Algebra of Classical 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.

Collective Referential Intentionality in the Semantics of Dialogue

The concept of a dialogue is considered in general terms from the standpoint of its referential presuppositions. The semantics of dialogue implies that dialogue participants must generally have a collective intentionality of agreed-upon references that is minimally sufficient for them to be able to disagree about other things, and ideally for outstanding disagreements to become clearer at successive stages of the dialogue. These points are detailed and illustrated in a fictional dialogue, in which precisely these kinds of referential confusions impede progress in shared understanding. It is only through a continuous exchange of question and answer in this dialogue case study that the meanings of key terms and anaphorical references are disambiguated, and a relevantly complete collective intentionality of shared meaning between dialogue participants is achieved. The importance of a minimally shared referential semantics for the terms entering into reasoning and argument in dialogue contexts broadly construed cannot be over-estimated. Where to draw the line between referential agreement and disagreement within any chosen dialogue, as participants work toward better mutual understanding in clearing up referential incongruities, is sometimes among the dialogue’s main points of dispute.