A Theory of the A Priori
In the first half of the Twentieth Century many philosophers—for instance, many logical positivists—treated analyticity, necessary truth, and the a priori as equivalent. There are, however, convincing arguments showing that each of these equivalences fails.1 An important corollary is that, even if (as Quineans hold) the notion of analyticity is suspect, it does not follow that modality and the a priori are suspect as well. In this paper I will assume that modality is acceptable. With that starting point, one of my main goals will be to show that the a priori is equally acceptable.
Two other alleged equivalences have been prominent, not just in Twentieth Century epistemology, but throughout the history of epistemology: the alleged equivalence between knowledge and justified true belief, and the alleged equivalence between justification and good evidence (good reasons). Clearly, if these two equivalences held, they would make the tie between knowledge and evidence very close indeed. But Gettier examples convincingly show that good evidence plus true belief is not sufficient for knowledge.2 Furthermore, various reliabilists and coherentists have questioned whether good evidence is even necessary for knowledge. Although that debate continues, there is nevertheless significant agreement that good evidence is at least required for the high grade of theoretical knowledge sought in science, mathematics, and philosophy. It certainly is required for critical understanding. Moreover, even if it should turn out that good evidence is not needed for certain kinds of nontheoretical knowledge (e.g., noninferential knowledge), it is very plausible that a successful general account of evidence would at least provide the explanatory tools needed to account for nontheoretical knowledge.3 This suggests that a promising approach to knowledge in general is through the topic of evidence. In particular, an account of the nature of evidence (reasons) in a priori theorizing should provide the basis for a unified account of a priori knowledge.
The paper will have three parts. First, a brief discussion of our use of intuitions as evidence (reasons) in the a priori disciplines—logic, mathematics, philosophy—and an argument showing that omitting intuitions from one’s body of evidence leads one to epistemic self-defeat. Second, an explanation of why intuitions are evidence. The explanation is provided by modal reliabilism—the theory that there is a certain kind of qualified modal tie between intuitions and the truth.4 Third, an explanation of why there should be such a tie between intuitions and the truth. According to the explanation, the tie does not have a mysterious, or supernatural, source (as perhaps it does in Gödel’s theory of mathematical intuition5); rather, it is simply a consequence of what, by definition, it is to possess—to understand—the concepts involved in our intuitions. Taken together, these three parts form the basis of a unified account of a priori evidence, an account which promises to clarify the relation between the empirical sciences and logic, mathematics, and philosophy (hereafter, ‘the a priori disciplines’).6
Our Standard Justificatory Procedure.
It is truistic that intuitions are used as evidence (or reasons) in our standard justificatory practices.7 For example, in elementary logic, number theory, and set theory. In philosophy, the use of intuitions as evidence is equally ubiquitous. Just recall the Gettier examples, Chisholm’s perceptual-relativity refutation of phenomenalism, the Chisholm-Geach-Putnam refutations of behaviorism, all the various twin-earth examples, Burge’s arthritis example, multiple-realizability, etc., etc. Each of these involve intuitions about whether certain situations are possible and whether relevant concepts would apply. It is safe to say that these intuitions—and conclusions based on them—determine the structure of contemporary debates in epistemology, metaphysics, and philosophy of logic, language, and mind. Clearly, it is our standard justificatory procedure to use intuitions as evidence (or as reasons). This, of course, does not entail that intuitions are evidence; showing that comes later.
By intuition, we do not mean a magical power or inner voice or a mysterious “faculty” or anything of the sort. For you to have an intuition that A is just for it to seem to you that A. Here ‘seems’ is understood, not as a cautionary or “hedging” term, but in its use as a term for a genuine kind of conscious episode. For example, when you first consider one of de Morgan’s laws, often it neither seems to be true nor seems to be false; after a moment's reflection, however, something new happens: suddenly it just seems true. Of course, this kind of seeming is intellectual, not sensory or introspective (or imaginative). For this reason, intuitions are counted as “data of reason” not “data of experience.”
In our context when we speak of intuition, we mean “rational intuition” or “a priori intuition.” This is distinguished from what physicists call “physical intuition.” We have a physical intuition that, when a house is undermined, it will fall. This does not count as a rational intuition, for it does not present itself as necessary: it does not seem that a house undermined must fall; plainly, it is possible for a house undermined to remain in its original position or, indeed, to rise up. By contrast, when we have a rational intuition, say, that if P then not not P, this presents itself as necessary: it seems that things could not be otherwise; it must be that if P then not not P.8
Intuition must also be distinguished from belief: belief is not a seeming; intuition is. For example, there are many mathematical theorems that I believe (because I have seen the proofs) but that do not seem to me to be true and that do not seem to me to be false; I do not have intuitions about them either way. Conversely, I have an intuition—it still seems to me—that the naive truth schema holds; this is so despite the fact that I do not believe that it holds (because I know of the Liar paradox).9 There is a rather similar phenomenon in sensory (vs. intellectual) seeming. In the Müller-Lyer illusion, it still seems to me that one of the arrows is longer than the other; this is so despite the fact that I do not believe that it is (because I have measured them). In each case, the seeming (intellectual or sensory) persists in spite of the countervailing belief.
It should be observed at this point that the existence of the paradoxes suggests that the infallibilist theory of intuition is mistaken: for example, the Liar Paradox shows that either our intuition of the naive truth schema or one or more of our intuitions about classical logic must be mistaken (or misreported).
This brings up a closely related difference between belief and intuition. Belief is highly plastic. Using (false) appeals to authority and so forth, you can get a person to believe almost anything, at least briefly. Not so for intuitions. Although there is disagreement about the degree of plasticity of intuitions (some people believe they are rather plastic; I do not), it is clear that, collectively, they are inherently more resistant to such influences than beliefs.
Similar phenomenological considerations make it clear that intuitions are likewise distinct from judgments, guesses, hunches, and common sense. My view is simply that, like sensory seeming, intellectual seeming (intuition) is just one more primitive propositional attitude.
I should note, finally, that the work of cognitive psychologists such as Wason, Johnson-Laird, Nisbett, Kahneman and Tversky tells us little about intuitions in our sense; these researchers have simply not been concerned with them. In other papers, I have defended the on-balance consistency of our elementary concrete-case intuitions against the attacks of “intuition-bashing” philosophers who think that psychological studies justify their aversion. To be sure, the logical paradoxes and other antinomies have shown that certain intuitions can be inconsistent. But this pales by comparison with a positive fact, namely, the on-balance consistency of our elementary concrete-case intuitions. Indeed, the on-balance consistency of our elementary concrete-case intuitions is one of the most impressive general facts about human cognition. This is all the more impressive when one realizes that most prima facie conflicts among intuitions can be reconciled by well-known rephrasal strategies.10
So far we have seen what intuitions are and that we use them as evidence. But using something as evidence does not show that it really is evidence; for example, simply using astrology charts as evidence for what will happen is hardly enough to make them evidence for what will happen.
One way to show that intuitions are truly evidence is to invoke various concrete-case intuitions about what sorts of things qualify as evidence; a variety of these concrete-case intuitions show straight off that intuitions themselves qualify as evidence. While this direct route is entirely correct, it does not convince the skeptic. To do that, one needs a special form of argument which is designed to persuade on their own terms people who are in the grips of a view which interferes with the effectiveness of ordinary, direct arguments. Self-defeat arguments fall into this category. In “The Incoherence of Empiricism” I gave three distinct self-defeat arguments showing that radical empiricists, who reject intuitions as evidence, end up with a self-defeating epistemology (i.e., an epistemology which, by its very own standards, is not justified).11 To give a feel for this style of argument I will sketch one designed to work specifically against radical empiricists of a Quinean persuasion.12 Bear in mind that non-Quineans might find the other self-defeat arguments more persuasive.
Quineans hold the following three principles:
A person's phenomenal experiences and/or observations comprise the person's evidence.
(ii) The principle of holism.
A theory is justified (acceptable, more reasonable than its competitors, legitimate, warranted) for a person if and only if it is, or belongs to, the simplest comprehensive theory that explains all, or most, of the person's evidence.13
The natural sciences (plus the logic and mathematics needed for them) constitute the simplest comprehensive theory that explains all, or most, of a person's phenomenal experiences and/or observations.
Quineans use these principles to obtain a number of strong negative conclusions. The following is an illustration. From principles (i) and (ii)—the principle of empiricism and the principle of holism—it follows that a theory is justified for a person if and only if it is, or belongs to, the simplest comprehensive theory that explains all, or most, of the person's phenomenal experiences and/or observations. From this conclusion and principle (iii)—the principle of naturalism—it follows that a theory is justified for a person if and only if it is, or belongs to, the natural sciences (plus the logic and mathematics needed for them). It is understood that this is to be the simplest regimented formulation of the natural sciences. By implementing various ingenious techniques of regimentation, Quineans give arguments showing that the underlying logic needed for this formulation of the natural sciences is just elementary extensional logic and, in turn, that no modal propositions (modal sentences) are found in this formulation of the natural sciences. If these arguments are sound, it follows that no modal proposition (sentence) is justified. Indeed, (the sentence expressing) the proposition that modal truths exist does not belong to the simplest regimented formulation of the natural sciences. Given this, it follows that it is unjustified even to assert the existence of modal truths. This, then, is how Quinean empiricism joins forces with naturalism to attack the modalities and modal knowledge.
Quineans mount much the same style of argument to attack analyticities, synonymies, intensional meanings, definitions, definitional truths, property identities, property reductions, and the associated ontology of intensional entities (concepts, ideas, properties, propositions, etc.). For, just as no modal propositions (sentences) belong to the simplest regimented formulation of the natural sciences, neither do propositions (sentences) to the effect that such and such is a definition (definitional truth, analytic, etc.). According to Quineans, the natural sciences on their simplest regimented formulation have no need to include definitions and the special apparatus of intensional logic and/or intensional semantics needed to state them. Likewise for propositions (sentences) about definitional truth, analyticity, synonymy, intensional meaning, property identity, property reduction, and so forth: to explain one's phenomenal experiences and/or observations, one always has a simpler formulation of the natural sciences that avoids these things. Therefore, given principles (i)-(iii), any theory that includes these things is unjustified. Quineans are surely right that principles (i)-(iii) do lead to these negative conclusions. This is extremely plausible when one realizes that, for our radical empiricists, techniques of regimentation need not conform to our intuitions; after all, for them, intuitions have no evidential weight whatsoever.
We are now ready for our argument that radical empiricism, as formulated, is epistemically self-defeating. The principle of holism and the principle of naturalism (or something like them) are quite plausible. Let us agree that some such principles are correct. It is the principle of empiricism that is questionable. For reductio, let us suppose that it too is correct. What is the justificatory status of principles (i)-(iii) themselves?
Notice that these principles contain the familiar terms ‘justified’, ‘simplest’, ‘theory’, ‘explain’, and ‘evidence’. These terms do not belong to the primitive vocabulary of the simplest regimented formulation of the natural sciences. Moreover, given the validity of the Quinean negative arguments, these terms cannot be defined within this formulation of the natural sciences (likewise they cannot be stated to be translations of other expressions; nor can they be stated to express the same properties as; or to be synonyms of—or abbreviations for—other expressions; etc.). The reason is that this formulation of the natural sciences does not contain an apparatus for indicating definitional relationships (or relationships of translation, synonymy, abbreviation, property identity, property reduction, or anything relevantly like them).14 It follows that the radical empiricists' principles (i)-(iii) do not belong to this formulation of the natural sciences and, therefore, that principles (i)-(iii) do not count as justified according to principles (i)-(iii). Hence, this version of empiricism is epistemically self-defeating. Moreover, as I show in “The Incoherence of Empiricism,” various sophisticated efforts to escape this conclusion within the Quinean framework fall prey to the same sort of problem.
As indicated, principles (ii) and (iii) are quite plausible. (Although there are reasonable alternatives to principle (ii), none of them is sufficiently different to enable radical empiricists to escape the self-defeat.) Principle (i) is the problem. If we replace it with the following principle, the problem disappears:
A person’s phenomenal experiences and intuitions comprise the person’s basic evidence.15
Unlike principle (i), this principle admits intuitions as evidence, and it is intuitions that provide the evidence needed to justify various philosophical theories—including, in particular, principles (i'), (ii), and (iii) themselves. In this way, the self-defeat is avoided.
The above self-defeat argument, coupled with certain other self-defeat arguments (including those in “The Incoherence of Empiricism”), lead to the following conclusion. Whoever engages in reflective epistemic appraisal of their beliefs and theories will end up in an epistemically self-defeating position unless they accept intuitions as evidence. Since all of us philosophers, in connection with our pursuit of critical understanding, must engage in such epistemic appraisal, we cannot rationally avoid the thesis that intuitions are evidence.
What explains why intuitions are evidence? In “Philosophical Limits of Scientific Essentialism” I argued that the only adequate explanation is some kind of truth-based (i.e., reliabilist) explanation. In Philosophical Limits of Science I develop these arguments in detail, dealing there with various alternative explanations—pragmatist, coherentist, conventionalist, contextualist, and rule-based (or practice-based). In the present context, I will assume that these arguments are successful and that we must turn to a truth-based explanation. This assumption will appeal to many readers independently of the indicated arguments.
Reliabilism has been associated with analyses of knowledge and justification, analyses which most philosophers today reject. Our topic, however, is not knowledge or justification but rather evidence. This difference is salutary, for here reliabilism is more promising. But not as a general theory of evidence: sources of evidence traditionally classified as nonbasic sources are subject to counterexamples much like those used against reliabilist theories of justification. For example, testimony would still provide an individual with evidence (reasons to believe) even if the individual has been exposed to systematic but undetectable lying. So reliability is not a necessary condition for something’s qualifying as a source of evidence. Nor is reliability a sufficient condition for something’s qualifying as a source of evidence: as in the case of justification, such things as nomologically reliable clairvoyance, etc. are prima facie counterexamples.
The natural response to these counterexamples is to demand just that basic sources of evidence be reliable: something is a basic source of evidence iff it has an appropriate kind of reliable tie to the truth.16 Then we would be free to adopt some alternative treatment of nonbasic sources; for example, something is a nonbasic source of evidence relative to a given subject iff it would be deemed (perhaps unreliably) to have a reliable tie to the truth by the best comprehensive theory based on the subject’s basic sources of evidence.17 If we accept the traditional thesis that phenomenal experience and intuition are our basic sources and that all other sources are nonbasic,18 then the above counterexamples would not fault this analysis of nonbasic sources of evidence. For example, even in the context of systematic undetectable lying, testimony would now rightly be counted as a source of evidence, for the best comprehensive theory based on the individual’s basic sources (phenomenal experience and intuition) would deem it to have a reliable tie to the truth (even if it in fact does not because of the envisaged lying). And in the examples of spurious nonbasic sources (reliable clairvoyance, etc.), if their reliability is not affirmed by the best comprehensive theory based on the individual’s basic sources, their deliverances would rightly not qualify as evidence.
Let us therefore agree that reliabilism should be restricted to basic sources of evidence: something is a basic source of evidence iff it has an appropriate kind of reliable tie to the truth. The fundamental question then concerns the character of this tie. Is it a contingent (nomological or causal) tie? Or is it some kind of necessary tie?
On this account, something counts as a basic source of evidence iff there is a contingent nomological tie between its deliverances and the truth. This account, however, is subject to counterexamples of the sort which faulted the original sufficiency condition above (nomologically reliable clairvoyance, etc.). Consider a creature who has a capacity for making reliable telepathically generated guesses. Phenomenologically, these guesses resemble those which people make in blind-sight experiments. The guesses at issue concern necessary truths of some very high degree of difficulty. These truths are known to the beings on a distant planet who have arrived at them by ordinary a priori means (theoretical systematization of intuitions, proof of consequences therefrom, etc.). These beings have intelligence far exceeding that of our creature or anyone else coinhabiting his planet. Indeed, the creature and his coinhabitants will never be able to establish any of these necessary truths (or even assess their consistency) by ordinary a priori means. Moreover, none of these creatures has any beliefs whatsoever about the superior beings and their intellectual accomplishments. Finally, suppose that the following holds as a matter of nomological necessity: the creature guesses that p is true iff p is one of these necessary truths and the superior beings telepathically induce the creature to guess that p is true when the question arises. But, plainly, guessing would not qualify as a basic source of evidence for the creature, contrary to contingent reliabilism.19 Would you say that, by virtue of just guessing that Fermat’s Last Theorem is true, the creature has evidence (reason to believe) that it is true?!
Given that contingent reliabilism fails, we are left with modal reliabilism, according to which something counts as a basic source of evidence iff there is an appropriate kind of strong modal tie between its deliverances and the truth. This formula provides us with a general scheme for analyzing what it takes for a candidate source of evidence to be basic. It is not itself an analysis: it is not intended that just any strong modal tie be necessary and sufficient for something’s being a basic source of evidence. Rather, this scheme provides us with an invitation to find the weakest natural (non-ad-hoc) modal tie that does the job—that is, the weakest such tie which lets in the right sources and excludes the wrong ones.20 The explanation of why intuition is a basic source of evidence then goes as follows. By definition, a candidate source of evidence is basic iff it has that sort of modal tie; intuition does have that sort of modal tie; therefore, intuition is a basic source of evidence. Likewise for phenomenal experience: it too has that sort of modal tie and so is a basic source of evidence. And we have an explanation of why other candidate sources are nonbasic: they lack that sort of modal tie.
We thus have an invitation to find the weakest non-ad-hoc modal tie that does the job. Clearly, infallibilism is out of the running: it posits too strong a tie. Some form of fallibilism is what is needed. A modal tie with the following characteristics seems to do the job: (1) it holds relative to some suitably good cognitive conditions, (2) it is holistic in character, and (3) it holds, not with absolute universality, but as Aristotle would say “for the most part.” This suggests an analysis along the following lines: a candidate source is basic iff for cognitive conditions of some suitably high quality, necessarily, if someone in those cognitive conditions were to process theoretically the deliverances of the candidate source, the resulting theory would provide a correct assessment as to the truth or falsity of most of those deliverances.21 In our own case, we might not be in the indicated sort of cognitive conditions. But, when we limit ourselves to suitably elementary propositions, then relative to them we approximate such cognitive conditions. For suitably elementary propositions, therefore, deliverances of our basic sources would provide in an approximate way the kind of pathway to the truth they would have generally in the envisaged high-level conditions.
This analysis does the job. It tells us in a natural, non-ad-hoc way what is common to the traditional basic sources of evidence—intuition and phenomenal experience.22 And it tells us what is lacking in all other candidate sources—those which are nonbasic and those which are not even sources of evidence, basic or nonbasic. Moreover, I can think of no natural modal tie that is weaker and still does the job. Finally, although there might be such a tie, it is plausible that it would at least resemble the foregoing.
Of course, the analysis, and others like it, would be vacuous if it were not at least possible for some subjects to be in cognitive conditions of the high quality indicated in the analysis and to arrive at the indicated sort of theory of the deliverances of each basic source—phenomenal experience and intuition. In the case of intuitions, this possibility, and the modal tie to the truth which such a theory would have, is important for the autonomy thesis discussed at the close of the paper.
A shortcoming of traditional empiricism was that it offered no explanation of why phenomenal experience is a basic source of evidence; this was just an unexplained dogma. By the same token, traditional rationalists (and also moderate empiricists who, like Hume, accepted intuition as a basic source of evidence) did not successfully explain why intuition is a basic source of evidence. Modal reliabilism provides a natural explanation filling in these two gaps. The explanation is in terms of the indicated modal tie between these sources and the truth. But why should there be such a tie to the truth? Neither traditional empiricism nor traditional rationalism provided a satisfactory explanation.23 The theory of concept possession promises to fill in this remaining gap.
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