Tag Archives: conjunction

Solving the Conjunction Problem of Russell’s Principles of Mathematics / Review of On the Genealogy of Universals

Volume 8.8 of The Journal for the History of Analytical Philosophy (JHAP) has now been published online, with full open-access.

It features an article by Gregory Landini entitled, “Solving the Conjunction Problem of Russell’s Principles of Mathematics”. Here is an abstract:

The quantification theory of propositions in Russell’s Principles of Mathematics has been the subject of an intensive study and in reconstruction has been found to be complete with respect to analogs of the truths of modern quantification theory. A difficulty arises in the reconstruction, however, because it presents universally quantified exportations of five of Russell’s axioms. This paper investigates whether a formal system can be found that is more faithful to Russell’s original prose. Russell offers axioms that are universally quantified implications that have antecedent clauses that are conjunctions. The presence of conjunctions as antecedent clauses seems to doom the theory from the onset, it will be found that there is no way to prove conjunctions so that, after universal instantiation, one can detach the needed antecedent clauses. Amalgamating two of Russell’s axioms, this paper overcomes the difficulty.

The volume also contains a review of Fraser MacBride, On the Genealogy of Universals: The Metaphysical Origins of Analytic Philosophy (Oxford: Oxford University Press, 2018), written by Landon D. C. Elkind.

JHAP is a free, open-access, peer-reviewed journal. It is available at https://jhaponline.org/. Submissions welcome!