Journal article
Solving the Conjunction Problem of Russell's Principles of Mathematics
The journal for the history of analytical philosophy, Vol.8(8), pp.1-11
09/01/2020
DOI: 10.15173/jhap.v8i8.4176
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.
Details
- Title: Subtitle
- Solving the Conjunction Problem of Russell's Principles of Mathematics
- Creators
- Gregory Landini - University of Iowa
- Resource Type
- Journal article
- Publication Details
- The journal for the history of analytical philosophy, Vol.8(8), pp.1-11
- DOI
- 10.15173/jhap.v8i8.4176
- ISSN
- 2159-0303
- eISSN
- 2159-0303
- Publisher
- MULPress
- Language
- English
- Date published
- 09/01/2020
- Academic Unit
- Philosophy
- Record Identifier
- 9984397192502771
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