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Sunday, March 13, 2022

This is the third in a series of posts about Locke’s theory of space.

Having raised, in the first post, a question about the qualitative constraints on the modes of space, I pointed out, in the second post, that such constraints can in principle be derived from constraints on the possible behavior of bodies in motion. In particular, I examined one of Thābit ibn Qurra’s proofs of the parallel postulate — a proof based on the principle that, when a solid body moves in a single direction, every point in the body moves along a straight line. Here I intend to show that Locke considers the principle in question (which I called “Thābit’s axiom”) to be an intuitively certain truth about bodies: considers it, that is, to be a fundamental truth of rational physics. I will also make a start at showing how Locke can use this principle to derive geometrical results.

This principle: but I ought to say, rather, instances of this principle. Highly abstract universal axioms such as this — in Locke’s terminology, “maxims” — don’t, according to him, themselves play any useful role in our demonstrations. To see why, we need to remember (1) what Locke thinks is the end of demonstration and (2) when and how he thinks demonstration is the right means to that end.

As to (1), the answer is deceptively obvious: the end of demonstration is knowledge. This seems so unobjectionable as to be not worth saying, until you realize just how seriously it is meant. Locke himself (like Spinoza) often introduces such deceptively obvious propositions — the most pertinent example here would be, that knowledge is conversant about ideas (4.1.1) — and he relies implicitly on this one, as well. Such propositions may even be “trifling”: that every demonstration aims to produce knowledge is probably supposed to follow from the definition Locke would give of the word “demonstration.” When we realize, to our surprise, what follows from taking them seriously, they are serving the proper purpose of trifling propositions, namely “to shew the Disingenuity of one, who will go from the Definitions of his own Terms, by reminding him sometimes of it” (4.8.5). Our surprise exposes our covert disingenuity: the definition we were prepared to accept was out of line with the consequences we were prepared to draw. It is always possible, indeed, that our error was in accepting the definition, and this technique, whether in Locke’s hands or in others’ — for example, in Socrates’ — may even have the aim of making us reject what seemed trifling as after all false. With some hesitation, however, I judge that in this case, and in many others, Locke’s aim is more direct. We are supposed to accept, or rather to realize that we have already accepted, the surprising consequences, which here include: that a demonstration is useless to anyone who already knows the conclusion, that is, perceives with certainty that the conclusion is true. This is why Locke thinks it clear that, if there are propositions such that everyone, upon entertaining them at all, instantly and certainly perceives their truth, then there can never be any use in demonstrating them:

He would be thought void of common Sense, who asked on the one side, or on the other side, went to give a Reason, Why it is impossible for the same thing to be, and not to be. It carries its own Light and Evidence with it, and needs no other Proof: He that understands the Terms, assents to it for its own sake, or else nothing will ever be able to prevail with him to do it. (1.3.4)[1]×Hamilton (Dissertations on Reid, Note A, p. 784b) takes Locke to be admitting here that “Common Sense or intellect, as the source, is the guarantee of the principle of contradiction.” This is an example of the unfortunate carelessness in interpretation that makes Hamilton’s formidable erudition so much less useful that one might hope. For, first of all, what common sense guarantees here is not the principle of contradiction, but rather the proposition I have been discussing, namely that demonstration presupposes doubt — which proposition is, as I have noted, probably “trifling,” according to Locke. That is: “common sense” in this place reveals no theoretical content. Furthermore, Locke does not regard this kind of maxim (maximally general proposition: see Hamilton’s own discussion of this term, pp. 766b–768a, misunderstanding Locke’s use of it at 767b) as a principle, that is, as a beginning point of knowledge. However, it is true that Locke thinks this maxim and all its instances (e.g. “Sweet is not bitter” and “A rod is not a cherry”) are not trifling and that they are intuitive, that is, perceived certainly to be true once proposed. Only, they cannot be proposed until we acquire, from experience, the ideas therein related. So, in Kant’s terminology: they are all synthetic a priori, but not pure a priori.

A demonstration, therefore, always occurs in the context of willing to know something which we do not, as yet, know, which is to say, in the context of doubt: “before the Demonstration there was a doubt” (4.2.5).

As to (2), then: given that knowledge is certain perception of the agreement or disagreement of ideas, the context of demonstration must be one in which ideas can be perceived without a perception of their agreement or disagreement: a context, that is, in which we do not have intuitive knowledge of the agreement or disagreement of the ideas in question, “where the Ideas themselves, by an immediate View, discover their Agreement or Disagreement one with another” (4.1.9). For without a perception of the ideas themselves, I could not will to perceive their agreement or disagreement; but if I already perceived that agreement or disagreement, there would be no doubt which a demonstration might resolve. But how is it possible to perceive two ideas clearly and yet not perceive whether they agree or disagree? For this Locke turns to just such a geometrical example as we have been discussing:

Thus the Mind being willing to know the Agreement or Disagreement in bigness, between the three Angles of a Triangle, and two right ones, cannot by an immediate View and comparing them, do it: Because the three Angles of a Triangle cannot be brought at once, and be compared with any one, or two Angles; and so of this the Mind has no immediate, no intuitive Knowledge. (4.2.2)

What allows doubt in this case — being willing to know, but not knowing — is that the two ideas in question can’t be directly compared. If they could be directly compared, on the other hand, then the agreement or disagreement would already be known, so that no doubt could intervene and there would be no use for a demonstration. If some general maxim is immediately certain, then, i.e. is a general truth about a sort of ideas that can, in each instance, be immediately compared, there can be no occasion for using the maxim, as such, in a demonstration. Whatever we might use it to demonstrate is already known.

When, at the end of my previous post, I spoke of showing that this axiom is intuitively certain, according to Locke, what I really should have said, then, is that every instance of the axiom is an intuitively certain truth. These “instances” themselves, granted, are typically only lower generalities, not fully concrete particulars. Angelic intellects, perhaps, can carry out and retain the results of an infinite number of particular demonstrations; but we can not, and so, “in this imperfect state,” are forced to deal instead with general ideas — for example, the idea of a triangle, “neither Oblique, nor Rectangle, neither Equilaterial, Equicrural, nor Scalenon” (4.7.9). Still, the instance of the maxim involved in any given demonstration is always specialized in some way or other. Such instances are not demonstrated, according to Locke, by showing that they are instances of the axiom: they are not demonstrated at all. Therefore the axiom, as a general principle, also is not used to demonstrate anything else. It does not appear as a premise in any demonstration. In fact, a demonstration doesn’t really have premises, according to Locke. A demonstration doesn’t proceed from a list of propositions (the premises), via various steps that allow us to write down other propositions (according to rules of inference), to a final proposition (the conclusion). Rather, a demonstration proceeds from one idea (the subject of the conclusion) to another idea (the predicate of the conclusion) via a series of intermediate ideas, such that, at each step, the adjacent ideas can be directly compared, and such that, in consequence, the agreement or disagreement of the adjacent ideas is immediately, i.e., intuitively, perceived.

Now, if I, unlike Locke, take Thābit’s axiom and other such general maxims to be worth our consideration, it is not so much that I disagree with him about (2) (although there are well known problems in reducing everything we call a “demonstration” to this form) as rather that I disagree with him about (1). I deny, namely, that the only or even the main purpose of demonstration is to move ourselves or others from doubt to certainty. Mathematicians, at any rate, seem to value demonstration mostly because they want to understand something about the structure of what we know: how one part depends on another. (This is why, among other things, even after a demonstration of some proposition has been discovered, they may continue to search for a more perspicuous demonstration, or one that proceeds on different premises.) In the context of geometry, in particular, one of the main questions is, so to speak, how much of the Euclideanness of space is required to make a given theorem come out true. This question may be asked, and has been historically been asked, even by people who regard it as immediately and self-evidently true that space is fully Euclidean, i.e. that every instance of every Euclidean axiom is true. Whether Locke has simply ignored the possibility of this kind of question, or whether he on purpose rejects it, I can’t say for sure.

Returning to Locke, then: note first that, in the way he describes the need for a demonstration of the triangle postulate, he implicitly supposes that instances of something like Thābit’s axiom are intuitively certain. The reason the three angles of a triangle cannot be directly compared to two right angles is, that the three angles can’t be “brought” to coincide with the two. This is because “two right angles” are, by definition, two equal, adjacent angles formed by one straight line and another (see Elements 1, def. 10, ed. Clavius [1574], fol. 5\(^{\rm v}\)). To compare some three angles directly to two right angles, they must be “brought” into adjacency — which, of course, can never be done to the three angles of a triangle, no matter how the triangle is moved. If, on the other hand, Locke implies, some angle can be “brought” to some other, then the two can be directly compared. This is the standard for geometric equality, which is to say, for agreement or disagreement of the second kind (qualitative agreement or disagreement) between geometric ideas. But Thābit’s axiom concerns specifically the way in which one thing can be “brought” to another for the purpose of direct comparison. If the axiom is true at all, therefore, then its instances must be intuitively certain. The standard of equality which is to be used at every step in a geometrical demonstration cannot itself depend on any demonstration.

What is the source of this intuitive certainty? That the axiom involves motion implies, as I pointed out in my previous post, that we are outside the realm of pure geometry: the parts of space as such are immovable. When we talk about a solid body, \(S\), which is “moved in its entirety to one side by a simple direct motion,” and a point, \(A\), fixed on \(S\), we must, according to Locke, be using the term “solid” in the physical, not the mathematical, acceptation. This idea of solidity is essential to that sort of substance that we call “body”: a body is something extended and solid. Notice that the idea of body is, therefore, quite different from the idea of almost any other sort (species) of substance. The complex idea of a substance differs from a mixed mode, according to Locke, in that the former, but not the latter, is supposed to reflect the qualities which, taken together, constitute a distinct sort of external thing. This means, on the one hand, that we must know that those qualities possibly coexist (which, in general, we can tell only by experiencing that they actually coexist). But it also means, on the other hand, that the coexistence of those qualities implies something about the thing in which they coexist. That is to say: it is supposed to follow, from the coexistence of those qualities in the external object of our idea, that it will also have certain further qualities. Our ideas of substance are, for this very reason, in general inadequate ideas. We do not, in general, perceive any necessary connection (nexus) between distinct ideas, and thus in general do not know (perceive with certainty) that the coexistence of certain qualities implies anything further. With one small, and yet important, exception:

In vain … shall we endeavour to discover by our Ideas … what other Ideas are to be found constantly joined with that of our complex Idea of any Substance: since we neither know the real Constitution of minute Parts, on which their Qualities do depend; nor, did we know them, could we discover any necessary Connexion between them, and any of the secondary Qualities: which is necessary to be done, before we can certainly know their necessary Co-existence. So that let our complex Idea of any Species of Substances, be what it will, we can hardly, from the simple Ideas contained in it, certainly determine the necessary Co-existence of any other Quality whatsoever. . . . Indeed, some few of the primary Qualities have a necessary Dependence, and visible Connexion one with another, as Figure necessarily supposes Extension, receiving or communicating Motion by impulse, supposes Solidity. But though these, and perhaps some other of our Ideas have: yet there are so few of them, that have a visible Connexion one with another, that we can by Intuition or Demonstration, discover the Co-existence of very few of the Qualities are to be found united in Substances. (4.3.14)

Because our idea of body is made up of primary qualities, namely extension and solidity, body is a sort of substance of which we know the real, not merely the nominal, essence, and the known properties of body then follow from this essence, with either intuitive or demonstrative certainty. Among these properties is the property of divisibility, which I discussed at length in the previous two posts. Divisibility follows from solidity, first of all, because solidity, as Locke says here, is a necessary condition for the reception or communication of motion by impulse. The extreme parts of a given body, considered simply as such, cannot, in general, move towards one another, but they can always move apart from one another: what could resist such motion would have to be another body, and our original body — again, considered simply as such — in no way makes it necessary that any other body exist beyond its own limits. But this motion requires division — that is, the creation of new superficies — because “upon the Solidity of Bodies also depends their mutual impulse, Resistance, and Protrusion” (2.4.5; my emphasis). Solidity is a necessary and sufficient condition, not only for resistance to the motion of other bodies as a whole, but also for any force that would cause them to distort as they moved. We understand, in common terms, what this means: motion through empty space does not tend to make a body stretch, flatten, bulge out, etc. One part of this can be expressed more precisely by saying that a body, in the absence of other bodies, is free to move without any change in the distance between its parts, and this is already enough to imply that bodies are divisible: if the extremities of a body move away from one another, any other parts can maintain a constant distance from one extremity or the other, but not from both. Another part of it, however, is expressed by Thābit’s axiom: a body is free to move such that its parts remain at constant distances from each other, in such a way that every point of the body, and every line in the direction of motion, moves along a straight line. This, then, is why every instance of Thābit’s axiom is intuitively certain.

It is easy to see, in general terms, why a principle like this can constrain space to be Euclidean. In a space of variable curvature, rigid motion is not, in general, possible at all: a figure which occupies one place simply will not fit into other places. But even in a space of constant (nonzero) curvature, where rigid motion is possible, rigid motion is not free of resistance, and it is not free of resistance because Thābit’s axiom is violated. Think of an airplane flying west to east along the equator as a model of motion along a straight line (geodesic) in a curved space. A second airplane flying just to its north cannot both fly straight ahead and maintain a constant distance from the first. No matter what direction the second airplane heads, it will, traveling along some great circle, eventually cross paths with the first. To maintain formation, the second airplane must continually swerve off from a “straight” (that is, great circle) course, and some force must be applied to make this happen. If we imagine that the two airplanes are connected by a solid metal bar, there will be constant stress on the bar.[2]×If we look at the two airplanes as traveling on curved paths in three-dimensional space, rather than as traveling through a curved two-dimensional space, then this force can be seen to arise from the difference between the centrifugal force on the two airplanes, or, in other words, the difference between the forces that are needed to hold each onto the surface of the Earth. From here we could go on to a more general discussion of the relationship between gravitation and geometry. And so, indeed, with the parts of a single airplane, or of any rigid shape: to move rigidly, it must, so to speak, constantly push against the shape of the space it is moving through, because its various points can never both maintain constant distance from one another and all move in straight lines (i.e., along geodesic curves). Thābit’s axiom says that space is flat because it says that rigid bodies — “solids” in the physical sense — can move through space without any such pushing. But just this, the fact that resistance requires solidity, i.e. that a body only needs to push when it is moving against another body, is the necessary relation between ideas that Locke thinks we perceive with certainty. With intuitive certainty, that is: meaning that the ideas themselves are perceived to have this relation in every instance, without any need for demonstration, and in particular without needing to appeal to Thābit’s axiom, or to any general principle or axiom, to make the connection.

To go from this insight about rigid motion and curvature to the proof of a specific theorem like the triangle postulate — to use instances of Thābit’s axiom, in other words, for that kind of specific constraint on the shape of a space — is, however, more complicated than one might at first expect. Indeed, it is more complicated than I at first expected, which is one reason there has been such a long interval since the previous installment in this series of posts. Locke himself perhaps underestimated the difficulty. All he says about how the proof will work is that “in this Case the Mind is fain to find out some other Angles, to which the three Angles of a Triangle have an Equality; and finding those equal to two right ones, comes to know their Equality to two right ones” (4.2.2). Given the way Euclid proves this, however (Elements 1.32, fol. 52\(^{\rm v}\)), we can guess which intermediate angles Locke has in mind. pict

Figure 1: Euclid’s proof of the triangle postulate (Elements 1.32).

Consider a triangle \(ABC\) whose base lies on the line \(BD\) (fig. 1). The proof proceeds by drawing a parallel \(CE\) to the side \(BA\) (that at least one such a parallel exists can be proved without relying on the parallel postulate). By the the alternate angle theorem (Elements 1.29, fol. 50\(^{\rm r}\)), \(\angle \,ABC = \angle \,ECD\) and \(\angle \,BAC = \angle \,ACE\). Therefore, etc. Here Locke’s intermediate angles are \(\angle \,ACB\), \(\angle \,ACE\), and \(\angle \,ECD\). These angles can be “brought,” for comparison, onto two right angles, and we have shown, on the other hand, that they are equal to the interior angles of the triangle. Or rather: Euclid has shown that, to his satisfaction, using the alternate angle theorem. The question is, however, how Locke thinks we can show it.


Figure 2: A simple proof of the triangle postulate using Thābit’s axiom, of the kind Locke may have contemplated.

Now, the alternate angle theorem is a consequence of the parallel postulate: in the Elements, in fact, the parallel postulate is first used in the proof of 1.29. If Thābit’s axiom can be used to prove the parallel postulate, therefore, it can be used — in combination with the other principles invoked in Euclid’s proof — to prove the alternate angle theorem, and hence to prove the triangle postulate, as well. Such a proof would be needlessly complex, however, since a version of the alternate angle theorem actually turns up as a lemma in Thābit’s overall demonstration of the parallel postulate (his Proposition 6). There must therefore be a more direct proof of the triangle postulate. Given, indeed, the resemblance between the current fig. 1 and fig. 4 in the previous post in this series, we might suspect that this more direct proof would be fairly simple. Thābit’s axiom implies (see fig. 2) that, if we imagine the triangle \(ABC\) as affixed to a solid body, then we can move that body rigidly left until \(\triangle \,ABC\) coincides with \(\triangle \,ECD\), in such a way that \(A\), \(C\), and \(D\) will lie on a single straight line. \(\angle \,ACB\), \(\angle \,ACE\), and \(\angle \,ECD\) will, once again, be the intermediate angles in Locke’s demonstration. It is perhaps intuitive, on the one hand, or, if not, then easily demonstrable, that their sum is equal to two right angles.[3]×See Elements 1.13, fol. 35\(^{\rm r}\), and see also 4.17.14, where Locke gives, as an example of an immediate and hence intuitive comparison of ideas, “that an Arch of a Circle is less than the whole Circle.” And it is, on the other hand, intuitively certain both that \(\angle \,ACB\) is equal to itself and (by rigid motion) that \(\angle \,ECD\) is equal to \(\angle \,ABC\). The question then is only, how to show that \(\angle \,ECA = \angle \,BAC\). It’s impossible to say for sure how Locke would have carried out that final step, but it seems natural to imagine a further application of Thābit’s axiom, this time sliding our solid body diagonally down until \(\triangle \,ABC\) coincides with \(\triangle \,CFG\). Now if we assume that the vertical angle theorem (Elements 1.15, fol. 36\(^{\rm r}\)) is either intuitively or demonstratively certain,[4]×I hope also to discuss in the following post how or whether Locke might be entitled to this assumption. then \(\angle \,ECA = \angle \,FCG = \angle \,BAC\).

My conjecture that Locke had a demonstration like this in mind is only a conjecture. It is an uncharitable conjecture, at that, because if Locke did contemplate a proof like this, he was neglecting something important. How do we know that \(F\), \(C\), and \(E\) lie along a single straight line? This must be true if the plane is Euclidean: it follows from Elements 1.27, fol. 48\(^{\rm r}\) that both \(EC\) and \(CF\) are parallel to \(AB\), and, by Playfair’s axiom, this means that \(EC\) and \(CF\) must be segments of the same line. But the proof of Elements 1.27 uses the exterior angle theorem, while Playfair’s axiom is equivalent (in the presence of the other axioms) to the parallel postulate. In a demonstration that space is Euclidean, then, one cannot take either of these for granted: if Thābit’s axiom is sufficient to demonstrate, via the procedure of fig. 2, that space is Euclidean, we will need to produce a demonstration that \(F\), \(C\), and \(E\) are collinear which does not rely on the parallel postulate or the external angle theorem. But the figure doesn’t make clear, at least, how that might be done.

The moral is not that Thābit’s axiom cannot be used to prove the triangle postulate: on the contrary, we still know that it can, since it can be used to prove the parallel postulate, which in turn can be used to prove the alternate angle theorem, which in turn can be used to prove the triangle postulate by Euclid’s procedure (fig. 1). We may still suspect, even, that there is a way to circumvent some of that complexity, since, as I pointed out above, Thābit proves a version of the alternate angle theorem before he proves the parallel postulate. It remains possible, indeed, that Locke had such a proof in mind, rather than the simpler but invalid one I just attributed to him. In the next post in this series I will show in detail how this would proceed, essentially just following Thābit’s tracks. When this is finished, it will show how the supposedly intuitive truths concerning the divisibility of bodies can be used to limit, a priori, the possible shapes of spaces in this one respect. At the same time, however, it will reveal a certain limit to Locke’s approach, because the proof, while it does not take for granted either the parallel postulate or the exterior angle theorem — does not, that is, take for granted that space is Euclidean as opposed to hyperbolic or elliptical — does take for granted something more basic, about the possibility of reflection. And it will be unclear whether that more basic assumption could be intuitive, according to Locke.

Tuesday, July 20, 2021

According to Berkeley, Locke’s doctrine of abstraction involves some kind of absurdity. The absurdity, whatever it is, has something to do with the separability of ideas:

It is agreed on all hands, that the Qualities or Modes of things do never really exist each of them apart by itself, and separared from all others, but are mix’d, as it were, and blended together, several in the same Object. But we are told, the Mind being able to consider each Quality singly, or abstracted from those other Qualities with which it is united, does by that means frame to it self abstract Ideas. For example, there is perceived by Sight an Object extended, coloured, and moved: This mix’d or compound Idea the mind resolving into its Simple, constituent Parts, and viewing each by it self, exclusive of the rest, does frame the abstract Ideas of Extension, Colour, and Motion. (Principles, Introduction, §7)

Berkeley and Locke (“all hands”) agree, that is, that qualities are inseparably mixed in their real existence, but when Locke further maintins that these qualities can be abstracted from one another in the idea — that is where an absurdity is supposed to come in. The passage Berkeley is alluding to reads, however, as follows:

Though the Qualities that affect our Senses, are, in the things themselves, so united and blended, that there is no separation, no distance between them; yet ’tis plain, the Ideas they produce in the Mind, enter by the Senses simple and unmixed. For though the Sight and Touch often take in from the same Object, at the fame time, different Ideas; as a Man sees at once Motion and Colour; the Hand feel[s] Softness and Warmth in the same piece of Wax: Yet the simple Ideas thus united in the same Subject, are as perfectly distinct, as those that come in by different senses. (Essay, 2.2.1)

Locke does describe a separation here, but it is not a separation of ideas, nor is it accomplished by any act of the mind. He places the separation in question rather between the thing (res), in which the qualities are united and blended, and the mind, into which the corresponding ideas enter already separated: simple and unmixed. The separation about which he and Berkeley disagree is supposed to occur, in other words, at a point which does not exist at all in Berkeley’s system, namely at the interface between the real and the ideal. Some care will therefore be needed in correctly expressing Berkeley’s objection.

Simple ideas, according to Locke, enter the mind only via an operation of perception, narrowly understood — that is, an operation either of sensation or of reflection. But this (passive) operation always precedes the active operation of abstraction:

The Senses at first let in particular Ideas, and furnish the yet empty Cabinet. . . . Afterward the Mind proceeding farther, abstracts them. (1.2.15)

These simple and unmixed ideas are, on their first entrance into the mind, particular, not abstract. To report the disagreement between Locke and Berkeley in neutral terms, then: it is a disagreement, first of all, about what particular ideas we have, and then only secondarily about the possibilities for what Locke calls “abstraction.” It is agreed on all hands that certain qualities are inseparably united and blended in real existence, but it is not agreed on all hands what “real existence” is: where Berkeley locates the (particular) res, namely in the mind, Locke sees only a particular idea, and there, he says, the separation has already occured — the inseparable blending was only in an external res whose very possibility Berkeley denies. To repeat, then: Locke’s particular ideas already contain the separation that Berkeley considers absurd.

The disagreement, moreover, does not reach every case of that supposed separation. Consider, for example, some particular apple. According to Locke, its secondary qualities — for example, its color and its smell — are all inseparably blended in the apple itself. This must be so, since secondary qualities, according to him, are bare powers: are not, that is, really distinct from the subject in which they inhere, and hence not really distinct from one another.[1]See 2.8.24, and see also Boyle, The Origine of Formes and Qualities, p. 19: “They are not in the Bodies that are Endow’d with them any Real or Distinct Entities, or differing from the Matter its self, furnish’d with such a Determinate Bigness, Shape, or other Mechanical Modifications.” And, on the other hand, Locke of course considers that these ideas of color and smell enter the mind simple and unmixed. But there is no disagreement with Berkeley. A thing (res) such as an apple is, according to Berkeley, a collection of distinct ideas:

Thus, for Example, a certain Colour, Taste, Smell, Figure and Consistence having been observed to go together, are accounted one distinct Thing, signified by the Name Apple. (Principles, Part I, §1)

The color and taste of a particular apple are, then, according to Berkeley, realiter distinct — distinct in the thing — and, therefore, consistent with his principles, he holds that each can be conceived separately from the other.

I may indeed divide in my Thoughts or conceive apart from each other those Things which, perhaps, I never perceived by Sense so divided. Thus I … conceive the Smell of a Rose without thinking on the Rose itself. So far I will not deny I can abstract, if that may properly be called Abstraction, which extends only to the conceiving separately such Objects, as it is possible may really exist or be actually perceived asunder. (Part I, §5)

What Locke affirms and Berkeley denies, in this case, is that there is somewhere (outside the mind) a real nexus between the color and smell: the regularity on which the compound reality of apples depends is, according to Berkeley, nothing more than a matter of arbitrary divine syntax.[2]Hence as far as things like apples are concerned, Berkeley’s answer to skepticism is the same as Descartes’s: God is not a deceiver — with the important difference that Descartes thinks this a speculative truth inolving the idea of the infinite, whereas for Berkeley it amounts to nothing more than an expression of my will (to leave by the door and not by the window).

In which cases, then, does Locke actually allow a separation that Berkeley does not? I count at least three, though I am not at all sure the list is exhaustive.[3]There are also some disagreements about the possibility of abstraction that do not depend in any obvious way on disagreements about separability of ideas. The abstract idea of color, for example, that is “neither White, nor Black, nor any particular Colour” (Principles, Introduction, §9), cannot possibly be explained by separating anything within these simple ideas. According to Locke’s actual explanation (Essay, 3.4.16), he would take “there is no human but has some color” to mean, roughly: “all humans have some quality perceptible only by vision.” To determine the true content of Berkeley’s complaint in this case would require a detour into many complications (for one thing, he and Locke do not agree about what “peception by vision” means).

First is the very case Locke mentions in the passage quoted above: ideas belonging to the same sense modality. The example Berkeley mentions most often concerns what might be called the visible primary qualities (visible extension, visible figure, etc.), which he thinks cannot occur without color. Throughout the Principles, indeed, and oddly enough, Berkeley seems to conceive of bodies primarily as visible things. It is difficult to say what Locke thinks about this case, however.[4]Locke says explicitly that the ideas of the primary qualities (except that of solidity!) can enter the mind either by way of sight or by way of touch (Essay, 2.5; 2.13.2). But his response to Molyneux’s question (2.9.8) shows that he doesn’t strictly consider the tangible and visible ideas to be the same. Moreover, since towers which look round from far off may appear square from close by (Med. 6.7, AT 7:76,23–4), visible figure should, by Locke’s own arguments, be accounted a secondary quality (as Berkeley points out: Principles Part I, §14; see also Dialogues III, p. 306, and note once again that Berkeley’s true response to skepticism is the same as Descartes’s). Finally, whatever the status of visible figure and extension, color, at least, is definitely a secondary quality according to Locke, and this implies that we can see no necessary connection between ideas of color and any other idea, or, in other words, that visible figure could in principle appear with no color at all. In one place (Essay, 2.23.11), Locke even appears to claim that this is all microscopic eyes would see. If that actually is his opinion, then the disagreement in this case concerns what is separable in (what Berkeley calls) real existence, not what is separable in the (mere) idea. The case of the tangible primary qualities, including solidity, is clearer. According to Locke, all our knowledge about geometry and rational physics is thanks to the manifest necessary connections between separate abstract ideas of these qualities: these ideas are separately conceivable, but we know that they cannot occur separately (or in the wrong proportions, etc.) in real existence. If the ideas are necessarily connected, moreover, then the corresponding qualities, i.e. powers, in bodies are also necessarily connected, and this establishes a resemblance (isomorphism) between our ideas and things. Berkeley denies that an inert thing can directly necessitate another: denies, that is, that mere affections as such (modes of pure receptivity) can ever resemble an active being. Hence he classifies some of this supposed knowledge as syntactically general representations of empirical regularities — that is, as an attempt to conform our will (qua productive of imagined signs) to the divine will (qua productive of the ideas of sense) — and the rest as trifling: that all figure is extended, for example, is for Berkeley not a connection between separate ideas at all, since every figured idea is also extended.

Second, ideas of pleasure and pain. Locke’s position is the very one that Philonous quickly gets Hylas to give up, namely that, for example, “Pain is something distinct from Heat, and the Consequence or Effect of it” (Dialogues I, p. 187), and similarly for pleasure. Once again, the disagreement is about the separability of, for example, moderate warmth and the pleasure consequent to it in a particular case, and only secondarily about the ability “to frame an abstract Idea of Happiness, prescinded from all particular Pleasure” (Principles Part I, §100). If the disagreement over primary qualities affects the basis of geometry and physics, then this disagreement affects the basis of what Locke projects as an even more important demonstrative science, namely ethics. In this case, Locke does not claim any theoretically manifest necessary connection between ideas,[5]Locke’s ethics is supposed to be demonstrative, but there is not any direct demonstration, as in Hobbes or Spinoza, of the connection between pain or pleasure and any other idea; rather, the connection is supposed to be established — in the Essay, at least — by way of the existence and nature of God. (The imperfection in myself which starts off Locke’s cosmological proof is not, as in the Third Meditation, doubt, i.e. a species of uneasiness, but rather, implicitly, the possessing a beginning in time: see 4.10.2–3.) but we do find, so to speak, a practically necessary connection: the desire of pleasure and the aversion to pain are “Innate Practical Principles, which (as practical Principles ought) do continue constantly to operate and influence all our Actions, without ceasing” (Essay, 1.3.3). Berkeley must deny that there are such general principles. Whether this can be connected to the larger ethcial and political disagreements between him and Locke, I do not know.

Third, and of most interest from a metaphysical point of view, are the transcendental ideas of existence and of unity, which “are suggested to the Understanding, by every Object without, and every Idea within” (2.7.7).[6]The idea of power (2.7.8) is in some respects similar to these, except that power is always only real (associated with the mediate object), not ideal (associated with the immediate object, i.e. the idea, itself). If to these three we add also the simple idea of limit, we obtain a list of four transcendental ideas corresponding to the categories of quantity (unity), quality (limit), relation (power), and modality (existence), or in Locke’s terms to the four sorts of agreement and disagreement of ideas (identity–difference, relation, necessary coexistence, real existence). According to Berkeley, there is no idea of power: I represent power by having power myself, not by having an idea of it. He also presumably would deny that there is a separable idea of limit, though I’m not aware of any place where he discusses that directly. Berkeley rejects the idea of unity as part of his critique of abstract arithmetic (Principles, Part I, §13), and, as for the idea of existence, he sees it as implicated in Locke’s absurd realism: “For can there be a nicer Strain of Abstraction than to distinguish the Existence of sensible Objects from their being perceived, so as to conceive them Existing unperceived?” (Part I, §5).

If Locke genuinely disagrees with Berkeley about this, he must hold that when I know or judge some thing, \(a\), to exist, my act involves two distinct ideas: the idea of \(a\), on the one hand, and the idea of existence, on the other. That in itself is strange enough. It becomes stranger still if we consider more closely the passage from 2.7.7 quoted above, along with what immediately follows there:

When Ideas are in our Minds, we consider them as being actually there, as well as we consider things to be actually without us; which is, that they Exist, or have Existence: And whatever we can consider as one thing, whether a real Being, or Idea, suggests to the Understanding, the Idea of Unity. (2.7.7)

If the same idea of existence, call it \(E\), covers both the ideal case (the existence of an idea) and the real (the existence of a thing, or in other words of a subject of powers and operations: a substance), then knowledge of existence, whether ideal or real, consists in the perceiving an agreement between that idea, \(E\), and some other idea.[7]Berkeley, for his part, denies that either “existence” or “knowledge” applies univocally to cases of ideas and of substances (spirits): see Principles, Part I, §142. Hence, to take Locke’s example: the demonstration of God’s existence, based in part on the intuitive premise that I myself, at least, exist (see Essay, 4.10.2 and 4.3.21), establishes an agreement between the idea of God and \(E\), mediated in part by the agreement between \(E\) and my idea of myself. Or, in general: if \(A\) is my idea of some thing, \(a\), then I know that \(a\) exists by perceiving an agreement between \(A\) and \(E\).[8]Note, incidentally, that there is no thing \(e\) that is the cause of my perceiving \(E\). Hence although \(E\) is not innate, it is what Kant would call a priori. The same holds for the other transcendental ideas listed above. What is strange, however, is that my knowledge that the idea itself, \(A\), exists, must also consist in a perceived agreement between \(A\) and \(E\). How can it be both?

Locke, unfortunately, says practically nothing about ideal existence. He does say quite a bit about real existence, though. Knowledge of real existence — perception of “actual real Existence agreeing to any Idea” (4.1.7) — is the fourth and last sort of knowledge on Locke’s list, corresponding to Kant’s category of modality. Now, this formulation may suggest a tempting way of evading the question posed above: why not think that the idea of “actual real existence” is simply a different idea, according to Locke, than the idea of ideal existence? Then to know that \(A\) exists would be to perceive agreement between \(A\) and one idea, call it \(E_{\text {ideal}}\), whereas to know that \(a\) exists would be to perceive agreement between \(A\) and some completely different idea, \(E_{\text {real}}\). But, besides that our passage at 2.7.7 speaks strongly against this solution, it would also lead to various undesirable consequences. Perhaps most importantly, it would mean that Locke is not strictly speaking a realist, that is, someone who believes that both ideas and things exist, since there would be no sense of “exist” that applies correctly to both.[9]This problem is serious for Locke and not for Berkeley because of their differences over the proper function of language. For Berkeley, “Both ideas and spirits exist” is a sentence meant to affect the will of the listener directly, rather than by means of any ideas that it may excite in the listener’s mind. For Locke, such a use of language would be illegitimate. So I will proceed on the assumption that there is only one idea of existence, \(E\), and ask: what sort of agreement can it be, between \(A\) and \(E\), such that the perception of that agreement constitutes the knowledge that the corresponding thing, \(a\), exists?

The simple and correct answer is, that it is the fourth sort: the sort of agreement, that is, that we perceive in knowing real existence, and not in any other case. This means, for one thing, that it is not agreement of the first sort, agreement by identity: to know that I exist is not to know that the idea of existence is identical to some component of my idea of myself; or, in other words, the proposition that I exist is not, in Kantian terminology, analytic (or as Locke would say: not “trifling”). But neither is it synthetic in the manner of “The interior angles of a triangle equal two right angles” (second sort of agreement) or “Every solid thing is divisible” (third sort). All of this is as it should be: we don’t want “I exist” to mean that I exist by definition, or that my degree of perfection is such that I exist, or that my qualities are necessarily connected to existence. In a word: all three of the other sorts of agreement give rise to knowledge of what is necessarily the case, whereas what I know here — what I know, in knowing that I exist — is something contingent. The fourth sort of agreement and disagreement between ideas is a contingent sort of agreement or disagreement.[10]If it be objected that, in that case, Locke’s demonstration shows God to exist only contingently: I think that must be conceded. The same is true of the Third Meditation proofs, moreover. A cosmological proof can directly establish necessary existence only if it begins with an imperfect being (world) whose imperfection is characterized as contingency.

It may seem, however, that this answer raises more problems than it solves. For can there truly be contingent agreement between ideas at all? And, even if there can, could there be contingent agreement between any idea and the idea of being or existence in particular? Doesn’t every idea, on the contrary, always represent its object as a being, that is, as existent?

Both of these objections, I think, overlook the same thing about the knowledge of real existence. Consider that Locke allows one other case, besides those of God and of myself, in which we have such knowledge — a case which he describes as neither intuitive nor demonstrative, but rather “sensible.” This third case is very narrow:

The Knowledge of the Existence of any other thing we can have only by Sensation: For there being no necessary Connexion of real Existence, with any Idea a Man hath in his Memory, nor of any other Existence but that of GOD, with the Existence of any particular Man; no particular Man can know the Existence of any other Being, but only when by actual operating upon him, it makes itself perceived by him. (4.11.1)

It would be wrong to conclude, however, from this passage, that such knowledge is so narrow that it concerns only present existence, or in other words that the past existence of the world is not certain, according to Locke, but at best only highly probable:

As when our Senses are actually employ’d about any Object, we do know that it does exist; so by our Memory we may be assured, that heretofore Things, that affected our Senses, have existed. And thus we have Knowledge of the past Existence of several Things, whereof our Senses having informed us, our Memories still retain the Ideas. (4.11.11)

What is true, rather, is that sensible knowledge always involves attributing real existence to the object at some determinate time: either, in sensation, at the present, or, in memory, in the past. Or, we might add, in expectation, in the future. For our possession of demonstrative science means that, in certain special cases, we can deduce the course of the future from our knowledge of the past and present.

This temporal determinacy therefore characterizes sensible knowledge: and not sensible knowledge alone, but, I think it clear, the fourth sort of agreement and disagreement in general. While every idea represents its object as possible, “actual real existence” — note that the expression is by no means redundant — is existence at a determinate time, and, at least in the case of an external object, in a determinate place. This is why, according to Locke, even though many, indeed most, of our ideas are abstract and general, the actual thing corresponding to any idea is always individual, and also why actual existence, in implying individuality, consequently implies spatiotemporal position:

From what has been said, ’tis easy to discover what is so much enquired after, the principium Individuationis, and that ’tis plain is Existence it self, which determines a Being of any sort to a particular time and place incommunicable to two Beings of the same kind. (2.27.3)

Thus both of the above objections are answered. There is always and necessarily agreement (I suppose it is of the second sort?) between every idea and the idea of existence, as attributed to the real object (I am not yet here talking about the ideal existence of the idea itself). But this agreement only means that the idea represents the real object as possible, that is, as existent at some indeterminate time and place. The actual existence of the real object requires a determination to time and place, and the latter determination is always contingent: there is no deriving, from an idea alone, the time and place, if any, at which the corresponding real object exists.

If any: we do have ideas of merely possible things. But Locke puts stringent limits on the cases and the senses in which that is so. A simple idea, for one thing, must always be the idea of something that at one time existed: if it is not a present sensation, it must be a memory. That is the whole content of Locke’s empiricism. The mind cannot make a new simple idea. It follows that, even if (as is usual) we cannot recall that particular time at which we first had some sort of sensation, we nevertheless never have a simple idea without the consciousness that it has been in our mind as a sensation at some determinate time in the past, and “to Remember, is to perceive any thing with Memory, or with a Consciousness, that it was known or perceived before: … This Consciousness of its having been in the Mind before, being that, which distinguishes Remembring from all other ways of Thinking” (1.4.20/21). With regard to their ultimate components, then, our ideas never refer to anything merely possible, but always to something that either exists now or has once existed. A complex idea of substance, moreover, since its corresponding real object is supposed to contain the unknown nexus on which the unity of its component ideas depends, is not adequate to our purposes unless that combination has actually occurred in the past:

No body joins the Voice of a Sheep, with the Shape of a Horse; nor the Colour of Lead, with the Weight and Fixedness of Gold, to be the complex Ideas of any real Substances; unless he has a mind to fill his Head with Chimera’s, and his Discourse with unintelligble Words. . . . For tho’ Men may make what complex Ideas they please, and give what Names to them they will; yet if they will be understood, when they speak of Things really existing, they must, in some degree, conform their Ideas to the Things they would speak of. (3.6.28; see also 2.30.5)

This is why, when meeting a skeptical doubt about the existence of external things, Locke thinks it sufficient to point out that we can distinguish, not between sensation and dreaming, but between sensation and memory:

For I ask any one, Whether he be not invincibly conscious to himself of a different Perception, when he looks on the Sun by Day, and thinks on it by Night; when he actually tastes Wormwood, or smells Rose, or only thinks on that Savour, or Odour? We as plainly find the difference there is between any Idea revived in our Minds by our own Memory, and actually coming into our Minds by our Senses, as we do between any two distinct Ideas. (4.2.14)

In the cases of modes and relations only do we have good (theoretical or practical) reasons to form complex ideas in which the combination depends on nothing but our will and is not intended to refer to anything actual, whether past or present. But, although Locke never says this explicitly, he appears to think that we can usefully form those ideas only within the bounds of the demonstrative sciences (mathematics, physics, and ethics), where a priori connections supply the place of past experience in limiting the range of possibility.

Now, abstraction, according to Locke, consists not in any arbitrary separation of one idea from another, but rather in separation of any idea from its contingent, temporally determinate agreement with real existence, which is the principle of individuation:

The Mind makes the particular Ideas, received from particular Objects, to become general; which is done by considering them as they are in the Mind such Appearances, separate from all other Existences, and the circumstances of real Existence, as Time, Place, or any other concomitant Ideas. This is called ABSTRACTION, wherby Ideas taken from particular Beings, become general Representatives of the same kind. (2.11.9)

The ideas that we have prior to this operation, including therefore all the ideas of infants (and of adult non-human animals) are particular:

The Senses at first let in particular Ideas, and furnish the yet empty Cabinet: And the Mind by degrees growing familiar with some of them, they are lodged in the Memory, and Names got to them. Aftewards the Mind proceeding farther, abstracts them, and be degrees learns the use of general Names. (1.2.15)

But these initial, purely particular ideas, are nevertheless simple: that is, as separated from other ideas as they could be. What a child knows before it gets the use of words is, for example, “the difference between the Ideas of Sweet and Bitter (i.e. That Sweet is not Bitter)” (1.2.15), and non-human animals never compound ideas very much, if at all (2.11.7). So what the beast or the infant has is, for example, the sensation of something sweet — that is, of some particular subject of the power to cause it to perceive sweet — here and now; either that, or the memory that such a thing was previously present, which sensation or memory is certainly correct:;

Because being nothing but the Effects of certain Powers in Things, fitted and ordained by GOD, to produce such Sensations in us, they cannot but be correspondent and adequate to those Powers: And we are sure they agree to the Reality of Things. For if Sugar produce in us the Ideas which we call Whiteness, and Sweetness, we are sure there is a Power in Sugar to produce those Ideas in our Minds, or else they could not have been produced by it. (2.31.2)

And, conversely, even if we put into a complex idea enough simple ones that only a single invidual is known to possess all the corresponding qualities (for example, in our idea of the sun: see 3.6.1), as soon as we consider that idea without its contingent, temporally determinate agreement with existence, it becomes fully as abstract as any other. Indeed, this would remain true even if, per impossibile, we could put into our complex particular idea the ideas of every quality belonging to some particular thing (see 2.31.8). In that case, all of those qualities would be known to be necessarily combined in the object of the idea (by the first sort of agreement), but the uniqueness of the object, or in other words the particularity of the idea, would be due neither to any of them severally nor to all of them collectively, but rather to the contingent existence of the object at some determinate time and place (that is, by the fourth sort of agreement). Take that away, and you have always an abstract general idea, to which many distinct objects might in principle correspond.

So much for real existence. Ideal existence is harder to understand. I know some, perhaps most, readers of Locke tend to think of ideas as the objects of reflection, which would at least promise to make real and ideal existence parallel cases. But to me that seems a fundamental mistake. The immediate object of a mental operation — whether of sensation, of reflection, or of any other — is always an idea, but the mediate (real) object never is. The mediate object is always something that is acting, or has acted, or might possibly act on me so as to cause me to perceive the immediate one. Thus the mediate object strictly speaking is a substance: either a body or a spirit. However, we can also think of the mediate object as the quality, that is, power, faculty, of that substance, by virtue of which it can so affect me. Or we can think of the object as the actual or potential operation of that quality. So if I see something white, for example, we can think of the object as the white substance (e.g., a snowball), or as the quality of whiteness in that substance (the whiteness of the snowball), or as the operation of that quality (its looking-white-to-me-now, so to speak). And similarly, when I reflect on myself qua sensing something, we can think of the object as the sensing substance (my mind), or as the quality of sensitivity in that substance (the faculty of sensation), or as the operation of that quality (this individual mental operation of sensation). In practice, Locke tends to mix the different ways of speaking: “our Observation [is] employ’d either about External sensible Objects; or about the Internal Operations of our Minds” (2.1.2). But, whatever reasons he may have for this,[11]It is perhaps connected to the fact that the mind has no primary qualities, since all its faculties are nominal, not real: see 2.21.6. I will return to this point below. it remains clear that no idea is mediate object, either in sensation or in reflection. On the contrary, when I reflect on sensation, the only idea that is my object at all is the immediate object, namely, the simple idea of sensation itself.

If an idea is only ever immediate object of perception, then there is no room for distinction between the time at which it is known to exist and the time at which it exists. If I now perceive some sort of agreement between an idea, \(A\), and the idea of existence, \(E\), and my perception of that agreement is supposed to consitute my knowledge that \(A\) exists, then what I know must be that \(A\) exists now. When I am no longer perceiving this idea (no longer perceiving numerically the same idea), I can no longer perceive its agreement or disagreement with anything. Every idea therefore agrees with the idea of existence always and necessarily in two quite different ways, and the difference is reflected in the different, indeed opposite, temporal character of the attributed existence: every idea represents some real object as existing at some completely indeterminate time, while the idea itself always exists now and at no other time whatsoever. Or perhaps I should say that there is only one agreement, which presents different aspects as we regard it either subjectively or objectively. This agreement — which, again, I guess is of the second sort — does not itself involve any temporal determination. So I perceive it to apply to the idea exactly when I perceive the idea itself, and I perceive it to apply to the mediate object at no determinate time. And this helps explain why Locke feels no need for a separate treatment of ideal existence: knowledge of actual ideal existence is really neither more nor less than knowledge of possible real existence.

This is the best I can do at present to make sense of what Locke says about these matters. I must admit that I am not entirely happy with it. The main question that bothers me: why, if all the above is correct, does Locke say that my sensible knowledge of the actual real existence of bodies is “not altogether so certain” (4.11.3) as my intuitive knowledge of my own actual real existence? My situation is the same in both cases. In case of memory or of sensation, I not only perceive the sort of agreement between the idea of existence and my idea \(A\) which constitutes knowledge of the (present) ideal existence of \(A\), but also another agreement, of the fourth sort, between the idea of existence and \(A\): the sort of agreement the perception of which constitutes knowledge of the (temporally determinate) existence of a substance \(a\) (a substance with the power to cause me to perceive \(A\)). What difference does it make which substance \(a\) happens to be? Why is this perception more certain if \(a\) is the substance that I myself (currently) am?

I suspect that I could answer this question if only I understood better what Locke is even saying. The certainty of sensible knowledge is different from any degree of probability, no matter how high. As I write these words, for example, it happens that no human beings other than myself are present to my senses, although I am not entirely alone: a cat is sleeping on the sofa across the room. Of the existence of other human beings, therefore, I have, according to Locke, only a highly probable judgment (opinion):

And therefore though it be highly probable, that Millions of Men do now exist, yet whilst I am alone writing this, I have not that Certainty of it, which we strictly call Knowledge; though the great Likelihood of it puts me past Doubt, and it be reasonable for me to do several Things upon the Confidence, that there are Men (and Men also of my Acquaintance, with whom I have to do) now in the World; But this is but Probability, not Knowledge. (4.11.9)

Of the cat’s existence, on the other hand, I do have such certainty (I can look at her directly while touch-typing these words). How can my certainty of the cat’s existence be, so to speak, more certain than any probability, and yet still not altogether so certain as the certainty of my own existence?

What occurs to me in this regard is that sensible knowledge has two parts, one of which is certain while the other is not. It is certain that some substance now operates so as to cause in me the perception of some ideas, which ideas belong to (although they do not exhaust) my complex idea of Lily, the cat. But that the substance in question is Lily, or even that it is a cat, can only be, at best, highly probable. And perhaps, according to Locke, it is not even quite certain that the substance in question is a body. Or at least: if that is certain (or would be certain if I were feeling Lily rather than merely seeing her, i.e. if I were perceiving her tangible primary qualities), it is not certain that the substance is different from my mind, since it is not certain, according to Locke, that my mind is not a body. When Locke offers evidence against skepticism, he aims to refute a skeptical doubt of this nature: due to the vast difference between seeing the sun and remembering having seen it, everyone, he says, “hath a certain Knowledge, that they are not both Memory, or Actions of his Mind, and Fancies only within him; but that actual seeing hath a Cause without” (4.11.5).[12]Hume uses this same phrase, “action of the mind,” and in the same sense, in his own discussion of real vs. ideal existence at Treatise It may be hard to notice this because, again, of the difference between what Hume and Locke think “real existence” is. To believe in the existence of an external thing, such as a table, is, according to Hume, to have an idea which is a copy of and draws force and vivacity from a certain impression, which impression we ordinally take to be, not a representation of the table, but rather the table itself. Similarly, to believe in the existence of a mental operation, e.g. an act of memory or imagination, is to have an idea which is a copy of an idea, and also a copy of that idea’s special je-ne-sais-quoi character of mental activity, which we ordinarily take to be, not a representaion of the mental operation, but rather the operation itself. Even though the first idea is a mere copy of the impression (i.e., of the table), its character of mental activity is original to it: in that respect, then, the first idea is an impression, and can be source of force and vivacity for the second. A similar question could not arise about my perception of myself, then, just because acts of reflection, since they do not represent any primary qualities, do not represent any substance at all per se. The mediate object of an act of reflection is represented simply as whatever substance operated to cause that act — to cause the perception of, for example, the idea of sensation:

When we see, hear, smell, taste, feel, meditate, or will any thing, we know that we do so. Thus it is always as to our present Sensations and Perceptions: And by this every one is to himself that which he calls Self ; it not being considered in this Case, whether the same Self be continued in the same, or divers Substances. (2.27.9)

There is no room for error here, not because the act of reflection has superior access to its object, but rather because it claims so little about it.

But although it would make sense for Locke to say this, I am unhappy because I can’t persuade myself that he actually is saying it. The passage I cite above, “he hath a certain Knowledge, that they are not both Memory,” actually seems to tell against it: Locke there explicitly attaches certainty to sensation in the very respect in which I suggested it leaves room for doubt (and this in the case of the sun, whose tangible primary qualities, I suppose, we never perceive[13]Unless someone could be said to perceive the tangible position of the sun by feeling the monthly variation of the tides?). So I remain confused as to what Locke means.

Returning, in any case, to the dispute with Berkeley: we may now observe that Berkeley, in maintaining that there is no separable idea of existence, is really maintaining both his idealism and his whole case against abstraction. In perceiving Locke’s fourth sort of agreement, we perceive that something actually is or was present, but only contingently, at the same time and place as our idea; hence we perceive the presence of something distinct from our idea. On the other hand, when we regard the same idea apart from that agreement, it represents its object as possibly present, at no determinate time and place, and in that way becomes general, in the sense that different substances, at different times and places, can all agree with it, just so long as they all have the power (quality) to cause perception of such an idea. Berkeley’s idea can never become general in Locke’s sense because it was never particular, in that sense, to begin with: we do not perceive in it any connection to a determinate temporal position. Its position depends only what cannot be perceived, namely, a will, whether human or divine.

Wednesday, September 23, 2020

This is a response to a several things, but, first of all, to a project of Andrea Sangiacomo’s, as reported in this article.[1]The article, which is clearly based on an interview with Sangiacomo, is available in both English and Dutch, but there is no indication I can see as to the relationship between the two versions nor as to the language(s) used in the original interview. I will mostly rely on the English version, for obvious reasons. As usual, I am ill-informed: I don’t know anything about Dr. Sangiacomo’s work besides what the article contains, and, given that such sources are not always very reliable, I can scarcely be said to know even that. I don’t know, for example, whether Sangiacomo has been accurately quoted, or whether his words, even when they are his, may have been taken out of context. So my remarks here should not be understood as criticism of Sangiacomo’s project, still less of him personally.

If not that, though, then what are they? Sangiacomo is reported to have said something to the point:

Many colleagues still consider philosophy to be purely a job for humans. And do not get me wrong, I generally agree with that. The most relevant philosophical insights are still being generated by people who reflect deeply.

The difference between human and non-human is not, as such, of much concern to me in this regard: if horses, oxen, or electronic computers can aid in the generation of relevant philosophical insights, then I am more than happy to share the glory of such with them. What does concern me is the difference between reflective and unreflective. To paraphrase Locke: I grant, AI’s will not come to deep reflection till they be more like humans; and I add, nor then, neither. Natural intelligence is fully capable of executing an algorithm.

I introduce this word, “algorithm” (which does occur, but not very prominently, in the article under consideration) with some hesitation, and not only because, as Popper somewhere notes, the word should really be “algorism.” What I want is a word for the thing non-human AI’s can definitely do, according to Sangiacomo, because to do that thing — to implement or execute what I am calling an algorithm — does not require deep reflection. “Algorithm” may or may not be the best choice for this, and I certainly don’t intend to import any of its technical content from theoretical or applied computer science. In what follows, it should taken to mean: a process that can be carried on without reflection. This I think an informative definition because, despite having read and been thoroughly confused by a whole canonfull of philosophers who all use the term “reflection” in various ways, I still find the definiens clearer than the definiendum.

With only slight exaggeration, then, I would say: the present post expresses a reflection prompted by the output of a certain algorithm. One stage of the algorithm in question, namely the part that made Martin Lenz’s link to the article come up on my Facebook feed, was implemented by electronic computers. But, before that, I would guess it was a human who decided that the University of Gronigen needed a story about this under “About us \(>\) Latest news \(>\) News \(>\) News articles,” and I know it was a human, by the name of Jorn Lelong, who actually wrote the story.[2]I find with some Googling that Jorn Lelong is a freelance journalist based in Ghent, Belgium, who has authored various pieces (in English) about developments in technology research for various different outlets, and who also has a Twitter account (in Dutch). There is even a picture of him, so, barring deepfakery, he is definitely an actual human being — a kind of cool, cheerful looking young human being in a bright red hoody and dark sunglasses. There is no credit for a translator. Perhaps this means that Lelong wrote both the Dutch and the English versions. But I mean no disrespect in saying that I doubt the humans in question required any deep reflection to perform these tasks, and in fact I even imagine that the best current AI might be trained up to do them tolerably well. Moreover, the main factor in the decision to publish the story is presumably what gets mentioned at the very end, namely that Sangiacomo has received an ERC grant of 1.5 million for a follow-up research project. How much deep reflection is involved in awarding such grants? I hope Martin will not be offended if I add that, whatever reflection he may have engaged in upon reading the article, it was likely not an essential part of his decision to post the link. And, as for my own decision to follow that link: what chance has reflection in the face of clickbait? In conclusion, then, Sangiacomo (as reported) and I (as self-reported) agree thus far: we both hold that philosophy requires reflection, and yet we both concede that the output of an unreflective, algorithmic process can present a useful occasion for such reflection.

The question, however, is whether some such algorithms are superior to others. Sangiacomo, in conjunction with the Data Science team at Gronigen’s Centre for Information Technology, has come up with a new algorithm to do this, and plans to spend 1.5 million following up on this work, because he is unsatisfied with the results of a different algorithm, namely, the one whose output he characterizes as “a few great works by a few great authors.”[3]At least: these words are in quotation marks in the article, which I think is supposed to imply that they are due to Sangiacomo, rather than to Lelong. This algorithm, too, has various stages which have been implemented on different hardware. The first and longest part was carried out by what you might call a neural network — anyway, it was a network of some kind, as Sangiacomo reportedly asserts. In a section of the article titled “The importance of a network,” Lelong writes:

Sangiacomo also found that social connections also have a significant role to play in the popularity of certain philosophical theories. As such, in addition to the shifts in meanings, he also sought to trace the mutual relationships and networks of early modern philosophers.

Working over the course of some centuries, this network has brought a few great authors to prominence. The second and shorter part is carried out by the current institutions of philosophy, as part of the process of professionalization: students, professors, journal editors, etc., are trained up to recognize these few great authors and to produce and respond selectively to the work of philosophical scholars which is confined, in a certain way, to a few great works by them.

That the first, long part of this process was algorithmic in the sense in which I am using that term, which it to say, not properly reflective, is Sangiacomo’s point when he (reportedly) goes on to say:

A priori, there are no obvious reasons as to why some philosophical theories become much more popular than others. Throughout history you sometimes see that really crazy ideas become mainstream, while good ideas are side-lined. To explain that, you have to look at social connections, because people are the real driving force of history. In that respect, this project provides a lot of information.[4]Again, these words are in quotation marks in the article.

Now, the discovery that some ideas are “really crazy” (Dutch: erg gekke) even though they have “become mainstream” (Dutch: mainstream worden), is, in other words, enlightenment. As such, it requires, one would think, significant philosophical insight, and must therefore depend on deep reflection. This calls up the image of an alternate version of history: a history in which the owl of Minerva gets up early in the morning and flaps around all day, pecking out the really crazy ideas and making sure that the good ones become mainstream. Sangiacomo, however, regardless of what he may or may not imagine, nevertheless does not propose either to apply reflection now, in order retrospectively to put such a history together, nor to try and institute the rule of reflection from now on. Instead, he offers a new algorithm.

But before considering Sangiacomo’s new algorithm: I have yet to describe the second, shorter stage of the old one. This stage, as it happens, is well describe by Martin Lenz himself in his own recent blog post:

People become enthusiastic if they recognise something. . . .  I think much the same is true of our talk of “great thinkers.” We applaud recognised patterns. But only applauding the right kinds of patterns and thinkers secures our belonging to the ingroup. . . .

This is why calling someone a “great thinker” is to a large extent self-congratulatory. It signals and reinforces canonical status. What’s important is that this works in three directions: it affirms that status of the figure, it affirms it for me, and it signals this affirmation to others. Thus, it signals where I (want to) belong and demonstrates which nuances of style and content are of the right sort.

The algorithm at this stage has a familiar purpose, one of the main things both artificial and natural intelligences are trained to do. It is an algorithm for recognizing patterns, and, more particularly, for recognizing places in a pattern: figures that stand out against a ground, enclosing what is inner and excluding what is outer. Some of the places, or topics, it is trained to recognize are great thinkers of the past, whereas others (metaphysics, philosophy of mind, etc.) are contemporary, but, one way or another, knowing how to recognize such topics; how to market oneself as belonging to one of them (or to the “intersection” of two of them); how, on the basis of this topic assignment, to enter into a mutually beneficial group of researchers who own that topic, in which everyone is bound to cite each other’s works; how (if one is a journal editor) to determine the topic of a submission and ensure that it is refereed by members of the group who own that topic — all this, and more of the like, is what professionalization in academic philosophy currently entails.

Or — and this will make a difference to our understanding of what Sangiacomo proposes to do — is that description already somewhat outdated? In using the term “topic” I allude, on the one hand, to Kant and, via Kant, to Aristotle. More on that below. But I also, on the other hand, allude to Brian Weatherson’s fascinating History of Philosophy Journals: Volume 1: Evidence from Topic Modeling, 1876–2013. Unlike Kant and Aristotle, Weatherson cannot be held responsible for the word: “topic modeling” is just the usual terminology for the type of algorithmic technique he uses. But still, it is interesting to inquire into what “topic” ends up meaning for him, i.e. what “topics” the algorithm comes up with when applied to the contents of philosophy journals during the indicated period. It is particularly interesting in the present connection because, to quote the Wikipedia article just linked to:

HLTA [a method of topic modeling][5]HTLA stands for hierarchical latent tree analysis. Weatherson uses a different method, LDA (latent Dirichlet allocation). For some technical details and, should you be interested, links to more, see the Wikipedia article in question and Weatherson’s chapter on methodology. was applied to a collection of recent research papers published at major AI and Machine Learning venues. The resulting model is called The AI Tree. The resulting topics are used to index the papers at to help researchers track research trends and identify papers to read, and help conference organizers and journal editors identify reviewers for submissions.

So, in other words: the AI researchers themselves feel that their algorithm, when implemented by artificial intelligence, can fulfill at least part of the function I assigned to professionalized human philosophers above — or rather, it can fulfill at least part of the corresponding function in that field. So an interesting question would be: will Weatherson’s related technique succeed in finding the corresponding kind of “topic” in philosophy, such that it, too, could be used for those purposes? The interesting answer, as I understand Weatherson’s results, is that his method can succeed in this respect, but only during a certain, relatively short period of the history of philosophy (and of the history of philosophy journals).

A perfect philosophical work, at whatever time and in whatever way written and/or published, ought to have a topic, a place, in a formal (logical) sense. That is: it ought to have some leading concept.[6]You might think the condition should instead be that the work have a leading judgment (a thesis). For Kant, however, such a unity of thesis depends on and presupposes a conceptual unity: “A judgment is the representation of the unity of the consciousness of different representations or the representation of their relation insofar as they make up a concept” (Jäsche Logic, §17, Ak. 9:101,5–7). For, as Kant says in the Amphiboly of the Pure Concepts of Reflection:

One can call any concept, any title under which many cognitions belong, a logical place [Ort]. Upon this is founded [gründet sich] the logical topics of Aristotle. (KrV A268/B324)[7]Kant, reasonably enough, treats τόποςtopos as the equivalent of Ort, and reserves Topik for a theory or system of such places (parallel to other terms such as Logik and Physik). But I will stick, somewhat reluctantly, to the more common practice of calling each individual logical place a topic. (Hume, following a different interpretation of the Topics, uses “topic” in yet another sense.)

The (logical) perfection of such a work would consist in the consequence of all its parts from, and their joint adequacy to, that single leading concept:

In every cognition of an object there is namely unity of the concept, which one can call qualitative unity, insofar as only the unity of the comprehension of what is manifold in the cognitions is thought thereunder, as, for example, the unity of theme in a play, an oration, a fable. Secondly, truth with regard to consequences. . . .  This one can call the qualitative plurality of the notes that belong to a concept as their common ground. . . . Finally, perfection, which consists in this, that this plurality, [taken] together, reduces, conversely, to the unity of the concept, and completely agrees to this [concept] and to no other, which one can call qualitative completeness (totality). (B114)

I hasten to add (in fact, this is the whole point of §12 of the B edition) that these three qualitative moments of quantity are necessary but not sufficient for reference, i.e. for “cognition of an object”; in other words, even a work that is logically perfect in this sense might lack a subject matter (what might be called an objective or material topic, although Kant never uses such expressions, to my knowledge). And then again, on the other hand, a work might be full of objective content and yet lack formal–logical perfection. This latter condition, roughly speaking, is what the methods of “topic modeling” assume: namely, that a given article will contain a mixture (in some determinate proportion) of the consequences (notes, characteristics) of various different logical topics. Words are used as proxies for such consequences, and a statistically recurring cluster of words is taken as the sign of an underlying conceptual unity from which all (and, ideally, only) the members of that cluster flow.

Even assuming, however, that all or most of the articles published in philosophy journals have at least such imperfect logical locality, it doesn’t follow that the topics located by topic modeling will be topics of the aforementioned kind, namely the topics that guide the current algorithm of professionalized philosophy. For one thing: if a topic is to be usable in that way, it must be, not only a logical place, but also, so to speak, a social or political one. It is not enough for it to comprehend, in a conceptual unity, what is manifold in certain cognitions; it must also comprehend, in a political unity, what is manifold in certain people. This is explicit enough in one part of the function of such topics: if the editor is to decide, based on the topic of a paper, who would be appropriate reviewers, or rather, to which reviewers that paper is appropriate, then there must be an identifiable group of people who have a right — in a broad sense, a property right — to the topic in question. This is the external deference to or recognition of the political structure which is owed by the journal editor; internally, the main political tie, is, as I have mentioned above, the implicit covenant to cite one another’s papers.[8]It came out recently, in certain infamous cases, that the editors of some journals had not paid this political deference to the owners of certain topics, e.g. trans studies, and, as a consequence, had accepted articles for publication that failed to cite the literature. No doubt these articles were also flawed in their content. I highly doubt they were based on deep reflection or contained many relevant philosophical insights. But people were quite right, in my view, to complain, not only about problems in content, but about the merely procedural errors in the acceptance process. This lack of deferral to experts was itself, indeed, an unjust act, given the way other topics are currently treated. Following the usual terminology, I will call such combined logico-political topics specialties. For topic modeling to pick up topics of the right kind, at a minimum, the constitution of professional philosophy — the constitution under which the body of writing to be analyzed was produced — must involve division into specialties.

In the absence of such a constitution, the method may well detect some topics, but these topics will not be specialties. It might still pick up the logical topics of individual works, even though, since these topics are not specialties, the information will not be usable by journal editors etc. in the contemplated ways. On the other hand, however, it might detect political topics directly, even though these are not specialties, i.e., not correlated with logical topics. A group of people who selectively read and mention each other, and selectively control one another’s ability to publish and otherwise flourish, will naturally develop some linguistic markers of their own. They would do so, I’m certain, even under an imagined constitution in which political topics were formed arbitrarily, say by lot, which means that topic modeling could easily discover even such purely political topics. Philosophy has never been so constituted, and I hope it never will be.[9]Some systems of academic patronage can contain elements of such a constitution, however. This may be what Sangiacomo has in mind when he (reportedly) talks about “the network of a well-known male author,” and also when he (reportedly) says that “people are the real driving force of history.” It’s not what you know but who you know, as they say. But philosophy has very often, in fact almost always, had another constitution that might produce, so to speak, an even stronger political signal. I refer to the system of philosophical schools, also known as sects: αἱρέσειςhaireseis. In this system, a few great authors — authors in the original sense, authorities — are treated, not as logical topics, conceptual themes that a philosophical work might be about, but rather as heresiarchs, mythical or historical originators and successive rulers of political topics that preserve themselves through time.

Maybe it seems that there is little to choose between our constitution of specialties and this older one of sects. Isn’t the latter just an alternate way of dividing up the same territory? But actually everything is different, because no sect ever owns its authorities. If anything, it is the other way around, although sovereignty should not be confused with property. In any case: this relationship, however it should be described, leaves the authorities still available to anyone else. The ancient Peripatetics and Stoics could not prevent, and had no right to prevent, the Neoplatonists from using Aristotle or Epictetus for their own purposes. The German Idealists might have many things against Schopenhauer, or the Marburgers against the Phenomenologists, and vice versa, but no one could coherently complain: Kant is ours. If Natorp gave a talk, and Husserl raised his hand during the Q&A, he would not have to begin his question with an apology: “This is not my field, but …”. The authorities were no one’s field. They remained a commons.[10]This is not to say that there can’t be problems about property rights to authorities. Problems will come up when we want to use an authority, e.g. Confucius, who belongs to an entirely different tradition, a tradition that has its own institutions of teaching and writing and need not necessarily welcome being appropriated by the Western academy (descended from Plato’s Academy). In general, a commons belongs to the village, not to the world.

And, sure enough, Weatherson does pick up at least two sects as “topics”: post-Kantian idealism (dominant in the earlier years of his journals) and ordinary language philosophy (peaking sometime in the 1950’s). Weatherson is well aware that these are not “topics” in the same sense as most of his others: he does call idealism a “school,” and he says of ordinary language philosophy that “what the model is finding is a style as much as a content,” although I think “school” (or “sect”) would be more appropriate in that case, as well. He explains here that, while the particular model that forms the basis of his book did not detect another sect, pragmatism, this sect did appear as a topic in many other runs. Since the reign of Analytic philosophy began with the capture of most of these journals by a single sect,[11]As discussed by Weatherson, ibid., referring in turn to an article by Joel Katzav and Krist Vaesen. most of the well-defined sects in the postwar period do not appear in his model, or at best have a very small signal.[12]Clear examples of this would be Straussians and Cavellians, both of whom tend to publish elsewhere. Continental philosophy, while it could be regarded from the outside as one big sect, also continued to have a stronger sect-based constitution internally during much of this period, but, again, their publication mostly did not appear in these journals. The nature and evolution of Continental philosophy’s internal constitution are beyond my scope here, and in part beyond my knowledge (though I do have some ideas).

But — and this needs to be emphasized because, even though the main events happened within living memory, they have already become hard to imagine, let alone recall — this does not mean that his method detects mostly specialties from, say, the late 1940’s on. On the contrary: no specialties yet existed, or at most very few (ancient philosophy might be an example). What we had instead was, to begin with, a single sect, Analytic philosophy, which then began the process of breaking into subsects. Ordinary language philosophy was an early and ultimately abortive example, but it is not hard to imagine an alternative future for our mid-to-late 20th century past in which Anglophone philosophy would have been divided up among followers of such figures as Popper, David Lewis, Dummett, Putnam, Rorty, etc., with none of those sects coming to own any logical topic. In other words: we might have Popperian logic, Lewisian logic, etc.; and likewise for metaphysics, political philosophy, philosophy of science, philosophy of language, philosophy of mind — each of these figures felt free to write about any of those logical topics, and so might all of their followers have felt free. In fact, Lewis, writing around 1988–9,[13]“Academic appointments: Why ignore the advantage of being right?,” first published in Ormond Papers (Ormond College, University of Melbourne, 1989), based on a lecture given at Ormond College in July 1988; now available in Papers in Ethics and Social Philosophy (Cambridge University Press, 2000, ISBN 978-0521587860), pp. 187–200. I have discussed this article, which abounds in relevant philosophical insights, at greater length elsewhere. seems to confidently assume that such a future is in store: the implicit bargaining between the members of his lucky philosophy department concerns which school[14]Lewis in this article conceives schools doxastically, as groups of people who happen to agree about certain things, rather than politically, as I do here. I take this as a piece of characteristically Lewisian irony. will get a new hire, not, as generally happens now, which AOS will get it. Allowing for Lewis’s perceptions of the profession to be a little out of date,[15]If that is really the explanation. He had perhaps already acknowledged Leibniz as a historical specialty earlier: “Anything I might say about Leibniz would be amateurish, undeserving of others’ attention, and better left unsaid” (On the Plurality of Worlds (Blackwell, 1986, ISBN 978-0631139942), p. viii). Alas, what I wouldn’t give to know Lewis’s amateurish thoughts on Leibniz! this agrees well with my own sense that the rise of specialties occurred sometime in the 1980’s. It also agrees with Weatherson’s characterization, here, of his Era 3 (1966–1981): “where the classic works of contemporary analytic philosophy were written by writers like Kripke, Lewis, Putnam, Rawls, Thomson, Singer and Frankfurt.” “Classic works of contemporary philosophy” (as I have had occasion to point out recently on Facebook) is, like “Classic New Coke,” a contradiction in terms. But we can all understand Weatherson’s meaning: since this was the era of the last authorities, the most influential works of this era — the ones that would have become central texts of newly emerging sects — are, so to speak, frozen in, as both “classic” and, at the same time, permanently “contemporary.” And this also explains why he describes his Era 4 (1982–1998) as “the one I have the hardest time conceptualising.” This era, being the era in which empire of specialties arose and grew to its maximum extent, is the era Weatherson (at least subconsciously[16]I don’t know Weatherson personally, nor have I read his extensive other professional publication, but his writing in this book is thoughtful (perhaps even contains some deep reflection and relevant philosophical insights), so I don’t want to suggest that he is unaware of the matters I bring up here. I should emphasize, as well, that he does not aim (at least, in what he has published so far) to study the change I am talking about; I am putting his work to a use somewhat different than what he intends. In particular: the author of an article is not among the data that his algorithm works with. Still, I think it not too unfair to say that his work is animated by a background feeling that division into specialties a normal state for philosophy.) imagines extending over the whole history of philosophy. How could he differentiate it in the way conceptualization requires?

I have one last matter to consider from Weatherson, before getting back to Sangiacomo and, by way of him, back to Kant (and Hume). This is the nature of his Era 5 (1999–2013), which he describes somewhat anticlimactically as “dominated by a number of distinctive topics, such as reasons, vagueness, contextualism and Williamsonian epistemology and metaphysics.” I suppose Era 5 is all of that, but it is also the period which saw the appearance of the “bad topic” he discusses here and again here. This bad topic (“bad” in the sense that it is not the kind of result Weatherson wants) does not appear in the list he eventually settled on; it resulted from an attempt apply too many iterated “refinements” to the same underlying model — I refer you to the above linked text for technical details. Here is Weatherson’s description of what happened:

One signature problem with the kind of text mining I’m doing is that it can’t tell the difference between a change of vocabulary that is the result of a change in subject matter, and a change of vocabulary that is the result of a change in verbal fashions. . . .

So after 100 iterations, we ended up with a model that wasn’t a philosophical topic at all, but was characterized by the buzzwords of recent philosophy.

To be specific, the words the over-refined model gave most weight in identifying this topic were: accounts, role, commitment, commitments, account, proposal, constitutive, practices, challenge, typically, claims, worry, approach, relevant, project, focus, features, issue, appeal, provide. I blush to say that I have relied on some of these myself in the past and that, even after having seen the list, I sometimes find it difficult to avoid them. Weatherson hesitates between two possible explanations of why a bad topic like this only appeared towards the end of his period:

  1. There has been a linguistic revolution over the last generation, and philosophers now write in a very different style to how they wrote a generation ago.
  2. This is an artifact of model building, and if you stopped the model at any time, and ran the same study I did, you’d get results like this. That is, doing what I did will get you weird results whenever there is linguistic drift, and there is always linguistic drift.

But, although I have not a shred of that meticulous empirical evidence which Weatherson requires and could supply, I don’t doubt for a moment that the answer is (1). This certainty of mine you should probably distrust: the old are always affronted by the language of the young, after all. I can only say how it seems to me. The rise of these buzzwords, namely, seems to me a sign that it is not only Weatherson’s algorithm that can’t tell the difference between subject matter and verbal fashion, but that, rather, the algorithms of professionalization themselves are beginning to have the same problem. We are beginning to train up producers and detectors of buzzwords.

Back to Sangiacomo, then. In place of the algorithmic — that is, as I am using the term: unreflective — process which has brought up a few works by a few great thinkers for our consideration, he offers a different algorithmic process which will bring up different pieces of text. Granted, there may be little reason to suppose, with Hegel, that the old algorithm, the algorithm of history, was suffused with the cunning of the spirit, such that it could be trusted always to output exactly what deep reflection requires. Whatever Hegel means by “the end of history,” it probably is not the kind of end we face now. Still, it would be reasonable to ask: what was wrong with the old algorithm, and how will the new one improve on it? Sangiacomo (reportedly) explains:

Our entire understanding of early modern philosophy is based on the works of five authors.[17]The five (or six) authors he counts, in the order in which Lelong lists them, are: Spinoza, Descartes, Hume, Locke, Newton “and, at least according to some, Kant.” A few other names, e.g. Leibniz, could probably have been added to this. So naturally, that is an incredibly distorted view. But what is the alternative?…

I realized that I would never be able to gain a complete picture of that period. Because if it turns out that there were actually as many as a thousand philosophers active during that time, what would be the advantage of adding ten to fifteen names to the existing canon? We need new tools.

How he arrived at the figure of (as many as) a thousand “active” philosophers, I can only guess. But I can say a few things about this. First of all, if the knowledge we need about our history, in order to make reflection possible, consists in knowing the views of as many as a thousand different people, then there is no hope for us, because there is no way we can possibly know that. Secondly, and worse: as philosophy is now constituted, we, the thousands upon thousands of philosophers who are said to be active now, are very far from knowing the views even of those five authors. Each of these authors constitutes a specialty (or rather, as things now stand, a relative specialty, which is a generality to the various specialties lying under it). The owners of a specialty are alone authorized to say, to one another, in the journals, what each one of these authors said, and always on the condition that they cite one another. The rest of us are authorized, more or less, to supply caricatures of them for the purposes of jokes at department meetings, lectures to undergraduates, and chronically unfunny comic strips. Adding ten or fifteen new history AOS’s would only make this situation worse. To be added to the canon, under our present constitution, is to be culturally appropriated: removed from the commons and brought under the corporate control of a specialty. After canonization, the figure in question is no longer known by us: from our point of view, they have been canceled. Canonization is appropriation is cancellation. Only those who are (still) too obscure to be claimed by any specialty can still be known by us at all.

What is the true fear, the true uneasiness, that finds expression as the fear that “our” “view” is “incredibly distorted”? There is an inconsistency between the way we understand contemporary philosophy (the classics of Weatherson’s Era 3, plus the vast output or Eras 4 and 5) and the way we — that is, the specialists among us — understand the history of philosophy. To know philosophy now, to be a professional, means (1) to know to which specialty one belongs, who else belongs to it, when to cite them, and so forth; and (2), increasingly, to be up on the latest verbal fashions, to know what buzzwords to emit. But no one knows anything parallel about philosophy before Era 3. It would be impossible to know (1), since specialties did not yet exist, but some historians, so-called contextualists, now supply a simulacrum by pretending that, say, Descartes, spent much of his time eagerly scanning the latest literature by every (active) member of his “field” (which was …?), as if he lay under our obligation to read recent things so as to able to spew a list of name–date pairs into the appropriate footnote. But this leaves (2) unaccounted for, and (2) is what Sangiacomo’s algorithm promises to supply. Along with his collaborator, Christian Marocico, and others at the CIT, he “used ShiCo (Shifting Concepts through Time), an open source tool developed by the Netherlands eScience Center and the University of Utrecht, to analyse shifts in words in a historical context.” Here is how it worked out:

Of course, the tool needed a little tinkering. ShiCo was developed to record conceptual shifts in 20th-century newspaper reports. Data scientist Marocico adapted the model so that the algorithm was able to analyse 70,000 letters exchanged between philosophers and academics during the 17th and 18th centuries. . . .  They investigated which word associations were formed for certain scientific concepts, and how this changed over the years. Sometimes this produced remarkable results. “For example, we found that in the 17th century the English word ‘spirit’ was used in both a chemical and a religious context. In the 18th century, however, we see that the word has lost its chemical meaning. It illustrates how concepts change.”

It may not be obvious that this result is remarkable, that is, worthy of remark.[18]Contrast it with Locke’s story about a related word: “I was once in a Meeting of very learned and ingenious Physicians, where by chance there arose a Question, whether any Liquor passed through the Filaments of the Nerves. The Debate having been manag’d a good while, by variety of Arguments on both sides, I … desired, That, before they went any further on in this Dispute, they would first examine, and establish amongst them, what the Word Liquor signified. . . .  They were pleased to comply with my Motion, and upon Examination found that the signification of that Word, was not so settled or certain, as they had all imagined; but that each of them made it a sign of a different complex Idea. This made them perceive that the Main of their Dispute was about the signification of that Term; … a thing which when considered, [they] thought it not worth the contending about.” (3.9.16) But we can appreciate what might make it remarkable by comparing it with what Weatherson (somewhere in here) says his algorithm has detected in its “bad topic”: “talking about the ‘commitments of an account’ rather than the ‘consequences of a theory’ is a way to mark one’s philosophical writing as being up to date with modern terminology.” This is the kind of thing a professional ought to know about the present, and so it must be important to know it about the past, as well.

Whether deep reflection, of the kind essential to philosophy, can ever be prompted by knowledge of verbal fashions — either contemporary verbal fashions or the verbal fashions of the 17th century — I honestly don’t know. The spirit, as that term is used in a Hegelian context, rather than a chemical or a religious one — the spirit, whose perfections non comprehendere, sed quocunque modo attingere cogitatione possumus, is always more cunning that we expect; it always overflows our concepts, shift them as we might. It is said to have revealed itself in cracked turtle shells, in images on toast, in words written on subway walls and tenement halls, in riddle games in the dark at the roots of the Hithaeglir, in comic strips, in superhero movies, in Facebook memes, in a brutal command to wipe out Amalek — perhaps, who can say, it reveals itself in philosophical buzzwords, as well. But, if we are to act on God’s apparent, presumptive, antecedent will, rather than his secret, decisive, consequent one, I would have to say that this method does not look promising.

What about the old algorithm, then — let’s say, the old algorithm as it operated (or: in one of the many ways it operated) before the rise of our current specialties? What reason is there, Hegel’s reasons aside, to expect anything useful from that? “Why,” to quote the title of Lenz’s blog post cited above, “would we want to call people ‘great thinkers’?” To tell the truth, although I have often used that phrase in the past, I am growing tired of it. To present day ears, at least, it sounds like an award we are giving to some people, as if we were doing something for them, rather than: that they did something for us, namely, made us possible. I am pleased to find that Justin E.H. Smith makes some remarks along the same lines in a newsletter I received as I was writing this, which I will quote, since he writes so much better than I do. Speaking of demands that we diversity our canon, he says:

An implicit premise … is that it is a good thing for a thinker to end up on a course syllabus, a sort of posthumous prize handed out to the dead by the living. Thus it is presumed that to study the old canon, as we inherited it, the canon of dead white men, is to honour these dead white men.

But scholarship is not a fan club, and to read Descartes or Kant is an undertaking that is entirely neutral with respect to whether they are praiseworthy as thinkers (a fortiori whether they are praiseworthy as people). When we study the history of philosophy we want, first, to know what happened, and second, to know how what happened shaped the world we inherited. This is not a celebration, but a solemn duty.[19]I received this essay as an edition of Smith’s newsletter, to which I urge you to subscribe, but for now you can see it online without a subscription here.

I disagree with some of this,[20]I agree that at least some of the complaints about the old canon arise from a thought like this: that assigning someone’s book is like building a monument to them (which, however, does rather undermine the meme about, “Won’t they be surprised to hear that we can learn history from books?”). But I doubt that all or most of the impetus for a new, more diverse canon can be traced to same source. What students want to see on the syllabus is not someone to whom an award is due, but someone who “looks like them,” who reminds them of themselves. And, in some sense, as I will go on to say, that is exactly what they should want. I can’t think that what is really desirable in this respect is to find someone in the reading list the same color or gender as yourself, but I can see that feeling alienated by the color and gender you exclusively do find might be an obstacle. We all face such obstacles, but some more than others. We should try to remove them if we can. and with some of the other things Smith says in his essay, but I agree with the main point: canonization is not a reward. So, although I continue to think that most of the canonized, if not all, were indeed praiseworthy, and in particular that they were praiseworthy as (finitely!) wise and good — wiser and better than me, at any rate — I would rather avoid calling them great anything. Let me call them my authorities.

How can reading an authority prompt deep reflection? What is “reflection”? It is reflective, reflex. I recognize a pattern, all right, something familiar, but the pattern, the παράδειγμαparadeigma, is familiar, not because I have previously picked it up with my buzzword detector, but because I myself am its image, ut esset tanquam nota artificis operi suo impressa; nec etiam opus est ut nota illa fit aliqua res ab opere ipso diversa. This kind of pattern recognition is called recollection, ἀνάμνησιςanamnesis, and it cannot be performed by algorithm: not because machines, in the end, really only know how to count; not because πᾶν τὸ πρὸς ἑαυτὸ ἐπιστρεπτικὸνpan to pros heauto epistreptikon ἀσώματόν ἐστινasomaton estin; not (if I may allude to a certain harasser) because recollection depends on the actual physical–chemical properties of actual human brains — but simply because recollection is reflection, and, as you will recall, I have defined an algorithm as a process that does not require reflection. To see an electronic computer perform ἀνάμνησιςanamnesis would surprise me no more than to see a human being do so, which is to say: it would surprise me a great deal, and always again surprise me even if I were to see it always and everywhere I looked (although, sadly, there is little prospect of that). But I would also know, of the computer or the human, that they could have performed this recollection only thanks to a reminder. The sign, the trace that can remind me in this way leads always beyond my shifting concepts, לעילא לעילא מכל ברכתא ושירתאle-ʿeila le-ʿeila mi-kol birchata ve-shirata, and is hence everywhere beyond needing any praise from me. But I need everything from it.

I close by coming back to Kant, and from Kant to Hume. What did Kant think was wrong in Hume? Not, alas, that he was a racist: Hume’s racism, if anything, thanks to its tentative, empirical nature, would scarcely have seemed racist enough for Kant. But he did think Hume had committed an error or two. The worst one, as it happens, was his failure to reflect, or rather, his failure to reflect in the right way. Reflection (I will assert here without evidence) is the (logical) topic Kant takes up in the Analytic of Principles, in its third Hauptstück, Of the Ground of the Distinction of all Objects in general into Phenomena and Noumena.[21]The distinction itself between phenomena and noumena is also a local distinction: it distinguishes what is within the bounds of experience (phenomena) from what is without (noumena). These two places constitute what Kant calls transcendental topic — or, in the terminology I have adopted here: they are the two transcendental topics (only, of course, that the second one is empty). Accordingly, he begins there by raising a question about everything that has preceded. Granted that everything you say is true, Kant, why tell us? (For, it must always be recalled: there is a negative duty not to lie, not, absurdly, a positive duty to say everything that is true.)

If, then, through this critical investigation, we learn no more than what, even without so subtle an inquiry [Nachforschung], we would anyway have executed [von selbst wol würden ausgeübt haben] in the merely empirical use of the intellect, then it seems that the advantage which one draws from it is not worth the effort and the preparation. (A237/B296)

Leaving aside the conclusion, where does the premise of this objection come from? Who says that we would have done the same thing, anyway, without this subtle inquiry? Who indeed. Who says, for example, that we would have employed the law of causality, that every event must have a cause, even if we not only could not demonstrate the truth of that judgment, but could not even show title to the concepts it contains? The answer is: Hume. Hume says that. So what does the whole apparatus of the Transcendental Analytic contribute that was missing in Hume? If we must, anyway, use the concept of a cause (when, for example, we speculate, rightly or wrongly, about the causes of certain historical–geographical trends), what good to us is a demonstration of the Second Analogy? Kant answers:

the intellect when occupied with its merely empirical use, which does not reflect [nicht nachsinnt] upon the sources of its own cognition,[22]Nachsinnung is not the official equivalent Kant later gives for reflexio (rather: Uberlegung — see A260/B316). But I feel the translation is justified, given that he is talking here about what he goes on to call “transcendental reflection”: investigating the relation of one’s cognitions to the faculties that are their “sources.” can indeed progress very well, but there is one thing it cannot achieve, namely, to determine of itself the limits of its use, and to know what may lie within or without its whole sphere.

What Kant thinks Hume failed to do — or perhaps did incorrectly, so as to obtain a negative (skeptical) result — was transcendental reflection; and he adds that Hume was therefore led to say (as, indeed, Hume does say quite clearly) that reason cannot set its own limits (i.e., transcendentally locate itself). Which, from Kant’s point of view, is an infinitely bad error, both theoretical and practical: reason’s theoretical self-limitation is the destruction of knowledge that makes room for faith, and reason’s practical self-limitation is self-legislation, autonomy. For Kant, Hume is guilty, not of making some particular moral error, but rather of asserting that morality, as such, is impossible.

So why would Kant want to call Hume a “great thinker” (or words to that effect)? Or, as I would rather say: why would Kant take Hume as an authority?

Because Hume is perhaps the most ingenious [the richest in spirit, geistreichste — not, one assumes, in the chemical sense] among all skeptics, and incontrovertibly the most eminent with respect to the influence which the skeptical procedure can have upon the awakening of a thoroughgoing rational self-examination [einer gründlichen Vernunftprüfung], it may well be worth the trouble to represent, insofar as it is appropriate to my aim, the course of his conclusions and the strayings [Verirrungen], which nevertheless began on the track of the truth,[23]It is difficult to translate this passage correctly. The idea is that, when we follow the course or path (Gang) of Hume’s reasoning, we will find that, at certain points, he takes off after the tracks or traces (Spur) of the truth, but nevertheless goes astray (verirren). of so insightful and estimable a man. (A764/B792)

Hume supplied the place — the authoritative topic, so to speak — of Kant’s awakening.

I freely confess: the recollection [Erinnerung] of David Hume was just that which, many years ago, first interrupted my dogmatic slumber and gave to my investigations in the field of speculative philosophy an entirely different direction. (Prolegomena, Ak. 4:260,6–9)

Hume himself — wrong, infinitely wrong as he may have been — was for Kant the trace of truth, the trail, the spoor, the path that leads right inward. In Kant’s terminology: one might say that Hume, in his life and thought, constituted a symbolic, indirect exhibition of the transcendental idea of freedom. The recollection of Hume was, then, for Kant, the recollection of his own true self, of his transcendental ego. To name a tower after such a one, even a monument as high as the moon; to put him on a syllabus, or even, like some notice about the plagiarism policy, on every syllabus; to hire a fantastic young scholar who specializes in his work, or even to hire a whole army of such young scholars, each more fantastic than the last — all this is nothing, not the smallest part of what we owe him, or, rather, what we would owe him, if he needed anything from the likes of us.[24]Here I am speaking about what we might owe Hume in common, not about what is owed to him by those specialists who have appropriated him and used him as a means, extracting the value of his labor to further their own careers. But these latter will have to make their own reckoning.

But do we need him! What have I just been saying, all this time, but that our dogmatic slumber now appears terminal? “Any prospect of awakening or coming to life to a dead man makes indifferent all times and places. The place where that may occur is always the same, and indescribably pleasant to all our senses” (Walden, 5.9). He is, incontrovertibly, the heresiarch most eminent with regard to what we require. We cannot receive him now, cannot receive anyone: Hume and all the others were already canceled the moment they were transformed from authorities into specialties. To quote someone else who had a morally wrong view here and there: only a god can save us. But, if and when the day should come, it has already been prophesied: et servus meus David princeps in medio eorum.