SCIENTIFIC KNOWLEDGE - Reeve, C. D. C.

2.1 Aristotelian Sciences

An Aristotelian science deals with a distinct, non-overlapping genus of beings that have forms or essences.¹ When appropriately regimented, it may be set out as a structure of demonstrations (apodeixeis), the indem-onstrable first principles of which are real (as opposed to nominal) defini-tions of those essences.² More precisely, the first principles special to a science are like this. Others that are common to all sciences, such as the principle of non-contradiction, have a somewhat different character (9.4).

Since all these first principles are necessary, and demonstration is necessity preserving, scientific theorems are also necessary.

Though we cannot grasp a first principle by demonstrating it from yet more primitive principles, it must—if we are to have any unqualified scientific knowledge at all—be “better known” than any of the science’s other theorems (EN VI 3 1139^b33–34). This better knowledge is provided by understanding (nous) and the process by which principles come within understanding’s ken is induction—epagôgê (1139^b28–29, 6 1141â7–8).³ Induction begins with perception of particulars, which in turn gives rise to retention of perceptual contents, or memory. When many perceptual contents have been retained in memory, we “come to have an account out of the retention of such things” (APo. II 19 100â1–3). Craft and science

1 APo. I 7 75^b17–20, 11 77â26–32, 23 84^b13–18, 28 87â38–39, 32 88â30–^b3;

Met. IV 2 1003^b19–21.

2 Sorabji, “Definitions: Why Necessary and in What Way?”

3 Aristotle’s canonical account of this process is given in APo. II 19. More compressed versions appear in Ph. I 1 and Met. I 1. Bolton, “Aristotle’s Method in Natural Science: Physics I,” carefully compares these three accounts, arguing per-suasively that they use “the same unusual language . . . to say the same thing.”

arise from experience, which is a unified set of such memories (100^a3–6),

“when, from many notions gained by experience, one universal supposi-tion about similar objects is produced” (Met. I 1 981^a1–7). Getting from particulars to universals, therefore, is a largely noninferential and epistemo-logically unproblematic process. If we simply attend to particular cases—

perhaps to all, perhaps to just one—and have some acumen (agchinoia), we will get there.⁴

The transition from experience to craft or science results in the grasp of universals, but so too does the earlier transition from memory to experi-ence: “To have a supposition that when Callias was ill of this disease, this did him good, and similarly in the case of Socrates, and in many other such cases, is a matter of experience. But to have a supposition that it has done good to all persons of a certain sort, marked off in a class, when they were ill of this disease, e.g., phlegmatic or bilious people when burning with fever, this is a matter of craft knowledge” (Met. I 1 981^a7–12). For recognizing a multiplicity of people as belonging to a single class, and a single type of treatment as having benefited all of them, clearly requires some grasp of universals. What the experienced lack, therefore, is not a grasp of universals generally, but a grasp of the special sort of universals required for scientific explanation—they “know (isasi) the that, but they do not know the why, while others [scientists] know the why, i.e., the cause” (981^a28–30). That is why they cannot provide the sort of formal instruction typically found in a craft or science: “In general it is a sign of the one who knows that he can teach, and therefore we think that craft is scientific knowledge to a higher degree than experience is; for the former [someone who knows] can teach and the latter [someone with mere experience] cannot” (981^b7–10).

The following text provides important insight into these two types of universals, and what moving from one to the other involves:

APo. II 19 100^a15–^b5 When [^a15] one of the undifferentiated items makes a stand, then for the first time there is a universal in the soul; for although one perceives particulars, perception is of universals—e.g., of man and not of Callias the man. Next, [^b1] a stand is made among these items, until something partless and universal makes a stand.

E.g., such-and-such an animal makes a stand, until animal does; and with animal a stand is made in the same way. Thus it is clear that we

4 APr. II 23 68^b15–29 (all); APo. I 31 88^a12–17, II 2 90^a24 –30 (one); APo. I 34 89^b10–13 (acumen).

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must get to know the first principles by induction; for this is the way in which perception instills universals.

The undifferentiated item that makes the stand referred to in â15 is “the entire (pantos) universal” (APo. II 19 100â6–7). In Physics I 1, where it is called “the whole (holon) universal” (184â25), it is characterized as “inde-terminate” and “better known in perception” (184â21–26). This is the sort of universal, therefore, that perception is “of ” (â15). When such undifferentiated or indeterminate universals are analyzed into their “ele-ments (stoicheia) and first principles,” they become intrinsically clear and unqualifiedly better known than their perceptible predecessors (184â16–

21). These elements and principles are the “partless” items that make the stand referred to in ^b1.

It is clear from this account of induction that first principles come in two varieties: ontological first principles or essences, which are fundamental causal factors in the world; and epistemic first principles, principles of our scientific knowledge of the world, which are accounts or definitions of these essences. Aristotle is not always careful to distinguish these. For example, he speaks of Socrates as not separating “the definitions,” when it is the essences that are their ontological correlates to which he is referring (Met. XIII 4 1078^b30–31). Such carelessness becomes at once intelligible and innocuous, however, when we recall that Aristotle is a realist about definition, as about truth, who requires a structural isomorphism between definiens and definiendum: “the definition is an account, and every ac-count has parts, and as the acac-count is to the thing, so the part of the account is to the part of the thing” (10 1034^b20–22).⁵

Like the step from memory to undifferentiated universals, the step from the latter to analyzed universals is itself inductive (APo. II 19 100^b3– 4).

Thus induction includes two rather different sorts of processes: the broadly perceptual (and somewhat physiologically conceived) one by which we reach unanalyzed universals from the perception of particulars, and the other, more intellectual and discursive one, by which we proceed from unanalyzed universals to analyzed ones and their definitions. When Aris-totle characterizes Socrates’ elenctic method as inductive (Met. XIII 4 1078^b28–29), it is presumably the latter process he has in mind.

The inductive path to first principles and scientific knowledge begins, then, with perception of particulars and of perceptually accessible, un-analyzed universals, and leads eventually to un-analyzed universals (first

prin-5 Also Cat. 12 14^b14 –22; Met. II 1 993^b30–31, IV 7 1011^b26–28.

ciples) and accounts (definitions) of them. Perception alone, unaided by understanding, cannot reach the end of this journey, therefore, but under-standing without experience cannot so much as begin it (APr. I 30 46^a17–

18, DA III 8 432^a7–9).

2.2 Dialectic and First Principles

Because the first principles proper to a science “are primary among all [the truths contained in it],” they cannot be demonstrated within that science.

They can, however, be defended by dialectic. For, since it “examines,” and does so by appeal not to scientific principles per se but to endoxa, dialectic

“provides a way to the first principles of all lines of inquiry” (Top. I 2 101^a36–^b4). In due course, we shall see what that way is. First, though, we need to understand what dialectic utilizes on the journey.

Endoxa are opinions that are accepted without demurral “by everyone or by the majority or by the wise, either by all of them or by most or by the most notable and reputable” (Top. I 1 100^b21–23), so that the many do not disagree with the wise about them, nor do “one or the other of these two classes disagree among themselves” (I 10 104^a8–11). Endoxa, therefore, are beliefs to which there is simply no worthwhile opposition (I 11 104^b19–

28). Merely apparent endoxa, by contrast, are opinions that mistakenly appear to have this uncontested status (I 1 100^b23–25, 10 104^a15–33).

Defending first principles on the basis of endoxa is a matter of going through the problems (aporiai) “on both sides of a subject” until they are solved (Top. I 2 101^a35). Suppose, for example, that the topic for dialectical investigation is this: Is being one and unchanging, or not? A competent dialectician will, first, follow out the consequences of each disjunct to see what problems they face. Second, he will go through the problems he has uncovered to determine which can be solved and which cannot (VIII 14 163^b9–12). As a result he will be well placed to attack or defend either disjunct in the strongest possible way.

Aporematic, which is the part of philosophy that deals with such prob-lems, is like dialectic in its methods, but differs from it in important respects. In a dialectical argument, for example, the opponent may refuse to accept a proposition that a philosopher would accept: “The premises of the philosopher’s deductions or those of the one investigating by himself, though true and familiar, may be refused by . . . [an opponent] because they lie too near to the original proposition, and so he sees what will happen if he grants them. But the philosopher is unconcerned about this.

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Indeed, he will presumably be eager that his axioms should be as familiar and as near to the question at hand as possible, since it is from premises of this sort that scientific deductions proceed” (Top. VIII 1 155^b10–16).⁶ Since the truth may well hinge on propositions whose status is just like these premises, there is no guarantee that what a dialectician might con-sider most defensible for the purposes of dispute will be true.

Drawing on this new class of endoxa, then, the philosopher examines both the claim that being is one and unchanging, and the claim that it is not, in just the way that the dialectician does. As a result, he determines, let us suppose, that the most defensible, or least problematic, conclusion is that in some senses of the terms being is one and unchanging, in others not. To reach this conclusion, however, he will have to disambiguate and reformu-late endoxa on both sides, partly accepting and partly rejecting them (Top.

VIII 14 164^b6–7). Others he may well have to reject outright. If so, some beliefs that initially seemed to be endoxa, that seemed to be unproblematic, will have emerged as only apparently such (I 1 100^b23–25). These he will have to explain away: “We must not only state the true view, but also give the explanation for the false one, since that promotes confidence. For when we have a clear and good account of why a false view appears true, that makes us more confident of the true view” (EN VII 14 1154^a22–25).

If, at the end of this process “the problems are solved and the endoxa are left, that,” Aristotle claims, “will be an adequate proof ” of the philoso-pher’s conclusion (1 1145^a6–7).

But in that claim lies a problem. For while dialectic treats things “only in relation to opinion,” philosophy must treat them “according to their truth” (Top. I 14 105^b30–31). Endoxa, however, are just opinions accepted without demurral by “everyone, or by the majority, or by the wise.” Since even such unopposed beliefs may nevertheless be false, how can an argu-ment that relies on them be guaranteed to reach the truth? The answer lies in peirastic (peirastikˆe)—in aporematic philosophy’s dialectical capacity to examine (I 1 101^b3).

Peirastic is “a type of dialectic which has in view not the person who knows but the one who pretends to know, but does not” (SE I 11 171^b4 – 6). In other words, it is the type especially useful in dealing with sophists (I 1 165^a21). We may best understand how it operates, and what it accom-plishes, however, by exploring sophistical refutations, which are its evil twin. For whereas peirastic exposes the genuine ignorance of someone

6 Also APr. I 30 46^a3–10; Top. I 14 105^b30–31.

who pretends to scientific knowledge, sophistical refutations give the ap-pearance of exposing the ignorance of someone who really does have such knowledge (I 6 168^b4 –10).

Sophistical refutations come in two varieties: an a-type, which is “an apparent deduction or refutation rather than a real one,” and a b-type, which is “a real deduction that is only apparently proper to the subject in question” (SE I 8 169^b20–23). Thus, while a-type sophistical refutations are invalid or eristic arguments, b-type are closely akin to paralogisms (I 11 171^b34 –37).

The paralogisms proper to a science are those based on its first princi-ples and conclusions (Top. I 11 171^b36–37). For example, someone who squares the circle by means of lunes produces a geometrical paralogism, since he “proceeds from principles that are proper to geometry” and

“cannot be adapted to any subject except geometry” (172^a4 –5).⁷ But someone who uses Bryson’s method of squaring the circle,⁸ or who uses Zeno’s argument that motion is impossible in order to refute a doctor’s claim that it is better to take a walk after dinner, has produced a b-type sophistical refutation. For Bryson’s and Zeno’s arguments are not proper to geometry or medicine but “common” (172^a8–9). Such arguments are paralogistic, moreover, even if they are sound: “Bryson’s method of squar-ing the circle, even if the circle is thereby squared, is still sophistical because it is not in accord with the relevant subject matter” (171^b16–18). Hence the difference between paralogisms and b-type sophistical refutations is that the former have premises proper to the relevant science but false, whereas the latter have premises that are not proper to it but true.

Because paralogisms depend on premises proper to a science, it is the business of the practitioner of that science to diagnose and refute them. It is not his business to deal with b-type sophistical refutations, however, since these depend on common things (koina). For “it is dialecticians who study a refutation that depends on common things, i.e., do not belong to any [special] craft” (SE I 9 170^a38–39). What these common things are, as this text suggests, are transcategorial attributes, such as being, unity, similarity, and so on, as well as such logical axioms as the principle of non-contra-diction, which, because they hold of beings in all genera, cannot be the

7 An argument of this sort, due to Hippocrates, is described in Heath, A History of Greek Mathematics Vol. 1, 183–201.

8 It is difficult to say just what this method amounted to. See Heath, A History of Greek Mathematics Vol. 1, 223–225.

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subject matter of a science that is, by its very nature, restricted to a single genus (2.1).⁹ Since these attributes and principles are not proper to a science, endoxa about them cannot be proper to it either.

For the same reason dialecticians must also deal with a-type sophistical refutations, such as Antiphon’s argument for squaring the circle. For this argument assumes that a circle is a polygon with a very large (but finite) number of sides. As a result, it “does away with the first principles of geometry” (Ph. I 2 185^a1–2)—specifically, the principle that magnitudes are divisible without limit.¹⁰ Consequently, it cannot be discussed in a way that presupposes that principle, and so must be discussed on the basis of endoxa (Top. I 2 101^a37-^b4).

Since what makes b-type sophistical refutations sophistical, then, is just the fact that they employ endoxa that aren’t proper to a science as if they were proper to it, we should expect that peirastic arguments will differ from them simply in having endoxa as premises that are in fact proper to it.

Aristotle’s somewhat opaque characterization of peirastic deductions con-firms this expectation. For these, he says, “deduce from premises that are accepted by the answerer [i.e., the one being examined], and that must be known (eidenai) by anyone who claims to have the [relevant] scientific knowledge (epistêmê)” (SE I 2 165^b4 –6). Such premises are “taken not from the things from which one knows (oiden),” he says, “or even from those proper to the subject in question, but from the consequences that a man can know (eidota) without knowing (eidenai) the craft in question, but which if he does not know (eidota), he is necessarily ignorant of the craft” (I 11 172â21–34). In other words, they are not first principles of the relevant science—not “things from which one knows”—or other principles proper to it, but “consequences” of them.

9 When the common things are logical axioms they are sometimes referred to as

“common opinions” (Met. III 2 996^b28, 997^a21), which makes them sound like endoxa (as I too hastily took them to be in “Dialectic and Philosophy in Aristotle”).

But Met. IV 3 1005^a27–28 makes it plain that these axioms are common because they hold in common of all things that share the transcategorial attribute being, and not because they are held in common by all people: “it is clear that it is qua being that these things [the logical axioms] hold of all things (since this [viz., being a being] is what is common to [all of ] them).” Some people, after all, do deny even the principle of non–contradiction (9.3). Nonetheless, koina and endoxa are closely related.

10 Heath, A History of Greek Mathematics Vol. 1, 221–222, citing Simplicius.

Later in the same passage these consequences are identified as endoxa:

“everybody, including those that do not possess a craft, makes use of dialectic as peirastic; for everyone tries to use peirastic to some extent in order to test those who claim to know things. And this is where the common things come in; for the testers know (isasin) these things for themselves just as well as those who do possess the craft—even if they seem to say quite inaccurate things” (SE I 11 172^a30–34). Hence, as we were led to expect by our investigation of b-type sophistical refutations, the prem-ises of peirastic arguments are indeed endoxa proper to the science that the one undergoing peirastic examination is claiming to know.

Peirastic premises can be known (eidenai, isasin) by someone who lacks scientific knowledge (epistˆemˆe), then, and are consequences of the princi-ples of a science. It follows that they are true, and potentially objects of scientific knowledge—a potential that would be realized if they were in fact demonstrated from first principles. Since such premises are endoxa, it follows that some endoxa also have these features. But why do endoxa have to have them in order to serve as peirastic premises?

A person who really does have scientific knowledge may yet be the victim of a sophistical refutation—he may find himself caught in a con-tradiction when he is interrogated by a clever sophist. The mere fact that someone can be bested in this way, therefore, is not enough to show that he lacks scientific knowledge. What is further required is, first, that this argu-ment not be a sophistical refutation, that its premises be true and proper to the science in question. But even that is not enough. For, second, they must also be premises that anyone who knows that science would have to know. Otherwise, an examinee could reject them and still know the sci-ence. Third, they must be premises it is possible to know without knowing the science. Otherwise, they could not figure in arguments available to nonscientists. Thus the various features that the premises of a peirastic argument must have are entailed by the purpose such arguments are in-tended to serve of enabling nonscientists to unmask the ignorant pretender to scientific knowledge.

As a generally educated person, the aporematic philosopher knows what it takes to be a genuine science of whatever sort: “In every study and investigation, humbler or more honorable alike, there appear to be two kinds of competence. One can properly be called scientific knowledge of the subject, the other as it were a sort of educatedness. For it is the mark of an educated person to be able to reach a judgment based on a sound

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