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)

Desires are contentful mental states. But what determines the content of a desire? Two different classic answers were proposed by Russell and by Wittgenstein, starting in the 1910s. Russell proposed a behaviorist account according to which the content of the desire is fixed by the type of state that puts an end to the relevant kind of behavior which was triggered by some initial discomfort. The desire’s content consists in its “satisfaction conditions”. Wittgenstein criticized such an account for neglecting the (...) crucial point that the relation between a desire and its content is a conceptual, internal one, not an external contingent one. Desires specify their own contents, their “fulfillment conditions”. Even though there is a lot to say in favor of Wittgenstein’s criticism, this paper argues that Russell pointed at an important aspect of desires which plays a crucial role for accounts of self-knowledge of one’s own desires. It turns out that fulfillment conditions and satisfaction conditions are tied together in rational self-knowledge of one’s own desires. In this sense, the views of Russell and Wittgenstein can be combined in a fruitful way. (shrink)