On Structural Features of the Implication Fragment of Frege’s Grundgesetze

Journal of Philosophical Logic 46 (4):443-456 (2017)
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Abstract

We set out the implication fragment of Frege’s Grundgesetze, clarifying the implication rules and showing that this system extends Absolute Implication, or the implication fragment of Intuitionist logic. We set out a sequent calculus which naturally captures Frege’s implication proofs, and draw particular attention to the Cut-like features of his Hypothetical Syllogism rule.

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10.1007/s10992-016-9406-x

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Andrew Tedder
University of Connecticut

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References found in this work

Foundations of mathematical logic.Haskell Brooks Curry - 1963 - New York: Dover Publications.
Grundzüge der theoretischen Logik.D. Hilbert & W. Ackermann - 1928 - Annalen der Philosophie Und Philosophischen Kritik 7:157-157.
Proof theory: sequent calculi and related formalisms.Katalin Bimbó - 2015 - Boca Raton: CRC Press, Taylor & Francis Group.
Combinators and structurally free logic.J. Dunn & R. Meyer - 1997 - Logic Journal of the IGPL 5 (4):505-537.
The Theory of Implication.Bertrand Russell - 1906 - American Journal of Mathematics 28:158-202.

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