On Value‐Attributions: Semantics and Beyond

This paper is driven by the idea that the contextualism‐relativism debate regarding the semantics of value‐attributions turns on certain extra‐semantic assumptions that are unwarranted. One is the assumption that the many‐place predicate of truth, deployed by compositional semantics, cannot be directly appealed to in theorizing about people's assessments of truth value but must be supplemented (if not replaced) by a different truth‐predicate, obtained through certain “postsemantic” principles. Another is the assumption that semantics assigns to sentences not only truth values (as a function of various parameters, such as contexts, worlds and times), but also semantic contents, and that what context‐sensitive expressions contribute to content are contextually determined elements. My first aim in this paper will be to show how the two assumptions have shaped two ways of understanding the debate between contextualism and relativism. My second aim will be to show that both assumptions belong outside semantics and are, moreover, questionable.     

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.     

Why the Liar Does not Matter

This paper develops a classical model for our ordinary use of the truth predicate (1) that is able to address the liar's paradox and (2) that satisfies a very strong version of deflationism. Since the model is a classical in the sense that it has no truth value gaps, the model is able to address Tarski's indictment of our ordinary use of the predicate as inconsistent. Moreover, since it is able to address the liar's paradox, it responds to arguments against deflationism based upon that paradox alone. The model is based upon a notion of the complexity of propositions that a fixed set of speakers might express. A context-sensitive definition of the truth predicate is then provided based upon a class of possible worlds defined in terms of these speakers. Reasonable constraints on the memories and lifetimes of ordinary speakers are used to limit the set of propositions that they might express so that deflationist requirements are satisfied.     

Reasoning from Suppositions

Two experiments investigated inferences based on suppositions. In Experiment 1, the subjects decided whether suppositions about individuals' veracity were consistent with their assertions—for example, whether the supposition “Ann is telling the truth and Beth is telling a lie”, is consistent with the premises: “Ann asserts: I am telling the truth and Beth is telling the truth. Beth asserts: Ann is telling the truth”. It showed that these inferences are more difficult than ones based on factual premises: “Ann asserts: I live in Dublin and Beth lives in Dublin”. There was no difference between problems about truthtellers and liars, who always told the truth or always lied, and normals, who sometimes told the truth and sometimes lied. In Experiment 2, the subjects made inferences about factual matters set in three contexts: a truth-inducing context in which friends confided their personality characteristics, a lie-inducing context in which business rivals advertised their products, and a neutral context in which computers printed their program characteristics. Given the supposition that the individuals were lying, it was more difficult to make inferences in a truth-inducing context than in the other two contexts. We discuss the implications of our results for everyday reasoning from suppositions, and for theories of reasoning based on models or inference rules.     

Reasoning about a rule

Two experiments were carried out to investigate the difficulty of making the contra-positive inference from conditional sentences of the form, “if P then Q.” This inference, that not-P follows from not-Q, requires the transformation of the information presented in the conditional sentence. It is suggested that the difficulty is due to a mental set for expecting a relation of truth, correspondence, or match to hold between sentences and states of affairs. The elicitation of the inference was not facilitated by attempting to induce two kinds of therapy designed to break this set. It is argued that the subjects did not give evidence of having acquired the characteristics of Piaget's “formal operational thought.”     

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。     

Gödelizing the Yablo Sequence

We investigate what happens when ‘truth’ is replaced with ‘provability’ in Yablo’s paradox. By diagonalization, appropriate sequences of sentences can be constructed. Such sequences contain no sentence decided by the background consistent and sufficiently strong arithmetical theory. If the provability predicate satisfies the derivability conditions, each such sentence is provably equivalent to the consistency statement and to the Gödel sentence. Thus each two such sentences are provably equivalent to each other. The same holds for the arithmetization of the existential Yablo paradox. We also look at a formulation which employs Rosser’s provability predicate.     

A Generic Framework for Adaptive Vague Logics

In this paper, we present a generic format for adaptive vague logics. Logics based on this format are able to (1) identify sentences as vague or non-vague in light of a given set of premises, and to (2) dynamically adjust the possible set of inferences in accordance with these identifications, i.e. sentences that are identified as vague allow only for the application of vague inference rules and sentences that are identified as non-vague also allow for the application of some extra set of classical logic rules. The generic format consists of a set of minimal criteria that must be satisfied by the vague logic in casu in order to be usable as a basis for an adaptive vague logic. The criteria focus on the way in which the logic deals with a special ⊡-operator. Depending on the kind of logic for vagueness that is used as a basis for the adaptive vague logic, this operator can be interpreted as completely true, definitely true, clearly true, etc. It is proven that a wide range of famous logics for vagueness satisfies these criteria when extended with a specific ⊡-operator, e.g. fuzzy basic logic and its well known extensions, cf. [7], super- and subvaluationist logics, cf. [6], [9], and clarity logic, cf. [13]. Also a fuzzy logic is presented that can be used for an adaptive vague logic that can deal with higher-order vagueness. To illustrate the theory, some toy-examples of adaptive vague proofs are provided.     

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.     

Truth and Gradability

Journal of Philosophical Logic - I argue for two claims: that the ordinary English truth predicate is a gradable adjective and that truth is a property that comes in degrees. The first is a...     

Demonstrative Induction and the Skeleton of Inference

It has been common wisdom for centuries that scientific inference cannot be deductive; if it is inference at all, it must be a distinctive kind of inductive inference. According to demonstrative theories of induction, however, important scientific inferences are not inductive in the sense of requiring ampliative inference rules at all. Rather, they are deductive inferences with sufficiently strong premises. General considerations about inferences suffice to show that there is no difference in justification between an inference construed demonstratively or ampliatively. The inductive risk may be shouldered by premises or rules, but it cannot be shirked. Demonstrative theories of induction might, nevertheless, better describe scientific practice. And there may be good methodological reasons for constructing our inferences one way rather than the other. By exploring the limits of these possible advantages, I argue that scientific inference is neither of essence deductive nor of essence inductive.     

The Content of Deduction

For deductive reasoning to be justified, it must be guaranteed to preserve truth from premises to conclusion; and for it to be useful to us, it must be capable of informing us of something. How can we capture this notion of information content, whilst respecting the fact that the content of the premises, if true, already secures the truth of the conclusion? This is the problem I address here. I begin by considering and rejecting several accounts of informational content. I then develop an account on which informational contents are indeterminate in their membership. This allows there to be cases in which it is indeterminate whether a given deduction is informative. Nevertheless, on the picture I present, there are determinate cases of informative (and determinate cases of uninformative) inferences. I argue that the model I offer is the best way for an account of content to respect the meaning of the logical constants and the inference rules associated with them without collapsing into a classical picture of content, unable to account for informative deductive inferences.     

The Neglect of Epistemic Considerations in Logic: The Case of Epistemic Assumptions

The two different layers of logical theory—epistemological and ontological—are considered and explained. Special attention is given to epistemic assumptions of the kind that a judgement is granted as known, and their role in validating rules of inference, namely to aid the inferential preservation of epistemic matters from premise judgements to conclusion judgement, while ordinary Natural Deduction assumptions (that propositions are true) serve to establish the holding of consequence from antecedent propositions to succedent proposition.

     

Fuzzy Logic and Arithmetical Hierarchy III

Fuzzy logic is understood as a logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies (identically true sentences) and satisfiable sentences (sentences true in at least one interpretation) as well of sets of provable formulas of the most important systems of fuzzy predicate logic is determined or at least estimated.     

The belief-bias effect in formal reasoning: The influence of knowledge on logic

The present study examines the applicability of a rational model of categorical inference (e.g., Revlis, 1975b) to account for the apparently irrational decisions students reach on categorical syllogisms. In Experiment 1, students judged the logical validity of emotionally neutral conclusions to controversial premises. Of the reasoners’ decisions, 80% can be accounted for by the application of rational rules to their idiosyncratic encoding of the syllogistic premises. In Experiment 2, students were asked to solve syllogisms whose conclusions varied in truth value. When asked to reason about controversial, if not emotional, material, students do not suspend rational choice, but rather, their decisions are judicious ones, flowing logically from their idiosyncratic understanding of the materials reasoned about. When errors do occur, they result from an interrupt to rational processes and reflect conflict between competing goals rather than a switch to irrational decision processes.     

Idealism and Williams's Semantic Paradox

Bernard Williams's essay ‘Wittgenstein and Idealism’ argues that that the conventionality of language entails the dependence of the truth of sentences and ultimately of corresponding states of affairs as truth‐makers on the existence of thinking subjects. Peter Winch and Colin Lyas try to avoid William's paradox by distinguishing between the existence conditions of a sentence and its assertion. The Winch‐Lyas solution is criticized and a stronger Winch‐Lays resistant version of Williams's paradox is proposed. A more satisfactory countercriticism is given, involving an ineliminable modal fallacy occurring in the paradox inference, that arises because of the argument's invalid combination of categorical and counterfactual assumptions and conclusions.     

Getting the Most Out of Inconsistency

In this paper we look at two classic methods of deriving consequences from inconsistent premises: Rescher-Manor and Schotch-Jennings. The overall goal of the project is to confine the method of drawing consequences from inconsistent sets to those that do not require reference to any information outside of very general facts about the set of premises. Methods in belief revision often require imposing assumptions on premises, e.g., which are the important premises, how the premises relate in non-logical ways. Such assumptions enable one to select a reasonable collection of formulas from all the formulas of the language (the set of consequences of an inconsistent set). Basic versions of the classic methods only use logical relations between the premises. We compare and criticize each of the classic views with an eye to combining the views to get the most out of inconsistent premises. We do this in a way that will respect the theoretical grounding of each view while meeting our other restrictions.