INTRODUCTION

By means that meet the standards of nominalism set by Nelson Goodman (in [1], section II, 3; and in [2]) we can define relations that behave in many ways like the membership relation of set theory. Though the agreement is imperfect, these pseudo-membership relations seem much closer to membership than to its usual nominalistic counterpart, the part-whole relation. Someone impressed by the diversity of set theories might regard the theories of these relations as peculiar set theories; someone more impressed by the non-diversity of the more successful set theories – ZF and its relatives – might prefer not to. This verbal dispute does not matter; what matters is that the gap between nominalistic and set-theoretic methods of construction is narrower than it seems.

PRELIMINARIES

A finitistic nominalist's world might consist of an enormous hypercubical array of space-time points, together with all wholes composed of one or more of those points. Each point in the array is next to certain others; nextness is a symmetric, irreflexive, intransitive relation among the points. We can (but the nominalist cannot) describe the array of points and the nextness relation more precisely by stipulating that the points can be placed in one-to-one correspondence with all the quadruples 〈x, y, z, t〉 of non-negative integers less than or equal to some very large integers xmax, ymax, zmax, tmax, respectively in such a way that one point is next to another iff the corresponding quadruples are alike in three coordinates and differ by exactly one in the remaining coordinate.

RADICAL EMPIRICISM AND SKEPTICISM

The conclusion of the preceding chapter was that the moderate empiricist approach to a priori justification does not succeed. Moderate empiricism turns out on examination to be in effect a mere schema for a position, one that is apparently incapable of being satisfactorily fleshed out into a realized view and that owes most of its initial appeal to this schematic character (and, I have suggested, to a pervasive failure to distinguish clearly between the various attempted realizations thereof).

What alternative then is left for the empiricist? The answer is both stark and obvious: if a priori justification cannot be accommodated within the empiricist framework in the way that the moderate empiricist attempts, then it must apparently be repudiated outright if empiricism is to be sustained. Such a course would have had very little appeal to most of the historical advocates of empiricism, with the single, somewhat problematic exception of Mill, but it has been seriously advocated in recent times, mainly by Quine and his followers. While this Quinean view seems to me very difficult to take seriously, the present chapter will be devoted to an attempt to understand and evaluate it.

Though it is not always so regarded, radical empiricism as thus understood is of course a form of skepticism, indeed seemingly one of the deepest and most threatening forms of skepticism.

This collection reprints almost all my previously published papers in philosophical logic, except for those that were previously reprinted in another collection, Philosophical Papers. Still omitted are (1) two papers in deontic logic; (2) a paper on counterfactual logic, which is superseded by proofs later published in my book Counterfactuals; and (3) two papers on immodest inductive methods, the first of them completely mistaken and the second one concerned with loose ends left over when the first was rebutted. I have taken the opportunity to correct typographical and editorial errors. But I have left the philosophical content as it originally was, rather than trying to rewrite the papers as I would write them today. A very few afterthoughts have been noted in new footnotes.

The first four papers have to do with the project of transplanting the methods of formal semantics from artificial formalized languages to natural languages, or to formalized approximations thereof. ‘Index, Context, and Content’ is a meta-theoretical paper, arguing that some supposedly competing formulations are no more than notational variants. The other three study particular constructions. ‘Adverbs of Quantification’ examines a neglected part of the quantificational apparatus of ordinary English: sentential adverbs like ‘always’, sometimes, ‘often’, et al. (I first became interested in these adverbs as a means to making my own technical writing more concise. Only afterward did it occur to me that they afforded a treatment of a class of problematic sentences in which it seemed that there was no satisfactory way to assign relative scopes to quantifier phrases.)

INTRODUCTION

Carnap's Aufbau sketches a remarkably ambitious construction. Given just one primitive phenomenal relation, he seeks to define enough concepts to provide a language adequate for all of science.

The constructed concepts are supposed to be coextensive with certain familiar ones. The Aufbau is commonly dismissed as a failure because discrepancies would appear under unfavorable circumstances. That verdict is premature. If there are few discrepancies under actual circumstances, the constructed concepts might be just as adequate for science as the familiar ones they approximate and replace. A mere chance of discrepancies is too bad, but not fatal. It would take frequent discrepancies to spoil the construction, by Carnap's own standards of success. The frequency has not been much investigated – understandably so; the needed computing power has become available only lately. Therefore it remains an open question whether the Aufbau succeeds or fails on its own terms.

If the original construction gives too many discrepancies, perhaps a more elaborate version would work better. The version presented, after all, is tentative; indeed it serves mostly as an illustration for Carnap's general discussion of logical constructions. There is plenty of room for improvement.

In particular, there are unexploited opportunities to police the construction. Spurious instances of a constructed concept, instances which do not fall under the familiar concept being approximated, often turn out to behave strangely later in the construction. Thereby they may be recognized as suspect and removed.

SYNOPSIS

If a grammar is to do its jobs as part of a systematic restatement of our common knowledge about our practices of linguistic communication, it must assign semantic values that determine which sentences are true in which contexts. If the semantic values of sentences also serve to help determine the semantic values of larger sentences having the given sentence as a constituent, then also the semantic values must determine how the truth of a sentence varies when certain features of context are shifted, one feature at a time.

Two sorts of dependence of truth on features of context are involved: context-dependence and index-dependence. A context is a location – time, place, and possible world – where a sentence is said. It has countless features, determined by the character of the location. An index is an n-tuple of features of context, but not necessarily features that go together in any possible context. Thus an index might consist of a speaker, a time before his birth, a world where he never lived at all, and so on. Since we are unlikely to think of all the features of context on which truth sometimes depends, and hence unlikely to construct adequately rich indices, we cannot get by without context-dependence as well as index-dependence. Since indices but not contexts can be shifted one feature at a time, we cannot get by without index-dependence as well as context-dependence.

THE NEED FOR THE A PRIORI

Perhaps the most pervasive conviction within the Western epistemological tradition is that in order for a person's belief to constitute knowledge it is necessary (though not sufficient) that it be justified or warranted or rationally grounded, that the person have an adequate reason for accepting it. Moreover, this justifying reason must be of the right sort: though one might accept a belief for moral reasons or pragmatic reasons or religious reasons or reasons of some still further sort and be thereby in a sense justified, such reasons cannot satisfy the requirements for knowledge, no matter how powerful, in their own distinctive ways, they may happen to be. Knowledge requires instead that the belief in question be justified or rational in a way that is internally connected to the defining goal of the cognitive enterprise, that is, that there be a reason that enhances, to an appropriate degree, the chances that the belief is true. Justification of this distinctive, truth-conducive sort will be here referred to as epistemic justification.

Historically, most epistemologists have distinguished two main sources from which the epistemic justification of a belief might arise. It has seemed obvious to all but a very few that many beliefs are justified by appeal to one's sensory (and introspective) experience of the world.

In [4] I offered an analysis of what it means to be (entirely) about a subject matter. I first repeat that analysis. Then I define several relations of relevance, for instance, between the premise and conclusion of an implication. I show that whenever a premise implies a conclusion, in the ordinary sense of truth-preservation, then also the premise is relevant to the conclusion in the sense of the present analysis. Pace Anderson and Belnap [1], there can be no such thing as a truth-preserving “fallacy of relevance”. Finally I remark that this does not by any means do away with all motivations for relevant logic.

SUBJECT MATTERS

We can think of a subject matter, sometimes, as a part of the world: the 17th Century is a subject matter, and also a part of this world. Or better, we can think of a subject matter as a part of the world in intension: a function which picks out, for any given world, the appropriate part – as it might be, that world's 17th Century. (If for some reason the world had no 17th Century, the function would be undefined.) We can say that two worlds are exactly alike with respect to a given subject matter. For instance two worlds are alike with respect to the 17th Century iff their 17th Centuries are exact intrinsic duplicates (or if neither one has a 17th Century).

This being exactly alike is an equivalence relation.

My aim in this book is to explain and defend a rationalist conception of a priori justification and knowledge: a view according to which there is genuine a priori justification that is not limited in its scope to tautologies or matters of definition. Though taken largely for granted throughout most of the history of philosophy, such a view has fallen into increasing disrepute in the last two centuries and has been generally repudiated in recent times. Nonetheless, as explained further in Chapter 1, it is arguably difficult or impossible to make good sense of most if not all claims of empirical knowledge, and indeed of reasoning generally, while eschewing any a priori appeal. What this indicates, I think, is that the prevailing forms of empiricism are in fact untenable, and that a re-examination of rationalism is sorely needed.

Though this book is not primarily meta-philosophical in character, the need for an account of genuine and non-tautological a priori justification seems to me especially urgent for philosophy itself. While it is not my purpose to argue the matter in detail here, my conviction is that philosophy is a priori if it is anything (or at least if it is anything intellectually respectable); and that the practice of even those who most explicitly reject the idea of substantive a priori justification inevitably involves tacit appeal to insights and modes of reasoning that can only be understood as a priori in character, if they are justified at all.

INTRODUCTION

Our discussion of a priori justification so far has been in the main relentlessly abstract, with only a few of the most obvious examples to enliven the way. While this seems to me appropriate where it is the very existence of non-tautological a priori justification that is at issue, it does leave the issue of the scope of a priori justification almost entirely unillumined. For all that has been argued so far, it would be possible that a priori justification of the rationalist kind, though genuinely existent, is confined entirely to the general kinds of examples discussed in §4.2. And if this were so, then such justification, though perhaps important in these limited areas, would have little significance for human knowledge in general and would in particular do almost nothing to solve the problem of observation-transcendent inference raised in §1.1. Radical empiricists would indeed be mistaken in their central claim, but their error would be of little consequence; their general epistemological position would still be closer to the truth than that of the rationalist in the ways that matter most.

My conviction is that, on the contrary, rationalistic a priori justification is of crucial importance for epistemology and indeed for philosophy generally.

J. R. Lucas serves warning that he stands ready to refute any sufficiently specific accusation that he is a machine. Let any mechanist say, to his face, that he is some particular machine M; Lucas will respond by producing forthwith a suitable Gödel sentence φM. Having produced φM, he will then argue that – given certain credible premises about himself – he could not have done so if the accusation that he was M had been true. Let the mechanist try again; Lucas will counter him again in the same way. It is not possible to accuse Lucas truly of being a machine.

I used to think that the accusing mechanist interlocutor was an expository frill, and that Lucas was really claiming to be able to do something that no machine could do. But I was wrong; Lucas insists that the interlocutor does play an essential role. He writes that “the argument is a dialectical one. It is not a direct proof that the mind is something more than a machine; but a schema of disproof for any particular version of mechanism that may be put forward. If the mechanist maintains any specific thesis, I show that a contradiction ensues. But only if. It depends on the mechanist making the first move and putting forward his claim for inspection.” Very well. I promise to take the dialectical character of Lucas's argument more seriously this time – and that shall be his downfall.

INTRODUCTION

The main conclusion of the preceding chapter was that the distinctively epistemological objections to rationalism, while perhaps not entirely without force, are very far from being decisive. Indeed, it is more natural to construe the epistemological objections, taken as a group, as merely revealing various limitations of our a priori capacities. These limitations are no doubt unfortunate, but they cannot plausibly be construed as serious reasons for taking the quixotic step of abandoning rational thought altogether, or at least any claim of cogency on its behalf – which is what we have seen that the rejection of rationalism would amount to.

In any case, though such a conjecture would be impossible to verify, it seems to me likely that the reasons for the widespread dismissal of rationalism lie on the metaphysical rather than the epistemological side of the ledger. I have already voiced the suspicion that the intellectual motives for the rejection of rationalism lie more in the realm of fashion than of argument, but even the relevant fashions seem primarily metaphysical in character. My purpose in this chapter is to examine and evaluate some of these metaphysical fashions and objections.

As was the case with the epistemological objections, the metaphysical objections to rationalism are only rarely spelled out and developed in any detail.

INTRODUCTION

The argument of the previous chapters leads to the striking or perhaps even startling conclusion that empiricist positions on a priori justification and knowledge, despite their apparent dominance throughout most of the twentieth century, are epistemological dead ends: the moderate empiricist attempt to reconcile a priori justification with empiricism by invoking the concept of analyticity does not succeed, indeed does not really get off the ground; and the radical empiricist attempt to dispense entirely with such justification ends in a nearly total skepticism. The indicated conclusion is that a viable non-skeptical epistemology, rather than downgrading or rejecting a priori insight, must accept it more or less at face value as a genuine and autonomous source of epistemic justification and knowledge. This is the main thesis of epistemological rationalism and also the central thesis of the present book.

Obviously, however, such a result can be no more than tentative until the rationalist view has been explored more fully and shown to be defensible. For even if the objections to the two positive empiricist views are indeed decisive, as claimed here, the possibility remains that the negative empiricist claim is correct: that a priori justification as understood by the rationalist simply does not exist.