Abstract
Wittgenstein’s philosophy is permeated by spatial imagery. This is true not only of the Tractatus Logico-Philosophicus with its prominent “logical space”, but also in his so-called middle-period, especially in the time from 1929 to 1933, one of the most productive episodes of his life: in this period he created ten manuscript volumes (MSS105–114) which form the backbone of much of his later philosophy. Later writings consist to a large extent in revisions of these remarks, leading to new directions the closer they get towards the Philosophical Investigations. One point where the “late” departs from the “middle” Wittgenstein is the apparent disappearance of the spatial expressions that were so conspicuous in the early 30s. What I would like to suggest in this chapter is not to neglect the methodical role of this imagery in Wittgenstein’s thinking and instead to take it as a central characteristic of his philosophy. What is hinted at with the usage of “space” and “geometry” in the early and middle period survives in the later writings where it appears under different names, but with largely similar functions.
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- 1.
The most famous instance of these remarks is: “I believe there is some truth in it when I think that I am actually only reproductive in my thinking. I believe I have never invented a move of thought, but it has always been given to me from someone else and I have only passionately taken it up for my clarificatory work. In this way, Hertz, Boltzmann, Schopenhauer, Frege, Russell, Kraus, Loos, Weininger, Spengler, Sraffa have influenced me” (MS154, 14v).
- 2.
The earliest version of the preface is from 1938, the last one from 1945. There he writes that the book had occupied him “for the last sixteen years”. So the word “today” refers to a larger span of time ranging from the late 20s to the 40s.
- 3.
Bertrand Russell’s first publication on mathematical philosophy was his Essay on the Foundations of Geometry. Michael Friedman has pointed out the importance of the history of geometry for many members of the Vienna Circle in his Reconsidering Logical Positivism (1999).
- 4.
Kant’s views on this issue changed during his career (cf. Caygill 1995, 367–373), but the a priori necessity of Euclidean Space became the background against which geometers and philosophers argued in the 19th century.
- 5.
On Hertz’s geometrization of mechanics see especially Lützen (2005).
- 6.
I quote them as leading representatives of the Cambridge and Vienna intellectuals with whom Wittgenstein was in contact: “I am convinced you are right in your main contention, that logical props are tautologies, which are not true in the sense that substantial props are true” (Wittgenstein 2004, Russell to Wittgenstein, 13 August 1919); “The most important insight I gained from his work was the conception that the truth of logical statements is based only on their logical structure and on the meaning of the terms. Logical statements are true under all conceivable circumstances; thus their truth is independent of the contingent facts of the world. On the other hand, it follows that these statements do not say anything about the world and thus have no factual content” (Carnap 1963, 24).
- 7.
Wittgenstein was probably familiar with these developments from his studies in theoretical physics or from Russell’s writings.
- 8.
Frank Ramsey had pointed out this problem to Wittgenstein: e.g. “No one could say that inference from ‘This is red’ to ‘This is not blue’ was formally guaranteed like the syllogism” (1990, 48).
- 9.
“It is the specific criterion of structure to find out which propositions have sense in it—not which ones are true. To search this is the method of philosophy” (MS105, 36); “This method is essentially the transition from the quest for truth to the quest for sense” (MS105, 45).
- 10.
See also: “Verification is not one indication of truth, but the sense of the proposition (Einstein: how a magnitude is measured, is what is measured)” (MS107, 142r).
- 11.
He distinguishes, e.g., between the space of generality from the disjunction of individual elements: “It is a different calculus to which the determination of generality belongs, and another one which yields that disjunction” (MS111, 65).
- 12.
Plaud (2011) has highlighted the role of “style” as a kind of a priori framework very similar to space in the middle period.
- 13.
See Stump 2015 for a good summary of the development and current trends in this debate.
References
Carnap, Rudolph. 1963. The Philosophy of Rudolph Carnap. Ed. by P. A. Schilpp. La Salle, Illinois: Open Court.
Cassirer, Ernst. 1922. Einstein’s Theory of Relativity. Considered from the Epistemological Standpoint. In: The Monist. Vol. 32, No. 3 (July, 1922). 412–448.
Caygill, Howard. 1995. A Kant Dictionary. Oxford: Blackwell Reference.
Einstein, Albert. 1920. Relativity. The Special and the General Theory. Tr. by Robert Lawson, London: Methuen & Co. Ltd.
Friedman, Michael. 1999. Reconsidering Logical Positivism. Cambridge University Press.
Friedman, Michael. 2001. Dynamics of Reason. Stanford: CSLI Publications.
Helmholtz, Hermann von. 1903. Über den Ursprung und die Bedeutung der geometrischen Axiome. In: Vorträge und Reden, vol. 2. Braunschweig: Vieweg.
Hertz, Heinrich. 1899. The Principles of Mechanics. London: Macmillan.
Hyder, David. 2002. The Mechanics of Meaning: Propositional Content and the Logical Space of Wittgenstein’s Tractatus. Berlin, New York: Walter de Gruyter.
Kant, Immanuel. 1999. The Critique of Pure Reason. Edited and translated by Paul Guyer and A.W. Wood. Cambridge University Press.
Kuusela, Oskari. 2008. The Struggle against Dogmatism. Harvard University Press.
Lützen, Jesper. 2005. Mechanistic Images in Geometric Form. Heinrich Hertz’s Principles of Mechanics. Oxford University Press.
Pilch, Martin. 2017. The Structure of Wittgenstein’s Logical Space. In: Wittgenstein-Studien, 8 (1). 15–60.
Plaud, Sabine. 2011. From ‘Styles of Thinking’ to ‘World-Pictures’: Wittgenstein and Spengler on Style. In: Unsocial Sociabilities. Wittgenstein’s Sources. Ed. by Esther Ramharter. Berlin: Parerga. 75–95.
Preston, J.M. 2017. Wittgenstein, Hertz and Boltzmann. In: A Companion to Wittgenstein. Ed. H.J.Glock and J. Hyman. Chichester: Wiley Blackwell. 110–124.
Ramsey, F.P. 1990. Philosophical Papers. Ed. by Hugh Mellor. Cambridge University Press.
Russell, Bertrand. 1968. The Autobiography, Vol. 2, 1914–1944. London: George Allen and Unwin.
Schulte, Joachim. 2006. Wittgenstein on Time (1929–33). In: Time and History. Zeit und Geschichte. Ed. by F. Stadler and M. Stöltzner. Frankfurt: Ontos Verlag.
Schulte, Joachim. 2018. Body and Soul. In: The Cambridge Companion to Wittgenstein. Ed. by H. Sluga and D. Stern. Cambridge University Press.
Stump, David. 2015. Conceptual Change and the Philosophy of Science. Alternative Interpretations of the A Priori. New York: Routledge.
Wittgenstein, Ludwig. 1922. Tractatus Logico-Philosophicus [TLP]. Tr. by C.K. Ogden and F.P. Ramsey. London: Routledge and Kegan Paul.
Wittgenstein, Ludwig.1929. Some Remarks on Logical Form. In: Proceedings of the Aristotelian Society, Supplementary Volumes, Vol. 9, Knowledge, Experience and Realism. 162–171.
Wittgenstein, Ludwig. 2004. Briefwechsel. Innsbrucker Elektronische Ausgabe. Ed. by M. Seekircher, B.F. McGuinness and A. Unterkircher.
Wittgenstein, Ludwig. 2009. Philosophical Investigations [PI]. Ed. and tr. by P. M. S. Hacker and J. Schulte, Oxford: Wiley-Blackwell.
Wittgenstein, Ludwig. 2015. Bergen Nachlass Edition. Ed. by A. Pichler, Wittgenstein Archives, University of Bergen. In: Wittgenstein Source (2009-) [wittgensteinsource.org]. Bergen: WAB.
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Zambito, P. (2020). Thinking in Spaces: A Characteristic of Wittgensteinian Philosophy. In: Wuppuluri, S., da Costa, N. (eds) WITTGENSTEINIAN (adj.). The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-030-27569-3_14
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