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}
}
  • R. Jeroslow
  • Published 1975
  • Computer Science, Mathematics
  • Journal of Philosophical Logic
  • 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

    Topics from this paper.

    Hilbert's program then and now
    • 54
    • Open Access
    Induction, Pure and Simple
    • 41
    • Open Access
    Generalizations of Gödel's Incompleteness theorems for ∑ n -Definable Theories of Arithmetic
    • 9
    • Highly Influenced
    • Open Access
    Logic and probabilistic systems
    • 7
    Gödel-Rosser's Incompleteness Theorem, generalized and optimized for definable theories
    • 7
    • Open Access
    Epistemic Entrenchment and Arithmetical Hierarchy
    • 4
    Self-reference and incompleteness in a non-monotonic setting
    • 5

    References

    Publications referenced by this paper.
    SHOWING 1-8 OF 8 REFERENCES
    Theory of Recursive Functions and Effective Computability
    • 3,672
    • Open Access
    The Completeness of the First-Order Functional Calculus
    • 395
    • Open Access
    Die Widerspruchsfreiheit der reinen Zahlentheorie
    • 454
    Limiting Recursion
    • 189
    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
    • 307
    • Open Access
    certe teorie non enumerabili (Sulle Limitazioni dei sistemi formali, I)‘,Ann
    • 1974