# Gödel, Tarski, Church, and The Liar

@article{Sereny1999GdelTC, title={G{\"o}del, Tarski, Church, and The Liar}, author={Gyorgy Sereny}, journal={Bulletin of Symbolic Logic}, year={1999}, volume={9}, pages={3 - 25} }

The fact that Gödel's famous incompleteness theorem and the archetype of all logical paradoxes, that of the Liar, are related closely is, of course, not only well known, but is a part of the common knowledge of the community of logicians. Indeed, almost every more or less formal treatment of the theorem makes a reference to this connection. Gödel himself remarked in the paper announcing his celebrated result (cf. [7]): The analogy between this result and Richard's antinomy leaps to the eye…

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## References

SHOWING 1-10 OF 29 REFERENCES

### Review: J. Findlay, Goedelian Sentences: A Non-Numerical Approach

- PhilosophyJournal of Symbolic Logic
- 1942

In a number of incidental passages the author flirts with symbolic logic proper, bu t with little evidence of serious intentions. The longest of these passages (pp. 186-188) proposes notions of…

### Infinity and the Mind

- PhilosophyThe Mathematical Gazette
- 1984

The inspector investigates the properties of such machines, and finally he sees their connection with the lock of a safe in Monte Carlo, and this enables him to find the missing combination. Most of…

### Some results on the length of proofs

- Mathematics, Computer Science
- 1973

This paper shall consider questions regarding the length of proofs of theories formalised in some language of thelower predicate calculus by means of a finite number of axioms, axiomschemata and schematic rules of inference, including Hilbert type and Gentzen type formalisations of classical and in-tuitionistic arithmetic.

### Languages in which self reference is possible

- PhilosophyJournal of Symbolic Logic
- 1957

This paper treats of semantical systems S of sufficient strength so that for any set W definable in S, there must exist a sentence X which is true in S if and only if it is an element of W .

### Truth and proof.

- PhilosophyScientific American
- 1969

The notion of truth and the notion of proof are discussed: the relationship between these two notions is discussed and the way the material has been arranged and knitted together is discussed.

### The Semantic Conception of Truth and the Foundations of Semantics

- Philosophy
- 1944

X is true if, and only if, p. [...] we shall call a definition of truth “adequate” if all these equivalences follow from it. [...] The definition of truth which was outlined above [...] implies all…

### Concatenation as a basis for arithmetic

- Computer ScienceJournal of Symbolic Logic
- 1946

General syntax, the formal part of the general theory of signs, has as its basic operation the operation of concatenation, expressed by the connective ‘⌢’ and understood as follows : where x and y…

### Advanced Logic for Applications

- Philosophy
- 1977

I. Henkin Sets and the Fundamental Theorem.- II. Derivation Rules and Completeness.- III. Gentzen Systems and Constructive Completeness Proofs.- IV. Quantification Theory with Identity and Functional…

### Computability and logic

- Computer Science, Philosophy
- 1974

This book discusses Computability Theory, Modal logic and provability, and its applications to first-order logic, which aims to clarify and clarify the role of language in the development of computability.