Bertrand Russell’s 1906 article ‘The Theory of Implication’ contains an algebraic weak completeness proof for classical propositional logic. Russell did not present it as such. We give an exposition of the proof and investigate Russell’s view of what he was about, whether he could have appreciated the proof for what it is, and why there is no parallel of the proof in Principia Mathematica.

In March 1912 A. N. Whitehead wrote a letter which sheds new and important light on his own view of his mathematical goals. In this article I publish the letter for the first time and relate its contents not only to his mathematical career but also to his scientific, philosophical and educational interests.

There are many wonderful puzzles concerning Principia Mathematica, but none are more striking than those arising from the crisis that befell Whitehead in November of 1910. Volume 1 appeared in December of 1910. Volume 2 on cardinal numbers and Russell's relation arithmetic might have appeared in 1911 but for Whitehead's having halted the printing. He discovered that inferences involving the typically ambiguous notation ‘Nc‘α’ for the cardinal number of α might generate fallacies. When the volume appeared in 1912, it was (...) extensively emended by Whitehead and accompanied by a Prefatory Statement of Symbolic Conventions. This paper endeavors to recover from Whitehead's bad emendations—including his bewildering thesis that since ‘‘α’ is ‘true whenever significant,’ ‘α is to be accepted. It is supposedly a fallacy to apply Modus Ponens and infer Nc‘α from ‘α and‘‘α. (shrink)

The use of the symbol ∨for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or,” vel. We show that the origin of the symbol ∨ for disjunction can be traced to Whitehead and (...) Russell’s pre-Principia work in formal logic. Because of Principia’s influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert’s adoption of ∨ in his Grundzüge der theoretischen Logik guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed. (shrink)

Name der Zeitschrift: Wittgenstein-Studien Jahrgang: 5 Heft: 1 Seiten: 101-132.

Tato studie je v první řadě studií z dějin filosofie. Jejím hlavním úkolem je popsat život a dílo autora, který byl v česko-slovenském intelektuálním prostředí dlouhou dobu opomíjen: anglo-amerického matematika, fyzika a filosofa Alfreda Northa Whiteheada. Jeho životní příběh bývá někdy popisován jako „příběh tří měst“: Cambridge v Anglii, Londýna a nakonec Cambridge v Massachusetts, kde sídlí Harvardova univerzita. Studie se soustředí na některé významné momenty ve filosofově životě a pokouší se je zdůraznit jako klíč k porozumění Whiteheadovu celoživotnímu projektu. (...) Na samotném závěru je dodáno několik poznámek o recepci Whiteheadových myšlenek v česko-slovenském myšlenkovém milieu. (shrink)