Post Post-Truth: Epistemologies of Disintegration and the Praxeology of Truth

Our truth culture has changed. Yet we are not living in a post-truth era but in a truth era – an observation of the ongoing debates shows a proliferation of invocations of truth. This paper argues that in order to grasp this transition, we should not refer to classical truth theories or common oppositions such as knowledge and belief, objectivity and subjectivity. Instead, we should focus on concrete practices in concrete situations: on “doing truth.” This paper introduces the concept of a “praxeology of truth,” which sets out to analyse truth by means of two parameters: “truth scenes” and “truth figures.” In suggesting that to ask about truth is to pose the question of power, it follows Michel Foucault, but it regards the invocation of truth as a technique of identity politics and truth as a social operator.

Logics based on linear orders of contaminating values

A wide family of many-valued logics—for instance, those based on the weak Kleene algebra—includes a non-classical truth-value that is ‘contaminating’ in the sense that whenever the value is assigned to a formula $\varphi $, any complex formula in which $\varphi $ appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with multiple contaminating values. In this paper, we consider the countably infinite family of multiple-conclusion consequence relations in which classical logic is enriched with one or more contaminating values whose behaviour is determined by a linear ordering between them. We consider some motivations and applications for such systems and provide general characterizations for all consequence relations in this family. Finally, we provide sequent calculi for a pair of four-valued logics including two linearly ordered contaminating values before defining two-sided sequent calculi corresponding to each of the infinite family of many-valued logics studied in this paper.

A FULLY CLASSICAL TRUTH THEORY CHARACTERIZED BY SUBSTRUCTURAL MEANS

We will present a three-valued consequence relation for metainferences, called CM, defined through ST and TS, two well known substructural consequence relations for inferences. While ST recovers every classically valid inference, it invalidates some classically valid metainferences. While CM works as ST at the inferential level, it also recovers every classically valid metainference. Moreover, CM can be safely expanded with a transparent truth predicate. Nevertheless, CM cannot recapture every classically valid meta-metainference. We will afterwards develop a hierarchy of consequence relations CMn for metainferences of level n (for 1 ≤ n < ω). Each CMn recovers every metainference of level n or less, and can be nontrivially expanded with a transparent truth predicate, but cannot recapture every classically valid metainferences of higher levels. Finally, we will present a logic CMω, based on the hierarchy of logics CMn, that is fully classical, in the sense that every classically valid metainference of any level is valid in it. Moreover, CMω can be nontrivially expanded with a transparent truth predicate.

Normality operators and classical recapture in many-valued logic

In this paper, we use a ‘normality operator’ in order to generate logics of formal inconsistency and logics of formal undeterminedness from any subclassical many-valued logic that enjoys a truth-functional semantics. Normality operators express, in any many-valued logic, that a given formula has a classical truth value. In the first part of the paper we provide some setup and focus on many-valued logics that satisfy some (or all) of the three properties, namely subclassicality and two properties that we call fixed-point negation property and conservativeness. In the second part of the paper, we introduce normality operators and explore their formal behaviour. In the third and final part of the paper, we establish a number of classical recapture results for systems of formal inconsistency and formal undeterminedness that satisfy some or all the properties above. These are the main formal results of the paper. Also, we illustrate concrete cases of recapture by discussing the logics $\mathsf{K}^{\circledast }_{3}$, $\mathsf{LP}^{\circledast }$, $\mathsf{K}^{w\circledast }_{3}$, $\mathsf{PWK}^{\circledast }$ and $\mathsf{E_{fde}}^{\circledast }$, that are in turn extensions of $\mathsf{{K}_{3}}$, $\mathsf{LP}$, $\mathsf{K}^{w}_{3}$, $\mathsf{PWK}$ and $\mathsf{E_{fde}}$, respectively.

Dummett, Michael Anthony Eardley (1925–2011)

For Michael Dummett, the core of philosophy lies in the theory of meaning. His exploration of meaning begins with the model proposed by Gottlob Frege, of whose work Dummett is a prime expositor. A central feature of that model is that the sense (content) of a sentence is given by a condition for its truth, displayed as deriving from its constituent structure. If sense so explicated is to explain linguistic practice, knowledge of these truth-conditions must be attributed to language users by identifying features of use in which it is manifested. Analysis of truth suggests we seek such manifestation in patterns of assertion. But scrutiny of those patterns shows that there is no distinction between use which manifests knowledge of classical truth-conditions, and use which manifests knowledge of a weaker kind of truth - for example, one which holds whenever we possess a potential warrant for a statement. Such considerations motivate reconstruing sense as given by conditions for this weaker kind of truth. But rejigging Fregean semantics in line with such a conception is highly nontrivial. Mathematical intuitionism, properly construed, gives us models for doing so with mathematical language; Dummett’s programme is to extend such work to everyday discourses. Since he further argues that realism consists in defending the classical semantics for a discourse, this programme amounts to probing the viability of antirealism about such things as the material world, other minds and past events.

Two meanings of “if”? Individual differences in the interpretation of conditionals

This work investigates the nature of two distinct response patterns in a probabilistic truth table evaluation task, in which people estimate the probability of a conditional on the basis of frequencies of the truth table cases. The conditional-probability pattern reflects an interpretation of conditionals as expressing a conditional probability. The conjunctive pattern suggests that some people treat conditionals as conjunctions, in line with a prediction of the mental-model theory. Experiments 1 and 2 rule out two alternative explanations of the conjunctive pattern. It does not arise from people believing that at least one case matching the conjunction of antecedent and consequent must exist for a conditional to be true, and it does not arise from people adding the converse to the given conditional. Experiment 3 establishes that people's response patterns in the probabilistic truth table task are very consistent across different conditionals, and that the two response patterns generalize to conditionals with negated antecedents and consequents. Individual differences in rating the probability of a conditional were loosely correlated with corresponding response patterns in a classical truth table evaluation task, but there was little association with people's evaluation of deductive inferences from conditionals as premises. A theoretical framework is proposed that integrates elements from the conditional-probability view with the theory of mental models.