From the ALWS archives: A selection of papers from the International Wittgenstein Symposia in Kirchberg am Wechsel

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1. The notion of the a priori underwent several changes since the time it came into existence in the Middle Ages. Originally it had been used to mark a certain form of argument, an argument that proceeds from what is prior to what is later, from cause to effect: demonstratio procedens ex causis ad effectum = demonstratio a priori. But this changed with Kant, for whom it meant not a form of argument but rather some special kind of knowledge (or elements thereof), namely knowledge that (a) is independent of particular experiences and (b) that makes experience in general (Erfahrung überhaupt) possible. Tied up with consciousness and the transcendental unity of apperception, Kant’s understanding of the a priori was in the spirit of his transcendental philosophy. But this understanding changed again with the rise of analytic philosophy, in which we still find the first characteristic but not the second anymore. The idea of Erfahrung überhaupt was given up, partly because one naturally wondered what exactly this notion of experience in general, or experience universally conceived, should be. Where should we get it from, if not by way of abstraction and generalization from individual cases of experience? And would this not make it an empirical concept, so that the whole project of asking for the conditions of its possibility would not lead us to the kind of certainty, necessity and universality we expect from a priori knowledge? There would be no guarantee that in the future we would not make discoveries that would give us new kinds of experiences or that would show us our experiences in a new light. Thus, we would have to admit that these experiences did not satisfy the conditions of experience we had set up originally. The a priori conditions would have to be revised.

It seems that Kant did trust in our rational abilities in ways we do not any more. Kant believed that reason can understand itself and that we can find certainty. But it seems we no longer have such optimism, belief, or hope for absolute and certain knowledge. The idea of final solutions has been given up in many areas of research, and instead we have learned to be content with temporary solutions and various kinds of relative or approximate a priori’s. Instead of requiring, as Kant did, that everything that happens must follow from something else according to strict and determinate universal rules, we are more modest now in merely demanding some kind of regularity. Part of Kant’s rather demanding idea of the a priori has thus been given up. But does the entire transcendental project have to go as well? Or did analytic philosophy go too far by disregarding the second aspect of the a priori and by giving up the quest for the conditions of the possibility of experience in general? Already Hegel, often ignored by many analytic philosophers, did know how to relativize the a priori by conceiving of absolute knowledge as being relative to his time: Absolute knowledge is reached at the end of the Phenomonology of Spirit after we have worked through the history of consciousness from its beginning stages to its state in Hegel’s day and age. From the very beginning of the Phenomenology, the present determines the perspective and limits of knowledge. Nevertheless, for Hegel as also for Heidegger in his analysis of Dasein as always already being-in-the-world, it is not a question of avoiding a vicious circle but of getting into the circle in the right way. Kant was still satisfied to acknowledge that in philosophy definitions come at the end of inquiry, and although Hegel expressed some reservations when he famously wrote in 1820, at the end of the preface to his Philosophy of Right, that philosophy always comes rather late (“die Eule der Minerva beginnt erst mit der einbrechenden Dämmerung ihren Flug”), both Kant and Hegel still trusted their holistic approaches and their preconceptions of Erfahrung überhaupt.

It is intrinsic to such a holistic approach that metaphysics and epistemology cannot be neatly separated. But since the development of modern modal logic and especially since Kripke taught us how to distinguish aprioricity from necessity, it now seems possible to make this separation. It is this kind of separation that I want to question. Kripke gave examples of statements that are necessary and a posteriori, or contingent anda priori. It is the latter, his notion of the continent a priori, that I want to criticize in what follows.

2. In his lectures, published as Naming and Necessity, Kripke states, “I guess the traditional characterization from Kant goes somewhat like: a priori truths are those which can be known independently of any experience” (35). Taking an example from Wittgenstein, he argues that the statement P: “Stick S is one meter long” is a priori (or known a priori) but nevertheless contingent. Wittgenstein actually wrote: “There is one thing of which one can say neither that it is one meter long nor that it is not one meter long, and that is the standard meter in Paris” (PI, par. 49). Kripke probably misinterprets Wittgenstein when he says, “I think he must be wrong” (NN 54), as has been shown, convincingly I think, by Heather J. Gert (see bibliography). But whether Kripke here misinterprets Wittgenstein or not, it seems to me that on purely systematic grounds and contrary to what Kripke claims P is not both contingent and a priori.

Kripke argues that the truth of P is contingent because heat could have been applied to the stick so that its length would have been different. He thinks of this as happening at the time of stipulation (NN, 55). In such a possible world the length of stick S would then not have been one meter. This is supposed to be part of the metaphysical status of P. On the other hand, the reference fixer knows P a priori because he knows that he used stick S to fix the reference of the expression “one meter.” According to Kripke, “he knows automatically, without further investigation, that S is one meter long” (NN, 56). This is supposed to be part of the epistemic status of P. All this seems to make sense, and not only at first blush. Even after much thinking and contemplation this somewhat paradoxical example seems to convincingly show that there are statements that are both contingent and a priori. Nevertheless, I think this example does not show what Kripke wants it to. Let us look at P in the actual world wa and in an imagined world wi.

    P(wa) = (stick S is 1 m long) (wa)

    = stick S(wa) is 1 m (wa) long

In order to know P(wa) a priori, the reference fixer has to keep in mind that he used stick S(wa) to fix the reference of what he calls “1 m”. That is, he has to think:

    1 m (wa) = 1 m (S(wa)) and

    P(wa) = stick S(wa) is 1 m (S(wa)) long.

    In fact, the same applies to P(wi):

    P(wi) = stick S(wi) is 1 m (S(wi)) long.

In wi stick S(wi) is used to carry out the stipulation, and therefore P(wi) turns out to be true as well; and the reference fixer in wi knows this a priori, as he did in wa. There is nothing special about wa in this respect. (I believe Kripke would not agree to this.) Nor is there anything special about the reference fixer. (Kripke would probably not accept this either.) We all know P a priori and the reference fixer is not in a privileged position. What we actually know a priori is not the statement P with respect to the particular stick S, but P with respect to any stick that happens to be the Urmeter. What we know a priori is the possibility of such a stipulation (which could be expressed in form of an if-then statement) and the fact that whatever we use as Urmeter is then “automatically”, as Kripke says, one meter long. In the end, what makes P a priori is an if-then statement. This is my first main objection to Kripke’s account. Evidently, Kripke wants to understand it all differently. He takes the truth of P to be contingent: in fact, he wants P to be false in wi. He wants us to think of P in wi as:

    Q = stick S(wi) is not 1 m (wa) long

Well, this statement is true, too, and we even know it a priori. But obviously this statement is different from P(wi). Now what should we take P to mean? How should we think of P in wi: as P(wi), as I suggest, or Q(wi), as Kripke wants it? As I said above, we have to think of “1 m” as being dependent on S. Otherwise we do not know P(wa) a priori. It is part of the meaning of “S” in P that it is the Urmeter. It is essential to S (in the context of P as known a priori) that it is the standard meter.

We cannot meaningfully say Q in wi, because you cannot refer to 1 m (wa) in wi. Kripke of course wants to say Q in wa and not in wi. But I think this changes the meaning of P. To know P a priori, the stick and the reference (the act of referring) to the meter have to be taken from the same world, because the latter depends on the former. This is my second objection to Kripke’s account.

Kripke does not tell us how he thinks the meter is defined in wi. He thinks this not important. In wi the meter cannot be fixed as the length of S(wa), because there is no way to, so to speak, “go back” from wi to wa. Kripke is silent about this. But I do not think that we can afford to be silent here. We cannot simply say that we don’t need to give an answer to this question just because we are dealing with the metaphysical aspect of P. Does God fix the reference of “1 m” in wi by taking it from wa ?

Let us have a closer look at wi while trying to make sense of what Kripke wants us to see, i.e., that P is false in wi. If S(wi) is the standard meter and is thus used to fix the reference of “1 m” in wi, P will be true. Thus Kripke must assume that S(wi) is not used as the standard meter and that the meter is defined differently in wi. Certainly the meter cannot be defined in wi by means of S(wa), because S(wa) does not exist in wi. It must be defined differently, by another stick, by means of the wavelength of light, or in some other way. But in whatever way this is done, whatever the definition of 1 m in wi might be, the probability that 1 m (wi) = 1 m (wa) is zero, because there are infinitely many, even uncountably many different lengths. (We can make sense of the intuitive idea that lengths between two worlds can be compared as long as these two worlds are not too different from each other, which we assume is the case between wa and wi.)

Of course S(wi) is longer than S(wa), and one can say that the length of stick S is contingent, that it just has the length it happens to have. But in the context of statement P, stick S has to be understood as the standard meter stick, be it in wa or in wi, and the reference of “1 m” has to be understood as being determined by stick S. Forgetting this in wi amounts to changing the meaning of P in wi.

Based on what I have said so far, it seems to me that Kripke has not given us an example of the contingent a priori.

Let us now have a look at Kant again. What would be a priori about P in Kant’s eyes is, I think, the knowledge that there is a certain order and continuity in the world, especially that lengths do not change chaotically, that the concept of length therefore makes sense, and that we can set up a standard of length. We know for instance that if a stick S’ is as long as S and another stick S’’ as long as S’, then S’’ is also as long as S; or that if S’ is twice as long as S and S’’ again twice as long a S’, then S’’ is four times the length of S. In fact, to know P a priori we have to know many things of that kind and statement P has to be read as telling, or presupposing, a whole story, namely the story of setting up a standard of length and whatever this requires. The a priori aspect of P can thus be suitably expressed by an if-then statement, where a long story underlies (or should be expressed by) the if-part.

Kripke thinks that contingency is a matter of metaphysics and not of epistemology, which leads him to say that S(wi) is not 1 m (wa) long. But this is not what P says when you look at it as known a priori. P is about the relation between the meter and the stick S in one and the same world (and not about two items from two different worlds). Kripke distorts the meaning of P when he argues that it is contingent. Furthermore, we know a priori not only that P, but in a way (by imagination) we also know a priori that S(wi) is not 1 m (wa) long. I do not see how we can distinguish metaphysics and epistemology here, nor how we can ever circumvent or undercut the latter.

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