The Importance of Confidence: Revisit the Kripkenstein Paradox and the Failure of Lewis’s Naturalist Response

The featured image is a picture of grue, according to Google Image

This is the term paper written for PH2242 Philosophy of Language. As usual, I only post the introduction and the conclusion here. Please feel free to contact me via email (refer to the Home page) if you would like to read some of my arguments in detail or offer any critic. 


Wittgenstein’s rule-following paradox states that “no course of action could be determined by a rule, because every course of action can be made out to accord with the rule” (201). Kripke regards the rule-following paradox as the central problem of Wittgenstein’s Philosophical Investigations and a new form of philosophical scepticism (7). He draws parallels between language use and rule-following as well as between the meaning of language and a course of action. Inspired by the rule-following paradox, Kripke argues that the meaning of language cannot be uniquely determined by the language one uses, because the meaning can be artificially made out to accord with the language. As a result, people cannot be certain about the meaning of their language. Inspired by Wittgenstein’s rule-following paradox, Kripke’ sceptical challenge is named the Kripkenstein paradox. Kripke develops this sceptical challenge first from a mathematical example and applies it to all meaningful uses of language. The mathematical example is the simple calculation “68 plus 57 is 125”. English speakers usually associate the word ‘plus’ with the mathematical symbol ‘+’ which denotes an elementary mathematical function valid for all real numbers. Kripke further elaborates that by means of the symbolic representation ‘+’ and one’s mental understanding, one grasps the rule for the linguistic term ‘plus’ (7, emphasis mine). In particular, although people in the English-speaking world have only encountered finitely many summations in their lives, they understand the word ‘plus’ as a timelessly valid rule: people’s “past intentions regarding addition determine a unique answer for indefinitely many new cases in the future” (Kripke 8). As such, when one computes ‘68 + 57’ for the first time in one’s life, one will well believe that the symbol ‘+’ means ‘addition’ and give the answer ‘125’. ‘125’ is deemed as the correct answer satisfying both the arithmetic function ‘plus’ as 125 is indeed the arithmetic sum of 68 and 57 and the metalinguistic ‘plus’ because one continues to apply one’s past understanding of the word. However, suppose one encounters a bizarre sceptic who faithfully subscribes to Wittgenstein’s rule-following paradox and questions the certainty of one’s meaning of using ‘plus’. The sceptic defines another word ‘quaddition’ as the following:


For the sake of subsequent discussions, I assume that when calculating 68+57, the person meets numbers larger than 56 for the first time in his life. The sceptic claims that in the past, the person always unknowingly misinterpreted the word ‘plus’ which in fact means ‘quus’. Moreover, ‘5’ should be the answer of ’68 plus 57’, and in the past one obtained the correct answer by chance because one’s past calculations only involved numbers smaller than 57. Absurd as the claim may seem, people never instruct themselves explicitly which meaning they should follow when using the word ‘plus’ (Kripke 8). Addition and quaddition are both compatible with the person’s grasp of the rule ‘plus’, but people do not have any evidence or facts to favour addition over quaddition. People therefore cannot assume, from their finite past encounters with the word ‘plus’, that their previous understanding universally applies to all future instances of ‘plus’. In other words, no facts can ground the belief that one really meant ‘addition’ rather than ‘quaddition’ in the past. Consequently, people cannot be certain of the meaning of the linguistic term ‘plus’.


To summarise, this essay reconstructs the Kripkenstein paradox using the examples of ‘quaddition’ and ‘grue’. The Kripkenstein paradox challenges that people can never be certain about their meaning of language, or all meaningful uses of languages. Although Lewis provides a promising solution to the paradox using the concept of naturalness, he cannot solve the paradox. In fact, Lewis’s criticism does not capture the guidance constraint explicitly set by Kripke, and people cannot use the concept of naturalness to justify their choice of meaning. I argue that Lewis’s response remains as an appealing solution, but it cannot go further to solve the paradox once for all. I present two related criticisms or perspectives to show that Lewis’s solution to the sceptical challenge cannot give people the absolute confidence in their meaning of linguistic terms, and Lewis’s response does not capture the guidance constraint. The Kripkenstein paradox, essentially a sceptical challenge with some important metaphysical insight, can still justify itself in front of Lewis’s solution.

Works Cited

Ahmed, Arif. Saul Kripke. London: Continuum, 2007. Print.

Kripke, Saul A. Wittgenstein on Rules and Private Language: An Elementary Exposition. Cambridge, Mass: Harvard University Press, 1982. Print.

Lewis, David. “New Work for a Theory of Universals.” Australasian Journal of Philosophy 61.4 (1983): 343-77. Print.

Merino-Rajme, Carla. “Why Lewis’ Appeal to Natural Properties Fails to Kripke’s Rule-Following Paradox.” Philosophical Studies 172.1 (2015): 163-75. Print.

Wittgenstein, Ludwig. Philosophical Investigations. New York Macmillan, 1953. Print.

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