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harmony

Logical harmony was a name coined by Sir Michael Dummett to talk about an idea about where meaning comes from that is powerfully summarised in a brief phrase of Gerhard Gentzen to the effect that we can take the introduction rules as giving the meaning of a connective. Harmony, then, referes to certain constraints that a proof theory must let hold between introduction and elimination rules for it to be meaningful, or in other words, for its inference rules to be meaning constituting. Semantics of this form has not provided a very great challenge to that sketched in Tarski's semantic theory of truth, but many philosophers interested in reconstituting the semantics of logic in a way that respects Ludwig Wittgenstein's meaning is use have felt that harmony holds the key.

Resources

  1. Wikipedia:Logical harmony, which was seeded from this one.
  2. Local Reduction Interesting thread at Brian Wetherson's weblog on this topic, highlights difference between what I call local harmony and global harmony.
  3. New Blog, Tonk, and Normalization A comment at Richard Zach's weblog points out Arnon Avron and I. Lev treat Prior's tonk in their paper on semantics via nondeterministic matrices paper ((1))
  4. Logical harmony is a topic Gillian Russell keeps revisiting at her weblog:
    1. 'Tonk' and Local Reduction
    2. Normalisation/local reduction
    3. Truth and Tonk
    4. Dummett on Harmony, Conservative Extensions and Local Reduction/Normalisation
  5. Intelim Rules for Truth and Names at Matt Wiener's weblog.
  6. Dummett on connectives at Kenneth Easwara's Antimeta weblog.