[by Corey McCall, Elmira College]
I’ve divided my post on the fifth chapter into two unequal parts. The first, lengthier part deals with modality and covers approximately the first two pages of Maimon’s text. Once I realized I’d never post anything worth reading if I kept going at this pace, I decided to wrap up with a much shorter section on the notion of the thing, which roughly covers the rest of the chapter. It amounts to a series of notes which are my attempt to make sense of what’s going on in the chapter. I discuss David Lachterman’s article “Mathematical Construction, Symbolic Cognition, and the Infinite Intellect: Reflections on Maimon and Maimonides,” Journal of the History of Philosophy, 30 (1992), pp. 497-522; I believe all the remaining texts that I cite have been cited by either Jon or Nick in their posts. I’m becoming increasingly interested in the role that the imagination plays in Maimon’s work, and I’m hoping to be able to write something more on this in my post on the symbolic cognition appendix during the first week in August. I’ll post on chapter six in the next couple days.
I take some comfort in the fact that I’m not alone in finding Maimon’s text terribly difficult (and I admit that I haven’t had as much time to read the secondary literature as I might have liked). What follows is a series of observations, questions, and notes on Chapter Five; hopefully they will be sufficient to start a good discussion.
It seems a good rule of thumb to begin to orient oneself in Maimon’s text by relating it to the relevant concepts in Kant’s thought. Chapter Five takes up the question of modality, a question that Kant pursues in The Critique of Pure Reason in terms of the categories of possibility, existence, and necessity. These three categories provide the basis for the postulates of empirical thinking, which Kant discusses beginning at A 218/B265. Kant defines the three postulates thusly:
1. Whatever agrees with the formal conditions of experience (in accordance with intuition and concepts) is possible.
2. That which is connected with the material conditions of experience (of sensation) is actual.
3. That whose connection with the actual is determined in accordance with general conditions of experience is (exists) necessarily.
One cannot get far in Maimon’s Essay without coming back to the quid facti question (the question of precisely determining precisely how a priori categories relate to sensation), and his presentation of modality in Chapter Five is no exception. In particular, the question of actuality and the relationship between actuality and possibility is at stake in the question of experience. For Kant, the categories condition possible experience, and actuality is defined in terms of the connection between particular sensations/intuitions which are passively received and the categories of the understanding which, when combined with sensations, actively produce experience (Kant will clearly distinguish judgments of experience–which demand universal assent–from judgments of perception-which don’t-in The Prolegomena to Any Future Metaphysics, but doesn’t make the distinction explicit in CPR). Possible experience is at stake in Kant’s conception of the limits of metaphysics. In her great introduction to the Critique of Pure Reason, Jill Vance Buroker reminds us that for Kant lunar inhabitants are part of our possible experience as well (A493/B521, cited by Buroker, 188). For Maimon, the problem isn’t primarily with possible experience but rather actual experience. Maimon famously sides with Hume and argues that Kant cannot account for the actuality of experience (that is, the fact that concepts and intuitions combine to constitute it) without begging the question, and the same problem applies to the principle of causality that provides the pinch of necessity in experience. Kant’s elegant solution to the problem of experience is to argue that actual experience is that which is simply connected to intuition, but Maimon finds this solution wanting.
Maimon contests Kant’s claims about experience both in terms of the causal necessity of experience claim and the limits of possible experience claim. A possible thing is opposed to both the impossible (i.e. it’s non-contradictory) and “to the formally nothing or to the formally problematically possible and impossible, and in this case ‘possible thing’ signifies a synthesis of which we have positive cognition and in which the predicate can belong to the subject as the determination to the determinable” (Essay, 56). In other words, a possible predicate can either belong to the subject or not, and has no necessary existence whatsoever. It can belong to the subject, but it isn’t intrinsic to it. This recalls Descartes’ conception of a substance as that which has independent existence. Maimon’s example here is a “straight line,” where line can be thought “both in itself as well as with other determinations (crooked),” while straightness requires the subject (line) in order to be thought at all (Essay, 56). Similarly, using Maimon’s terminology Descartes would describe accidents such as color as determinations that inhere in a subject (of course, such talk of subjects and accidents takes us ultimately back to Aristotle via the Scholastics). The relationship between the determination (straightness) and the determinable (line) is a thus a one sided one without reciprocity. A synthesis of relational concepts entails reciprocity between the parts, so that none of the parts can be thought independently of one another. Maimon cites the concept of causation, in which neither cause nor effect can be thought apart from one another. Although it’s not mentioned by Maimon, a more interesting possibility presents itself in the concept of an organism, especially given Kant’s treatment of teleological reason in the second part of the 3rd Critique and the importance for this concept in later German idealism as well as in predecessors such as Leibniz. “But if several things that can each be thought in itself are taken together arbitrarily, then this synthesis is formally problematic and opposed to the possible” (Essay, 57). An organism (per Kant, at least as a regulative idea) would be a thing whose parts are reciprocally implicated and cannot be thought apart from one another.
In his chapter on Maimon in The Fate of Reason, Beiser discusses the important role that this notion of the determinable plays in both the Essay and in his later Logic:
The central thesis of Maimon’s principle of determinability is that if a judgment is to attain the status of real thought, then its terms must be able to stand in a relation of one-sided or non-reciprocal dependence. One term must be independent and conceivable by itself; and the other term must be dependent upon and conceivable only through the other […] Maimon insists that such one-sided dependence is the distinctive feature of real thought in contrast to formal or arbitrary thought. in other words, only a judgment whose terms can stand in such a relation is either true or false of reality (Beiser, 314).
Determinability thus becomes the criterion by which we distinguish true judgments from false judgments. True judgments, in which the predicate is dependent upon the subject, are objectively valid and not just valid for the subject (i.e. in a formal sense).
The possible is next opposed “to the materially nothing.” This, explains Maimon, “signifies the given intuition that comprises the substratum of a synthesis,” without which the synthesis would lack “objective reality.” The question of course is what Maimon means by objective reality. He cannot mean it in the pre-critical sense that thinkers such as Descartes and Hume used the term. With this conception of the possible, we return to the affection problem Jon discussed in his post on Chapter 2, but this is also a problem for the Cartesian, and later, the Humean skeptic. Without the guarantee that my thoughts conform to the world, science is impossible. Descartes attempts to come to terms with this by using God as a (literal) deus ex machina that will guarantee the truth of my perceptions if they are found to be “clear and distinct,” while Hume essentially shrugs his shoulders and goes to play billiards (I know this is somewhat glib, but at times so was Hume). Kant’s critical philosophy is famously meant to reconceive this problematic in such a way that the spontaneous understanding imposes the rules (categories) upon given appearances (intuitions) such that they can be judged objectively valid regardless of whether these appearances correspond to things as they truly are. But how do we know what causes these appearances? We can’t (and yet we must). As Beiser notes, Friedrich Jacobi first raised the problem of the thing-in-itself: “it was necessary to affirm it in order to explain the origins of experience; and it was necessary to deny it in order to remain within possible experience” (Beiser, 306). Of course, for Kant objectivity isn’t about the conformity of appearances to reality but rather about the relationship between my judgments and our judgments; for a judgment to be objectively valid simply means that we must all agree with it. If I don’t, something is simply wrong with the way I have come to this judgment. (If we stop here, it’s relatively simple, but of course the question is how precisely I have come to the particular judgments I have arrived at.) Maimon writes that the possible thing signifies the substratum of the synthesis that renders it objective, which seems to me to be closely allied to the Kantian conception of objectivity rather than the pre-critical one. Subjectivity and objectivity must be distinguished from one another from within the immanence of consciousness. Beiser claims in The Fate of Reason that this is Maimon’s mature view, and cites Mamon’s Logic: “the Fundamentum divisionis is not in the source but the content of our knowledge” (cited by Beiser, 308). In order to remain true to the principles of critical philosophy, Maimon argues that philosophers must remain silent about the nature of the Ding-an-sich.
Like Kant in “The Postulates of Empirical Thought” section of “The Analytic of Principles,” Maimon next contrasts possibility with actuality and necessity. A possible thing in this sense would be contrasted to a contingent concept or to essential matter (an idea). Maimon’s example of a contingent concept is that of a mere concept of a triangle, absent the imagination that links it with space and time. The example of an idea is that of the asymptotes of a curved line in which the finite and infinite understanding coincide. “In this second kind the synthesis of a finite and the synthesis an infinite understanding are formally identical and only materially different in that a finite understanding can make only part of the synthesis intuitive while the rest remains merely symbolic, whereas an infinite understanding represents everything to itself intuitively” (Essay, 57). With these two examples we can see the importance that Maimon places on construction (cf. David Lachterman’s work on construction in The Ethics of Geometry). Equally pertinent is Lachterman’s 1991 article “Mathematical Construction, Symbolic Cognition and the Infinite Intellect: Reflections on Maimon and Maimonides.” He cites Maimonides characterization of God from his 1793 Über die Progressen die Philosophie:
God, as an infinite power of representation, from all eternity, thinks himself as all possible essences, that is, he thinks himself as restricted in every possible way. He does not think as we do, [namely], discursively; rather, his thoughts are at one and the same time presentations/complete exhibitions [Darstellungen]. If someone objects that we have no concept of such a style of thinking, my answer is: we do in fact have a concept of it, since we partly have this style in our possession. All mathematical concepts are thought by us and at the same time exhibited as real objects [reelle Objecte] through construction a priori. Thus, we are in this respect similar to God (IV, 20).
Lachterman glosses Maimon’s text as follows:
Maimon’s formulation is, on first hearing, an extreme version of Kant’s quite Cartesian appraisal in the first Critique, viz., that the method of constructing concepts in pure intuition a priori “becomes, so to speak, the master of nature’ (A725/B753). (On closer hearing the resonances of Maimon’s similarity thesis echo not only Descartes and Kant, but his special reading of Maimonides as well.) (Lachterman, 499).
For Kant, a synthetic a priori arithmetic construction occurs in time, while a geometrical one occurs in space. The concept of a triangle is presented through a transcendental act of the imagination that temporalizes or spatializes it. Lachterman reminds us that Maimon follows Leibniz in conceptualizing space and time, so as to avoid the problem of the heterogeneity of space and time (as pure a priori forms of sensibility) and concepts of the understanding. As a result, the distinction between the formal and the material must differ from the distinction in Kant’s thought. Lachterman argues that “space and time are in the first place concepts and “afterwards” intuitions only by way of the imagination’s ‘licit fictions’ ” (Lachterman, 503). A purely formal or conceptual notion of space would be an undetermined diversity, with determination coming about as a result of schematizing:
At this purely formal or conceptual level, spatiality and temporality are devoid of any “material” characteristics, e.g., three- or n-dimensionality (VII, 80), infinite divisibility, isotrophy, equable succession, and the like. Such “material” characteristics belong, not to space and time as a priori concepts (specifically of pure diversity), but to their schemata or images produced by the imagination and wedded to the particular sets of empirical objects appearing in, or to, sensible intuition (Lachterman, 502).
I’d be interested in hearing about how Lachterman’s account of the role of imagination in mathematical construction relates to Buzaglo’s discussion of Maimon’s philosophy of mathematics (I’ve ordered Buzaglo’s book and plan to get to it soon). I hope to have more to say about this when I get around to posting on the “Symbolic Cognition” appendix later on.
Thus far, Maimon has been discussing not just possibility as such, but possible things. I’ll spare everyone the lengthy excursus on things (e.g. a discussion of Heidegger’s lecture course What is a Thing?, etc.) since this post is already somewhat long-winded as it stands, except to point out the obvious fact that the concept has had a rather interesting career in Kant and post-Kantian thought under the guise of the Ding-an-sich. A thing is negatively possible if it’s predicates or determinations are non-contradictory (this relates back to Beiser’s discussion of the principle of determinability cited above), while it’s positively possible if in addition to non-contradictory determinations it possesses an intuition “that grounds the concept along with the relation thought in that intuition” as well as “an objective ground of possibility” so as to avoid arbitrary (merely subjective) determination. Finally, we must be able to account for the thing’s genesis.
Actuality is not defined strictly in terms of complete dertermination, since something can be completely determined without being actual (. Furthermore, how can an actual thing be completely determined; or, more significantly how can I know that an actual thing is completely determined? That is, how can I know all of the relations that have combined to make this thing the thing that it is? Here Maimon sounds a skeptical note that relates back to his skeptical critique of Kant’s project. All we can know of a thing’s concrete relations is a posteriori, so the laws of the understanding cannot completely determine the thing–the predicates of a lump of gold can be thought independently of one another. In other words, the predicates that determine the thing are necessary but not sufficient for an understanding of the nature of the thing (provided that I’ve adequately understood Maimon’s point here). Maimon defines an object’s ground as the rule by which it can be represented, but it remains insufficient, an idea of reasonOur description of a thing’s properties will always remain incomplete, a function of the finitude of our intellectual capabilities (Essay, 58-60).
Obviously, there’s much more that needs to be said about this chapter, but I hope this will suffice as a beginning.