Abstract
This Tractatus’s engagement with the issue of the nature of truth and falsity emerged from engagement with Russell. This engagement reverberated through the Vienna Circle and in particular affected Gödel. The Tractatus’s “elementary sentences” must be seen against the backdrop of Russell’s “multiple relation theory of judgment”, his theory of truth in Principia Mathematica, which Wittgenstein discussed at length with Russell in 1912–1913 and Gödel studied in 1929–1932. Russell’s approach was directed against both Idealism and William James’s pragmatist view of truth. It aimed at a direct treatment of the distinction between truth and falsity in terms of particular, logically simple beliefs (judgments lacking in truth-functional and quantification complexity). Schlick rejected Russell’s view in favor of his more holistic correspondence theory, one which, however, tipped easily into pragmatism, conventionalism and verificationism. The Tractatus begins, rather, with Russell’s bottom-up approach truth, and then draws in two further ideas: (1) The need for a medium of representation and (2) The importance of modality (possibility and necessity) to logic. This approach was developed further in his later work, i.e., Philosophical Investigations.
Aware of the Tractatus and Russell’s engagement with Wittgenstein on truth, Gödel continued to engage with Russell’s multiple relation theory of truth and Principia philosophically up through 1944. The parallel yet distinct engagements of Gödel and Wittgenstein with Russell on truth (and Vienna positivism) show that each regarded Russell’s view as requiring amendment. However, their philosophical differences with one another are not merely to be understood in terms of the dichotomy between conventionalism (the usual view of Wittgenstein) and Platonism (the usual view of Gödel). They must rather be seen to emerge from the original approach to truth we find in Russell.
I am honored by Friedrich Stadler for the invitation to address the Institut Wiener Kreis’s June 2021 conference in honor of the centennial of the Tractatus. Stadler’s history of philosophy in and emigrating from Austria and the Vienna Circle has taught us much, and has inspired me for many years. The audience at the conference provided me with questions that led to the improvement of this paper, as well as an anonymous referee to whom I am grateful for comments on the final version. To Zeynep Soysal I owe many stimulating discussions about truth, and very timely help assembling the final version: without her the paper would not have been written. To Sanford Shieh I owe a great debt for many years of conversation about Russell, Gödel, Wittgenstein, and the Tractatus in particular. His views have influenced me in all that follows, and he greatly improved the final version of this essay.
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Notes
- 1.
The literature on whether Wittgenstein refuted Russell’s MRT and how, or whether he endorsed it, in adapted form, is very large and rapidly evolving. The best brief introduction to the thorny nest of reconstructed criticisms and Russellian replies, including a good review of the literature, is Shieh (forthcoming). See also the editors’ introduction to Russell (1913).
- 2.
See the Introduction to Russell (1913).
- 3.
- 4.
Floyd and Kanamori (2016, §6, p. 310).
- 5.
Floyd and Kanamori (2016, §§3–6).
- 6.
See Russell (1940), his William James lecture at Harvard. In his account of the Vienna Circle Stadler (2001, 91) identifies a realist and objectivist strand in the Austrian tradition, associating Gödel with it. On the importance of pragmatism to the Vienna Circle see Pihlström et al. (2017) and compare, for a more general characterization of the role of pragmatism in the history of 20th century European philosophy, Baghramian and Marchetti (2017).
- 7.
Whitehead and Russell 1919, Introduction, Chapter II, Section III, “Definition and Systematic Ambiguity of Truth and Falsehood”, 42ff. Compare Floyd and Kanamori (2016).
- 8.
Gödel remarked to Wang in 1976 that he had already seen by 1930 that the notion of arithmetic truth cannot be defined within arithmetic, thereby getting to that part of Tarski’s undefinability result on his own (Wang 1996, 82). On hesitations Russell, Wittgenstein and Gödel expressed about the usefulness of Tarski’s analysis to treat the most fundamental problem of the distinction between truth and falsity see Russell (1940), Diamond (2002), and Floyd and Kanamori (2016).
- 9.
Levine (2013) gives a nice account of Russell’s Principia treatment which he argues does not, like the Tractatus, separate molecular from atomic facts at the first level of truth; Levine argues that one of Wittgenstein’s main troubles with Russell’s MRT concerned the status of logical laws, in particular the issue of the Law of Excluded Middle.
- 10.
- 11.
Whitehead and Russell 1919, Introduction, Chapter II, Section III, “Definition and Systematic Ambiguity of Truth and Falsehood”, 42ff. Compare Floyd and Kanamori (2016, §4.2).
- 12.
Compare Russell’s later notes on James in Russell (2015–2016).
- 13.
- 14.
The primacy of the issue of anti-dogmatism in Wittgenstein’s thought is stressed in Kuusela (2008).
- 15.
Laugier (2020, 397f.) explains the importance of the Tractatus’s response to the top-down Lotzean idea of “validity” [Geltung], which joined cognition and ethics in a theory of “value as such” [Wert]. The price of this top-down joining, she argues, opened ethics up to the non-cognitivist criticisms of empiricists. By contrast, the Tractatus overturns the very idea of using such notions as top-down, substantial or “simple” ones, treating them as “formal”. Compare Wiggins (2004). This is the sense in which value-as-such “has no value” (TLP 6.4f.): Truth as such is not true. Humanity must treat as a “dream” the idea of a “simple” sphere of questions whose answers would unite in a symmetrical closed structure a priori, i.e., in which sentences would be valid-as-such, (or valuable as such) and the simple would be the sign of the true (TLP 5.4541). Instead, the symmetrical closed structure of logic, which is a priori, consists of tautologies and contradictions, which are sinnlos according to the Tractatus and hence only “true” in a limiting sense (not really true at all, for they carry zero information). Floyd (2020, 2022) elaborate these points.
- 16.
- 17.
See also Floyd (2021b, §4.1), where MS 160, 27r is adduced in justification of this reading.
- 18.
Floyd and Kanamori (2016, §§4.1–4.2).
- 19.
See Floyd and Kanamori (2016, 287, 291, 304) on Gödel, an infinitary perspective on the MRT, and Gödel’s remarks on “noticing”. Thanks to Sanford Shieh for making me aware of the distinction between “perceiving” and “noticing” in Russell (1913): this may well have been appreciated by Gödel, careful reader of Russell as he was.
- 20.
Wittgenstein critically responds to this older view in “modern epistemology” at TLP 5.54f., as well as Russell’s version of the MRT.
- 21.
See Levine and Linsky (forthcoming).
- 22.
The image is by Théodore Chassériau, Plate 6 in Le Cahiers de l’Amateur, Rue Lafitte 2 (1844), in the public domain at https://www.metmuseum.org/art/collection/search/371334 (accessed March 13, 2022).
- 23.
Our anachronism is intended to help the reader appreciate the MRT. Of course, the analysis of the ordered pair in terms of sets was not at issue for Russell, and Wittgenstein’s non-extensionalism would never have allowed him to speak quite this way (see Floyd and Mühlhölzer 2020). Russell did however firmly believe that such a material relation would be an external, and not an internal one. Compare the Tractatus’s distinction between material and “internal” relations at TLP 4.122.
- 24.
Floyd and Kanamori (2016, §6).
- 25.
Floyd and Kanamori (2016, §6.3).
- 26.
Quoted in Floyd and Kanamori (2016, 274).
- 27.
Floyd and Kanamori (2016, 279).
- 28.
Floyd and Kanamori (2016, 254). The Tractatus had dismissed this Axiom as non-logical, because “it is possible to imagine a world in which [it] is not valid” (6.1232f.). This reflects Wittgenstein’s non-extensionalist, potential-infinity stance in the Tractatus.
- 29.
On 7 October 1932 Gödel copied out into his notebook an extract from Russell’s (1927, 171, Chap. XVII) in which Russell explicitly agrees with Wittgenstein’s Tractatus view that logical “truths” are tautologies, and then goes beyond Wittgenstein (“though here Wittgenstein might dissent”) to say that mathematics also consists of tautologies. He was highlighting an impact on Russell with which he deeply disagreed.
- 30.
Floyd and Kanamori (2016, §§3, 5.0).
- 31.
Floyd and Kanamori (2016, 269).
- 32.
Diamond (2002, 270) is concerned to argue that all talk of necessity with an ontological cast “falls into incoherence”. I am not in disagreement, I join Diamond in agreeing with Goldfarb (1997, 66) that “our understanding of possibility … arises simply from our understanding of and our operating with the sensical sentences of our language”. But like Shieh (2019) I take the entrance of possibility and necessity into early analytic philosophy in the Tractatus to be essential to Wittgenstein’s intervention and diagnosis of truth. For more on modality see Floyd (2022).
- 33.
- 34.
Floyd (2019) discusses this actualism.
- 35.
Compare Diamond (2002, 277 n. 33).
- 36.
Compare Wittgenstein’s letter to Russell (August 19, 1919, 1995, 98f.), answering Russell’s question about the constituents of thoughts: “I don’t know what the constituents of a thought are but I know that it must have such constituents which correspond to the words of Language. Again the kind of relation of the constituents of thought and of the pictured fact is irrelevant. It would be a matter of psychology to find it out.”
- 37.
- 38.
Wang (1987, 270); compare Floyd and Kanamori p. 268.
- 39.
Thomas Ricketts pointed out that the quotation marks here, as in Wittgenstein’s early draft in his 1914 Moore Notes (see 1979, p. 119) are not playing the role of metalinguistic mention-devices, describing uninterpreted sentence-structures, but rather allude to a whole situation in which the correlations between names and objects, arbitrary in themselves, are nevertheless taken to have been fixed, and the affirming-as-true is in place. Compare Diamond (2002, n. 33).
- 40.
- 41.
See Floyd (2021a, 42f).
- 42.
Russell at first resisted neutral monism, but later on, in his 1921, he came to advocate it. Russell (1927, 10), refers to Sheffer explicitly. To do this Russell moved beyond his 1912, which assumed we could be acquainted with our own self, and which analyzed belief in terms of a believing subject. In 1913 Chapter 3, Russell holds that we can “attend to” or select from a group of objects with which we are directly acquainted, attending to this. We may then know who we are through a description (“the subject attending to ‘this’), rather than acquaintance with a self. However, Russell’s (1921), with its oddly dual emphasis on behaviorism and on first-person introspection, failed to satisfy Wittgenstein, who was closer to Sheffer in “grammaticalizing” James’s view. Russell (1921) did much to stimulate Wittgenstein in his writings on private language.
- 43.
- 44.
Travis (2006) applies this notion to a reading of Philosophical Investigations, stressing the affinities between the mature Wittgenstein and Frege on the issue of truth and falsity, with Wittgenstein adding in a notion of “occasion sensitivity”, which Travis does not take to be a form of relativism.
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Floyd, J. (2023). Truth in Russell, Early Wittgenstein and Gödel. In: Stadler, F. (eds) Wittgenstein and the Vienna Circle. Vienna Circle Institute Yearbook, vol 28. Springer, Cham. https://doi.org/10.1007/978-3-031-07789-0_9
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