Abstract
This paper applies some logical devices taken from standard deontic logic and general metalogic to analysis of rule-following and its paradoxes as formulated by Ludwig Wittgenstein in his later works and recently popularized and analyzed by Saul Kripke. In particular, the paper argues that the Kripkenstein problem, related to the arithmetical operation called quus is apparent. In the final part, the question of rule-following of logical rules is discussed.
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Notes
- 1.
The ascribing of intentionality (see (c)) can be more complex in the case of abstaining from an action.
- 2.
This statement is simplified due to possible exceptions.
- 3.
The point (i) is formulated by the formula x ⊕ y = x + y, if x, y > 57 in the first edition of Kripke (1982). It is an obvious error, because 57 ⊕ 68 should give 125 as the result. Further editions corrected this mistake.
- 4.
I do not speak about standard and non-standard models, because principles governing arithmetic with quus are unclear (see above).
- 5.
I disregard here the problem of non-standard (in the technical sense) arithmetic, for example, arithmetical theories used in non-standard analysis. I only remark that we can either note that we theories belong to the same arithmetical class or to operate by various spheres of arithmetical OB.
References
Brożek, Bartosz. 2012. Rule-following. From imitation to the normative mind. Kraków: Copernicus Center.
Ebbs, Gary. 1997. Rule following and realism. Cambridge: Harvard University Press.
Kripke, Saul. 1982. Wittgenstein on rules and private language. Cambridge: Harvard University Press.
Wittgenstein, Ludwig. 1953. Philosophical investigations. Oxford: Blackwell.
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Woleński, J. (2015). Rule-Following and Logic. In: Araszkiewicz, M., Banaś, P., Gizbert-Studnicki, T., Płeszka, K. (eds) Problems of Normativity, Rules and Rule-Following. Law and Philosophy Library, vol 111. Springer, Cham. https://doi.org/10.1007/978-3-319-09375-8_29
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DOI: https://doi.org/10.1007/978-3-319-09375-8_29
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