Implied-Meaning Analysis of the Currian Conditional

Expanding on the recent research of Stephen Read and Catarina Dutilh Novaes concerning Thomas Bradwardine's theory of truth, the present paper makes an effort to analyse the Currian conditional in terms of the so-called ‘Bradwardine principle’, i.e. the principle that meaning is closed under entailment. Based upon two possible applications of this approach, alternative solutions to the issues of semantic pathology and trivialisation of deductive systems are presented.     

Plural signification and the Liar paradox

In recent years, speech-act theory has mooted the possibility that one utterance can signify a number of different things. This pluralist conception of signification lies at the heart of Thomas Bradwardine’s solution to the insolubles, logical puzzles such as the semantic paradoxes, presented in Oxford in the early 1320s. His leading assumption was that signification is closed under consequence, that is, that a proposition signifies everything which follows from what it signifies. Then any proposition signifying its own falsity, he showed, also signifies its own truth and so, since it signifies things which cannot both obtain, it is simply false. Bradwardine himself, and his contemporaries, did not elaborate this pluralist theory, or say much in its defence. It can be shown to accord closely, however, with the prevailing conception of logical consequence in England in the fourteenth century. Recent pluralist theories of signification, such as Grice’s, also endorse Bradwardine’s closure postulate as a plausible constraint on signification, and so his analysis of the semantic paradoxes is seen to be both well-grounded and plausible.

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。     

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.     

Entailments are Cancellable

Several philosophers have recently claimed that if a proposition is cancellable from an uttered sentence then that proposition is not entailed by that uttered sentence. The claim should be a familiar one. It has become a standard device in the philosopher's tool‐kit. I argue that this claim is false. There is a kind of entailment—which I call “modal entailment”—that is context‐sensitive and, because of this, cancellable. So cancellability does not show that a proposition is not entailed by an uttered sentence. I close the paper by describing an implication this has for a disagreement between J. L. Austin and Grice concerning the relation between felicity and truth. 1     

The paradox of negation in Nāgārjuna's philosophy

This essay discusses the paradox of the Nāgārjunian negation as presented in his Vigrahavyāvartani. In Part One it is argued that as the Naiyāyika remarks, Nāgārjuna's speech act ‘No proposition has its own intrinsic thesis’ seemingly contradicts his famous claim that he has no negation whatsoever. In Parts Two and Three I consider the traditional as well as modem responses to this paradox and offer my own. I argue that Nāgārjuna's speech act does not generate a paradox for two reasons: (a) the equivalence thesis of the kind‐?P = ?P is obviously false; and (b) since Nāgārjuna's speech act is situated in the dialogical/conversational universe of discourse as opposed to the argumentative/systematic universe of discourse, the teaching of the non‐intrinsic thesis of all statements that it purports, holds for all statements in its class, including itself. Lastly, it is argued that even though the Nāgārjunian speech act is not a negation situated in the argumentative universe of discourse, it serves both philosophical and soteriological purposes.     

Thomas Bradwardine on God and the Foundations of Modality

Scholars have claimed that the fourteenth-century thinker Thomas Bradwardine held that God's will freely determined what was necessary, possible and impossible and in this regard, he was a medieval precursor to Descartes. In this article, I argue against this interpretation of Bradwardine. I show that Bradwardine held that objects derive their modal status based on whether God's necessary and immutable being isrepugnant or non-repugnant to their existence. I offer readings of thepassages in which Bradwardine appears to state that God's will determines modality that render them consistent with the non-voluntarist interpretation of his modal theory.     

Val Plumwood

Miller's reply to Nelson misses the point because it does not attend to the difference between identifying the truth conditions for a proposition and explaining why those conditions are the ones in which the proposition is true.     

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.     

SIMPLIFYING ALETHIC PLURALISM

What is truth? What precisely is it that truths have that falsehoods lack? Pluralists about truth (or “alethic pluralists”) tend to answer these questions by saying that there is more than one way for a proposition, sentence, belief—or any chosen truth‐bearer—to be true. In this paper, I argue that two of the most influential formations of alethic pluralism, those of Wright (1992, 2003a ) and Lynch (2009 ), are subject to serious problems. I outline a new formulation, which I call “simple determination pluralism,” that I claim offers better prospects for alethic pluralism, with the potential to have applications for pluralist theories beyond truth.     

Evidence and the openness of knowledge

The paper argues that knowledge is not closed under logical inference. The argument proceeds from the openness of evidential support and the dependence of empirical knowledge on evidence, to the conclusion that knowledge is open. Without attempting to provide a full-fledged theory of evidence, we show that on the modest assumption that evidence cannot support both a proposition and its negation, or, alternatively, that information that reduces the probability of a proposition cannot constitute evidence for its truth, the relation of evidential support is not closed under known entailment. Therefore the evidence-for relation is deductively open regardless of whether evidence is probabilistic or not. Given even a weak dependence of empirical knowledge on evidence, we argue that empirical knowledge is also open. On this basis, we also respond to the strongest argument in support of knowledge closure (Hawthorne 2004a). Finally, we present a number of significant benefits of our position, namely, offering a unified explanation for a range of epistemological puzzles.     

Visual content of words delays negation

Many studies have shown the advantage of processing visualizable words over non-visualizables due to the associated image code. The present paper reports the case of negation in which imagery could slow down processing. Negation reverses the truth value of a proposition from false to true or vice versa. Consequently, negation works only on propositions (reversing their truth value) and cannot apply directly to other forms of knowledge representation such as images (although they can be veridical or not). This leads to a paradoxical hypothesis: despite the advantage of visualizable words for general processing, the negation of clauses containing words related to the representation of an image would be more difficult than negation containing non-visualizable words. Two experiments support this hypothesis by showing that sentences with a previously negated visualizable word took longer to be read than sentences with previously negated non-visualizable words. The results suggest that a verbal code is used to process negation.     

Two Notions of Circularity

Crispin Wright’s epistemic response to McKinsey’s paradox is to argue that introspective knowledge of the first premise fails to transmit across the semantic externalist entailment in the second premise to the conclusion that one has such untoward knowledge of the external world. This paper argues first that Stewart Cohen and Jonathan Vogel’s bootstrapping arguments suffer from a novel kind of epistemic circularity, which triggers failure of transmission but allows for the possibility of basic perceptual knowledge. It is then argued that McKinsey’s paradox falls out as a special case of this template for transmission failure. The circularity in play is semantic: the paradox illicitly imports semantically relevant properties of knowledge-individuating sources into the contents of the knowledge states that those sources individuate by instantiating those properties. Importantly, this diagnosis permits the possibility of basic introspective knowledge as propounded by Tyler Burge and other semantic externalists.     

An Approach to Emerson’s Writing Style from a Daoist Perspective

There is a clear and controlling philosophical concern that governs Ralph Waldo Emerson’s essays: freedom from limitation and self-reliance from external authority. What makes it difficult to understand his essays, however, is his style, which is characterized by disconnection, paradox, and negation. These rhetorical techniques make the meaning of his writings elusive and slippery. Though many scholars have analyzed Emerson’s style, none have approached it through the writings of Laozi, an ancient Chinese philosopher. There are two reasons I compare Emerson and Laozi. First, in spite of their differences, there are important parallel themes and stylistic innovations in their writings. Second, attentiveness to a key figure in the Eastern philosophical tradition can help to explain how Emerson’s thoughts disappoint Western readers, precisely because they employ techniques beyond the method of habitual intellect in the Western frame. This essay tries to approach several features in Emerson’s writing style from a Daoist perspective to show that both philosophers purposefully use linguistic strategies such as disconnection, paradox, and negation to provoke readers into participating in understanding truth, instead of telling them directly what truth is.     

WARRANTED ASSERTIBILITY AND THE NORMS OF ASSERTORIC PRACTICE: WHY TRUTH AND WARRANTED ASSERTIBILITY ARE NOT COINCIDENT NORMS

Crispin Wright has argued that truth and warranted assertibility are coincident but non‐co‐extensive norms of assertoric practice and that this fact inflates deflationary theories of truth. Wright's inflationary argument has generated much discussion in the literature. By contrast, relatively little has been said about the coincidence claim that is the focus of this paper. Wright's argument for the claim that truth and warranted assertibility are coincident norms is first presented. It is then suggested that the argument trades on an ambiguity in ‘justified’ and ‘warrantedly assertible’. Finally, it is argued that, once the ambiguity is removed, there is reason to reject the claim that truth and epistemic warrant are coincident norms of assertoric practice. One important result is that no epistemic theory of truth can satisfy what Wright takes to be a key platitude about assertion.     

On field's argument for substantivalism

In this article I subject to criticism Field's argument, according to which field theory takes space‐time to be à substance since it ascribes field properties to space‐time points. There is petitio principii error made in this reasoning because Field does not give any justification for his controversial assumption that fields are properties of space‐time points. What is more, I suggest, Field's interpretation of field theory is incompatible with the way this theory is understood and utilized by its users, namely scientists. My criticism is based on the assumption that one cannot propose an ontology of a given scientific theory, at the same time imposing on it an interpretation which clashes with the interpretation current among its users. I also suggest that in order to establish the ontology of a scientific theory one should also take into account the way it has been constructed. According to this criterion, field theory does indeed take space‐time to be a substance.     

Something amazing about the Peripatetic of Pallet: Abaelard's development of Boethius' account of conditional propositions

Mediaeval logicians inherited from Boethius an account of conditional propositions and the syllogisms which may be constructed using them. In the following paper it is shown that there are considerable difficulties with Boethius' account which arise from his failure to understand the nature of compound propositions and in particular to provide for their negation. Boethius suggests that there are two different conditions which may be imposed for the truth of a conditional proposition but he really gives no adequate account of how such propositions may be obtained. The true greatness of Peter Abaelard as a philosophical logician is revealed in what he is able to do with the material which he found in Boethius. It is shown that he developed a precise theory of conditionals giving an account of how true conditionals may be obtained and principles which may be used to reject others as false. Unlike Boethius Abaelard properly appreciates that conjunctions must be treated as logical units. Even he, however, falls victim to difficulties which arise when this connective is brought into contact with negation and the conditions which he lays down for the truth of a conditional.     

Non‐Classical Knowledge

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely‐held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single‐premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker‐than‐classical K₃ logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to—whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non‐classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities.     

Are Propositions Essentially Representational?

Jeffrey King argues that nothing has truth conditions except by being taken to be true or false by rational agents. But – for good reason – King claims that propositions possess truth conditions essentially and intrinsically. I will argue that King cannot have both: if the truth conditions of a proposition depend on the reactions of rational agents, then the possession of truth conditions can't follow from the intrinsic nature or existence of the proposition. This leaves two options. Either, nothing can do the job that motivates positing propositions. Or, there is no need to explain what bestows a truth condition on a proposition.