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9. Wittgenstein, Philosophical Investigations, p. 218.


How can a sentence be undetectably true unless the rule embodied in its content--the condition the world has to satisfy to confer truth upon it--can permissibly be thought of as extending, so to speak, of itself into areas where we cannot follow it and there determining, without any contribution from us or our reactive natures, that a certain state of affairs complies with it? 10.

P. F. Strawson expresses the resistance to the "Wittgensteinian" story very effectively: It is an "externalist" point of view on our language and therefore false to the phenomena.

As thinkers and speakers ourselves, confronted with the claim that the Wittgensteinian picture exhausts the phenomena, says all there is to say, we may well find the claim impossible to believe, may well be tempted to say that it simply is not true to our most evident experience; for, we may be tempted to say, we do not merely experience compulsions, merely find it natural to say, in general what (we can observe that) others say too, or to agree with this or to question that; rather, we understand the meaning of what we say and hear well enough to be able, sometimes at least, to recognize, in what is said, inconsistencies and consequences which are attributable solely to the sense or meaning of what is said. 11.


I would like to be able to understand Wittgenstein's position in a resolutely antireductionist way that did not leave it open to such objections. The trouble is that some of his most frequently quoted remarks seem to encourage us to go on beyond the point at which he maintains there is nothing more to


10. Truth and Objectivity ( Harvard University Press, 1992), p. 228.
11. Skepticism and Naturalism: Some Varieties ( Columbia University Press, 1983), pp. 90-1.


be said; and we would have to explain why that is a misunderstanding. For instance:

"How am I able to obey a rule?"--if this is not a question about causes, then it is about the justification for my following the rule in the way I do.

If I have exhausted the justifications I have reached bedrock, and my spade is turned. Then I am inclined to say: "This is simply what I do."

"All the steps are really already taken" means: I no longer have any choice. The rule, once stamped with a particular meaning, traces the lines along which it is to be followed through the whole of space.--But if something of this sort really were the case, how would it help?

No; my description only made sense if it was to be understood symbolically.--I should have said: This is how it strikes me.

When I obey a rule, I do not choose.

I obey the rule blindly. 12.

It is true that at a certain point justifications come to an end, and that at that point I draw conclusions without further justification. I do not require further justification, because I have been told what to do. But the slogans "This is simply what I do" and "I obey the rule blindly" suggest a faulty picture, which I think can't be in accord with Wittgenstein's intentions. 13. They suggest that the final and correct conception of what I am doing when I add, for example, is that I am simply producing responses which are natural to me, which I cannot help giving in the circumstances (including the circumstances of my having been taught in a certain way). But to think this would be to get outside of my arithmetical thoughts in a way


12. Philosophical Investigations, sees. 217, 219.
13. For an illuminating presentation of a similar view, see Stanley Cavell , "The Argument of the Ordinary," in his Conditions Handsome and Unhandsome ( University of Chicago Press, 1990). He emphasizes the easily overlooked fact that Wittgenstein says only that he is inclined to say: "This is simply what I do." He stops short of actually saying it.


that would be inconsistent with them. My final judgment must be simply the arithmetical one, not the thought "This is simply what I do."

Perhaps it is possible to understand the statement "I obey the rule blindly" in this way: It might be said that if I think that what I'm doing is just something I can't help, I am not really obeying the rule of addition blindly. To obey it blindly could be taken to mean simply drawing the conclusion which it mandates, with no further explanation than that that is the right answer.

This leaves Wittgenstein without a positive theory of meaning or entailment, but perhaps that is just as well, given much of what he says about the aim of philosophy. We can understand him to claim that a certain level of agreement in usage and in judgments is a necessary condition for meaning, and for the possibility of giving sense to the distinction between correct and incorrect--but that this cannot be turned into a sufficient condition--either a truth condition or an assertability condition. This would be in effect to accept the reassurance Wittgenstein offers at section 242: "If language is to be a means of communication there must be agreement not only in definitions but also (queer as this may sound) in judgments. This seems to abolish logic, but does not do so" (my italics).

That makes the view much less startling, though it does require us to reject the question "What is it to mean addition by 'plus'?" as one that cannot be given a nontrivial answer. If that is so, then Wittgenstein's name has been taken in vain to endorse relativistic positions.

Barry Stroud has stated effectively the impossible demand to which all failed theories of meaning, including those perhaps misascribed to Wittgenstein, are responses:

We think we must find some facts, the recognition of which would not require that we already speak and understand a language, and some rules which would tell us what, given those facts, it was correct to say. Familiar, everyday state-


ments of what a particular expression means cannot serve. They make essential use of words that are already "alive", that already have a meaning, so they seem incapable of explaining in the right way how any words come to have any meaning or come to be understood at all. 14.

It is this perpetual desire to get outside of our thoughts that we must find some way of resisting, and it is pretty clear that the best interpretation of Wittgenstein should show him as offering us a way to do that. One interpreter who makes this claim is Cora Diamond, who explains Wittgenstein's opposition to the traditional enterprise of philosophy as follows:

The demands we make for philosophical explanations come, seem to come, from a position in which we are as it were looking down onto the relation between ourselves and some reality, some kind of fact or real possibility. We think that we mean something by our questions about it. Our questions are formed from notions of ordinary life, but the ways we usually ask and answer questions, our practices, our interests, the forms our reasoning and inquiries take, look from such a position to be the 'rags.' Our own linguistic constructions, cut free from the constraints of their ordinary functioning, take us in: the characteristic form of the illusion is precisely of philosophy as an area of inquiry, in the sense in which we are familiar with it. 15.


14. "Wittgenstein on Meaning, Understanding, and Community," in R. Haller and J. Brandl, eds., Wittgenstein--Towards a Re-Evaluation: Proceedings of the 14th International Wittgenstein-Symposium ( Hölder-PichlerTempsky, 1990), p. 35.
15. The Realistic Spirit ( MIT Press, 1991), pp. 69-70. The 'rags' are those referred to in Philosophical Investigations sec. 52: "If I am inclined to suppose that a mouse has come into being by spontaneous generation out of grey rags and dust, I shall do well to examine those rags very closely to see how a mouse may have hidden in them, how it may have got there and so on. But if I am convinced that a mouse cannot come into being from these things, then this investigation will perhaps be superfluous. But first we must learn to understand what it is that opposes such an examination of details in philosophy."


But if that is Wittgenstein's intention, his method of looking at the details of linguistic practice doesn't seem to me to have the desired effect. I, at least, am left with the feeling that there must be much more to it--some recognition that these practices reach far beyond themselves.

This may seem incoherent. How can I form the idea that our linguistic practices reach "beyond themselves"? It looks as if I am here cutting my words free of the constraints of their ordinary function and assuming that they will still work--that I have a concept of addition, for example, which is independent of the ordinary conditions of the application of that word, and which it is mysterious that those conditions should enable us to capture. Is it not absurd to ask, "How can a finite practice such as my everyday use of the word 'addition' enable me to refer to the infinite function addition?" The second occurrence, after all, is just one of my uses of the word. I cannot possibly use a concept to cast doubt on its normal conditions of application!

But matters are more complicated than this. When the normal conditions of application seem insufficient to support the content of a powerful concept, it is possible that we have misinterpreted the concept, but it is also possible that we have misunderstood the conditions of application. I think this may be what happens when we take an anthropological view of the ordinary practices of calculation, such as addition. They lose their meaning. But when I use the word "addition"--when I am inside arithmetic--it is evident that its scope is of a completely different order from anything revealed by the type of detailed observation of linguistic practices that Wittgenstein seems to recommend as a way to cure the transcendent philosophical impulse. What the apparently absurd question does is to reveal the huge gap between this view from inside and the view from outside the language.

I am pretty well convinced by Diamond's claim that when he says "What has to be accepted, the given, is--so one could


say--forms of life," 16. Wittgenstein is not proposing a "given" in the traditional sense of that in terms of which we must try to make philosophical sense of everything else. But how is detailed attention to our forms of life supposed to enable us to escape from the conviction that there is something to be explained here (even if we cannot explain it) about how our forms of life enable us to talk about all those things that are not part of our forms of life?

Ordinary explanations of the meaning of an expression do not explain how meaning is possible. Diamond believes Wittgenstein has shown we must abandon the pursuit of that explanation as a fantasy--not as something merely unattainable:

Realism in philosophy, the hardest thing, is open-eyedly giving up the quest for such an elucidation, the demand that a philosophical account of what I mean make clear how it is fixed, out of all the possible continuations, out of some real semantic space, which I mean. Open-eyedly: that is, not just stopping, but with an understanding of the quest as dependent on fantasy. 17.

Perhaps there is no deeper understanding of the reach of meaning than that involved in our ordinary understanding of the expressions themselves. But then that understanding is not adequately represented by the sort of facial description of our practices that Wittgenstein recommends as an instrument of demystification. I would prefer to say that the infinite reach of mathematical language can be understood only from inside it, by engaging in that form of life. That means that we cannot understand even the form of life by describing its practices from outside. The order of explanation is the reverse of that


16. Philosophical Investigations, p. 226.
17. The Realistic Spirit, p. 69. She is alluding to Wittgenstein Remarks on the Foundations of Mathematics ( Blackwell, 1956), p. 325: "Not empiricism and yet realism in philosophy, that is the hardest thing."


in the common (mis)interpretation of Wittgenstein: The rule-following practices of our linguistic community can be understood only through the substantive content of our thoughts--for example, the arithmetical ones. Otherwise they are impotent rituals. We cannot make sense of them by viewing them as items of natural history.





Most of the reasoning we engage in is not deductive but empirical, moral, and more broadly practical; but I want to begin my discussion of specific types of reason with the sort of logical and mathematical examples that have already figured in the discussion of Wittgenstein's views. Simple arithmetical or logical thoughts are examples of reason if anything is, however difficult it may be to understand exactly what is going on, and they are pervasive elements of the thought of anyone who can think at all. If we can understand how they exclude the possibility of a relativizing external view, it may help with more complicated cases, but all my discussion will be completely general: This chapter is not about the content of logic.

The simplest of such thoughts are immune to doubt. Whatever else we may be able to imagine as different, including the possibility that we ourselves should be incapable of thinking that 2 + 2 = 4, none of it tends to confer the slightest glimmer of possibility on that proposition's failing to be true, or being true only in some qualified sense. 1. If we are capable of thinking it at all, then it simply cannot be dislodged by any other suppositions, however extravagant.


1. Of course I may be unsure of the truth of the same proposition expressed in binary notation; but that is because I am not familiar enough with that notation to be able to think in it directly, without translating: I have to figure out what "10 + 10 = 100" expresses.


If, for example, someone says to me, "You only believe that 2 + 2 = 4 because you were in love with your second grade arithmetic teacher," this fails to qualify as a challenge. I may call up the long-buried image of Miss Gardbaum, with her soft hair, prominent bosom, and dark blue skirt powdered with chalk dust, and acknowledge that yes, I was in love with her and wanted to believe everything she told me--but these reflections will be powerless to make me reconsider my conviction that 2 + 2 = 4, because it lies beyond their reach and does not depend on anything which they call into question. I cannot come to consider it, even temporarily, as a mere appearance.

The range of logical and mathematical reasoning is wide, and any particular example may be indubitable to some people but not to others. A good example is contraposition (modus tollens): "If p then q" plus "Not q" implies "Not p." Not everyone recognizes that implication automatically, and some people may have trouble getting used to the idea. 2. Yet it too cannot be called into question or given a subjective reading by psychological observations about how it was learned or about variations in its acceptance or use among different groups. Even someone who is a bit shaky in its application must recognize it as a principle which, if true, has universal validity, and not just some local or perspectival variety. To think of it merely as a practice or habit of thought would be to misunderstand it: It is a principle of logic. Of course it is a habit of thought too (for some), and there are interesting questions about which valid principles it is practically reasonable or even possible to employ in our thinking, given limitations of time and mental capacity. 3. But to think of reason as an


2. In fact, failure to employ it is involved in some of the most common forms of faulty reasoning studied by psychologists. See Stephen Stich, The Fragmentation of Reason ( MIT Press, 1990), chapter 1, for some references.
3. For discussion, see Stich, The Fragmentation of Reason, and Gilbert Harman , Change in View ( MIT Press, 1986). Stich, however, offers the unhelpful proposal that we should give up truth as the aim of reasoning.


abstraction from the contingent psychological phenomena of human reasoning is to get things backward. The judgment that it is impossible or inconceivable that the premises of a proof be true and the conclusion false relies on our capacities and incapacities to conceive of different possibilities, but it is not a judgment about those capacities, and its object is not something that depends on them.

This is glaringly clear when we follow any actual course of compelling deductive reasoning. It is what makes Plato's example of the boy in the Meno so irresistible. When Socrates gets him to see that a square double in area to a given square must be the square on the diagonal, he does so by an argument that is completely persuasive, and we recognize the boy's assent as the product of the argument's validity, which he and we understand: There is no glimmer of explanation in the opposite direction.

Or consider Euclid's simple proof that there are infinitely many prime numbers: If we suppose that there are finitely many we get a contradiction, since the product of all of them, plus one, will be divisible by none of them without remainder but by each of them with a remainder of one. It is therefore either itself prime or divisible by another prime not in the original set. There is no room here for someone to fail to "go on in the same way." If, when presented with this argument, someone said that the product of all the finitely many primes plus one would be divisible by one of them without remainder, we could only treat it as either dim-wittedness or gibberish.

We can of course be mistaken in some of our judgments about what is and is not inconceivable. But such mistakes must be corrected at the same level at which they are made. That is, we must come to have some kind of positive understanding that we formerly lacked of how the proposition whose falsity we were unable to imagine might after all fail to be true, and the understanding must be in terms of the proposition itself: Mere external information about how we came to believe the


proposition, or about circumstances in which we would have failed to believe it, are not enough.

The same can be said about the judgment that something is conceivable. We may think we have conceived of something but then discover that we have misdescribed what we are doing and that we are really conceiving of something different. 4. But again, such corrections must go on at the level of the conceptions themselves. It is not enough to say, "Your inability (or ability) to conceive of the falsity of this proposition is merely a cultural or psychological fact about you." This is a general truth: Skepticism cannot be produced entirely from the "outside." We have to have or develop some internal understanding of the possibility that a belief might be false before any suppositions external to it can bring us to abandon it. 5.

We have here a clear example of one type of thought being superior in authority to others: When we juxtapose simple logical or mathematical thoughts with any other thoughts whatever, they remain subject only to their own standards and cannot be made the object of an external, purely psychological evaluation. In logic we cannot leave the object language behind, even temporarily. We may acknowledge that we are products of biological development and environmental influence, contingently constituted beings with contingent psychologies, speaking and thinking in contingent languages with contingent notations, and formed by contingent cultures. We may acknowledge that in various respects we might have been different, and also that there might have been no creatures like us at all. But none of these thoughts can get underneath


4. This technique is used by Saul Kripke to defend the necessity of certain identity statements despite an initial appearance of contingency. See Naming and Necessity ( Harvard University Press, 1980), lecture 3.
5. Sometimes external factors may prompt us to search for such an understanding (as apparently happened with Einstein and absolute time). But they cannot provide it by themselves.


the thought that 2 + 2 = 4 or that contraposition is a valid form of implication or that the product of any finite collection of primes, plus 1, is not divisible by any of them without remainder; or perhaps the preferable image is that none of these empirical thoughts enable us to rise above the logical thought, thinking about it while withholding commitment from its content. We cannot even momentarily "bracket" the ground-level thought that contraposition is valid and substitute for it the purely psychological observation that we find the falsity of that proposition inconceivable. It forms part of the framework of everything we can think about ourselves.


Descartes himself (in the First Meditation) refuses to recognize this priority. I believe he is wrong to entertain even temporarily the hypothesis that an evil demon may be scrambling his mind to make him think falsely that 2 + 3 = 5 or that a square has four sides. That would require him to think the following: "I can't decide between two possibilities: (a) that I believe that 2 + 3 = 5 because it's true; (b) that I believe it only because an evil demon is manipulating my mind. In the latter case, my belief may be false and 2 + 3 may be 4 or 3 or something else."

This thought is unintelligible, for two reasons. First, it includes the "thought" that perhaps 2 + 3 = 4, which has not been given a sense and cannot acquire one by being conjoined with the extraneous, nonarithmetical thought that an evil demon might be manipulating his mind. 6. Second, the judgment


6. A qualification is necessary here. "2 + 3 = 4" is not gibberish. It has enough sense to be necessarily false, and it can enter into reasoning as the premise or conclusion of a reductio ad absurdum. Nevertheless, though one can suppose for the purpose of argument that 2 + 3 = 4, or observe that it follows from certain assumptions that 2 + 3 = 4, it is not possible to think that (perhaps) 2 + 3 = 4.


that there are two such mutually exclusive alternatives and that he has no basis for deciding between them is itself an exercise of reason, and by engaging in it Descartes has already implicitly displayed his unshakeable attachment to first-order logical thought, undisturbed by the possibility that his mind is being manipulated. In other words, he can't even consider the implications of that possibility without implicitly ruling it out.

Descartes also held that God could have made the eternal truths of arithmetic different--could have made 2 + 3 = 4, I suppose--but this is unintelligible for the same reason. (See Objections and Replies V and VI to the Meditations.) He rests the weight of this possibility on his confidence in the idea of God's omnipotence and responsibility for everything, which is greater than his confidence in his judgments of mathematical inconceivability:

Again, there is no need to ask how God could have brought it about from eternity that it was not true that twice four make eight, and so on; for I admit this is unintelligible to us. Yet on the other hand I do understand, quite correctly, that there cannot be any class of entity that does not depend on God; I also understand that it would have been easy for God to ordain certain things such that we men cannot understand the possibility of their being otherwise than they are. And therefore it would be irrational for us to doubt what we do understand correctly just because there is something which we do not understand and which, so far as we can see, there is no reason why we should understand. 7.

This implies a hierarchy among a priori judgments that is unpersuasive. The idea is that if we believe G, and G provides an explanation of why I would seem to us inconceivable even


7. Objections and Replies VI, sec. 8. The Philosophical Writings of Descartes ( Cambridge University Press, 1984), vol. 2, p. 294 (vol. 7, p. 436, in the Adam and Tannery edition).


if it really wasn't, then it is reasonable to regard I as possible though we cannot conceive how. This makes sense as a general account of how we can come to distrust a modal intuition. The trouble is that in this case, the inconceivability of I is so unshakeable that (by contraposition) it undermines confidence in G: It is impossible to believe that God is responsible for the truths of arithmetic if that implies that it could have been false that twice four is eight. (And it won't help to add that God could also have made contraposition invalid!) Structurally, this argument of Descartes is precisely the same as is offered by those who want to ground logic in psychology or forms of life, and the same thing is wrong with it. 8.

However reasonable it may be to entertain doubts as to the validity of some of what one does under the heading of reasoning, such doubts cannot avoid involving some form of reasoning themselves, and the priorities I have been talking about show up in what we fall back on as we try to distance ourselves from more and more thoughts. Strategically, I think Descartes was right about this aspect of the appropriate response to skepticism, even if he was much too expansive about the range of things about which we could suspend belief. 9. Certain forms of thought can't be intelligibly doubted because they force themselves into every attempt to think about anything. Every hypothesis is a hypothesis about how things are and comes with logic built into it. The same is true of every doubt or counterproposal. To dislodge a belief requires argument, and the argument has to show that some incompatible alternative is at least as plausible.


8. Derek Parfit has remarked to me that similar objections could be made to the idea that God is the source of moral truth. The argument against it has to come from within morality.
9. A perennially interesting issue is whether he was right to think we could intelligibly suspend belief in all empirical propositions about the external world. Cf. Donald Davidson, "A Coherence Theory of Truth and Knowledge," in Ernest LePore, ed., Truth and Interpretation ( Blackwell, 1986).


As a limiting case, suppose someone argues as follows (somewhat in the vein of Descartes's evil genius hypothesis):

If my brains are being scrambled, I can't rely on any of my thoughts, including basic logical thoughts whose invalidity is so inconceivable to me that they seem to rule out anything, including scrambled brains, which would imply their invalidity--for the reply would always be, "Maybe that's just your scrambled brains talking." Therefore I can't safely accord objective validity to any hierarchy among my thoughts.

But it is not possible to argue this way, because it is an instance of the sort of argument it purports to undermine. The argument proposes a possibility, purports to show that it cannot be ruled out, and draws conclusions from this. To do these things is to rely on judgments of what is and is not conceivable. There just isn't room for skepticism about basic logic, because there is no place to stand where we can formulate or think it without immediately contradicting ourselves by relying on it. The impossibility of thinking "If my brains are being scrambled, then perhaps contraposition is invalid or 2 + 2 doesn't equal 4 " is just a special case of the impossibility of thinking "If my brains are being scrambled, none of my inferences are valid, including this one." I can't regard it as a possibility that my brains are being scrambled, because I can't regard it as a possibility that I'm not thinking. Nor can I appeal to the possibility of a gap, in a case as simple as this, between what I can't think and what can't be true.

Date: 2015-12-24; view: 81

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