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The Phrenetic Calculus: A Logician's View of Disordered Logical Thinking in Schizophrenia

Robert Klee
Behavior and Philosophy
Vol. 20/21, Vol. 20, no. 2 - Vol. 21, no. 1 (1993), pp. 49-61
Stable URL: http://www.jstor.org/stable/27759283
Page Count: 13
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The Phrenetic Calculus: A Logician's View of Disordered Logical Thinking in Schizophrenia
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Abstract

This paper contains a preliminary investigation of an experimental, first-order logic with identity which encodes as an inference rule the faulty reasoning which Von Domarus (1944) suggested underwrote much of the bizarre thinking seen in certain forms of schizophrenia. I begin with a discussion of the "Von Domarus thesis," note its fate under statistical testing, and remark on its continued explanatory power in the hands of certain psychiatrists. I next discuss a proof calculus which contains a rule representing Von Domarus reasoning — the phrenetic calculus — and present several nonstandard theorems which are provable in this system. In an appendix the phrenetic calculus is proven to be absolutely consistent, but unsound, yet complete. After a brief aside which addresses certain caveats and restrictions required in order to avoid rendering the calculus trivial, I close with a discussion of three of the nonstandard theorems, each of which are consistent in interesting ways with known schizophrenic cognitive deficits.

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