Tarski's Theory of Truth

Overview

• Tarski aimed to define "truth" clearly, avoiding problematic concepts.
• Philosophers were skeptical about the concept of truth.

Constraints on Defining Truth

Formal Correctness

• Definition must use clear expressions.
• Avoids presupposing the notion of truth.

Material Adequacy

• Conforms to classical conception of truth.
• Example: "Snow is white" is true if and only if snow is white.
• Generalized as:
  • X is true if and only if p.

Other Constraints

• Should not entail false sentences or paradoxes (e.g., Liar Paradox).

Tarski's Definition of Truth

Truth in a Language

• Truth must be language-specific.

Quantifying into Quotation

• Critiques of defining truth by quantifying over sentences.
• Importance of distinguishing variables in definitions.

Truth and Satisfaction

• Truth involves semantic notions like satisfaction.
• Finite Language: Defined truth as a list.
• Simple Language (Infinite Sentences): Uses inductive definitions.
• Language with Function Symbols: Requires definitions beyond lists.

Definitions of Designation and Satisfaction

• Analogous to truth definitions.
• Need to define for infinite terms and predicates.

Language with Quantifiers

• Introduces complexity beyond atomic sentences.
• Requires handling quantified sentences differently.

Liar Paradox and Language Hierarchy

• Avoid semantically closed languages.
• Distinguishes object-language and meta-language.

Importance of Tarski's Definition

Response to Truth Skepticism

• Proof of a rigorously defined truth predicate.

Definition of Logical Consequence

• Relation between truth and logical consequence.

Natural vs. Formalized Languages

Challenges with Natural Languages

• Lack formal structure for precise truth definition.
• Semantic closure issues similar to Liar Paradox.

Tarski's View on Natural Languages

• Belief that they are inconsistent due to universality.

Further Reading

• Soames, "Understanding Truth"
• Anil Gupta in the "Routledge Encyclopedia of Philosophy".