Kripkenstein, the coalesced monster of a position; it represents neither Wittgenstein nor Kripke, but something beyond. In Wittgenstein on Rules and Private Language, the former delves into Wittgenstein’s notion of the private language and the rule following paradox.
Let’s set the pretext. Assume two individuals – the agent and the skeptic. As presented in the work, the agent is attempting to add two numbers: 68 and 67. Well, 68 + 57 = 125… not quite. The skeptic challenges, that with the addition operation, “plus” (+), the agent didn’t mean the arithmetic operation rather a new one: quus
quus: \(x \bigoplus{} y = x + y, \text{ if } x,y < 57\)
\(5\), otherwise
Note, the skeptic does not question the validity of addition as arithmetic. But the ‘plus’, the certainty that it did signify addition as arithmetic. For until the particular example “68 + 57 = 125”, both plus and quus are consistent rules for addition given context. Also the skeptic does accept a common language L and reserves any skepticism for rules in the language.
A formalism of the skeptical argument
Consider a common language L and a rule R in it. The rule is abstract, such that it outputs O, given certain concrete parameters P. Take the current parameters as Pc and its corresponding output Oc.
Then, the skeptic’s (process of) contention can be characterized as: produce a new rule Rn, such that for the finite set of all parameters used until now in relation with the rule, denoted by F[P], the output is the corresponding O – the historical one. However, for Pc it is some Q
generalized quus: \(R(P_{i}) = O_{i}, \text{ if } P_{i} \in F\)
\(Q\) otherwise
Now, let’s begin.
Kripkenstein: The Mistaken Signifier – Notice that Kripkenstein, ultimately, is an issue of the signifier. That two agents can, at any moment, realize the discrepancy in the respective signifiers they mean. As mentioned, the skeptic’s mistrust is not of the arithmetic operator rather the meta-linguistic ‘plus’ not signifying arithmetic addition. Instead it denotes quus, an operation built on the arithmetic one.
As shown in The Hallucinatory Sign, the a posteriori law of identity becomes that of the signifiers.
That in a Language L, between two agents (for simplicity), the signifier Si represents the same signified for both. Formally, say the common signifier is Si and the signified for A is SdA, for B SdB. Then, the maximal a posteriori law of identity becomes
SdA = SdB
However, doesn’t Kripkenstein contradict this? Not necessarily. The skeptic still assumes a common language L, only rules the target of doubt. How can we know of the ‘true’ rule, so to speak? In Kripke’s words, how to resolve the challenge that “[…] there can be no such thing as meaning anything by any word”?
Recursive Reconstruction – While Kripkenstein does pose the problem of mistaken signifier, it doesn’t destroy meaning itself. As one reclaims meaning through recursive reconstruction, as I will conceptualize here.
Pass over the premises again. Common language L, accepted by the agent and the skeptic. For each rule R, the skeptic substitutes a modified rule Rn. An argument against Kripkenstein is that upon showing the skeptic how R works, say ‘plus’, the paradox is resolved. However, the skeptic can recursively apply rule modification; even to the rules that sustain the rule, the initial one.
As Kripke writes –
Many readers, I should suppose, have long been impatient to protest that our problem arises only because of a ridiculous model of the instruction I gave myself regarding ‘addition’ …
Rather I learned – and internalized instructions for – a rule which determines how addition is to be continued. What was the rule? Well, say, to take it in its most primitive form: suppose we wish to add x and y. Take a huge bunch of marbles. First count out x marbles in one heap. Then count out y marbles in another. Put the two heaps together and count out the number of marbles in the union thus formed. The result is x+y. …
Despite the initial plausibility of this objection, the sceptic’s response is all too obvious. True, if ‘count’, as I used the word in the past, referred to the act of counting …
In particular, he can claim that by ‘count’ I formerly meant quount, where to ‘quount’ a heap is to count it in the ordinary sense, unless the heap was formed as the union of two heaps, one of which has 57 or more items, in which case one must automatically give the answer’ 5′ …
A solution exists in recursive skepticism itself. Eventually, the rule modification reaches a final rule Rf, that can be described with non-rule entities in language L. As it is commonly accepted, the skeptic cannot doubt L. Then, one recursively reconstructs the argument; until it reaches the point of certainty.
Language in God’s Shadows – However, it still doesn’t absolve the original ‘paradox’? No basis exists to identify that a paradox… unless we already start from the Shadows of God.
Even the meaning of ‘paradox’, in here, assumes a normative truth about the meaning of words – as consistent universals; a fact non-existent in reality. Language acts as a vacuous shell for claiming safety after God died. To start from naked truth, a maximal skepticism, the Pyrrhonian tradition: the grounds are found in Truth, Language and Certainty.
That Kripkensteinian reconstruction permeates reality.
New struggles.- After Buddha was dead, his shadow was still shown for centuries in a cave-a tremendous. gruesome shadow. God is dead;l but given the way of men, there may still be caves for thousands of years in which his shadow will be shown. -And we-we still have to vanquish his shadow, too.
The Gay Science, Friedrich Nietzsche
References
Kripke, Saul. Wittgenstein on Rules and Private Language. 1982.
Krishna, Niranjan. The Hallucinatory Sign. 2023.
Krishna, Niranjan. Truth, Certainty and Language. 2023.
Nietzsche, Friedrich. The Gay Science. 1882.
Wittgenstein, Ludwig. Philosophical Investigations. 1953.