Language, Partial Truth, and Logic (original) (raw)
Related papers
Some Arguments for the Operational Reading of Truth Expressions
Analiza i Egzystencja, 2013
The main question of our article is: What is the logical form of statements containing expressions such as “… is true” and “it is true that …”? We claim that these expressions are generally not used in order to assign a certain property to sentences. We indicate that a predicative interpretation of these expressions was rejected by Frege and adherents to the prosentential conception of truth. We treat these expressions as operators. The main advantage of our operational reading is the fact that it adequately represents how the words “true” and “truth” function in everyday speech. Our approach confirms the intuition that so-called T-equivalences are not contingent truths, and explains why they seem to be—in some sense—necessary sentences. Moreover, our operational reading of truth
An Observation about Truth (with Implications for Meaning and Language) [PhD dissertation]
This dissertation is a philosophical analysis of the concept of truth. It is a development and defense of the “stratified” or “language-level” conception of truth, first advanced in Alfred Tarski’s 1933 monograph The Concept of Truth in Formalized Languages. Although Tarski’s paper had seminal influence both in philosophy and in more technical disciplines, its central philosophical claim has not been generally accepted. This work has two central goals: (a) to give a detailed and analytic presentation of Tarski’s theory and the problems it faces; (b) to offer a solution to these problems and assess the philosophical significance of this solution. The essay is divided in two parts. Part One contains a detailed and analytic presentation and interpretation of the stratified conception of truth. The analysis contains several steps: (a) Crucial basic assumptions, such as the limitation to formalized languages and the requirement of explicit definitions, are stated explicitly, motivated, and their philosophical significance discussed. (b) The main negative result of the stratified conception, the impossibility of semantic closure and of a universal language, is given in detail and interpreted. (c) Tarski’s criterion for adequate truth definitions, known as Convention T, is stated and motivated. (d) The deep structure of Tarski-style truth definitions and the necessary conditions for their availability are analyzed. In particular, the philosophical significance of Tarski’s notion of “essential richness” is discussed. (e) Finally, several problems are raised for the stratified conception, chief among them the unity objection, according to which the stratified conception is not a viable analysis of the concept of truth, since (by (a) above) an analysis should take the form of a definition, and on the stratified conception different languages have different definitions. There is therefore no one analysis of the concept. Part Two is a development of answers to the problems raised at the end of Part One. The crux of the answer to the unity objection is that Convention T, the adequacy criterion, connects the many definitions of truth into a single concept. However, in order to fulfill that role Convention T must apply universally, and a universal language was shown to be impossible ((c) above). The task of Part Two is therefore to develop a mode of expression that allows the universal applicability of Convention T without commitment to a universal metalanguage. The procedure is as follows. (a) Convention T is formalized in order to isolate the place in which universal applicability is required. (b) A new expressive resource of “abstract generality” is developed. To this purpose a digression into the semantics of natural language indexicals is undertaken. David Kaplan’s thesis of the direct reference of indexicals is analyzed and a new formal system is proposed that embodies it. It is shown that this formal system expresses abstract generality. (c) The notion of abstract generality is adapted to languages without indexicals and it isviii shown that Convention T can be expressed without assuming a universal language. (d) A reconstrual of the task of concept analysis is proposed, which is a generalization of the answer to the unity objection. It is often complained against Tarski’s stratified conception of truth that it is of limited philosophical significance. In this work I show that, on the contrary, the problems it faces and the solutions that can be advanced to answer these problems have substantive philosophical consequences. The notion of abstract generality gives rise to a distinction between two fundamentally different modes of discourse: a universal but merely abstract methodological discourse on the one hand, and a concrete but inevitably restricted theoretical discourse on the other. This distinction has many important implications for our understanding of the concepts of truth, meaning and language.
Some Arguments For the Operational Reading of Truth Expressions (co-author: Jan Wawrzyniak)
The main question of our article is: what is the logical form of statements containing expressions such as “… is true” and “it is true that …”? We claim that these expressions are generally not used in order to assign a certain property to sentences. We indicate that a predicative interpretation of these expressions was rejected by Frege and adherents of the prosentential conception of truth. We treat these expressions as operators. The main advantage of our operational reading is the fact that it adequately represents how words “true” and “truth” function in everyday speech. Our approach confirms the intuition that so-called T-equivalences are not contingent truths and explains why they seem to be – in some sense – necessary sentences. Moreover, our operational reading of truth expressions dissolves problems arising from the belief that there is some specific property – truth. The fact that we reject that truth is a certain property does not mean that we deny that the concept of truth plays a very important role in our language, and hence in our life. We indicate that the concept of truth is inseparable from the concept of sentence and vice versa – it is impossible to explicate one of these concepts without an appeal to the other. Analiza i Egzystencja, 24 (2013), pp. 61-86
Inquiry, 2018
Much philosophical attention has been devoted to the truth predicates of natural language and their logic. However, lexical truth predicates are neither necessary nor sufficient for a truthattribution to occur, which warrants closer attention to the grammar of truth attribution. A unified analysis of five constructions is offered here, in two of which the lexical truth predicate occurs (It's true that John left and That John left is true), while in the three remaining, it does not (John left; It seems that John left; and It's that John left). This analysis is philosophically significant for four reasons. First, it explains why speakers of natural language find standard instances of Tarski-inspired equivalences (e.g., That John left is true iff John left) intuitively compelling. Second, it derives the widespread 'deflationist' intuition that truth has no substantive content. Third, insofar as the deflationist sees insights on truth as flowing from understanding our practice of truth attribution, it furthers the deflationist agenda through a new analysis of such attributions. Finally, it advances the philosophical project of the 'naturalization' of truth by reducing our understanding of truth to our competence in the grammar of truth, as an aspect of our biological endowment.
Problems and Issues with Half- Truths
Rescher 1967 discusses the pros and cons of having hybrid truth-values vis-à-vis triviality and the loss or gain of tautologies and antilogies. We argue that hybrid truth-values are not an option for systems within the scope of the hexagon of oppositions, and try to clarify certain issues of many-valued logics, such as the basic distinction between half-truths and teratologies.
Defining "False": Towards a Unified Theory of Truth
Tarski’s semantic conception of truth was first stated by Aristotle: ‘To say of what is that it is not, or of what is that it is not, is false, while to say of what is that it is, or of what is not that it is not, is true’ (Metaphysics, 1011b 26-28). Tarski takes his T-biconditional from this. However, whereas Aristotle defines ‘true’ before ‘false’ Tarski defines only ‘true’. I reformulate the definitions of ‘false’ and ‘true’ of various contemporary theories of truth. In the reformulations ‘false’ is defined first. I hope to uncover some structural features that are common to all theories of truth and conjecture how these can be weaved into a fabric from which we can ultimately tailor a unified theory of truth. My main aim is to arrive historically, with my reversal, at the Tarskian biconditional F: “‘p’ is false if and only if not-p,” which will replace Tarski’s biconditional T: “‘p’ is true if and only if p.” Now, ‘true’ will be defined as: “‘p’ is true if and only if not-not-p.” But by double negation this is equivalent to Tarski’s original convention T. So what is the big deal? If truth is simply a logical concept then the truth functional equivalence of double negation with affirmation is sufficient to establish the identity of Tarski’s biconditional T with my reformulated Tarskian biconditional T. However, if truth is a concept involving some extra-logical, linguistic, ontological, metaphysical, epistemological, or psychological dimensions, then there is a significant difference between the definition of ‘true’ that involves an affirmation and the one that involves a double negation. Furthermore, some intuitionist systems of logic reject double negation as a rule. Hence, defining ‘true’ in terms of ‘false’ will not even be logically equivalent to defining ‘false’ in terms of ‘true’. I will demonstrate that with this reversal of definitions we will get a better rendition of the liar’s paradox, which usually begins with a statement like ‘This sentence is not true.’ I will begin with falsehood and then the paradox is unveiled. The result is that whereas Tarski’s actual version of the liar’s antinomy appeals to the rule of double negation, my version does not. Nonetheless Tarski’s original proof can also be revised to avoid use of the rule of double negation. I also consider the possibility of the indefinability of truth, as proposed by Donald Davidson, and defend robust as well as deflationary theories in their search for truth and reject indefinability. In doing so, I take on an exercise in philosophical methodology of Plato and its influence on contemporary analytic philosophy.
On the Truth of Linguistic Propositions
Problems of Methodology and Philosophy in Linguistics
In the present paper I analyse propositions functioning in linguistics from the point of view of the criteria of truth imposed on the propositions within the so-called correspondence theory of truth, coherence theory of truth, and pragmatic theory of truth in its sociological version. There exists in linguistic circulation a certain group of propositions which on some assumptions are in agreement with Tarski's explication. The truth of each sentence from the second group can be predicated only when they are juxtaposed with sentences belonging to a concrete system of propositions. The analysed sentence will be recognised as false in a different system. Some systems of sentences may recognise the criteria of evaluation as inadequate, they are, however, not sufficiently sharp so as to enable to make the final decision about the supremacy of one concrete system of sentences over the others. In linguistics there also exist many sentences which are true in linguists' view, although they are not coherent with a certain system of sentences-the propositions belonging to this system may lead to different conclusions. It is the last group of sentences that in the eyes of postmodernists constitutes an argument supporting the thesis that in science (particularly in the humanities) we deal only with accumulating narratives. The major objective of this paper is, however, to prove that the propositions which belong to the third group, although frequent in linguistics, do not belong to its centre-they are only a complement of what may be described by the name of linguistic discourse.