Friday, September 2, 2011

Broccoli Logic

This "Broccoli joke" jab at Tarskian semantics turns up at least a dozen times in Girard's writings. Here is a particularly clear form of it, from "Truth, Modality, Intersubjectivity," which should be available in the ARCHIVES.
Truth according to Tarski
Long ago, Tarski gave a definition of truth of the form :
A ∧ B is true iff A is true and B is true. All the other cases being treated in the same way, to sum up :
A is true iff A holds. Such a definition discouraged generations of mathematicians from even thinking at logic ; moreover, logicians developed a sort of esthetics of the meta ensuring that you must be dumb if you don’t understand the depth of such definitions . But the king is naked and one must say it : the arrogant essentialism of the Tarskian approach hides the absence of any interesting idea as to truth. It relies on a fantasy of objectivity reused by logical hustlers to develop systems of their own, typically :
A broccoli B is true iff A is true broccoli B is true.
the logic of broccoli, which is not even edible! This is the triumph of discretionary definitions : the absence of a decent subjective dimension in the logical explanation eventually leads to subjectivism.

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