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  1. Three Logical Theories.John Corcoran - 1969 - Philosophy of Science 36 (2):153-177.
    This study concerns logical systems considered as theories. By searching for the problems which the traditionally given systems may reasonably be intended to solve, we clarify the rationales for the adequacy criteria commonly applied to logical systems. From this point of view there appear to be three basic types of logical systems: those concerned with logical truth; those concerned with logical truth and with logical consequence; and those concerned with deduction per se as well as with logical truth and logical (...)
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2014-12-19
Three-logical-theories redux.

JOHN CORCORAN AND HASSAN MASOUD, Three-logical-theories redux.

  The 1969 paper, “Three logical theories” [1], considers three logical systems all based on the same interpreted language and having the same semantics.

  The first, a logistic system LS, codifies tautologies (logical truths)—using tautological axioms and tautology-preserving rules that are not required to be consequence-preserving.

  The second, a consequence system CS, codifies valid premise-conclusion arguments—using tautological axioms and consequence-preserving rules that are not required to be cogency-preserving [2]. A rule is cogency-preserving if in every application the conclusion is known to follow from its premises if the premises are all known to follow from their premises.

  The third, a deductive system DS, codifies deductions, or cogent argumentations [2]—using cogency-preserving rules. The derivations in a DS represent deduction: the process by which conclusions are deduced from premises, i. e. the way knowledge of argument validity is achieved in practice. Thus, deductive systems are all natural-deduction systems in the strict intuitive sense.

  The 1969 paper presupposed audiences that accept deductive systems—natural-deduction—as epistemically fundamental and that regard logistic systems and consequence systems as technically sound but artificial constructs. This paper aims for wider audiences including logicians who regard logistic or consequence systems as epistemically fundamental and take natural-deduction to be “psychological”, “heuristic”, or in some other way scientifically inferior or even inadequate.

  Moreover, this paper also discusses epistemic foundations. How do proponents of logistic systems propose to explain how knowledge of tautologousness is acquired? How do proponents of consequence systems propose to explain how knowledge of consequence-preservation is acquired? How do proponents of deductive systems propose to explain how knowledge of cogency-preservation is acquired?

  [1] JOHN CORCORAN, Three logical theories, Philosophy of Science, vol. 36 (1969), pp. 153–77.

  [2] JOHN CORCORAN, Argumentations and logic, Argumentation, vol. 3 (1989), pp. 17–43.