Teaching the PARC System of Natural Deduction
Daryl Close · American Association of Philosophy Teachers Studies in Pedagogy · 2015
PARC is an "appended numeral" system of natural deduction that I learned as an undergraduate and have taught for many years.Despite its considerable pedagogical strengths, PARC appears to have never been published.The system features explicit "tracking" of premises and assumptions throughout a derivation, the collapsing of indirect proofs into conditional proofs, and a very simple set of quantificational rules without the long list of exceptions that bedevil students learning existential instantiation and universal generalization.The system can be used with any Copi-style set of inference rules so it is quite adaptable to many mainstream symbolic logic textbooks.Consequently, PARC may be especially attractive to logic teachers who find Jaśkowski/Gentzen-style introduction/elimination rules to be far less "natural" than Copi-style rules.The PARC system is also keyboardfriendly in comparison to the widely adopted Jaśkowski-style graphical subproof system of natural deduction, viz., Fitch diagrams and Copi "bent arrow" diagrams.The pedagogy of most contemporary symbolic logic textbooks is firmly rooted in the natural deduction systems of Stanisław Jaśkowski 1 and Gerhard Gentzen. 2 First-order logic can be also be taught as an axiomatic system after Frege, Russell, and Hilbert, or using a Gentzen sequent calculus, but this is rare in undergraduate textbooks.Unhappily, the natural deduction systems developed and employed in logic textbooks over the past 80 years vary widely in what is considered "natural."3 Symbolic logic teachers who teach natural deduction thus continue to face substantial pedagogical choices and challenges.In what follows, I describe a system of natural deduction that I learned as an undergraduate and have taught for many years.I call the system "PARC," an initialism for the four deduction metarules of sentential and predicate logic, P, A, R, and C. PARC appears to date from the mid-1960s and is clearly derived in part from Patrick Suppes' classic 1957 textbook, Introduction to Logic, 4 although there are substantial differences.Other central aspects of PARC appear to be derived from the third edition of Copi's Symbolic Logic.5 A number of textbooks 6