Abstract
In Lecture III of The Philosophy of Logical Atomism, Russell says “When I was lecturing on this subject at Harvard I argued that there are negative facts, and it nearly produced a riot: the class would not hear of there being negative facts at all. I am inclined to think that there are. However, one of the men to whom I was lecturing at Harvard, Mr. Demos, subsequently wrote an article in Mind to explain why there are not negative facts. It is in Mind for April 1917.” (CPBR 8, 107) There are two sets of notes on Russell’s lectures in Philosophy 21 Advanced Logic at Harvard in 1914. One, well known, consists of notes by T.S. Eliot, who was then a graduate student writing his dissertation. Another set of notes, recently located at Trinity College Connecticut, are by Harry T. Costello. Russell brought Wittgenstein’s “Notes on Logic” with him to Harvard in March of 1914, and years later, in 1956, Costello published them in the Journal of Philosophy. Costello’s notes on the lectures, and a letter from Russell to Ottoline Morrell on April 15th, show that the lecture that “nearly produced a riot” was likely given in Philosophy 21 on April 11, 1914. The Costello notes will be used as evidence for this claim. That lecture appears to have been devoted to explaining ideas from Wittgenstein’s “Notes on Logic”. Another letter, this from Raphael Demos to Bertrand Russell, dated February 11th, 1918, suggests that Demos attended at least Lecture III of The Philosophy of Logical Atomism, on “the previous Tuesday” which would have been February 5th. I will conclude with a discussion of Russell’s views on Demos’ paper, and, more generally, why Russell would have taken negative facts seriously, but not conjunctive or disjunctive facts.
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Notes
- 1.
- 2.
Wittgenstein uses “a” and “b” instead of “t” and “f “ with this notation both in the “Notes on Logic” and Tractatus.
- 3.
This is likely the session of May 12, cited above. The notes for that day continue: “Dr. Costello then read a note on two topics: one on the nature of the so-called logical entities, insisting on their abstractness; the other on the contrast between statistical probability and the kind of probability you get when you verify an hypothesis, which may be called systematic probability.”
- 4.
Presumably, this refers to Husserl’s Logical Investigations.
- 5.
The Notes on Logic has: “Propositions, which are symbols having reference to facts, are themselves facts” (Costello 1957a: 236).
- 6.
Grover Smith (Costello 1963: 5) reports that the enrolled students were A.P. Brogan, N.N. Sen Gupta, Raphael Demos, E.W. Friend, C.E. Kellogg, Victor F. Lenzen, and Robert L.M. Underhill. T.S. Eliot is described as an “auditor”. Lenzen’s notes from Philosophy 21 do not survive, although his notes for Russell’s other course, Philosophy 9, “Theory of Knowledge”, are preserved in the Bertrand Russell Archives.
- 7.
One is also struck by the familiarity with Meinong at Harvard which is indicated here, and frequently in Costello’s notes on Royce’s seminar. T.S. Eliot mentions Meinong in his presentation to Royce’s seminar, and also several times in his thesis (Eliot 1964), which was completed in 1916.
- 8.
In a letter to Ottoline Morrell on November 1, 1911, Russell says of Wittgenstein, who he had just met and did not know well enough to know that he was Austrian: “My German engineer very argumentative and tiresome. He wouldn’t admit that it was certain that there was not a rhinoceros in the room.” Wittgenstein followed Russell to his rooms after the lecture and continued the argument. On the next day (November 2) the argument continued: “He thinks nothing empirical is knowable—I asked him to admit that there was not a rhinoceros in the room, but he wouldn’t.” (Monk 1990: 39). This issue is presented as a question of epistemology, but still seems to be a debate over how a negative proposition (or fact) is known.
- 9.
- 10.
Proof: (1) First observe that Double Negation Elimination (DNE) can be derived using ~E. Assume that ~~A. Then further if we suppose ~A, that subordinate assumption leads to a contradiction, ~A and ~ ~A, so by ~E we can derive A, based only on the first assumption, ~ ~A. Thus DNE is shown valid. (2) Now we show that ~ I can be derived using ~E. Suppose that a contradiction follows from some sentence B. We know that the same contradiction can be derived from ~ ~B, by one use of DNE followed by the derivation of the contradiction. But then we have a contradiction derived from ~ ~B, and so a proof of ~B by ~E. But now we have derived ~B on the supposition that B leads to a contradiction, and this is exactly what the rule ~ I allows.
- 11.
⊥ is also called “bottom” to recognize its place as the bottom value in a Boolean algebra, as well as “eet” to indicate that it is the inverse of “tee” the name of the letter “T”.
- 12.
See Linsky (2011) for an account of the Introduction to the Second Edition of Principia Mathematica where Russell shows how the body of the text can be based on the Sheffer stroke.
- 13.
See Linsky (2016) for an account of the changes in Russell’s choices of primitive connectives for propositional logic between The Principles of Mathematics and Principia Mathematica.
References
Works by Other Authors
Costello, Harry T. (1957a). “Notes on Logic.” Journal of Philosophy, Vol. 54, No. 9: 230–245.
Costello, Harry T. (1957b). “Logic in 1914 and Now”, The Journal of Philosophy, Vol. 54, No. 9: 245–265.
Costello, Harry T. (1963). Josiah Royce’s Seminar, 1913–14, ed. Grover Smith. New Brunswick: Rutgers University Press.
Demos, R. (1917). “A Discussion of a Certain Type of Negative Proposition”. Mind, Vol. 26 No. 102: 188–196.
Eliot, T. S. (1964). Knowledge and Experience in the Philosophy of F. H. Bradley. New York: Columbia University Press.
Korhonen, Anssi (2013). Logic as Universal Science: Russell’s Early Logicism and its Philosophical Context, Basingstoke: Palgrave Macmillan.
Linsky, Bernard (2011). The Evolution of Principia Mathematica: Bertrand Russell’s Manuscripts and Notes for the Second Edition, Cambridge: Cambridge University Press.
Linsky, Bernard (2016). “Propositional Logic from The Principles of Mathematics to Principia Mathematica.” In Early Analytic Philosophy: New Perspectives on the Tradition, ed. Sorin Costreie. London: Springer. 213–229.
Monk, Ray (1990). Ludwig Wittgenstein: The Duty of Genius, New York: Macmillan.
Potter, Michael (2009). Wittgenstein’s Notes on Logic, Oxford: Oxford University Press.
Van Heijenoort, Jan (1967). “Logic as Language and Logic as Calculus.” Synthese, Vol. 17: 324–330.
Wittgenstein, Ludwig (1913). “Notes on Logic.” In L. Wittgenstein, Notebooks 1914–16. Ed. G. H. von Wright and G. E. M. Anscombe. Oxford: Basil Blackwell: 93–106.
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Linsky, B. (2018). The Near Riot Over Negative Facts. In: Elkind, L., Landini, G. (eds) The Philosophy of Logical Atomism. History of Analytic Philosophy. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-94364-0_8
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