*Leon Horsten*

- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262015868
- eISBN:
- 9780262298643
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262015868.003.0042
- Subject:
- Philosophy, General

This chapter is concerned with how Tarski set out to define truth. According to Tarski, truth could not be defined in the object language and has to be done in an essentially stronger metalanguage. ...
More

This chapter is concerned with how Tarski set out to define truth. According to Tarski, truth could not be defined in the object language and has to be done in an essentially stronger metalanguage. Although he first develops his theory in natural language enriched by some mathematical symbols, Tarski is aware of the need for a precisely defined metalanguage that allows for strict formal proofs. His truth theory, which assigned a crucial role to the Tarski-biconditionals, is the point of departure for most, if not all, recent publications on truth. Deflationist philosophers of today rely on Tarski-biconditionals as the axioms of the theory of truth. This chapter does not aim to provide a detailed historical account of Tarski’s truth theories; rather, it focuses on their most pertinent features that are vital for later developments.Less

This chapter is concerned with how Tarski set out to define truth. According to Tarski, truth could not be defined in the object language and has to be done in an essentially stronger metalanguage. Although he first develops his theory in natural language enriched by some mathematical symbols, Tarski is aware of the need for a precisely defined metalanguage that allows for strict formal proofs. His truth theory, which assigned a crucial role to the Tarski-biconditionals, is the point of departure for most, if not all, recent publications on truth. Deflationist philosophers of today rely on Tarski-biconditionals as the axioms of the theory of truth. This chapter does not aim to provide a detailed historical account of Tarski’s truth theories; rather, it focuses on their most pertinent features that are vital for later developments.

*Jody Azzouni*

- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780195159882
- eISBN:
- 9780199834990
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195159888.003.0002
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

A version of the indispensability of the truth of applied mathematical doctrine and empirical scientific law is established in this and the next chapter. This chapter begins the argument with a ...
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A version of the indispensability of the truth of applied mathematical doctrine and empirical scientific law is established in this and the next chapter. This chapter begins the argument with a description of how the truth idiom, when used to make blind truth ascriptions, is indispensable to scientific practice. Tarski’s biconditionals enable the assertion of laws and applications of law schemas which cannot be explicitly stated. That the needs of science requires the univocality of a truth idiom is shown.Less

A version of the indispensability of the truth of applied mathematical doctrine and empirical scientific law is established in this and the next chapter. This chapter begins the argument with a description of how the truth idiom, when used to make blind truth ascriptions, is indispensable to scientific practice. Tarski’s biconditionals enable the assertion of laws and applications of law schemas which cannot be explicitly stated. That the needs of science requires the univocality of a truth idiom is shown.

*Leon Horsten*

- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262015868
- eISBN:
- 9780262298643
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262015868.003.0021
- Subject:
- Philosophy, General

This chapter discusses Tarski’s theorem that states that no sufficiently expressive language can define its own truth predicate. This theorem is the starting point of contemporary axiomatic theories ...
More

This chapter discusses Tarski’s theorem that states that no sufficiently expressive language can define its own truth predicate. This theorem is the starting point of contemporary axiomatic theories of truth, since it implies that no consistent truth theory implies all the Tarski-biconditionals. Although Tarski’s theorem on the undefinability of truth has negative consequences for axiomatic theories of truth, Gödel’s techniques, which prove that no sufficiently consistent mathematical theory proves its own consistency, can be used to prove them. This leads to the realization that “naive” attempts to construct an axiomatic theory of truth fail miserably. Versions of Tarski’s theorem and other metatheorems used here and in the succeeding chapters are also reviewed.Less

This chapter discusses Tarski’s theorem that states that no sufficiently expressive language can define its own truth predicate. This theorem is the starting point of contemporary axiomatic theories of truth, since it implies that no consistent truth theory implies all the Tarski-biconditionals. Although Tarski’s theorem on the undefinability of truth has negative consequences for axiomatic theories of truth, Gödel’s techniques, which prove that no sufficiently consistent mathematical theory proves its own consistency, can be used to prove them. This leads to the realization that “naive” attempts to construct an axiomatic theory of truth fail miserably. Versions of Tarski’s theorem and other metatheorems used here and in the succeeding chapters are also reviewed.

*Leon Horsten*

- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262015868
- eISBN:
- 9780262298643
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262015868.003.0062
- Subject:
- Philosophy, General

This chapter explores and examines a second axiomatic theory that is directly inspired by Tarski’s work on truth. It was earlier argued that proving many Tarski-biconditionals is a necessary ...
More

This chapter explores and examines a second axiomatic theory that is directly inspired by Tarski’s work on truth. It was earlier argued that proving many Tarski-biconditionals is a necessary condition for being a sound theory of truth; now, however, it becomes evident that deriving these Tarski-biconditionals is not a sufficient condition. A sound theory of truth must additionally do justice to its compositional nature. The intuition that truth is compositional is just as basic as our intuition that truth is a disquotational device. The truth theory presented here has an obligation to either do justice to it or explain what is wrong with it. Tarski’s definition of truth inspires an axiomatic theory that explains the compositional nature of truth. Through his definition, the advantages of the compositional theory over the disquotational theory become evident.Less

This chapter explores and examines a second axiomatic theory that is directly inspired by Tarski’s work on truth. It was earlier argued that proving many Tarski-biconditionals is a necessary condition for being a sound theory of truth; now, however, it becomes evident that deriving these Tarski-biconditionals is not a sufficient condition. A sound theory of truth must additionally do justice to its compositional nature. The intuition that truth is compositional is just as basic as our intuition that truth is a disquotational device. The truth theory presented here has an obligation to either do justice to it or explain what is wrong with it. Tarski’s definition of truth inspires an axiomatic theory that explains the compositional nature of truth. Through his definition, the advantages of the compositional theory over the disquotational theory become evident.