# Experimental logics and Δinf2sup0- theories

@article{Jeroslow1975ExperimentalLA, title={Experimental logics and Δinf2sup0- theories}, author={R. Jeroslow}, journal={Journal of Philosophical Logic}, year={1975}, volume={4}, pages={253-267} }

In this paper, we explore the concept of a logic which proceeds by trial-anderror, and deduce consequences which follow from relatively weak assumptions about these experimental logics. One of the consequences (Theorem 2) is analogous to, and in a rigorous sense it extends, Godel’s First Incompleteness Theorem. A second result (Theorem 5) stands in contrast to the corresponding result for ordinary formal systems, since it is not in general possible to mechanically find true but unprovable… CONTINUE READING

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- 1990

- 26

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- 2017

- 9
- Highly Influenced
- Open Access

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- 7
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#### References

##### Publications referenced by this paper.

SHOWING 1-8 OF 8 REFERENCES

The Completeness of the First-Order Functional Calculus

- Mathematics, Computer Science
- 1949

- 395
- Open Access

On Godel’s Consistency Theorem’, manuscript from the School of Mathematics, University of Minnesota, dated July

- 1971

Significato e verita nell aritmetica plan&ma (Sulle limitazioni dei sistemi formali, II)‘, to appear in Ann

- 1973

Trial and Error Predicates and the Solution to a Problem of Mostowski

- Mathematics, Computer Science
- 1965

- 307
- Open Access

certe teorie non enumerabili (Sulle Limitazioni dei sistemi formali, I)‘,Ann

- 1974