Kripkenstein: Rule and Indeterminacy
Xin Sheen Liu
Quine's indeterminacy differs from Wittgenstein's in several aspects. First, Wittgenstein and Kripke's indeterminacy applies to a single individual in isolation and this indeterminacy disappears when the single person is brought into a wider community. Thus, this indeterminacy is only logically possible or hypothetical. Second, in Quine's problem, two translation manuals are distinguishable; while Wittgenstein's hypotheses, such as 'plus' and 'quus' and many others, are indistinguishable for the subject's past and the subject would never aware of the distinctions. Third, in Wittgenstein's view, whether a member follows the rules or not can be determined by 'outward criterion'. Quine's indeterminacy denies the existence of such 'outward criterion' for his two translation manuals.
Goodman's hypothesis of 'grue' is quite different from the above two indeterminacy in terms of both objective of introducing the concept and the usage of it. Goodman's issue is to search for the rules in screening out 'bad' assumptions in induction. This induction issue is not indeterminacy of Wittgenstein's skeptic arguments or Quine's radical translation.
Wittgenstein and Kripke's conclusion that that rules are brute facts seems to be questionable. Form of life is one of Wittgenstein's key concepts in his theory on rules and is linked to rules in some crucial ways. A community cannot agree on arbitrary rules and rules other than some highly selected ones cannot bind a community together. What a community agree or disagree is not an arbitrary game.
Kripke presents Wittgenstein's theory on rules in his book Wittgenstein on Rules and Private Language. The topic is difficult and the presentation seems to inherit some characteristics of the original work, which "is not presented in the form of a deductive argument with definitive theses as conclusions,..." (Kripke, 1982, p.3). Kripke tells the reader: "The point to be made here is that, at the same time the second part is important for an ultimate understanding of the first.'' (1982, p.84) "In this way the relation ship between the first and the second portions... is reciprocal." (1982, p.85). We find that a reciprocal reading helps me to understand and absorb the main points and arguments. In this paper we will pursue the discussion of Kripke and Wittgenstein's doctrine of rules in the reciprocal order as a summary, and then discuss some other issues about indeterminacy of human thinking, such as raised by Hume, Quine, and Goodman.
Other people in a subject's community have justification conditions for attributing correct or incorrect rule following to him, and these conditions will not be simply that the subject's own authority is unconditionally to be accepted. In Wittgenstein's view, rules are produced collectively in a community. It is meaningless to talk about rules for a single person in isolation. Wittgenstein solution of private language does not allow us to speak whether a single individual in isolation follows rules or not. (1)
Three of Wittgenstein's key concepts are agreement, form of life, (2) and criteria. Agreement is essential for our game of ascribing rules and concepts to each other. Form of life is about how activities are organized in a community. The commercial and trade activity in a community requires accounting and calculations. These activities may determine the usage of rule of 'plus' instead of 'quus'. Criteria sets up standards to check and make judgment on whether a subject follows a specific rules or not. Others in the community can check whether a subject follows rule of usage of 'table' by checking his particular responses to the question 'what is this' in front a thing that they endorse the usage of 'table' to the thing. The way they check this, in general, "a primitive part of the language game" (Kripke, 1982, p.102). Special problem arises for individual sensations, which is not available to the public. Wittgenstein states that it need not operate the way it does in the case of 'table'. 'Outward criteria' for sensations such as pain are simply the way this general requirement of our game of attributing concepts to others works out in the behaviorist's way in the case of sensations. (3) Criteria can be regarded as the set of rules to oversee the rule following.
In such a sense, it is impossible to find necessary and sufficient truth conditions for following rules, without winding up blindly or circularly. In Wittgenstein's view, it is important for us to realize that we cannot find the necessary and sufficient conditions for following a rule. To be practical, "we are not looking for necessary and sufficient conditions for following a rule, or an analysis of what such rule-following 'consists in'." (Kripke, 1982, p.87) Instead of necessary and sufficient conditions for following a rule, Wittgenstein proposes assertability conditions or justification conditions: "under what circumstances are we allowed to make a given assertion." (Kripke, 1982, p.74) What can substantive content such conditionals have? Since rules are based upon a collective agreement, the notion of a rule as guiding a single person in isolation who adopts it can have no substantive content. Only a person considered as interacting with a wider community, he is subject to correction and assertion by others, to judge a new response to be 'correct' or 'wrong'.
I was brought to an island by an accident, like what happened to Robinson Crusoe. Only a sceptic lived on the island. I did not know where he was from. He, like any sceptics, doubts about everything and was even more bizarre. Following was a piece of conversation between us.
S(sceptic): Show me your usage of 'plus'. Your answer must satisfy two conditions: (1) condition of facts: must give an account of what fact it is (about my mental state) that constitutes your meaning plus. (2) condition of justification: show how you are justified in giving the answer to 68+57.
I: It agrees with my past use by following the rules of 'plus'.
S: What do you mean by the rules of 'plus'?
I: For example, 68+57, I add 8 and 7 to get 15, that I put down 5 and carry 1 and so on.
S: How do you justify the rule of 'carry'?
I: We have a decimal system, we 'carry' (4) for every sum of ten?
S: How do you justify your decimal system?
First time I keep introducing new rules to explain previous rules. Finally I have to agreed that I have no more new rules as explanations and I accept that I act unhesitatingly but blindly. (5) Then he allows me to try again.
I: My rule of carry can be proved by counting.
S: I have many hypotheses about your usage of the rule of 'plus', you may have always meant by something else. Do you agree that those hypotheses are not a priori, logically impossible? For example, your hand calculator has maximum 8 digits, and any sum above 99,999,999 it always gives 99,999,999 as the answer. Suppose you have such a pair of large numbers that you never have time to do counting, how do you prove 'counting rule' is not 'quounting rule' ?
I: I could do it easily by the rule of 'plus'.
S: You are asked about 'plus' and now you try to prove 'counting' by 'plus'. There are many possibilities that you are doing something other than 'plus', such as 'quus', 'blus', 'clus', ... We do not have the facts to justify any of those cases, including your use of 'plus'. Our life time is limited, but we need to prove your usage for infinite pair of numbers. This problem does not limit to your usage of 'plus', actually all of your language usage...
I: I don't...!
S: Calm down. Let's do a simple experiment. (He showed me a photo of a wood structure with a rectangular board and four legs less than a foot tall.) Is this a 'table'?
I: (I have never seen such things before. My past usage and my inclination have no facts at all that give guide to my new usage. I try to follow my past usage anyway.) It is a bench, not a table.
S: Your concept 'table' may be 'tzuble'. (6) 'Tzuble' excludes Japanese table, 'tzukue' shown on this photo, in its extension. I have to emphasize that I am not even sure about your concept, even though you have given me a definite answer. You may have made a mistake under some whim or fatigue of your exhausting adventure, but you are thinking that you are still following the same rule as usual.
Then the sceptic showed me that many concepts that I have no doubt before seemed to become fuzzy, such as 'green', 'blue', etc.... (7)
I: I have to say I am using the simplest concepts. I don't want to make things unnecessarily complicated.
S: You are talking about the principle of simplicity. Let's look at the case of 'table', you simply did not know what new cases would arise so that you even did not know what hypotheses are there and the simplicity simply does not arise. Even we concedes that there be two hypotheses, say 'table' and 'tzuble', you can argue the concept of 'table' is simpler than 'tzuble', but I can do the other way equally well. No unique answer to the question of simplicity.
I realized that, without the consensus of my community, I am not so sure about a particular usage of a word and nothing tells me what I ought to do in each new instance. I have no either facts nor truth conditions corresponding to my inclination of following a specific rule. What I can say is whatever is going to seem right to me is right. This is the only proof, a viciously circular one, of my usage of concepts I can give. Therefore, as the sceptic said, here I can't talk about right and wrong any more. (8) (9)
Wittgenstein and Kripke's indeterminacy principle on rules and language, as Quine's indeterminacy of radical translation, raises some questions on our knowledge and understanding. But Quine's indeterminacy (1960, 1967, 1985) differs from Wittgenstein's in several aspects.
(1) As Kripke points out, Quine's behaviorist position does not allow the introspection, by which Wittgenstein pursues his argument on his indeterminacy of rules. Quine sees the philosophy of language within a framework of behaviorism , he thinks of problems about meaning as problems of disposition to behavior. Thus, Wittgenstein's indeterminacy does not arise in Quine's frame work.
(2) Wittgenstein and Kripke's indeterminacy applies to a single individual in isolation and this indeterminacy disappears when the single person is brought into a wider community. Thus, this indeterminacy is only logically possible or hypothetical. Quine bases his argument from the outset on behavioristic premises. Hence, Quine's indeterminacy only exist in a community, at least composed of a subject and an observer.
(3) In Quine's problem, two translation manuals are distinguishable. These are distinct hypotheses. Wittgenstein's hypotheses, such as 'plus' and 'quus' and many others, are indistinguishable for the subject's past and the subject would never aware of the distinctions. As an isolated person, he would never aware of his usage, even though a new issue arises. (10)
(4) In Wittgenstein's view, whether a member follows the rules or not can be determined by 'outward criterion'. Quine's indeterminacy denies the existence of such 'outward criterion' for his two translation manuals. Imagine the community makes a rule that only one of the translation manual is allowed and every member in the community must follow this manual not the other. Quine's objection is that no 'outward criterion' would be able to tell whether a member violates the rule in using the wrong manual instead of the right one. In this sense, Quine's indeterminacy of translation raises question on Wittgenstein's 'outward criterion', at least for some cases.
Goodman's hypothesis of 'grue' is quite different from the above two indeterminacy in terms of both objective of introducing the concept and the usage of it.
(1) Goodman's issue is to search for the rules in screening out 'bad' assumptions in induction. This induction issue is not indeterminacy of Wittgenstein's sceptic arguments or Quine's radical translation.
(2) Goodman implicitly assumes that every body knows the usage of 'green' and 'grue'. In Wittgenstein's problem of 'plus' and 'quus', a subject is not aware of the differences between the two concept and even does not know the existence of the alternative concepts. Wittgenstein's indeterminacy does not arise in Goodman's induction problem.
(3) Rules, in Wittgenstein and Kripke's sense, are brute facts, the agreements of community. (11) Goodman tries to explain why we have the deduction rules. (12) He agrees that we are not able to avoid circular proof, but this circle is a virtue one: "I have said that deductive inferences are justified by their conformity to valid general rules, and that general rules are justified by their conformity to valid inferences. But this circle is a virtuous one." (Goodman, The New Riddle of Induction, p.64) In other words, deductive inferences are justified by their conformity to valid general rules, and that general rules are justified by their conformity to valid inferences. "justified by their conformity to valid inferences' means 'justified by deduction'.
Goodman seems to mixes up two different processes, confirming process and application process, in his claim of a virtue circle. In the confirming process, we start with empirical facts as premises and apply the deduction rules to get inferences. Those inferences are empirically verifiable. The application process starts with a empirical fact, then apply the deduction rule to get an inference which is not verifiable or we do not want to verify empirically. We take the inference as a valid result of the deduction process. These two processes are different and can be differentiated. There are some cases, the two processes are entangled each other. For example, modern particle physics makes assumptions about quarks based on existing empirical data, and then goes through a long deduction processes to get some observable inferences. Empirical verification of the inferences become crucial evidences of the hypothesis of quarks. If the empirical facts do not agree with the inferences, should we reject deduction rules or the hypothesis? In practice of science, the hypothesis is normally rejected and save the key component of the core of the science paradigm, deduction. If the empirical facts do agree with the inferences, do we accept the existence of quarks? Objections have been raise to an answer of yes.
Goodman's intention is to find the induction rules, which enable to eliminate the invalid assumptions (13) and find the rigid procedures as those of deduction. Supposing we have the rigid inductive rules as deductive and the rules to generate all the valid assumptions, does it mean that a super-computer can induce and deduce all the knowledge for us? Does it means that we can predict the future with certainty? Do we still need creativity? The answer seems to me, we would never have such rules for induction in the same sense for deduction. Induction controls the interface between human mind and the external world and deduction is a process inside the mind. External world presents itself in time and expanding space. Control of the channel between the mind and external world needs to be loosen up, not tighten up. Induction is creative activity and open ended. Hypothesis, like 'grue', 'quus', are not absurd but possible ones. Creativity should be allowed leap from any possible world to another. Einstein's physics in some sense is 'quus' corresponding to Newton's classical mechanics 'plus'. Many creative ideas are regarded as odd or crazy ideas. Concept of 'quark' is believed to have some connection with Chinese mythic book Yi-Jing. Similarity exists between every thing to every thing, even though we do not have empirical proof of them. Creativity is the link between them. It is not that we have too many bad hypothesis; on the contrary, it is that we need to break the limit of our imagination and we need more creative hypotheses.
Wittgenstein and Kripke's conclusion that that rules are brute facts seems to be questionable. (14) The theory on rules should not stop here. Form of life is one of Wittgenstein's key concepts in his theory on rules and is linked to rules in some crucial ways. Kripke says: "Beings who agreed in consistently giving bizarre quus-like responses would share in another form of life. By definition, such another form of life would be bizarre and incomprehensible to us." (p.96) Hence, Wittgenstein believes that form of life provides some constraints on the rules a community possibly agree on. If form of life for a community is not accidental, it offers explanations on why we have certain rules not others, or at least, why we do not have certain rules like 'quus'. (15) Not only it is true that a community may agrees on rules, but also the reversal is true, rules shapes a community. History has shown that the societies adopts particular rules may be unstable and eventually destroy themselves. A community cannot agree on arbitrary rules and rules other than some highly selected ones cannot bind a community together.
Furthermore, agreement is only a half truth of a community and disagreement is the other half of the story. A community, even a family, in an absolute harmony is only a dream. In many cases, a community cannot reach an agreement and results in social conflict, even civil war. Examples are abortion, homosexual, social benefit, and even scientific believes. If what we agree on are brute facts, then what we disagree on are brute facts too. However, many conflicts on scientific and social issues have reasons, either natural or social, and some of the issues can be explained. What a community agrees or disagrees is not an arbitrary game. (16)
Disagreement accompanies every new scientific theory and disagreement is settled not by agreement. Human community can be so divided that the agreement is impossible to be reached between two sides, for example, those who supported either vitalism or physicalism on the basic scientific rules of life. The final settlement of the issue is the new discovery of facts on nature. It is not that it is the rule because we agree on, but we agree on it because it is supported by nature.
For this example, the causal relation is irreversible. Wittgenstein and Kripke's, like Humean, (17) (18) alleges that use of causal powers in a strong sense to explain the regularity is meaningless. Rather we play a language game that allows us to attribute such a causal power to some phenomena as long as the regularity holds up. The regularity must be taken as a brute fact. (19) However, the rules and regularities can be justified or rejected based on empirical facts. Is linguistic grammar a brute facts or explainable based on science? Chomsky's answer is that it is physical science and explainable. Like other science, say biology, different community or individuals may reason about human's heritage according to different rules. Which rule is correct can be verified by the information coded on human gene. Chomsky claims that eventually brain science will discovery the information physically encoded in human brain. Chomsky's UG may be proved wrong. If so, it is not because language rules are brute facts, but because of new discovery of empirical facts.
The author is grateful to Professor Philip L. Peterson, Syracuse University, for his many comments and remarks on this paper.
(1) "The impossibility of private language emerges as a corollary of his sceptical solution of his own paradox, as does the impossibility of 'private causation' in Hume. It turns out that the sceptical solution does not allow us to speak of a single individual, considered by himself and in isolation, as ever meaning anything. " (Kripke, 1982, p.69)
(2) Putnam's concept of divisions of linguistic labor seems to be related to Wittgenstein's concepts of agreement and form of life. A community agrees to call a specific metal 'gold'. The members of the community respond unhesitatingly to the question what it is, when they are asked in front of the metal. However, different divisions of linguistic labor do have some different aspects of form of life. Therefore, their rules and usage have subtle differences.
(3) Kripke claims that 'outward criteria' is deduced. "It should then be clear that the demand for 'outward criteria' is no verificationist or behaviorist premise that Wittgenstein takes for granted in his 'private language argument'. If anything, it is deduced, in a sense of deduction akin to Kant's. (Kripke, 1982, p.100)
(4) We have a real example of 'quarry'. Chinese pound (jin) used to be 16 Chinese ounces (liang). In 1950s Chinese government adopted 1 Chinese pound=10 Chinese ounces. Therefore, the people must carry for sixteen before t and carry for ten after time t. Similar to 'grue', these two rules of carry can be defended as 'quarry'. Carry can be defined for any number. Computer algorithm carries for 2, time carries for 60, etc. Those can be defined as 'quarry' as well.
(5) Kripke suggests that eventually we wind up with no explanations any more and he does not consider an alternative to go circularly. He says: "The entire point of the sceptical argument is that ultimately we reach a level where we act without any reason in terms of which we can justify our action. We act unhesitatingly but blindly." (Kripke, 1982, p.87)
(6) I modified Kripke's example of 'tabair', in order to make the description easier.
(7) "The problems are compounded if, as in linguistics, the rules are thought of as tacit, to be reconstructed by the scientist and inferred as an explanation of behavior. The matter deserves an extended discussion elsewhere." (Kripke, 1982, p31)
(8) Kripke, 1982, p24.
(9) Kripke's discussion on machine is confusing. It seems to me, the discussion has to be under the condition of a single, isolated machine or the condition that prohibits the person to give the machine any judgment. Otherwise, a machine and a man can be regarded as a community, and the person who dominates the community can judge the right or wrong functions that the machine performs. Kripke's discussion assumes a designer or someone else accompanies the machine. Under such condition, the designer can determine if the machine follows the rules or not.
(10) Kripke comments: "...if Wittgenstein is right, and no amount of access to my mind can reveal whether I mean plus or quus, may the same not hold for rabbit and rabbit-state? So perhaps Quine's problem arises even for non-behaviorists." Rabbit and rabbit-stage are distinct for the past. If introspection is possible, the subject should be able to tell whether he means rabbit or rabbit-stage. But quus and plus are essentially the same for the subject's past, even the introspection would not tell the difference. Therefore, Kripke's comments seem to be not correct. Quine's problem does not arises for Wittgenstein's non-behaviorist aspect, introspect; it does arises for his behaviorist aspect, 'outward criterion'.
(11) A community can adjust the definition of a word through agreement. We can change the definition of 'fish' to include whale or exclude whale and keep the definition. Those are the periphery of human knowledge. The basic principles in the core of human knowledge cannot be changed arbitrarily. "We try to compose out of already understood words an expression that will apply to the familiar objects that standard usage calls trees, and that will not apply to objects that standard usage refuses to call trees. A proposal that plainly violates either condition is rejected; while a definition that meets these tests may be adopted and used to decide cases that are not already settled by actual usage." (Goodman, The New Riddle of Induction, p.66)
(12) For Goodman, deduction rules are not brute facts and their acceptance is determined by their inferences. He says: " how is the validity of rules of deduction to be determined? Their validity depends upon accordance with the particular deductive inferences we actually make and sanction. If a rule yields unacceptable inferences, we drop it as invalid." (Goodman, The New Riddle of Induction, p.63-64) "A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend." (Goodman, The New Riddle of Induction, p.64). He does not spell out why we accept or reject an inference.
(13) "Only a statement that is lawlike-regardless of its truth or falsity or its scientific importance-is capable of receiving confirmation from an instance of it; accidental statements are not." (Goodman, p.73).
(14) In Kripkenstein's sense, agreements is a brute fact without further explanations. "Rather our license to say of each other we mean addition by '+' is part of a 'language game' that sustains itself only because of the brute fact that we generally agree." (Kripke, p.97)
(15) Many theory have been trying to offer explanations on the economic and political forms of human society, on state and law. It is wrong to simply deny all of those theories.
(16) Wittgenstein's theory on rules reminds me Jean-Jacques Rousseau's concepts of social contract. Rousseau said in his The Social Contract: "Each of us puts his person and all his power in common under the supreme direction of the general will; and we as a body receive each member as an indivisible part of the whole." Rousseau believe that general will leads to agreement and the object of a society's general will is the good of that society.
(17) When an event of one kind frequently follows upon an event of another kind in experience, a habit is formed that leads the mind, when confronted with a new event of the first kind, to pass to the idea of an event of the second kind. (Goodman, p60) "we may wish to explain the observed concomitance of fire and heat by a causal, heat-producing, 'power' in the fire. the causal nexus whereby a past event necessitates a future one, and the inductive inferential nexus from the past to the future. when one prediction rather than another? the level prediction is one that accords with a past regularity, because this regularity has established a habit. Thus among alternative statements about a future moment, one statement is distinguished by its consonance with habit and thus with regularities observed in the past. (Goodman, p60)
(18) It is not that any antecedent conditions necessitate that some event b must take place; rather the conditional commits us, whenever we know that an event a of type A occurs and is not followed by an event of type B, to deny that there is a causal connection between the two event types. (Kripke, p.94)
(19) "The idea of necessary connection comes from the 'feeling of customary transition' between our ideas of these event types." (Kripke, p.67) "Only when the particular events a and b are though of as subsumed under two respective event types, A and B, can a be said to 'cause' b. When the events a and b are considered by themselves alone, no causal notions are applicable. This Humean conclusion might be called: the impossibility of private causation." (Kripke, p.68)
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Goodman, N., Fact, Fiction, and Forecast, Bobbs-Merrill, 1973.
Kripke, S.A., Wittgenstein on Rules and Private Language, Harvard University Press, 1982.
Quine, W.V.O., Word and Object, MIT Press, 1960.
Quine, W.V.O., Journal of Philosophy, 1967, 67, pp.178-183.
Quine, W.V.O., "Meaning", The Philosophy of Language, 1985, pp.446-455.
Rousseau, J.J., Discourse on Plitical Economy and Social Contract, Oxford University Press, 1994.