紧缩论,证明与保守性

紧缩论者主张真谓词表达了一种逻辑概念,它的全部意义都体现在所有塔斯基式的T-语句中。Shapiro近来论证说,将紧缩论的公理添加到一阶皮亚诺算术公理系统(PA)中,在该扩张理论中能够证明PA的可靠性,并在此基础上证明PA的一致性,这表明紧缩论不具有保守性,因此真谓词不是紧缩的。本文论证,扩张理论预设了反射原则,这导致它推出了更多的东西,而反射原则是可证性谓词定义的推论,这才是造成扩张理论非保守性的真正根源。针对紧缩论的非保守性论证因此失效了。     

Missed It By That Much: Austin on Norms of Truth

A principal challenge for a deflationary theory is to explain the value of truth: why we aim for true beliefs, abhor dishonesty, and so on. The problem arises because deflationism sees truth as a mere logical property and the truth predicate as serving primarily as a device of generalization. Paul Horwich, attempts to show how deflationism can account for the value of truth. Drawing on the work of J. L. Austin, I argue that his account, which focuses on belief, cannot adequately accommodate the complex role that truth plays in the norms governing assertion and similar speech acts.     

Leave Truth Alone: On Deflationism and Contextualism

Abstract: According to deflationism, grasp of the concept of truth consists in nothing more than a disposition to accept a priori (non‐paradoxical) instances of the schema: (DS) It is true that p if and only if p. According to contextualism, the same expression with the same meaning might, on different occasions of use, express different propositions bearing different truth‐conditions (where this does not result from indexicality and the like). On this view, what is expressed in an utterance depends in a non‐negligible way on the circumstances. Charles Travis claims that contextualism shows that ‘deflationism is a mistake’, that truth is a more substantive notion than deflationism allows. In this paper, I examine Travis's arguments in support of this ‘inflationary’ claim and argue that they are unsuccessful.     

The Logics of Strict-Tolerant Logic

Adding a transparent truth predicate to a language completely governed by classical logic is not possible. The trouble, as is well-known, comes from paradoxes such as the Liar and Curry. Recently, Cobreros, Egré, Ripley and van Rooij have put forward an approach based on a non-transitive notion of consequence which is suitable to deal with semantic paradoxes while having a transparent truth predicate together with classical logic. Nevertheless, there are some interesting issues concerning the set of metainferences validated by this logic. In this paper, we show that this logic, once it is adequately understood, is weaker than classical logic. Moreover, the logic is in a way similar to the paraconsistent logic LP.     

Probability,Approximate Truth,and Truthlikeness: More Ways out of the Preface Paradox

The so-called Preface Paradox seems to show that one can rationally believe two logically incompatible propositions. We address this puzzle, relying on the notions of truthlikeness and approximate truth as studied within the post-Popperian research programme on verisimilitude. In particular, we show that adequately combining probability, approximate truth, and truthlikeness leads to an explanation of how rational belief is possible in the face of the Preface Paradox. We argue that our account is superior to other solutions of the paradox, including a recent one advanced by Hannes Leitgeb (Analysis 74.1).     

What Truth Depends on

What kinds of sentences with truth predicate may be inserted plausibly and consistently into the T-scheme? We state an answer in terms of dependence: those sentences which depend directly or indirectly on non-semantic states of affairs (only). In order to make this precise we introduce a theory of dependence according to which a sentence φ is said to depend on a set Φ of sentences iff the truth value of φ supervenes on the presence or absence of the sentences of Φ in/from the extension of the truth predicate. Both φ and the members of Φ are allowed to contain the truth predicate. On that basis we are able define notions such as ungroundedness or self-referentiality within a classical semantics, and we can show that there is an adequate definition of truth for the class of sentences which depend on non-semantic states of affairs.     

Reasoning with Truth

The aim of the paper is to formulate rules of inference for the predicate 'is true' applied to sentences. A distinction is recognised between (ordinary) truth and definite truth and consequently between two notions of validity, depending on whether truth or definite truth is the property preserved in valid arguments. Appropriate sets of rules of inference governing the two predicates are devised. In each case the consequence relation is in harmony with the respective predicate. Particularly appealing is a set of ND rules for ordinary truth in which premises and assumptions play different roles, premises being taken to assert definite truth, assumptions to suppose truth. This set of rules can be said to capture everyday reasoning with truth. Also presented are formal characterisations, in the meta-language and in the object language, of paradoxical and 'truth teller'-like sentences.     

Realism,inferential semantics,and the truth norm

Characteristic of neo-pragmatism is a commitment to deflationism about semantic properties, and inferentialism about conceptual content. It is usually thought that deflationism undermines the distinction between realistic discourses and others, and that the neo-pragmatists, unlike the classical pragmatists, cannot recognize that truth is a norm of belief and inquiry. I argue, however, that (1) the distinction between realistic discourses and others can be maintained even in the face of a commitment to deflationism, and (2) that deflationists can recognize that truth is a norm of belief and inquiry. If deflationism is true, realistic discourses, it turns out, are those that are inferentially integrated with a large body of other commitments, whereas those that call for an anti-realist treatment are inferentially isolated. Now, Grimm has persuasively argued that inquiry aims at achieving understanding, and that to understand something is, roughly, to grasp a large body of inferential connections in which it features. So, if he is right, realistic discourses are those in which the aim of inquiry can be achieved. This fact, together with an inferential theory of conceptual content, will, I argue, allow neo-pragmatists to recognize truth as a norm of belief and inquiry, despite their commitment to deflationism.

     

Perfect validity,entailment and paraconsistency

This paper treats entailment as a subrelation of classical consequence and deducibility. Working with a Gentzen set-sequent system, we define an entailment as a substitution instance of a valid sequent all of whose premisses and conclusions are necessary for its classical validity. We also define a sequent Proof as one in which there are no applications of cut or dilution. The main result is that the entailments are exactly the Provable sequents. There are several important corollaries. Every unsatisfiable set is Provably inconsistent. Every logical consequence of a satisfiable set is Provable therefrom. Thus our system is adequate for ordinary mathematical practice. Moreover, transitivity of Proof fails upon accumulation of Proofs only when the newly combined premisses are inconsistent anyway, or the conclusion is a logical truth. In either case Proofs that show this can be effectively determined from the Proofs given. Thus transitivity fails where it least matters — arguably, where it ought to fail! We show also that entailments hold by virtue of logical form insufficient either to render the premisses inconsistent or to render the conclusion logically true. The Lewis paradoxes are not Provable. Our system is distinct from Anderson and Belnap's system of first degree entailments, and Johansson's minimal logic. Although the Curry set paradox is still Provable within naive set theory, our system offers the prospect of a more sensitive paraconsistent reconstruction of mathematics. It may also find applications within the logic of knowledge and belief.     

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‐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.     

论弗雷格的“真之收缩”思想

弗雷格运用逻辑分析的方法,提出了自己独特的"真"之思想,形成了关于"真"的完整理论。在他看来,"真"不具有实体属性,不存在与客体在存在方式或存在状况的符合与对应,"真"只用来表达断定句形式中的断定力。当"5是素数"这个句子带有断定力时,真也就被表达出来,它与"5是素数是真的"表达了同样的内容。另外,他将"真"作为初始概念,认为真是不可定义的。如果对"真"进行定义,将走入"定义的循环"。因为要知道什么是"真",就需要论证表象与现实的一致性,而二者的一致又依赖于"真"的定义。这种思路与做法必将导致循环定义,故弗雷格认为"真"是不可定义的。基于以上两点的分析,他再次对符合论提出批评。他认为,如果符合论对"真"的理解是正确的话,那么结论是"事实比真更为基本,应该在事实的基础上定义真",但这显然是错误的,因为我们总是通过真来确定事实,而不是通过事实来确定真。我们似乎可以在弗雷格思想中找到收缩论的雏型,因为他关于"真"的认识与收缩论在很大程度上是一致的。收缩论最重要的观点在于说"P是真的"和说"P"有相同的涵义,谓词"是真的"是多余的。"真"本身是可收缩的,不带有实体性质。于是,我们可把弗雷格作为表达真之收缩观点的第一位哲学家,虽然他并不是坚定的收缩论者。     

Minimalism deflated: independence without substance

The paper examines Wright’s attempt to inflate deflationism about truth. It accepts the details of Wright’s argument but contends that it should best be seen as posing a dilemma for the deflationist: either truth is independent of norms of warranted assertibility—in which case it is substantial—or it is not—in which case epistemicism about truth is a consequence. Some concerns about epistemicism are raised in avoiding the second horn. The first is avoided by distinguishing between independence and substantiality and arguing that only the first applies to truth and only the second is worrisome to deflationism. So, despite its sub-title, the following is not a diatribe against Home Rule but a modest defence of deflationism.     

试论语义悖论的弗完全理论

弗完全理论通过限制排中律的使用,弱化经典逻辑,采用非经典的三值语言来处理语义悖论,最终使得形式语言能够一致地包含自身的真谓词。文中我们讨论了弗完全理论的两种基本形式——基础的弗完全理论和高级的弗完全理论。基础的弗完全理论引入了＂真值空缺＂的思想,认为句子除了真假之外还有＂既不真也不假＂的第三值,像说谎者这样的语义悖论语句就落在真假之空缺中,该理论借助于对不动点的归纳构造过程证明了形式语言中真谓词的存在性。高级弗完全理论在前者的基础上引入一个适当的条件句,定义了一个＂更强的真＂,发展出了既满足真的素朴模式又具有不动点解释的、一致的高级弗完全理论。     

Truth and Nonsense: A Unified Reading of the Tractatus

Upon reading the Tractatus Logico-Philosophicus, readers might be confused about the nature of the book, since there seems to be a paradox introduced by the author’s two claims: a) the book conveys truths; b) propositions in the book are nonsense. Commentators disagree as to how best to resolve this paradox. Some hold that there are ineffable truths conveyed by nonsense propositions. Others deny this kind of truth, arguing that the book is not all nonsense, for there are some propositions in the book expressing at least the therapeutic truth that philosophical propositions are just nonsense. Recently, some interpreters have claimed that there is no truth at all. While the incoherence of the context is genuine, the purpose of the book is ethical. By diagnosing these interpretations, this paper intends to provide a new perspective toward reading the book by resolving the paradox. The truth of the Tractatus is not a propositional truth, but a specific true thought. The nonsense of the Tractatus is a transcending nonsense, rather than a pure nonsense. The book intends to attain the true thought about the mystical ethics by way of transcending nonsense. In this case, the Tractatus is not an incoherent work at all, since the paradox is not genuine. The fact that the nonsense part is a means to fulfill its ethical purpose makes the book a unified whole.     

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 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.     

A complete minimal logic of the propositional contents of thought

Our purpose is to formulate a complete logic of propositions that takes into account the fact that propositions are both senses provided with truth values and contents of conceptual thoughts. In our formalization, propositions are more complex entities than simple functions from possible worlds into truth values. They have a structure of constituents (a content) in addition to truth conditions. The formalization is adequate for the purposes of the logic of speech acts. It imposes a stronger criterion of propositional identity than strict equivalence. Two propositions P and Q are identical if and only if, for any illocutionary force F, it is not possible to perform with success a speech act of the form F(P) without also performing with success a speech act of the form F(Q). Unlike hyperintensional logic, our logic of propositions is compatible with the classical Boolean laws of propositional identity such as the symmetry and the associativity of conjunction and the reduction of double negation.Presented byJan Zygmunt     

Relative truth and the first person

In recent work on context-dependency, it has been argued that certain types of sentences give rise to a notion of relative truth. In particular, sentences containing predicates of personal taste and moral or aesthetic evaluation as well as epistemic modals are held to express a proposition (relative to a context of use) which is true or false not only relative to a world of evaluation, but other parameters as well, such as standards of taste or knowledge or an agent. I will argue that the sentences that apparently give rise to relative truth should be understood by relating them in a certain way to the first person. More precisely, such sentences express what I will call ‘first-person-based genericity’, a form of generalization that is based on an essential first-person application of the predicate. The account differs from standard relative truth account in crucial respects: it is not the truth of the proposition expressed that is relative to the first person; the proposition expressed by a sentence with a predicate of taste rather has absolute truth conditions. Instead it is the propositional content itself that requires a first-personal cognitive access whenever it is entertained. This account, I will argue, avoids a range of problems that standard relative truth theories of the sentences in question face and explains a number of further peculiarities that such sentences display.