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The Vagueness of the Muse—The Logic of Peirce’s Humble Argument for the Reality of God


Published in 1908, C.S. Peirce’s ‘A Neglected Argument for the Reality of God’ is one of his most difficult articles. Presenting a peculiar entanglement of scientific method and theology, it sketches a ‘humble’ argument for the reality—and not the existence—of God for Musers, that is, those who pursue the activity he calls ‘Musement’. In Musement, Peirce claims, we can achieve a kind of perception of the intertwinement of the three universes of experience: of feeling, of brute fact, and of reason. He also somehow relates each universe to a distinct phase of inquiry, which is described by the use of induction, deduction, and abduction or retroduction. The way that he develops his claims allows him to outline God as an abductive vague hypothesis to explain how those three universes make up a single whole. The hypothesis being vague means that the principle of contradiction does not hold for it. In this presentation, we aim at throwing some light at these points, focusing on the concept of Musement and what is understood as the vagueness of the hypothesis.

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  1. Peirce’s philosophy of religion includes but is not exhausted by his belief in God, and even though the concept of Musement appears as an essential step to his Humble Argument for the Reality of God, it is not a strictly religious concept, not at all, as we shall see. The pioneering works by V. Potter (1973) and (1988), D. Orange (1984), M. Raposa (1989), and D. Anderson (1995a) construe Peirce’s religious ideas within the broader context of his philosophical thought and are obligatory references to the day, though for not exactly the same topics. A. Robinson (2010) is a more recent deep-breath study of Peirce’s philosophy of religion in relation to his whole system, specially his semiotics. See also C. Hookway (2000), especially Chapter 11, M. Slater (2014), chap. 3, and E. Salas (1999), to get a more in-depth account of specific issues.

  2. The system of quotations for Peirce’s works follows what is internationally accepted by the Peircean scholarship in general lines. I will provide the dates for every one of Peirce’s texts I quote from, except for the Neglected Argument itself, for that is already said. Explanations of acronyms are to be found in the respective references Peirce (1931–1958), (1982–2010), (1998).

  3. See B. Canteñs (2004), p. 779; J. Nubiola (2004). C. Delaney (1992) discusses exactly this point, but without mentioning Musement. K. Hull (2005) clearly shows, in a very thorough discussion of the importance of Musement for mathematical discovery, that Musement ‘is likened to all creative reasoning processes’ (2005, p. 493). J. C. Clanton (2014), going on the opposite direction I take here, describes how Peirce defends the link with abduction and criticizes his attempt, claiming that it fails to deliver what it promises.

  4. F. Kruse (2010, p. 388 ff.), claims Peirce’s Musement is his ‘esthetic moment’, with deep roots in the Transcendentalism of R. W. Emerson, despite the differences between the two philosophers. See Potter [1988] as well.

  5. Salas also remembers that Peirce’s Musement has roots in F. W. J. von Schiller’s Spieltrieb, ‘play impulse’, an author who deeply impressed Peirce in his youth, though quoted very few times in his work (Salas, 2009, pp. 469 ff). On this, see Orange (1984), Chapter 1.

  6. The vague character of Musement and the Idea of God has not passed unnoticed. The main reference on the subject seems still to be Potter (1973). But, on the whole, the majority of the interpretations have stressed only that vagueness requires further determination and that this determination can only happen in practical conduct, not deepening the account of the logic of vagueness as I do here. For instance, see Orange (1984), Anderson (1995a), and Hookway (2000). Raposa (1989, 17 ff.) stresses a bit more the importance of Peirce’s logic of relatives for his arguments, but he does not aim at explicating it in detail; his efforts are rather directed to clarifying Peirce’s realism.

  7. This will ultimately lead Peirce to develop a genetic evolutionary cosmology, trying to explain how the world came to be what it is now from the same primordial beginning. It is not the aim of this paper to go deep into Peirce’s full cosmological system here, what would be impossible for a single article. See Robinson (2010), Potter (1973), Parker (1998), and Hookway (2000) for different presentations of Peirce’s cosmology.

  8. See W 8: 106, 1890. See also Ibri (2000).

  9. For a detailed discussion of real chance, that is, Peirce’s defense of ontological, and not just epistemological chance, see Salatiel (2009). In sum, the argument is that chance is not only due to our ignorance of hidden causes, but is ontologically working in events; it is ‘absolute’, and not only relative to us. Chance operates in reality as an inexhaustible residuum of possibilities that can never be completely determined. Chance is vague, in other words.

  10. Cf. Hookway (2011).

  11. Cf. Stewart (2000) for more on Musement and investigation.

  12. A short reminder: the sign Σ is introduced by Peirce in 1867 to stand for logical sum [W 2.60] and the sign Π, in 1870, for the product [W 2.392]. In 1880, this notation will suffer an important change, when the same signs will not stand for operations anymore and will be applied directly to expressions such as L i : M i , understood however as numerical coefficients [W 4.205]. Cf. Brady (2000), Chapters 1 and 2.

  13. In EP 2.284 and 353, vagueness is linked to particularity. Singularity, particularity, and universality are presumably taken from Hegel’s jargon, which was dominant in philosophy during the nineteenth century.

  14. Aristotle (1928), De Interpretatione, 17b13 ff.

  15. The universal proposition could be written in this way: ‘ (x)(fxgx)’.

  16. Cf. the succintest explanation by Stjernfelt (2007), pp. 17–20, whose exposition I follow here. But see also Tiercelin (2005), 232 ff.

  17. This is a point also held by Hempel (1965, pp. 123–126), even using Peirce’s own vocabulary as well as the very same examples, but without acknowledging it.

  18. An equivalent particular proposition could be written like this: ‘∃(x)(fxgx)’. Frege defines the existential and universal quantifiers in 1879 basically in the same way, at least 5 years before Peirce. The full development of Peirce’s theory of quantifiers is achieved, independently from Frege, in the 1885 article on the algebra of logic. The thrust of Peirce’s theory was taken from O. H. Mitchell’s ‘On the Albebra of Logic’, published in the 1883 volume edited by Peirce when he was teaching at Johns Hopkins University. Mitchell was Peirce’s pupil then and his paper brings a reference to the first edition of Frege’s Begriffsschrift, but from that alone, one cannot infer Peirce’s acquaintance with Frege’s ideas. Worth noticing is H. Putnam’s claim that though Frege was historically the first to develop quantifying logic in a modern way, the actual discovery of the quantifiers, however, should be attributed to Peirce. So, the origins of modern quantification theory should be searched in Peirce’s works, not in Frege’s. And truly the latter remained unknown until B. Russell rescued his works, but this was only after E. Schröder published his works. Schröder himself was heavily influenced by Peirce, and in a review of the Begriffschrift written in 1880, Frege hardly could have missed; he quotes Peirce four times. Cf. Schröder (1880). In 1895, Frege also published a review of Schröder’s Vorlesung über die Algebra der Logik, a work to which Peirce is more than a distant influence. Of course, one cannot infer from this that he knew any of Peirce’s works quoted by Schröder. Cf. Putnam (1982). Brady (2000) furnishes more grounds to Putnam’s claim, presenting a detailed history of the Peircean influence over Schröder. The aftermath of this history reaches Skolem and Löwenheim in the twentieth century. See also BocheŃski (1961), pp. 327–328; 347 ff.; Brady (1997); Hawkins, Jr. (1997), pp. 134–139; Sluga (1987); Houser, introduction to W 4. lviii–lix; Anellis (2012); Molczanow (2012), especially pp. 20 ff, but also ch. 3 and ch. 4.

  19. Cf. Boler (2005); Pich (2005).

  20. Haecceitas being a term Peirce avowedly adopts from Duns Scotus [CP 6.318]. See Boler (1963) and (2005), and for a more critical discussion of Peirce’s assessments on Scotus, cf. Pich (2005).

  21. See Kessler (1998), p. 3 ff. Canteñs (2004), p. 776 ff.

  22. Cf. CP 7.578, wherein Peirce refers to the ‘onement’ of science and religion.

  23. See Rodrigues (2003), p. 96; Raposa (2012), p. 211, states the same conclusion, but from a different—Daoist, he claims—perspective.


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Correspondence to Cassiano Terra Rodrigues.

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Rodrigues, C.T. The Vagueness of the Muse—The Logic of Peirce’s Humble Argument for the Reality of God. SOPHIA 56, 163–182 (2017).

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  • Peirce
  • Vagueness
  • God
  • Humble argument
  • Musement