Abstract
The laws of classical logic are taken to be logical truths, which in turn are taken to hold objectively. However, we might question our faith in these truths: why are they true? One general approach, proposed by Putnam [8] and more recently Dickson [3] or Maddy [5], is to adopt empiricism about logic. On this view, logical truths are true because they are true of the world alone – this gives logical truths an air of objectivity. Putnam and Dickson both take logical truths to be true in virtue of the world’s structure, given by our best empirical theory, quantum mechanics. This assumes a determinate logical structure of the world given by quantum mechanics. Here, I argue that this assumption is false, and that the world’s logical structure, and hence the related ‘true’ logic, are underdetermined. This leads to what I call empirical conventionalism.
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Notes
- 1.
Warren [12], p. 120.
- 2.
- 3.
Maddy [5], p. 226.
- 4.
Putnam [8], p. 179.
- 5.
Dickson [3], p. 2.
- 6.
The span of two subspaces is the plane containing them and their superpositions.
- 7.
Maudlin [6], p. 479.
- 8.
Bacciagaluppi [1], p. 19.
- 9.
Dickson [3], p. 4.
- 10.
For an exposition of the logical behavior of ‘⋁QL’, see Humberstone [4], pp. 913-917.
- 11.
See Bohm [2].
- 12.
Bacciagaluppi [1], p. 31.
- 13.
For more on decoherence or the status of ‘worlds’ in EM, see Wallace [11].
- 14.
Sklar [10], p. 958.
- 15.
Putnam [7], p. 33.
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Chua, E. (2017). An Empirical Route to Logical ‘Conventionalism’. In: Baltag, A., Seligman, J., Yamada, T. (eds) Logic, Rationality, and Interaction. LORI 2017. Lecture Notes in Computer Science(), vol 10455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55665-8_43
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