By John F. Hoffmeyer
This e-book argues that Hegel's philosophy powerfully articulates a good judgment of freedom.
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Extra info for The Advent of Freedom: The Presence of the Future in Hegel's Logic
Cut) ε, βsseqC As we have the subformula principle for higher-level natural deduction, it holds for the higher-level sequent calculus as well, if we only allow for cuts of the form described in the weak cut elimination theorem. Therefore cuts of this special form are harmless, although perhaps not most elegant. That we do not have full cut elimination is demonstrated by the sequent-calculus translation of our example (8): 22 P. Schroeder-Heister B ∇B A ∇A (∧ L) (⇒ L) A, (A ⇒ B ∧C) ∇ B ∧C B ∧C ∇ B (Cut) .
N. edu. 39. Schroeder-Heister, P. (2013). Definitional reflection and Basic Logic. Annals of Pure and Applied Logic (Special issue, Festschrift 60th Birthday Giovanni Sambin), 164, 491–501. 40. Schroeder-Heister, P. (2014). Harmony in proof-theoretic semantics: A reductive analysis. In H. ), Dag Prawitz on Proofs and Meaning, Heidelberg: Springer. 41. Tennant, N. (1992). Autologic. Edinburgh: Edinburgh University Press. 42. Tennant, N. (2002). Ultimate normal forms for parallelized natural deductions.
13) In fact, if we consider a purely implicational system with (→ L)◦ of the multi-ary form ε ∇ A1 . . ε ∇ An ε, A1 → (. . (An → B) . 17 Analogously, the purely implicational natural deduction system with the following rule for implication 17 Avron also remarks that the standard (→ L) rule is a way of avoiding the multi-ary character of this rule, which cannot be effected by means of (→ L)◦ alone (if conjunction is not available). Negri and von Plato  (p. 184) mention the rule (→ L)◦ as a sequent calculus rule corresponding to modus ponens, followed by a counterexample to cut analogous to (12), which is based on implication only.