How to be a good philosopher?

Are there any rules?^

Abstract: The paper represents an attempt to present and discuss a puzzle derived from Ludwig Wittgenstein’s rule-following considerations, aiming to avoid the existent ambiguities and conceptual misunderstandings. It is shown that the traditional logical approach to language is in principle unable to solve the puzzle. Although this result was taken to balance the odds in the favour of a naturalistic approach to the aim of producing a philosophical theory of natural language, it is also shown that this approach is equally wrong-headed. A few more general considerations with respect to the implications of this negative result are formulated in the end.

1. It has been said more than once about philosophical questions that they are meaningless. And it might be true of at least some questions usually asked by philosophers that they are so indeed. As philosophers, we cannot just rely on our own natural linguistic abilities and hope that this will do. Several examples have been produced, if only in the philosophical literature of the last century, illustrating situations in which sentences that we would be inclined to consider meaningful prove to be, after a more careful examination, quite meaningless¹. As a consequence, having a solid theory of language to provide us with the criteria for distinguishing between meaningful and meaningless sentences could be regarded as a prerequisite task for a philosophical investigation. I believe that such a theory will rest at least on the following assumption²:

(A) There is a set of rules that govern our linguistic activities, such that, for any linguistic utterance, we are able to say if it breaks or agrees with some of these rules. We can point out which rules were supposed to apply to the considered situation and which, if this is the case, have not been correctly followed. In the second case, not only can we state that a rule that was supposed to be followed has been broken, but we can also reasonably argue, by making appeal to the rule, that it so happened.

Accordingly, the theory will aim to state the rules one must obey if one wishes to speak meaningfully. It will also provide a procedure to apply the rules to each possible utterance, in order to see if it agrees with the rules or not. Were we armed with the set of rules and the procedure to apply them correctly to each case, we would be able to detect, for any question we might want to raise, whether it is meaningful or not. Thus, we could start a philosophical investigation being completely assured that the question we are trying to answer is not a meaningless one.

The problem is that (A) is wrong and it should be rejected. The most radical criticism of (A) is fostered by the later Wittgenstein's rule-following considerations. In what follows I will do little more (if any) than re-enact Wittgenstein’s arguments. With respect to this, I do not wish to get into disputes regarding what Wittgenstein's rule-following considerations (RFC) really mean³. I would rather take it for granted that I understood Wittgenstein correctly. I am, however, mostly willing to accept that I did not if the arguments presented here turn out to be feeble. But if someone accepts them, then I think the whole credit should be given to Wittgenstein⁴. The structure of this paper is as follows. I will first show how Wittgenstein’s RFC lead to the conclusion that if the rules are seen as some sort of entities (linguistic, abstract or perhaps mental), then it is not possible to bridge the gap between them and our linguistic practice. This, I think, is enough to show that the traditional logical/analytical approach to language is in principle wrong-headed. I will not insist on this point because it seems to me that it has been lately understood, and the consequences of Wittgenstein’s arguments in this respect have been gradually gaining acceptance. The last part of my paper will be dedicated to showing that an attempt to offer a naturalistic explanation of the relation between semantic rules and linguistic activities, usually presented as an alternative to the analytical approach, is equally mistaken. A few general conclusions will be presented in the end.

2. Let us begin by looking at an example. Suppose that we have two extremely simple languages⁵, L₁ and L₂. Each of them has only three sentences. For the purpose of this presentation there is no point in getting into the internal structure of these sentences so, since both L₁ and L₂ are finite, we could skip formation rules and define our languages in a descriptive manner:

L₁ - {'A', 'B', 'C'}

L₂ - {'1', '2', '3'}

A text written in L₁ will look like this: ‘A. C. A. B. C.’⁶

The same text could be written in L₂ like this: ‘1. 3. 1. 2. 3.’

Now we state the following general rule for translating⁷ from L₁ into L₂:

(R) The n^th sentence from L₁ is correctly translated into L₂ if it is replaced by the n^th sentence from L_2.

Suppose now that we give to a person trained to translate from L₁ into L₂ the following text:

(t1) ‘C. B. A. C. A. B. C.’

Our translator will start with the first three sentences as expected, by writing '3. 2. 1.' She will nevertheless continue in a most strange way:

'1. 2. 3. 3.'

Confronted with the rule (R) she will answer that all the sentences were translated according to the rule, but she interpreted the phrase "replacing a sentence by another", as it appears in (R), in a different manner. She might express her interpretation like this:

(I1) For any two formal languages which both contain m sentences, replacing the n^th sentence from one language with the n^th sentence from the other means writing instead of the n^th sentence from the first language, alternately, once the n^th sentence from the second language and once the {n+1}(mod m)^th sentence from the second language.

In order to prevent such deviant interpretations we will make our intended interpretation explicit:

(I1') For any two formal languages which both contain m sentences, replacing the n^th sentence from one language with the n^th sentence from the other means writing the n^th sentence from the second language in the place of every apparition of the n^th sentence from the first language.

Now our translator will retranslate (t1) correctly:

'3. 2. 1. 3. 1. 2. 3.'

We make another try with the following text:

(t2) “C. B. C. A.”

This, however, produces an unexpected result: ‘1. 3. 2. 3.’ Again our translator claims that she agrees to the rule (R) and to the interpretation (I1'). Only that this time she has interpreted (I1') differently:

(I2) Writing an expression in the place of another which appears within one string of symbols is to create a mirror image of the string and substitute the expression accordingly.

Let us stop here for a bit and turn to some more general considerations⁸. For any two languages described as sets of sentences we could regard the translation rules as functions from the sentences of one set to the sentences of the other. The idea of correspondence between sentences must be somehow expressed in the rules. Some phrase marking the correspondence will appear in the formulation of the rule, playing the role the equality sign has in the definition of a function. This phrase could always be misinterpreted. We can imagine an entire class of non-standard interpretations of the translation rule in the following way:

For two finite sets of sentences having n elements, S₁…S_n and S’₁…S’_n, there are nⁿ possible functions which associate elements from the second set to elements from the first set (of which, n! are bijections). Let f₁ be the standard mapping function and m the number of possible functions. There are m! possible arrangements of the mapping functions in a row (m! is still a finite number). Let f₁ … f_m be such a series. The pattern of a non-standard interpretation, then, could be:

(P) Up to the i^th occurrence of S_k the replacement should be made according to f₁; from the (i+1)^th occurrence to the (i+j)^th the replacement should be made according to f₂ etc.

Since i, j etc. are arbitrarily large numbers, it is obvious that there is an infinite number of possible interpretations of the translation rule⁹. Other patterns of non-standard interpretations are also possible, of course. There are non-standard interpretations of this sort, which will produce, in fact, the same result as f₁¹⁰. So there is no point in saying that the standard translation rule should be privileged because it does not make the application of the function dependent on the number of occurrences of the symbols which are to be processed¹¹. There is no point either in trying to escape the difficulty by replacing the phrase expressing the correspondence relation in the formulation of the rule by the phrase used by the recalcitrant translator in his interpretation of the rule (the phrase “the replacement should be made” in (P), for instance). For, since the same phrase appearing in the context of different sentences could be interpreted differently, nothing prevents our translator to interpret the phrase differently, now that it appears within a different sentence from his. And there is, of course, no point in saying that it is not plausible that one would take “=” to mean something so different from what it means to us. Finally, specifying that “each occurrence of S_k must be translated in the same way” is useless, since “each” and “the same way” could be interpreted differently from what we intend them to mean¹².

It should have become clear by now that regardless of our stipulation of the translation rules, the correct interpretation of the rules, the correct interpretation of the interpretation of the rules and so on, the translator might always interpret all our explicit stipulations in a way such that both the translations which seem to agree with our intended rules and those which seem to break our intended rules can be made to agree with the explicit stipulations¹³.

Perhaps one might want to reply now that our paradox appears only because we take the translator not to understand the metalanguage in which we formulate the translation rules. The metalanguage that the translator uses differs from ours in very few respects, though. Actually, the differences regard just some phrases used to express correspondence relations in the context of the sentences stating the translation rules. Apart from that, nothing is different. However, we cannot point to these differences properly without making appeal to the semantic rules that govern the use of those expressions in metalanguage. And here we only have an infinite regress. It is important to note, however, that the initial case had nothing to do with matters concerning meaning directly. The fact that our translator understands the meaning of ‘A’, ‘B’ ‘C’ and ‘1’, ‘2’, ‘3’ bears no relevance on the example¹⁴. What we can say is that he does not understand “correctly translating from L₁ to L₂” as we understand it¹⁵. But I would like to suggest that, at least for now, we put matters concerning meaning and understanding apart and keep focussing on the relation between rules and their applications¹⁶. Our trouble, therefore, seems to be that it follows from the above example that we cannot distinguish between a correct translation and an incorrect translation by making appeal to the translation stipulations (rules, interpretations of the rules and the like).

Before going any further, there is one more point I wish to make. In the example above there are a limited number of cases that a translator has to deal with. This shows that our problems are in no way related to the fact that in applying a rule we might encounter new, unheard of, situations¹⁷. Nevertheless, each situation we would refer to as an “application of a rule” is, in a sense, a new case¹⁸. Only that this has not so much to do with the complexity of the activities (verbal or not) the rules regulate.

3. Our problems seem to arise when we try to bridge the gap between rules and their applications. We feel that a rule has to determine, so to speak, its correct applications in a necessary manner¹⁹. But insofar as we take the rule to be a linguistic entity, i.e. a sentence, we cannot argue for this strong feeling of ours. One might think that all our trouble comes from that fact that we took rules to be linguistic entities. If we could regard the rule as something which precludes the need for further interpretation, the paradox should disappear. Indeed, it could be said that a sentence could only be the expression of a rule and not the rule itself. The rule itself could be perhaps thought of as an abstract entity, which, by its own nature, contains its interpretation. All the cases in accordance with the rule are, somehow, determined by it. The problem with this view is that there is no apparent way in which we could trace the relation between the rule, seen as an abstract object, i.e. not existing in space and time²⁰, and the actual situations in which we say that someone has followed the rule. The cases in accordance with the rule could not be causally determined by the rule. There has to be another sort of relation. In order to show what this relation consists in, we must talk of some correspondence. And here a version of Plato’s “third man” argument will surely apply.

Another strategy would be to speak of the rule as a mental object. The problem with our recalcitrant translator seems to be, on this view, that he has not grasped the translation rule yet. The rule is not “in his mind”, so to speak. Were the rule “in his mind”, there would be no more questions of interpreting or applying it wrongly. What the above example shows is at best that we cannot “put the rule in the mind of the translator” by using rational arguments. This does not make using rational arguments unnecessary, of course. We could show to someone who has already grasped the rule that he had broken it in one particular case by using such arguments. Let us ask now what sort of mental object the rule is. Suppose it is a mental representation. For the case presented above, grasping the rule might be, for instance, having the representation of a translation table. The table will perhaps look like this:

A → 1

B → 2

C → 3

We still have the problem of using the table in actual cases. The three arrows could be regarded as a single symbol, which provides a substitution rule for ‘A’, ‘B’, ‘C’ and ‘1’, ‘2’, ‘3’²¹. As a single symbol, it may stand for any substitution rule, of course. One might try to answer to this problem by saying that we actually have three different representations, one for each row of the table, which are kept apart from each other in our mind. I will put aside for now the objection that if the three representations are kept apart from each other there is no indication that they have something in common, which they should, since they relate to the same rule. Let’s accept for now that things are this way. In order to prevent further misinterpretations, we could even eliminate the arrows. The three representations will then look like this:

A1

B2

C3

One problem with ‘A1’, ‘B2’ and ‘C3’ is that they contain no hint that they have anything to do with a rule. But even if we accept that the person who represents ‘A1’ to herself somehow knows that ‘A1’ is a rule, she still might get the rule wrong. There are many ways in which one can make substitutions while having in mind the three representations from above. The string ‘A. C. B. C’, for instance, could produce any of the following results:

‘A. CCC. BB. CCC.’

‘1. 333. 22. 333.’

‘A1. C3. B2. C3.’

‘A. B. C. C.’²²

‘1CBC. A3B3. AC2C’

etc.

We expected the translator to read ‘A’, ‘B’, ‘C’ and ‘1’, ‘2’, ‘3’ appearing in his mental representations as iconic symbols for the signs she has to work with. It is obvious that she did not do so and is not at all clear why she should have done that. And here there still is a correspondence relation we seem to have overlooked, namely that between the elements of our representation (‘A’, ‘1’, ‘2’ as images in our mind) and the components of the cases to which our representations ought to apply (‘A’, ‘1’, ‘2’ written on a piece of paper).

This amounts to the conclusion that grasping the rule is not having a mental representation. Let us now substitute the concept of “a sign looking like ‘A’” for the mental representation of ‘A’, the concept of “a sign looking like ‘1’” for the mental representation of ‘1’ and so on. The person who has grasped the rule that ‘A’ should be replaced by ‘1’, then, must possess, apart from mental representations of ‘A’ and ‘1’, the concept of a sign which looks like ‘A’ and the concept of a sign which looks like ‘1’. She must also possess the concept of “substituting one sign for another”. And now the rule could be regarded as a proposition formulated in the language of thought:

(R-LOT) Substitute the sign, which looks like ‘1’ for the sign which looks like ‘A’.

The fact that this is a thought and she possesses the right concepts, we think, prevents any misinterpretations of the rule. But here we are in no better position than when we spoke of the rule as an abstract object. Neither an abstract object, nor a mental one has feelers to touch the reality with²³. This is perhaps inherent to the way we usually speak of objects and relations: one object does not contain the relation it has with another.

4. Let us now think that we have a large enough set of cards. Some of them have ‘A’ written on one side and ‘1’ on the other. Others have ‘B’ written on one side and ‘2’ on the other. Those with ‘C’ written on one side will display ‘3’ when turned over. A text written in L₁ by using the cards could be correctly translated into L₂ by turning all the cards to the other side. I will further assume that this is done mechanically. Perhaps we could say that the mechanism formed by the cards and the means to turn them over is correctly translating from L₁ to L₂. The translation rules are somehow physically instantiated in this mechanism, and the relation between the rules and their correct applications is a causal relation. And now it may occur to us that we are not in a very different position. Our brains are, in a sense, such mechanisms, though far more complicated. This is the starting point of a naturalist approach. The problem with our puzzle, as it may occur to the naturalist, was due to the fact that we were trying to get from rules to their correct applications by using a “logical path”, so to speak. This choice was enforced upon us by our preference for the method of conceptual analysis. Yet, this was not the only available alternative. Another way of getting from the translation rule of our example to the set of appropriate translations would be that of stating the causal laws which describe the functioning of the mechanism translating from L₁ into L₂²⁴.

The approach proceeds with the remark that grasping a rule is some sort of ability or disposition²⁵. However, it will be conceded that when we speak of dispositions or abilities we actually speak of certain processes going on in our brains, processes which cause us to behave as we do when we act according to the rules. Explaining the relation between rules and acting according to rules is nothing else but constructing an empirical theory about those processes and the relations between them and our behaviour.

Let us now try to figure out how a theory explaining the relation between (R) and correctly translating from L₁ to L₂ would look like. One model for the facts the theory must apply to is this:

Translation Input → Translating Mechanism → Translated Output

The theory, then, will include some general principles or laws that govern the functioning of the Translating Mechanism. From these laws, with the aid of some derivation principles, we should be able to obtain predictions of the form:

(P) Under the circumstances C₁&…&C_n, if state IS obtains in the mechanism, then state OS will also occur.

‘IS’ and ‘OS’ are two states of the Translating Mechanism, which correspond to a Translation Input and to a Translated Output respectively²⁶. Here it is clear that our example helps us to keep things simple: there is no need to speak of an infinite number of states occurring in the mechanism²⁷. There are three IS states and three OS states. The C₁,…,C_n conditions are required in order to “cut the causal relations” between the functioning of the mechanism and everything else going on in the universe (my head included)²⁸.

There is a question that could be raised now: How general are the laws of the theory? We could think of many different mechanisms, apart from our brains, performing what we would call “translations from L₁ to L₂”. We could use water pipes, strings, electric wires etc. in order to build such mechanisms. The Translation Input will be coded differently, for each such mechanism, of course. If we build a different theory for each, then we should say that there are different rules for “translating from L₁ to L₂ with a computer”, “translating by using a human brain” and so on. On the other hand, it is obvious that the functioning of a machine using water is governed by different physical laws from those concerning the functioning of an electrical machine. The idea of coding the input and the output brings some problems too: we could think of exactly the same states of a mechanism coding a different input or output. For instance, let L₃ be a language which contains only three sentences: ‘I’, ‘II’, and ‘III’. It is clear that exactly the same theory that explains the functioning of our first mechanism using cards to perform the translation will work as an explanation of a translation from L₃ to L₂. Should we say that we only have one translation rule or two? I will suppose, for the sake of the argument, that the laws of our theory apply only to human brains²⁹ and that we could somehow circumvent the idea of coding by speaking of the causal relation between the input and the output, on one hand, and the brain states, on the other. Thus, the occurrences of the sentences from L₃ will produce different states in our brain from those produced by the occurrences of the sentences from L₁. But we might still feel that there is something not completely in order here. How is it possible that we could derive only three predictions (connecting the state of reading ‘A’ with the state of writing down ‘1’, the state of reading ‘B’ with that of writing down ‘2’, and the state of reading ‘C’ with the state of writing down ‘3’) from our theory? Were the languages L₁ and L₂ one sentence bigger, would we have to construct a completely different theory? To this one could answer that perhaps there are two kind of laws or principles: some general principles which will perhaps explain all the cases of the ‘writing something instead of something else’ kind, and some particular laws which, when added to those general principles, produce only the three predictions we were looking for³⁰.

Suppose now that we have completed this theory. Its structure could be roughly represented like this:

T = <GL, PL, DP, M>

where GL is the set of general laws of the theory, PL is the set of its particular laws, DP is the set of derivation principles and M is the meta-theoretical assertion that the theory offers an explanation for what is to perform a correct translation from L₁ to L₂. Maybe one would like to say that the rule (R) was replaced in this theory by the laws from the PL set. This, I think, is not a very good move, since it instantly brings forward questions related to the distinction between norms and natural laws. So perhaps is better not to try to pin the rules on any assertion of the theory³¹. The consistent naturalist will probably say that it is not the case to think of the rule as a linguistic entity anymore and therefore it makes not sense to speak of a distinction between two types of statements. That is a fair enough remark, I think.

Yet, there might be a problem with this naturalist account³². Since T is an empirical theory, it should be at least in principle refutable. Let us try to find out what would count as an empirical infirmation of T. Let us think of a translator who translates correctly from L₁ to L₂. The states described by the theory occur in his brain, according to T’s laws and all, the conditions C₁,…,C_n are satisfied and the IS corresponding to reading ‘A’ also obtains. Yet he makes something which we would usually call a mistake. This happens perhaps due to a disturbing factor which the theory did not account for. There are two different ways in which we could modify our theory to fit the empirical facts. One is to add the condition that the disturbing factor does not occur to the conditions C₁,…,C_n. Another possibility is to extend the laws of the theory such as to cover these cases and predict the translator reactions in these situations too. Only that in this situation our theory will not be a theory of “correctly translating from L₁ to L₂” anymore³³. But why do we say that? This was not an infirmation of M. Since a correct translation is whatever the theory describes, why not adopt the second choice? And if we do not adopt it, is it not because we make appeal to the rule?

Let us now imagine a different situation. Our translator makes the same mistake. And now we realise that this too can be accounted for by the theory. We have thought that there are only three predictions that could be derived from T, but we applied the principles from the DP set incorrectly. And we realise that the translator’s behaviour could be also predicted by our theory. So there is no empirical infirmation here. We have discovered that the explanatory power of our theory is greater than what we have thought. Still, we wish to change our theory. Why is that so?

Perhaps our problem can be pointed at directly in the following way. If T is to be an empirical theory, then M too, since it is a part of it, must be refutable by the experience³⁴. But how can we speak of an empirical infirmation of M without making appeal to the non-naturalised concept of the translation rule? Being a meta-theoretical statement, M states a relation between the rest of the theory and the non-naturalised rule. It is obvious that we cannot give M up. But what can we make of it?

The naturalist’s reply, as I imagine it, could run as follows: “What guides our investigation is the model of a mechanism which never makes mistakes. Our theories are empirical in the sense that they are only approximations of such a model. The more factors which could affect the correct functioning of the translating mechanism we discover and eliminate, the better our approximations of the ideal model are. So M states the relation between our theory and this ideal model. We don’t make appeal to a non-naturalised rule, but to an ideal model within which the causal relation between the processes instantiating the rule and those counting as applications of the rule is never affected by disturbing factors.” This account, however, seems to contradict our common view about the scientific progress. We use to think that science advances by offering models that are less ideal and more close to the facts³⁵. In this vein, one may think that Classical Mechanics is a more abstract model of the physical interactions than the Relativity Theory, which offers a more accurate description of the facts³⁶. Why would anyone want to go the other way round? But I will leave that aside for now. Let us imagine that we have two such ideal models. One is that of a regular translator who never makes mistakes. The other one is a model of one of our deviant translators who never diverges from the way he is performing the translation. Why do we choose to be guided by the first and not by the last model? How could the naturalist motivate his choice of the first model without speaking of the translation rule? And even if he could somehow motivate his choice, there still is a problem left. On the new reading, what M says is that there is a relation between T\{M} and the ideal model. Since the ideal model is not a physical object, it follows that the relation cannot be a causal one, which makes it obvious that M could not be empirically infirmed. If the naturalist is not bothered by that, it is only because he does not realise that now he is in exactly the same position as the conceptual analyst. Namely, if he wants to hold on M, he must speak of the relation between an abstract object (the ideal model) and actual situations and processes. If he only wants to speak of the functioning of our brain, then nothing will be objected to that. But then he will not be in a position to claim that he has answered a naturalised version of the question regarding the relation between rules and their applications.

5. If it is true that the both adumbrated approaches fail to account for the relation between rules and their applications, then it is hard to see how a mixture of the two will succeed to do the job. And it is useless, of course, to try to state rules if we cannot relate them to their applications properly. What is wrong with (A), then? Perhaps it is wrong to speak of rules and their application as if they were two different things. Anyway, I am not going to try to advance a solution to our problem here but only to evaluate the import of the arguments presented above.

To prevent any misunderstandings, it does not follow from the above presentation that we cannot communicate, compute, that our social institutions are illusory or anything of the kind. Nor do I think that any relativist conclusions are supported by this account alone. What the arguments from above amount to is only that we cannot produce normative theories³⁷. Again, this is not to say that there are no values, norms or rules. They can be taught, transmitted, even enforced. They sometimes collide. There is nothing wrong with normative talk either, as long as we do not take normative talk for what it is not, namely a descriptive account of norms, rules and values³⁸. Rejection of theorizing about norms and values might be taken by some to lead to some sort of irrationalism. Since we cannot provide theories and arguments about what is morally, prudentially, practically or in some other way reasonable to do in this or that situation, one may think, it is as if we have no reasons at all. I do not agree with this view. Discussing these matters is, however, far beyond the topic of my paper.

*

It seems quite radical, to say the least, to maintain, as Wittgenstein usually does, that all the traditional philosophical questions are meaningless. It is difficult, nevertheless, to remove the suspicion that some of them might actually be nothing more than nonsensical puzzles. We do not have solid, ultimate criteria to distinguish between meaningful and meaningless sentences. And it might be the case that is in principle not possible to have such criteria. Trying to discover by philosophical analysis the rules that govern the distinction and to state them is doomed to be a Sisyphean activity. Constructing scientific theories which explain what happens in our brains when we learn to use the language or when we actually distinguish between meaningful and meaningless sentences could be informative, but will not help us a single bit to remove the shadow of suspicion cast upon our philosophical activities. Most philosophers, I do hope, will not think that ignoring Kant and plunging into traditional metaphysics would be very wise. And some would perhaps agree that ignoring the later Wittgenstein or interpreting him such that his views do not endanger our philosophical habits is not advisable either.

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