Algebra of Theoretical Term Reductions in the Sciences

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

Anselm’s Metaphysics of Nonbeing

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

On the Relation of Informal to Formal Logic

The distinction between formal and informal logic is clarified as a prelude to considering their ideal relation. Aristotle\u27s syllogistic describes forms of valid inference, and is in that sense a formal logic. Yet the square of opposition and rules of middle term distribution of positive or negative propositions in an argument\u27s premises and conclusion are standardly received as devices of so-called informal logic and critical reasoning. I propose a more exact criterion for distinguishing between formal and informal logic, and then defend a model for fruitful interaction between informal and formal methods of investigating and critically assessing the logic of arguments

Qualities, Relations, and Property Exemplification

The question whether qualities are metaphysically more fundamental than or mere limiting cases of relations can be addressed in an applied symbolic logic. There exists a logical equivalence between qualitative and relational predications, in which qualities are represented as one-argument-place property predicates, and relations as more-than-one-argument-place predicates. An interpretation is first considered, according to which the logical equivalence of qualitative and relational predications logically permits us ontically to eliminate qualities in favor of relations, or relations in favor of qualities. If metaphysics is understood at least in part as an exercise in ontic economy, then we may be encouraged to adopt a property ontology of qualities without quality-irreducible relations, or relations without relation-irreducible qualities. If either strategy is followed, the choice of reducing qualities to relations or relations to qualities will need to be justified on extra-logical grounds. These might include a perceived greater intuitiveness, explanatory fecundity, compatibility with cognitive ontogeny or developmental psychology, expressive or explanatory elegance or cumbersomeness, and an open-ended list of philosophical motivations that could reasonably favor the ontic prioritization of qualities over relations or relations over qualities. Despite its intuitive appeal, the thesis that logical equivalence together with extra-logical preferences justifies unidirectional ontic reduction of relations to qualities or qualities to relations is rejected in light of the more defensible proposition that the logical equivalence of qualitative and relational predications actually supports the opposite conclusion, that both qualities and relations are logically indispensable to a complete ontology of properties. The logical equivalence of qualitative and relational predications, insofar as we continue to observe the distinction, makes it logically necessary ontically for both qualities and relations to exist whenever either one exists. That logically equivalent qualitative and relational predications have as their truth-makers the exemplification by objects of both qualities and relations as equi-foundational properties further suggests that there is no deeper logical distinction between qualities and relations, but only two convenient lexical-grammatical designations for property predications involving one- versus more-than-one-argument-plac

Slingshot Arguments and the Intensionality of Identity

It is argued that the slingshot argument does not soundly challenge the truth-maker correspondence theory of truth, by which at least some distinct true propositions are expected to have distinct truth- makers. Objections are presented to possible exact interpretations of the essential slingshot assumption, in which no fully acceptable reconstruction is discovered. A streamlined version of the slingshot is evaluated, in which explicit contradiction results, on the assumption that identity and nonidentity contexts are purely extensional relations, effectively establishing the intensionality of identity