Tarski’s definition of truth

Alfred Tarski’s definition of truth is unlike any that philosophers have given in their long struggle to understand the concept of truth. Tarski’s definition is more clear and precise than any previous definition, but it is also unusual in character and more restricted in scope. Tarski does not provide a general definition of truth. He provides instead a method of constructing, for a range of formalized languages L, definitions of the notions ‘true sentence of L’. A remarkable feature of Tarski’s work on truth is his ‘Criterion T’, which lays down a general condition that any definition of ‘true sentence of L’ must satisfy. Tarski’s ideas have exercised an enormous influence in philosophy. They have played an important role in the formulation and defence of a range of views in logic, semantics and metaphysics.

Missing-link conditionals: pragmatically infelicitous or semantically defective?

According to virtually all major theories of conditionals, conditionals with a true antecedent and a true consequent are true. Yet conditionals whose antecedent and consequent have nothing to do with each other—so-called missing-link conditionals—strike us as odd, regardless of the truth values of their constituent clauses. Most theorists attribute this apparent oddness to pragmatics, but on a recent proposal, it rather betokens a semantic defect. Research in experimental pragmatics suggests that people can be more or less sensitive to pragmatic cues and may be inclined to differing degrees to evaluate a true sentence carrying a false implicature as false. We report the results of an empirical study that investigated whether people’s sensitivity to false implicatures is associated with how they tend to evaluate missing-link conditionals with true clauses. These results shed light on the question of whether missing-link conditionals are best seen as pragmatically infelicitous or rather as semantically defective.

Carnap's Contribution to Tarski's Truth.

<div class="page" title="Page 1"><div class="layoutArea"><div class="column">In his seminal work “The Concept of Truth in Formalized Languages” (1933), Alfred Tarski showed how to construct a formally correct and materially adequate definition of true sentence for certain formalized languages. These results have, eventually, been accepted and applauded by philosophers and logicians nearly in unison. Its Postscript, written two years later, however, has given rise to a considerable amount of controversy. There is an ongoing debate on what Tarski really said in the postscript. These discussions often regard Tarski as putatively changing his logical framework from type theory to set<br />theory.<br /><br />In what follows, we will compare the original results with those presented two years later. After a brief outline of Carnap’s program in The Logical Syntax of Language we will determine its significance for Tarski’s final results.</div></div></div>

On the syntactical construction of systems of modal logic

When C. I. Lewis developed his theory of strict implication, he left open the question which of his various systems should be regarded as being closest to our intuitions—though he was inclined to favor the system S2. There are to be found in the literature numerous discussions of this question; most of these have condemned S2 as being too strong, and have proposed ways of weakening it.In the present paper I shall attempt to throw some light on this question by setting up a syntactical definition of “possibility.” I shall show that every system of modal logic constructed on the basis of this definition is at least as strong as the Lewis system S4.As the intuitive basis for the syntactical definition of possibility, I take the position that to say a sentence is possible means that there exists a true sentence of the same form. Thus, for example, it would be said that the sentence, “Lions are indigenous to Alaska,” is possible, because of the fact that the sentence, “Lions are indigenous to Africa,” has the same form and is true.

An Overlooked Type of Inference

A Detailed analysis of single statements corroborates more and more our conviction that the elements of Hindu mentality (viz. philosophy, religion, and fine arts) are subject to certain fixed and common rules of thinking. If we acknowledge any one analytical method—of course the most general possible—as sufficient and adequate, we can presume that whatever may at any time be the object of our analysis must follow the method adopted. If we accept as a principle for the veracity of all judgments that they must be subjected to the rule of sapakṣe sattva and vipakṣe asattva, then the analysis will show that in reality all statements are measurable under the aspect of those two criteria. The only breach in this principle was made by a Jaina logical school which, while anticipating the principles of our “implication”, admits the syllogism fulfilling the anyathānupapannatva condition, i.e. it accepts as true conditional sentences of which the protasis does not reach beyond the sphere of the predicated subject (pakṣa). In other words: the argument, when predicating a fact, forms a true sentence, even if it does not predicate the class to which the fact belongs. Whilst the Buddhist syllogism oscillates between class inference and sentence calculus (sapakṣa and vipakṣa being the necessary conditions), the Jaina syllogism advances exclusively the sentence calculus, and the validity of the predication is confined merely to the implication in question.