖论及有向图的特征。本文证明了在使用说谎者悖论证明塔斯基定理时,在并且仅在有向图中含有奇循环时,说谎者悖论才会导致矛盾;在使用佐丹卡片悖论证明塔斯基定理时,在并且仅在有向图中含有高度不能被4整除的循环时,佐丹卡片悖论才会导致矛盾,这表明当T-模式拓展到有向图时,哥德尔关于"认识论悖论"应用于不完全性证明的思想能够被非平庸地类推于真之不可定义性的证明中。     

Non-Naturalist Moral Realism and the Limits of Rational Reflection

This essay develops the epistemic challenge to non-naturalist moral realism. While evolutionary considerations do not support the strongest claims made by ‘debunkers’, they do provide the basis for an inductive argument that our moral dispositions and starting beliefs are at best partially reliable. So, we need some method for separating truth from falsity. Many non-naturalists think that rational reflection can play this role. But rational reflection cannot be expected to bring us to truth even from reasonably accurate starting points. Reflection selects views that are coherent and conflict-free, yet there is no reason to think that the non-natural moral truth must be like this. Inasmuch as we seek coherent, conflict-free, ethical viewpoints, that suggests that our goal is not non-natural truth at all.     

Truth,Predication and a Family of Contingent Paradoxes

In truth theory one aims at general formal laws governing the attribution of truth to statements. Gupta’s and Belnap’s revision-theoretic approach provides various well-motivated theories of truth, in particular T* and T#, which tame the Liar and related paradoxes without a Tarskian hierarchy of languages. In property theory, one similarly aims at general formal laws governing the predication of properties. To avoid Russell’s paradox in this area a recourse to type theory is still popular, as testified by recent work in formal metaphysics by Williamson and Hale. There is a contingent Liar that has been taken to be a problem for type theory. But this is because this Liar has been presented without an explicit recourse to a truth predicate. Thus, type theory could avoid this paradox by incorporating such a predicate and accepting an appropriate theory of truth. There is however a contingent paradox of predication that more clearly undermines the viability of type theory. It is then suggested that a type-free property theory is a better option. One can pursue it, by generalizing the revision-theoretic approach to predication, as it has been done by Orilia with his system P*, based on T*. Although Gupta and Belnap do not explicitly declare a preference for T# over T*, they show that the latter has some advantages, such as the recovery of intuitively acceptable principles concerning truth and a better reconstruction of informal arguments involving this notion. A type-free system based on T# rather than T* extends these advantages to predication and thus fares better than P* in the intended applications of property theory.

     

The Paradox of Belief Instability and a Revision Theory of Belief

The epistemic paradox of 'belief instability' has recently received notable attention from many philosophers. In this paper I offer a new proposal, which I call a 'revision theory of belief'. This theory is in many respects an application of Gupta's and Belnap's revision theory of truth. They argue that the Liar paradox arises because our notion of truth is circular. I offer a similar proposal for handling the paradox of belief instability. In particular, I argue that our notion involved in the paradox of belief instability is circular, and this circularity of belief is the source of the paradox.     

Does God Know What It is Like to be Me?

Does God knows what it is like to be me? Scripture and religious tradition seem quite clear that God knows everything about us, even the deepest secrets of our hearts. There is nothing hidden from him. And this is an answer backed up by a more philosophical theology; for among the traditional list of divine attributes is omniscience: knowing everything that there is to know. The idea, moreover, seems essential to the ordinary religious consciousness, for how can God really help us, or fairly judge us, unless he knows exactly what things are like for us?     

SCHIFFER ON VAGUENESS

Abstract:  I go through, and criticize, Stephen Schiffer's account of vagueness and the sorites paradox. I discuss his notion of a happy-face solution to a paradox, his appeal to vagueness-related partial belief, his claim that indeterminacy is a psychological notion, and his view that the sorites premise and the inference rule of modus ponens are indeterminate.     

Feeling at home in language

What do we learn about language from reading Wittgenstein'sPhilosophical Investigations? This question gains urgency from Wittgenstein's alleged animus against philosophical theorizing and his indirectness. Section 1 argues that Wittgenstein's goal is to prevent philosophical questioning about the foundations of language from the beginning. This conception of his aim is not in tension with Wittgenstein's use of the notion of community; “community interpretations” of his views betray a misguided commitment to the coherence of the idea that language might need grounding. Wittgenstein's goal is not to enjoin us not to step “outside of language-games”, but to show that we have insufficiently clear grasp of the terms we try to use to express the limits of intelligibility. Section 2 suggests that appreciating Wittgenstein's moral concerning the relation between language and philosophizing about it involves allowing him to teach us how to read his book. What makes readingPhilosophical Investigations possible is openness to learning how not to forget our lives in language.     

The myth of phenomenological overflow

In this paper I examine the dispute between Hakwan Lau, Ned Block, and David Rosenthal over the extent to which empirical results can help us decide between first-order and higher-order theories of consciousness. What emerges from this is an overall argument to the best explanation against the first-order view of consciousness and the dispelling of the mythological notion of phenomenological overflow that comes with it.     

Aiming at Truth: Doxastic vs. Epistemic Goals

Belief is generally thought to be the primary cognitive state representing the world as being a certain way, regulating our behavior and guiding us around the world. It is thus regarded as being constitutively linked with the truth of its content. This feature of belief has been famously captured in the thesis that believing is a purposive state aiming at truth. It has however proved to be notoriously difficult to explain what the thesis really involves. In this paper, I begin by critically examining a number of recent attempts to unpack the metaphor. I shall then proceed to highlight an error that seems to cripple most of these attempts. This involves the confusion between, what I call, doxastic and epistemic goals. Finally, having offered my own positive account of the aim-of-belief thesis, I shall underline its deflationary nature by distinguishing between aiming at truth and hitting that target (truth). I end by comparing the account with certain prominent inflationary theories of the nature of belief. I am grateful to Muhammed Legenhausen, David Velleman and an anonymous referee of this journal for helpful comments on earlier drafts of this paper.     

The Ontology of Causal Process Theories

There is a widespread belief that the so-called process theories of causation developed by Wesley Salmon and Phil Dowe have given us an original account of what causation really is. In this paper, I show that this is a misconception. The notion of ??causal process?? does not offer us a new ontological account of causation. I make this argument by explicating the implicit ontological commitments in Salmon and Dowe??s theories. From this, it is clear that Salmon??s Mark Transmission Theory collapses to a counterfactual theory of causation, while the Conserved Quantity Theory collapses to David Fair??s phsyicalist reduction of causation.     

Simplicity as a criterion of theory choice in metaphysics

Metaphysicians frequently appeal to the idea that theoretical simplicity is truth conducive in metaphysics, in the sense that, all other things being equal, simpler metaphysical theories are more likely to be true. In this paper I defend the notion that theoretical simplicity is truth conducive in metaphysics, against several recent objections. I do not give any direct arguments for the thesis that simplicity is truth conducive in metaphysics, since I am aware of no such arguments. I do argue, however, that there is no special problem with the notion that simplicity is truth conducive in metaphysics. More specifically, I argue that if you accept the idea that simplicity is truth conducive in science, then it would be objectionably arbitrary to reject the idea that simplicity is truth conducive in metaphysics.     

Liar,Reducibility and Language

First, language and axioms of Church's paper 'Comparison of Russell's Resolution of the Semantical Antinomies with that of Tarski' are slightly modified and a version of the Liar paradox tentatively reconstructed. An obvious natural solution of the paradox leads to a hierarchy of truth predicates which is of a different kind from the one defined by Church: it depends on the enlargement of the semantical vocabulary and its levels do not differ in the ramified-type-theoretical sense. Second, two attempts are made in order to justify the Russellian, and perhaps Churchian, idea that language should not be fragmented beyond what is required by type distinctions. After all, because of reducibility, which seems to allow a semantics without propositions, this comes out to be possible only at the cost of resorting to two disputable theses. This revised version was published online in June 2006 with corrections to the Cover Date.     

The No-No Paradox Is a Paradox

The No-No Paradox consists of a pair of statements, each of which ‘says’ the other is false. Roy Sorensen claims that the No-No Paradox provides an example of a true statement that has no truthmaker: Given the relevant instances of the T-schema, one of the two statements comprising the ‘paradox’ must be true (and the other false), but symmetry constraints prevent us from determining which, and thus prevent there being a truthmaker grounding the relevant assignment of truth values. Sorensen's view is mistaken: situated within an appropriate background theory of truth, the statements comprising the No-No Paradox are genuinely paradoxical in the same sense as is the Liar (and thus, on Sorensen's view, must fail to have truth values). This result has consequences beyond Sorensen's semantic framework. In particular, the No-No Paradox, properly understood, is not only a new paradox, but also provides us with a new type of paradox, one which depends upon a general background theory of the truth predicate in a way that the Liar Paradox and similar constructions do not.     

Deutscher's problem is not Popper's problem

The so-called knowability paradox results from Fitch's argument that if there are any unknown truths, then there are unknowable truths. This threatens recent versions of semantical antirealism, the central thesis of which is that truth is epistemic. When this is taken to mean that all truths are knowable, antirealism is thus committed to the conclusion that no truths are unknown. The correct antirealistic response to the paradox should be to deny that the fundamental thesis of the epistemic nature of truth entails the knowability of all truths. Correctly understood, the antirealistic conditions on a proposition's truth do not require that the proposition possess a verification-procedure which, when executed under the given conditions, issues in an agent's recognition of truth, but merely that there be a verification-procedure which, under these conditions, takes the value true. The knowability paradox and the related idealism problem (that antirealism seems, but is not, committed to the necessary existence of an epistemic agent) draw attention to the fact that certain propositions, those that are about verification-procedures themselves, may under certain conditions take the value true despite their unperformability under these circumstances. Thus these propositions' procedures can only be performed when the propositions are false, and they gain the appearance of antirealistic impossibility (e.g., that there is an unknown truth). This differs from the unperformability that antirealists object to, pertaining merely to matters of execution rather than to the logical structure of the procedures themselves. The force of antirealism's notion of epistemic truth is piecemeal, rather than consisting in a blanket characterization of truth as knowable.