Abstract
The rise of modern logic had a deep impact on the philosophical reflection on logical form. This chapter explains how logical form became a primary topic of interest between the end of the nineteenth century and the beginning of the twentieth century. In particular, we will focus on Frege, Russell, and Wittgenstein. Their works contributed in different ways to shape a thought that moulded the beginning the analytic tradition, the thought that the logical form of the sentences of natural language can at least in principle be displayed by sentences of a logically perfect language.
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Notes
- 1.
- 2.
In later works, Frege talks of the “thought” expressed by a sentence as the primary bearer of its truth or falsity, see Frege (1918).
- 3.
The view that predicates denote functions from object to truth values is not explicitly stated in Begriffsschrift, but becomes clear in Frege (1891).
- 4.
Pietroski (2009), pp. 10–23, explains how Frege’s notation can solve some problematic cases that emerged in connection with previous attempts.
- 5.
Frege (1879), p. 7.
- 6.
Russell (1905).
- 7.
Russell (1905), p. 482.
- 8.
Russell (1905), pp. 482–484.
- 9.
Russell (1905), pp. 485–490.
- 10.
- 11.
Russell (1905), pp. 485–489.
- 12.
Russell used ‘proposition’ instead of ‘sentence’. But here it will be assumed that the two terms are not synonymous.
- 13.
Russell (1998) advances this line of thought.
- 14.
Wittgenstein (1992). Like Russell, Wittgenstein uses ‘proposition’ instead of ‘sentence’.
- 15.
Wittgenstein (1992), pp. 31–35, 89.
- 16.
Wittgenstein (1992), pp. 39–41.
- 17.
Wittgenstein (1992). p. 103 and ff.
- 18.
Wittgenstein (1992), p. 41.
- 19.
Wittgenstein (1992), pp. 41–43.
- 20.
Russell (1913), p. 113. To explain that the logical form of a complex is not itself a constituent of the complex, Russell says that the former is not an entity. But the distinction between object and entity is not clear, and Russell does not provide conclusive arguments to the effect that logical forms are not entities.
- 21.
Bonino (2008), pp. 170–192, explains Russell’s motivation.
- 22.
Wittgenstein himself, in Wittgenstein (1993), shows how some central claims of the Tractatus can be abandoned without giving up the term ‘logical form’.
- 23.
This is the definition of perspicuity outlined in Sainsbury (1991), p. 344.
- 24.
Here (34), (36) and (37) are described without taking into account the fact that names such as ‘Tom’ can also be affected by vagueness, ambiguity or context sensitivity. This is obviously a simplification, but it is harmless.
- 25.
The hypothesis that distinct names denote distinct objects will be considered in Sects. 6.2 and 6.4. Wittgenstein’s claim about quantification is expressed in Wittgenstein (1992), pp. 135 and 153. In reality, his view is not so clear, given that he denies that universally quantified sentences are conjunctions, and that existentially quantified sentences are disjunctions. Marconi (1995) provides some elucidations about Wittgenstein’s claim, and the reasons that led him to abandon it after the Tractatus.
- 26.
It is not entirely obvious that Russell and Wittgenstein have the second problem, as it is not entirely obvious that they understand simplicity as an absolute property.
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Iacona, A. (2018). The Ideal of Logical Perfection. In: Logical Form. Synthese Library, vol 393. Springer, Cham. https://doi.org/10.1007/978-3-319-74154-3_2
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