The argument diagramming method developed by Monroe C. Beardsley in his (1950) book Practical Logic, which has since become the gold standard for diagramming arguments in informal logic, makes it possible to map the relation between premises and conclusions of a chain of reasoning in relatively complex ways. The method has since been adapted and developed in a number of directions by many contemporary informal logicians and argumentation theorists. It has proved useful in practical applications and especially pedagogically in teaching (...) basic logic and critical reasoning skills at all levels of scientific education. I propose in this essay to build on Beardsley diagramming techniques to refine and supplement their structural tools for visualizing logical relationships in a number of categories not originally accommodated by Beardsley diagramming, including circular reasoning, reductio ad absurdum arguments, and efforts to dispute and contradict arguments, with applications and analysis. (shrink)

An elementary algebra identifies conceptual and corresponding applicational limitations in John Kemeny and Paul Oppenheim’s (K-O) 1956 model of theoretical reduction in the sciences. The K-O model was once widely accepted, at least in spirit, but seems afterward to have been discredited, or in any event superceeded. Today, the K-O reduction model is seldom mentioned, except to clarify when a reduction in the Kemeny-Oppenheim sense is not intended. The present essay takes a fresh look at the basic mathematics of K-O (...) comparative vocabulary theoretical term reductions, from historical and philosophical standpoints, as a contribution to the history of the philosophy of science. The K-O theoretical reduction model qualifies a theory replacement as a successful reduction when preconditions of explanatory adequacy and comparable systematicization are met, and there occur fewer numbers of theoretical terms identified as replicable syntax types in the most economical statement of a theory’s putative propositional truths, as compared with the theoretical term count for the theory it replaces. The challenge to the historical model developed here, to help explain its scope and limitations, involves the potential for equivocal theoretical meanings of multiple theoretical term tokens of the same syntactical type. (shrink)

In his eleventh century dialogue De Casu Diaboli, Anselm seeks to avoid the problem of evil for theodicy and explain the fall of Satan as attributable to Satan’s own self-creating wrongful will. It is something, as such, for which God as Satan’s divine Creator cannot be held causally or morally responsible. The distinctions on which Anselm relies presuppose an interesting metaphysics of nonbeing, and of the nonbeing of evil in particular as a privation of good, worthy of critical philosophical investigation (...) in its own right. Anselm’s concept of nonbeing does not resolve the philosophical problem of evil implied by Satan’s fall from grace, but is shown perhaps more unexpectedly to enable Anselm’s proof for the inconceivable nonexistence of God as the greatest conceivable intended object of thought to avoid Kant’s Critique of Pure Reason objection to the general category of ”ontological’ arguments. (shrink)