*Tim Maudlin*

- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780199247295
- eISBN:
- 9780191601781
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199247293.001.0001
- Subject:
- Philosophy, Philosophy of Language

At least since the work of Tarski, the Liar paradox has stood in the way of an acceptable account of the notion of truth. It has been less noticed that once one admits a truth predicate into a formal ...
More

At least since the work of Tarski, the Liar paradox has stood in the way of an acceptable account of the notion of truth. It has been less noticed that once one admits a truth predicate into a formal language, along with intuitively valid inferences involving the truth predicate, standard classical logic becomes inconsistent. So, any acceptable account of truth must both explicate how sentences get the truth values they have and amend classical logic to avoid the inconsistency. A natural account of a trivalent semantics arises from treating the problem of assigning truth values to sentences as akin to a boundary‐value problem in physics. The resulting theory solves the Liar paradox while avoiding the usual ‘revenge’ problems. It also suggests a natural modification of classical logic that blocks the paradoxical reasoning. This semantic theory is wedded to an account of the normative standards governing assertion and denial of sentence and a metaphysical analysis truth and factuality. The result is an account in which sentences like the Liar sentence are neither true nor false, and correspond to no facts.Less

At least since the work of Tarski, the Liar paradox has stood in the way of an acceptable account of the notion of truth. It has been less noticed that once one admits a truth predicate into a formal language, along with intuitively valid inferences involving the truth predicate, standard classical logic becomes inconsistent. So, any acceptable account of truth must both explicate how sentences get the truth values they have and amend classical logic to avoid the inconsistency. A natural account of a trivalent semantics arises from treating the problem of assigning truth values to sentences as akin to a boundary‐value problem in physics. The resulting theory solves the Liar paradox while avoiding the usual ‘revenge’ problems. It also suggests a natural modification of classical logic that blocks the paradoxical reasoning. This semantic theory is wedded to an account of the normative standards governing assertion and denial of sentence and a metaphysical analysis truth and factuality. The result is an account in which sentences like the Liar sentence are neither true nor false, and correspond to no facts.

*Tim Maudlin*

- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780199247295
- eISBN:
- 9780191601781
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199247293.003.0001
- Subject:
- Philosophy, Philosophy of Language

Reviews the standard semantic paradoxes, and constructs a simple formal language in which the paradoxical reasoning can be reconstructed. Particular attention is paid to Löb's paradox, which allows ...
More

Reviews the standard semantic paradoxes, and constructs a simple formal language in which the paradoxical reasoning can be reconstructed. Particular attention is paid to Löb's paradox, which allows for the derivation of any sentence in the language as a theorem. The advantages of a natural deduction system over an axiomatic logic is discussed.Less

Reviews the standard semantic paradoxes, and constructs a simple formal language in which the paradoxical reasoning can be reconstructed. Particular attention is paid to Löb's paradox, which allows for the derivation of any sentence in the language as a theorem. The advantages of a natural deduction system over an axiomatic logic is discussed.

*Tim Maudlin*

- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780199247295
- eISBN:
- 9780191601781
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199247293.003.0002
- Subject:
- Philosophy, Philosophy of Language

The formal language developed in ch. 1 is modelled as a directed graph with a boundary, and the problem of assigning truth values to sentences assimilated to a boundary‐value problem. A trivalent ...
More

The formal language developed in ch. 1 is modelled as a directed graph with a boundary, and the problem of assigning truth values to sentences assimilated to a boundary‐value problem. A trivalent semantics, with true, false, and ungrounded sentences results. The nature of the third truth‐value imposes constraints on the possible truth‐functional connectives in the language.Less

The formal language developed in ch. 1 is modelled as a directed graph with a boundary, and the problem of assigning truth values to sentences assimilated to a boundary‐value problem. A trivalent semantics, with true, false, and ungrounded sentences results. The nature of the third truth‐value imposes constraints on the possible truth‐functional connectives in the language.