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Impossible logical skepticism is different from the ordinary epistemological kind, because the latter depends on an unchallenged capacity to conceive of alternative possibilities and derive implications from them. The epistemological skeptic argues that we could be in an epistemically identical situation


if we were hallucinating totally, or dreaming, or if the world had come into existence five minutes ago. Even under the hypothesis that one is being manipulated by an evil demon or science-fictional brain stabbers, these thoughts about what is possible are usually not themselves supposed to be threatened.

But in skepticism about logic, we can never reach a point at which we have two possibilities with which all the "evidence" is compatible and between which it is therefore impossible to choose. The forms of thought that must be used in any attempt to set up such an alternative force themselves to the top of the heap. I cannot think, for example, that I would be in an epistemically identical situation if 2 + 2 equaled 5 but my brains were being scrambled--because I cannot conceive of 2 + 2 being equal to 5 . The epistemological skeptic relies on reason to get us to a neutral point above the level of the thoughts that are the object of skepticism. The logical skeptic can offer no such external platform.

That does not apply, of course, to all propositions of logic or arithmetic. It is possible for a mathematician to have a belief about a controversial proposition like the continuum hypothesis which he neither finds self-evident nor is able to establish by a proof whose elements are themselves selfevident. And on a more mundane level, if I come to believe a moderately complicated arithmetical proposition after five minutes of calculation, it will not be inconceivable to me that I might be mistaken. If I were told that someone had spiked my coffee in advance, or that I had made a slip of the pen along the way, I would suspend judgment. That is because nonarithmetical beliefs about my calculations are essential to the support of the more complicated arithmetical belief. But with contraposition or "2 + 2 = 4," nothing external to logic or arithmetic is involved. Provided I have the concepts necessary to form such a thought, any confrontation between it and any empirical suppositions whatever must be regarded as unreal.


What we have here is a hierarchy in which some thoughts dominate others. The thought that contraposition is a valid form of implication dominates all psychological, historical, or biological propositions--categorical, hypothetical, or modal-that might be brought in to qualify, relativize, or cast doubt on its truth. In particular, it dominates the propositions that we learned it in a certain way, or that we cannot help believing it, or that we cannot conceive of its not being true, or that if circumstances had been different we might not have been able to think it. The thought itself, in other words, dominates all thoughts about itself, considered as a psychological phenomenon. As with the cogito, one cannot get outside of it, and nothing outside of it can call it into question.

Simple logical thoughts dominate all others and are dominated by none, because there is no intellectual position we can occupy from which it is possible to scrutinize those thoughts without presupposing them. That is why they are exempt from skepticism: They cannot be put into question by an imaginative process that essentially relies on them. All alternative possibilities that we can dream up, however extravagant, must conform to the simple truths of arithmetic and logic, so even if we imagine ourselves or others different in some way that makes us fail to recognize the truth of those propositions, part of what we have to imagine is that we would be ignorant, or mistaken, or worse. (And if the proposition is simple enough, we cannot conceive of anyone positively believing it is false, because we cannot attribute both understanding of and disbelief in it to the same person.)

But the consequences of this kind of dominance include more than the impossibility of skepticism. They include the impossibility of any sort of relativistic, anthropological, or "pragmatist" interpretation. To say that we cannot get outside them means that the last word, with respect to such beliefs, belongs to the content of the thought itself rather than to anything that can be said about it. No further comments on its


origin or psychological character can in any way qualify it, in particular not the comment that it is just something I cannot help believing, or that it occupies a hierarchically dominant position in my system of beliefs. All that is secondary to the judgment itself.

As I have already indicated, not all propositions we believe to be necessarily true have this status. We can discover that we were mistaken to think that the falsity of a certain proposition was inconceivable--that our inability to conceive of its falsity was due to a failure of logical or conceptual or theoretical imagination. Some of the most important human discoveries--relativistic space-time, transfinite numbers, the incompleteness of arithmetic, limited government--are of this kind. But to reach such a conclusion we must still rely on logic of a simpler kind, whose validity we regard as universal and not subjective. We must find the newly discovered possibility consistent, and if we come to believe it not merely possible but actual, that will be because it is more consistent than the alternatives with other things we have good reason to believe. Not everything can be revised, because something must be used to determine whether a revision is warrantedeven if the proposition at issue is a very fundamental one. I am not here appealing merely to the image of Neurath's boat. No doubt, as Quine says, "our statements about the external world face the tribunal of sense experience not individually but only as a corporate body" 10. --but the board of directors can't be fired.

Thought itself has priority over its description, because its description necessarily involves thought. The use of language has priority over its analysis, because the analysis of language necessarily involves its use. And in general, every external view of ourselves, every understanding of the contingency of


10. Two Dogmas of Empiricism ( 1951), in his From a Logical Point of View ( Harvard University Press, 1953), p. 41.


our makeup and our responses as creatures in the world, has to be rooted in immediate first-order thought about the world. However successfully we may get outside of ourselves in certain respects, thereby subjecting ourselves to doubt, criticism, and revision, all of it must be done by some part of us that we haven't got outside of, which simply has the thoughts, draws the inferences, forms the beliefs, makes the statements.


If I try to get outside of my logical or arithmetical thoughts by regarding them as mere manifestations of my nature, then I will be left with biology or psychology or sociology as the final level of first-order thought. This is clearly no advance, for not only does it contain a good deal of material more superficial than arithmetic--it also contains logic and arithmetic as inextricable components. When I try to regard such a thought as a mere phenomenon, I cannot avoid also thinking its content-cannot retreat to thinking of it merely as words or pictures going through my head, for example. That content is a logical proposition, which would be true even if I were not in existence or were unable to think it. The thought is therefore about something independent of my mind, of my conceptual capacities, and of my existence, and this too I cannot get outside of, for every supposition that might be brought forward to cast doubt on it simply repeats it to me again.

The subjectivist would no doubt reply that he can avoid offending against common sense, since he is merely analyzing what we ordinarily say, not recommending that we change it. For example, he can agree that contraposition would be valid even if we didn't think it was, because this simply follows from its being valid, and that is something we are all prepared to say, and are therefore prepared to say is true. All of the rationalist claims to mind-independence are preserved within the


system of statements that the subjectivist is prepared to endorse and to interpret as expressions of our basic responses. But this reply is useless.

The reason it will not work is that the subjectivist always has something further to say, which does not fit into this framework but is supposed to be a comment on the significance and ultimate basis (in human practices) of the whole thing. And that comment simultaneously contradicts the true content of the original statements of reason, and contradicts itself by being intelligible only as an objective claim not grounded merely in our inescapable responses.

There is a general moral to be drawn from these observations, a moral that applies also to forms of reasoning very different from the simple, self-evident principles we have been considering so far, and it is this: Reflection about anything leads us inexorably to certain thoughts in which "I" plays no part-thoughts that are completely free of first-person content. (This can be understood to include the first person plural for good measure.) Such "impersonal" thoughts are simply misrepresented by any attempt to say that the real ground of their truth or necessity is that we can't help having them, or that this is one of our fundamental and not further grounded responses or practices--to reinterpret or diagnose them in a personal or communal form. 11. And one cannot evade the objection by admitting that such a diagnosis is not stateable within the linguistic practice to which it applies but can be seen to be right nonetheless. On the contrary, we can see that it couldn't be right.

Many thoughts that lack first-person content depend in


11. It is true that Descartes's first step on the road to an objective, impersonal reality is the cogito, a first-person thought which he takes to have objective implications. But the philosophical point of the cogito is not firstpersonal: It is that you cannot stay with the first person. I think he is right even here, but see Bernard Williams criticisms of him on this point: Descartes: The Project of Pure Inquiry ( Penguin, 1978), p. 100.


part on others that have it and that serve as evidence or grounds for the impersonal thoughts. But in explaining how they serve as grounds, one will reach still other thoughts, including those of logic and arithmetic, which are free-standing. While they are had by us, they do not in any way refer to us, even implicitly. It is in this region of impersonal thoughts that do not depend on any personal ones that the operation of reason must be located. Reason, so understood, permits us to develop the conception of the world in which we, our impressions, and our practices are contained, because it does not depend on our personal perspective.

We cannot judge any type of thought to be merely personal except from a standpoint that is impersonal. The aim of situating everything in a non-first-person framework--a conception of how things are--is one to which there is no alternative. But that does not tell us what specific types of thought belong to this finally impersonal domain. What I have said so far is consistent with Kantian idealism, physicalistic realism, or any number of other views. There is no telling in advance whether nearly everything objective rests on a fairly narrow logical base, with everything else coming from particular points of view, or whether great ranges of judgments, including those of ethics and contingent statements about empirical reality, depend on inescapably non-first-person thoughts in their own right.

This is the heart of the issue over the scope of reason, which includes those general forms or methods of impersonal thought, whatever they are, that we reach at the end of every line of questioning and every search for justification, and that we cannot in the end consider merely as a very deeply entrenched aspect of our point of view. I have been discussing particular logical and arithmetical examples, but the real character of reason is not found in belief in a set of "foundational" propositions, nor even in a set of procedures or rules for


drawing inferences, but rather in any forms of thought to which there is no alternative. 12.

This does not mean "no alternative for me," or "for us." It means "no alternative," period. That implies universal validity. The thing to which there is no alternative may include some specific beliefs, but in general it will not have that character. Rather, it will be a framework of methods and forms of thought that reappear whenever we call any specific propositions into question. This framework will be part of even the most general thoughts about our intellectual and linguistic practices considered as psychological or social phenomena. Instead of logic resting on agreement in judgments and usage by members of a community, the agreement, where it exists, has to be explained in terms of the logic whose validity we all recognize.

Again, let me emphasize that I am not talking about a set of unrevisable beliefs (though I believe the simplest rules of logic are unrevisable). The aim of universal validity is compatible with the willingness always to consider alternatives and counterarguments--but they must be considered as candidates for objectively valid alternatives and arguments. It is possible to accept a form of rationalism without committing oneself to a closed set of self-evident foundational truths.


What seems permanently puzzling about the phenomenon of reason, and what makes it so difficult to arrive at a satisfactory attitude toward it, is the relation it establishes between the


12. Cf. David Wiggins's invocation of the idea that "there is really nothing else to think but that p" (that 7 + 5 = 12, for example); Moral Cognitivism, Moral Relativism and Motivating Moral Beliefs, Proceedings of the Aristotelian Society 91 ( 1990-90), pp. 66f.


particular and the universal. If there is such a thing as reason, it is a local activity of finite creatures that somehow enables them to make contact with universal truths, often of infinite range. There is always a powerful temptation to think that this is impossible, and that an interpretation of reason must be found that reduces it to something more local and finite. It therefore may be useful to reflect directly on the employment of reason that gives us our knowledge of infinity itself.

Part of the idea of logical or arithmetical reasoning is that the truths we could ever come to know in this way are only a small sample of the infinity of such truths. The infinite logical space in which known examples are located is given as part of the system of thought that reveals them--a strong case of mind-independence. For example, we know that (x)(y)(3z)(x + y = z), but this is a judgment of reason about an infinite domain that at the same time our procedures of reasoning cannot fill out in detail--though it is a further fact of reason that if iterated often enough, those procedures could reach any true proposition of the form "a + b = c." The existence of truth in mathematics outruns both decision procedures and proof procedures, but even where there is a decision procedure, we cannot apply it to infinitely many cases: Our capacities are not only finite but quite meager. Even where there is no decision procedure, or we don't have one, we may nevertheless be constrained to think that there is a right answer, and methods of trying to get it which are not guaranteed to succeed.

The infinity of the natural numbers is something we come to grasp through our recognition that in a sense we cannot grasp all of it, while at the same time we see that there is something there which we cannot grasp. So we give the set a name, even though we cannot reach all of its members. Once we are able to count at all, we have the basis for realizing that every number has a successor, larger by one. This is easier if we already use a repeating notation for counting, like the


decimal system, which is itself an infinite series; but someone whose numerical language was finite, like an alphabet, could come to see that every number had a successor larger by one, even though he had names for only the first twenty-six of them. (I would guess that infinitely repeating numerical notations were the product, rather than the source, of this insight.)

The idea of infinity would not arise from just any fixed sequence of symbols, such as those used to designate in order the stages of a dance, or the steps that go into building a house. That would not give rise to the idea that every step has a successor. To get that idea, we need to be operating with the concept of numbers as the sizes of sets, which can have anything whatever as their elements. What we understand, then, is that the numbers we use to count things in everyday life are merely the first part of a series that never ends.

This thought is a paradigm of the way reason allows us to reach vastly beyond ourselves. The local, finite practice of counting contains within itself the implication that the series is not completable by us: It has, so to speak, a built-in immunity to attempts at reduction. Though our direct acquaintance with and designation of specific numbers is extremely limited, we cannot make sense of it except by putting them, and ourselves, in the context of something larger, something whose existence is independent of our fragmentary experience of it. Yet we draw this access to infinity out of our distinctly finite ability to count, in virtue of its evident incompleteness. When we think about the finite activity of counting, we come to realize that it can only be understood as part of something infinite. The idea of reducing the apparently infinite to the finite is therefore ruled out: Instead, the apparently finite must be explained in terms of the infinite.

The reason this is a model for the irreducibility of reason in general is that it illustrates the way in which the application of certain concepts from inside overpowers the attempt to grasp that application from outside and to describe it as a


finite and local practice. It may look small and "natural" from outside, but once one gets inside it, it opens out to burst the boundaries of that external naturalistic view. It is like stepping into what looks like a small windowless hut and finding oneself suddenly in the middle of a vast landscape stretching endlessly out to the horizon.

And it is precisely by posing the reductive question that we come to see this. We discover infinity when we ask whether these numbers we can name are all there is, whether we can understand counting as just a finite human practice in which speakers of the language come to relatively easy agreement. From inside the practice itself comes a negative answer: The view from inside dominates the view from outside, unless the latter somehow expands to include a version of the former. (There is an analogy here with the philosophy of mind: An external view of the mental cannot be adequate unless it expands to incorporate in some form the internal view.)


It is natural to want to understand ourselves, including our capacity to reason. But our understanding of ourselves must be part of our understanding of the world of which we form a part. And that means this understanding cannot close over itself completely: We have to remain inside it, and we cannot tell a story about ourselves and our rational capacities that is incompatible with the understanding of the world to which any story about ourselves must belong. The description of ourselves, including our rational capacities, must therefore be subordinate to the description of the world that our exercise of those capacities reveals to us. In particular, the description of what happens when we count must include the relation of that activity to the infinite series of natural numbers, since that is part of what our operation with the concept of number makes evident.


So counting, even small samples of it, must be understood as the application of a successor relation that generates an infinite series. Any external view of the practice that leaves this out or makes it mysterious is thereby shown to be inadequate, by the standards evident from within the practice. From inside, the incompleteness of any finite sequence of natural numbers is an evident logical consequence of the concept of number. That internal view has to be in some way made part of any adequate external view.

This is the general form of all failures of reduction. The perspective from inside the region of discourse or thought to be reduced shows us something that is not captured by the reducing discourse. Behavioristic reductions and their descendants do not work in the philosophy of mind because the phenomenological and intentional features that are evident from inside the mind are never adequately accounted for from the purely external perspective that the reducing theories limit themselves to, under the mistaken impression that an external perspective alone is compatible with a scientific worldview. The internal perspective of consciousness dominates any attempt to subordinate it to the external perspective of physiology and behavior, so the "external" account of the mind must somehow incorporate what is evident from inside it.

The strongest refutations of this sort show that even the reducing discourse itself must presuppose the independent perspective of the ostensibly reduced discourse. For example, phenomenalism--the analysis of all statements about the physical world in terms of actual and hypothetical sense experience--is refuted by the observation that the conditional statements about what perceptual experiences we would have if (for example) we looked in the refrigerator, on which it relies for its analysis of statements about the unperceived contents of the refrigerator, are unintelligible unless explained by nonconditional facts about the external world, by virtue of which they are true.


Still more decisive is the example of Gödel's Incompleteness Theorem, the best antireductionist argument of all time. Mathematical truth cannot be reduced to provability in an axiom system, because, first, the fact that a sentence is or is not provable in a given axiom system is itself a mathematical truth (so the reducing discourse itself presupposes a prior idea of mathematical truth), and second, in such a system, it is possible to construct sentences which assert the mathematical proposition that they are not provable in it.

The moral is that any attempt to account for one segment of our world picture in terms of others must leave us with a total world picture that is consistent with our having it. It cannot include a description of ourselves that is inconsistent with what we know--for example that there are infinitely many natural numbers. And the same test applies to everything else, from psychology to physics to ethics. A proposed reduction in any of these domains must be powerful enough to either accommodate or overcome what we think we know from inside them. It cannot prevail simply because the external view of what organisms like ourselves do can always be presumed to be more objective than the internal one. That is not the case; what appears to external empirical observation is not necessarily a more fundamental part of our knowledge than a priori mathematical reasoning or moral judgment or understanding of what a sentence means. Any reduction of these things to something else must leave us with a more credible world picture than one that keeps them in, unreduced.

We seem to be left with a question that has no imaginable answer: How is it possible for finite beings like us to think infinite thoughts--and even if they take priority over any possible outside view of them, what outside view can we take that is at least consistent with their content? The constant temptation toward reductionism--the explanation of reason in terms of something less fundamental--comes from treating our ca-


pacity to engage in it as the primary clue to what it is. The greatest monument to this temptation is the Kantian project, which tries to explain the mind-independent features of reason and the world in an ultimately mind-dependent form. I think the only way to avoid such subjectivism is to make sure the explanation is in a certain sense circular: that it accounts for our capacity to think these things in a way that presupposes their independent validity. The problem then will be not how, if we engage in it, reason can be valid, but how, if it is universally valid, we can engage in it.

There are not many candidates for an answer to this question. Probably the most popular nonsubjectivist answer nowadays is an evolutionary naturalism: We can reason in these ways because it is the consequence of a more primitive capacity of belief formation that had survival value during the period when the human brain was evolving. This explanation has always seemed to me laughably inadequate. 13. I shall say more about it in chapter 7.

The other well-known answer is the religious one: The universe is intelligible to us because it and our minds were made for each other. We find this not only in its Cartesian form, as an answer to skepticism, but also going in the opposite direction, as an "epistemological" argument for the existence of God--the hypothesis which provides the best explanation of why we can understand the universe by the exercise of our reason. 14. While I think such arguments are unjustly neglected in contemporary secular philosophy, I have never been able to understand the idea of God well enough to see such a theory as truly explanatory: It seems rather to stand for a still unspecified purposiveness that itself remains unex-


13. For reasons I try to explain in The View from Nowhere ( Oxford University Press, 1986), pp. 78-81.
14. A good recent statement of this position is John Polkinghorne, Science and Creation ( New Science Library, 1989).


plained. But perhaps this is due to my inadequate understanding of religious concepts.

Apart from Subjectivism, Evolution, and God, what are the alternatives? One possibility is that some things can't be explained because they have to enter into every explanation. The question "How can human beings add?" is not like the question "How can electronic calculators add?" In ascribing that capacity to a person, I interpret what he does in terms of my own capacity. And since I can't get outside of it, how can I hope to get outside of and explain the corresponding thing in anyone else? To follow a rule is not to obey a natural law. Perhaps there is something wrong with the hope of arriving at a complete understanding of the world that includes an understanding of ourselves as beings within it possessing the capacity for that very understanding.

I think something of the kind must be true. There are inevitably going to be limits on the closure achievable by turning our procedures of understanding on themselves. If that is so, then the outer boundaries of our understanding will always be reached in unqualified, objective reasoning about the real world rather than in the interpretation and expression of our own perspective--personal or social. To engage in such reasoning is to try to bring one's individual thoughts under the control of a universal standard that prescribes to each person those beliefs, available from his point of view, which can form part of a consistent set of objective beliefs dispersed over all rational persons. It enables us all to live in part of the truth.





There is more to reason than logic and mathematics. Subjectivism about logic is directly self-defeating. Subjectivism about other kinds of reasoning can be refuted only by showing that it is in direct competition with claims internal to that reasoning and that in a fair contest, it loses. With respect to science, or history, or ethics, resistance to the external view comes from inside the domains being challenged, though not, as with logic, because they are presupposed by the challenge itself.

Date: 2015-12-24; view: 79

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