Maimon Reading Group: Chapter 2 – A Rejoinder

I think Jon’s summary of the issues in chapter 2 is as comprehensive as it could be, considering the medium of our discussion, so my points here will mostly be related to things I’d like to reemphasize and draw attention to in terms of my own interests and my own reactions to the chapter. I wanted to post this immediately after Jon’s summary, but having gone through several reads of the chapter, I have continuously struggled to formulate my ideas as precisely as possible. So the resulting post is shorter and, hopefully, more concentrated. Plus, I of course got distracted and had to go look for my copy of Hermann Cohen’s Kants Theorie der Erfahrung because he was compared to Maimon in Atlas’s discussion of the latter’s theory of infinitesimals. [Cohen’s essay on Infinitesmal-Methode is available online] So, long story short, here goes.

As I previously stated, I find Kantian theory of sensibility/perception to be quite interesting, especially in terms of his understanding of space/time. I know that there are plenty of issues with it and I’m always excited about a debate, however something about his formulations vis-a-vis space/time being forms of intuition strikes me as if not solid, then certainly incredibly interesting, so my main interest in Chapter 2 is the business of the “infinitesimals of perception/extension” and Maimon’s original rethinking of perception as such, and consequently his rethinking of Kantian threesome of sensibility – understanding – imagination.

Differentials: infinitesimal of sensation/extension is like a geometrical point. This is not exactly how Maimon formulates his point in the very opening of the chapter, but I think it is useful to try and imagine it this way. What is so peculiar about a geometrical point? It is an ideal point, i.e., one cannot really point to a point and say “Here we have a point” (that is to say, of course, we can draw a point, but just like a drawing of a triangle and a triangle are not the same, so a drawing of a point is not really a point), and yet it constitutes lines and figures and so on.  Maimon’s opening point is that we must think of perceptions as consisting of physical point (“differentials of an extension) that are, nonetheless, akin to mathematical points. I think this interplay between “ideal” and “real” is rather intriguing part of Maimon’s discussion of sensation/perception.

As Atlas notes in his chapter on “infinitesimals of sensation” (Chapter VI), Maimon does not really pursue this theory further in his later writings. What exactly is this whole business of infinitesimals and differentials? I think this is a larger question that deserves additional attention, but for now I just want to make some brief observations.

“The way objects arise” (mode of generation): new theory of sensation/sensibility. Maimon’s discussion of infinitesimals is a discussion of perception or “the way objects arise” – Atlas translates the first note [19/27] this way: “In mathematics as well as in philosophy infinitesimals are mere ideas; they are not objects but represent the mode of generation of objects, that is, they are mere limiting concepts, which we can always approach but never attain. They arise through a process of reduction ad infinitum of the consciousness of an intuition.” [116]

By rethinking what takes place in perception Maimon, in this sense, tackles the “myth of the given” from a rather original angle: infinitesimals as individual elements of perception are not given as such, yet they are there as the process of their unification in thinking creates/determines (“creates” is appropriate here, I think, but reads better if coupled with “determines”) objects. Atlas puts it this way:

“Sensibility thus furnishes the differential elements of consciousness; the imagination produces out of these elements a definite object of intuition and perception; and the understanding establishes the relation of the objects of intuition, i.e. the sensuous objects resulting from the integration of the various differential elements of sensation.” [110]

Compare with Maimon: “Sensibility thus provides the differentials to a determined consciousness; out of them, the imagination produces a finite (determined) object of intuition; out of the relations of these different differentials, which are its objects, the understanding produces the relation of the sensible objects arising from them.” [21/31-2]

It is in light of this articulation (much more nuanced, I think, in the text itself, even if somewhat confusing and all-over-the-place upon the first reading) that we need to take Maimon’s reformulation of noumena and phenomena.

Solution to the problem of quid juris: skepticism. The problem that Maimon encounters in Kant – how do pure concepts of understanding relate to intuitions/sensations – is solved by adding the new level of the infinitesimal elements. Here’s Atlas again: ” The pure concepts of understanding are not to be directly related to the intuitions, to the sensations, but to their infinitesimal elements, which are ideas of the generation of these intuitions.” [113] More precisely, Kant’s problem was, it seems, that we had to explain the relationship between given objects and pure concepts (roughly put). In Maimon’s articulation, the only “given” we have are infinitely small magnitudes that are not perceived directly as sensuous qualities of objects, but allow us to form objects through the process of unification we call “perception” – this is certainly an idealist position through and through. The relationship between “outside” objects and “inside” concepts is now a relationship between ideas. Where did thing-in-itself go then?

Rethinking noumena and phenomena. Probably the most interesting suggestion in chapter 2 is the following:

“[The] differentials of objects are the so-called noumena; but the objects themselves arising from them are the phenomena… These noumena are ideas of reason serving as principles to explain how objects arise according to certain rules of the understanding.” [21-2/32]

Thing-in-itself as a metaphysical entity existing before and outside of determined object of perception/understanding is a chimera. If Kant was ambiguous about it, then he shouldn’t have been, i.e., whenever he talks about it in a way that suggests its independent existence, he is wrong, according to Maimon (although he doesn’t quite put it this way, but we can help him here). Noumena are fictions that serve a purpose: to help understanding determine an object. The business of understanding is thinking, i.e. the production of unity in the manifold. Yet “understanding cannot think an object as having already arisen but only as arising” – sensibility provides infinitesimals, understanding provides a rule by which an object arises [22/33].

Concepts and intuitions (once more). There is an interesting couple of thoughts in Chapter 2 that pertain to the discussion of concepts and intuitions, especially in terms of illustrating Maimon’s general view of the matter. He uses the example of the concepts of cause and effect: “The concepts of cause and effect contain the condition that if something determined, A, is arbitrarily posited, something else that is necessarily determined (by means of the former), B, must be posted.” [29/46] This is how concepts works, and in this case, the concepts of cause and effect are posited in a way that establishes a necessary relationship between A and B. Now the real question is not whether the concepts of cause and effect are formulated correctly, but whether it is possible to see the fire burn next to the stone and, having touched the stone and discovered that it is warm, conclude that fire is a cause of the stone’s warmth. The question (at this point) then is whether I would ever even think of making the connection between sun and warmth were I not already equipped with the concepts of cause and effect? Where does the concept cause/effect come from? This is the key to Maimon’s skepticism (and his quid facti problem):

“Kant derives the concept of cause from the form of the hypothetical judgment in logic. But we could raise the question: how does logic itself come by this peculiar form, that if one thing a is posted, another thing b must necessarily also be posted?… We have presumably abstracted it from its use with real objects, and transfered it into logic; as a result we must put the reality of its use beyond doubt before ascribing reality to it as a form of thought in logic; but the questions is not whether we can use it legitimately, which is the question quid juris?, but whether the fact is true, namely that we do use it with actual objects.” [42/72]

In other words, to put it bluntly, the problem is not how we can legitimately (quid juris) apply the concept of cause/effect to fire and warmth (event A and event B), but whether our concept of cause/effect is truly an a priori concept and is not in fact based on the uncritical assumption that real objects already interact in some cause/effect fashion, assumption derived from simple observation of contingent events A and B (“subjective necessity (arising from habit) that is wrongly passed off  as an objective necessity” [43/73])? To put it yet another way, the issue of legitimate application of a priori concepts to a posteriori intuitions takes the independent existence of both for granted while neither is really as obvious as Kant makes them out to be – the most important question here is the question of quid facti, not quid juris. This is where, of course, the ghost of Hume makes his entrance.

I have a heap of notes and jotted down observations still in front of me and I can hardly hope to go through all of them in order to address every single issue in Chapter 2 I found interesting, so the best strategy here is just to stop and press “publish”.

11 thoughts on “Maimon Reading Group: Chapter 2 – A Rejoinder

  1. Pingback: Maimon Reading Group (Summer 2010) « Perverse Egalitarianism

  2. So this might be a bit out of the blue kind of question, but where does Maimon’s theory of infinitesimals come from? That is to say, does he have any real explanation or is it just dogmatically posed? I realized that he relies on Leibniz and mathematical examples, but, let’s be honest here, how does saying that perception consists in some almost subconscious integration of infinitesimals of extension differ from any other random/arbitrary theory of reality (like, I don’t know, claiming that all objects at the core contain a small amount of orange juice or something like that)?

    I’m not asking you to defend Maimon’s theory as such, but in light of often posed criticism of some recent speculative ontologies, how does one approach a theory like Maimon’s? Is that why he claims to have been a “rational dogmatist“? Is there any attempt to prove or deduce this sort of theory in Maimon (as I haven’t seen a real argument in Chapter 2)?

  3. First of all, thanks for reading along. It’s always nice to know someone’s following along even if I can see that posts are getting some hits in stats.

    Your questions is more than legitimate, especially in light of the questions of dogmatism and skepticism. Reading the sections of Chapter 2 dedicated to the theory of infinitesimals again, I don’t see Maimon being dogmatic here in the following sense: the idea that our perception is hard at work before any sort of representation takes place (“presentation” as Maimon puts it and not “representation” – the latter is a “mere making present of what is not now present” [20/29] – if I’m not mistaken here, Nick could help, the German here is Vorstellung vs Darstellung) come from theorizing about our experience/perception, not from a mere postulation of some first principle as traditional dogmatic position would require.

    In this sense, Reinhold’s “principle of consciousness” could be labeled dogmatic, or any other principle that is posited as true without any demonstration or justification. Of course, our usual skeptical position could always be “how do you know that?” and this is where Maimon’s skepticism is different, and I hope to see more of it in the text as we go forward.

    The discussion of infitinesimals, I think, is ultimately very interesting because it is rather reasonably argued for, even if in the text of the Essay this argument is all over the place (I would mainly look to Maimon’s examples). When we think about perception in terms of “how is perception taking place?” we immediately realize that it is not merely a combination of raw given data and rules of understanding that make sense of that data, but that on the level of the “given” there is plenty of activity of basic “putting-together” of smaller sensations into larger units. There’s a kind of creation of sensations at hand, not a simple reading off data from already existing objects – objects come together in presentation as objects, there are no independently (and metaphysically) existing objects with substances/accidents and so on (maybe I’m taking Maimon too far here), objects arise (are generated) in the work of presentation. How does Maimon know that? Through a simple deduction: if the elements from which we get our objects are small, so small that we are not consciousness aware of them, then how small can they be? the idea of infinitely small magnitudes is the next logical step, and so on. I do agree that this deduction needs a stricter and more elegant presentation, but it’s certain there.

    I don’t think science today is any different on the matter (simplifying it of course) – Oliver Sacks has an essay in the most recent New Yorker that opens with a case of a writer losing his ability to read after a stroke – as weird as it sounds, everything was functioning normally (including his ability to write) but he could not decipher letters and put them into words, they were gibberish. Imagine a scenario in which you cannot read what you just wrote. Now, of course, this is just an example, and Sacks goes on to explain how our basic perception of letters and attachment of meaning etc etc we call “reading” is a rather complex perceptual event that involves a great number of small elements. It is fair to assume than, by analogy, that these small elements are present in every act of perception and, Maimon’s step, they in fact make up those larger more or less solid/sensuous objects we then perceive and so on.

  4. I see, I think reading the chapter again helps put these sorts of issues in perspective and I do think Maimon could have used a better presentation of the concept of infinitesimals (although, as I think you’ve mentioned, Atlas writes that Maimon never really returns to this theory and expands on it) – I wonder if it’s fair to suggest that in Maimon’s eyes these sorts of themes are familiar to the reading public from Wolff/Leibniz?

  5. There does seem to me to be a difference between the example you offer (from Sacks, but it really could be any scientific example) and Maimon’s infinitesimal: namely, that the former are not, well, infinitesimal. They seem rather to me to be much closer to Berkeley’s “smallest perceivable.” (Which, incidentally, does seem to be of a piece with Berkeley’s famous dismissal of Leibniz’s calculus as dependent upon ‘ghosts of departed quantities.’) I think one could argue that for any contact to occur, it cannot be a contact with an infinitesimal, but that there must be some delimited quanta (and I note that even contemporary physical theory depends upon a certain granularity of matter and energy in quanta, i.e., things are not infinitely divisible). Maimon seems to me to be closer to Badiou here, insofar as his infinitesimal is like Badiou’s undecidable. (In fact, this whole discussion has made me understand a little better why people read Badiou as an idealist, when he so clearly demands overtly to be read as a materialist.) If we are going to have recourse to infinitesimals, then we must argue not only that “on the level of the “given” there is plenty of activity of basic “putting-together” of smaller sensations into larger units,” as you put it, but that this putting-together goes all the way down the stack of turtles, indefinitely and indeed infinitely. I don’t have a problem with this, exactly (in fact I sort of like it), but it does diverge from physical science both in fact and I think even in principle (insofar as it courts an infinite regress).

    It’s possible that I’ve misunderstood your comment, though, Mikhail.

  6. No, Bryan, I don’t think you have misunderstood me. I’m actually thinking that you are correct in your assertions that we need to distinguish between infinitesimals and “smallest perceivables” here (I’d love to follow up on this Berkeley’s idea – do you know where he talks about this?) – if I understand you correctly, your reading of my comment goes further than I was willing to go, but I’m sort of okay with it in the same way as you are: yes, infinitesimals here must bring with them the idea of “turtles all the way down” and it’s not really as shocking and strange as it might seem, especially if you think about traditional philosophical question of infinite divisibility of space or some such. My only question here is maybe an awkward one: if there’s a kind of infinite “putting-together” (must it be infinite if there’s an infinite number of things that are being put together? or am I completely misreading the notion of infinitesimal here?), then when/where does it start and when/where does it end? Is perception, in other words, a kind of “middle of the road” image that allows us to grasp reality (or better, that allow reality to come in for a “perceiving opportunity”)?

    Maybe an unrelated thought, but reading Descartes’ concern with “I think, I exist” in Meditations as a basic concern of continuity (what carries me over from one “I think” to the next), is Maimon’s theory not a set up for the triumphant entrance of God/infinite mind a la Descartes’ Third meditation? That is to say, if we speak of infinitesimals and so on, then are we not imaging a world in need of some overarching (and ultimately “caring”) deity that would tie all of our ends together?

  7. Smallest perceivable = minimum sensibile. There’s a discussion of it in Treatise concerning the principles of human knowledge (ed. Kenneth Winkler), ex. Part I, section 132. Hope this helps.

  8. Matt is correct, though I was thinking of Berkeley’s Theory of Vision. An interesting paper on the matter is HERE (I use the caps-lock because links don’t show up well in these comments); the author, David M. Levy, argues that this finitism of Berkeley’s had ramifications for social and political philosophy, in particular Adam Smith.

  9. Re. God & infinity: I think you are right that Cartesian continuity, the “smooth” transitions between the ramifications of clear and distinct ideas, is an interesting puzzle for any step-by-step (and hence quantized) finitism. As you note, Decsartes becomes a sort of occasionalist in referring these transitions ultimately to God. Badiou is quite explicit that his appropriation of Cantorian transfinites is an argument against this, meant to “laicize” infinity, i.e., to dispel the whiff of deity that hangs about it. (He wants to yoke infinity to thought and not vice-versa.) My own suspicion is that the question of God and infinity is a “meaning-of-infinity” question (already yawned at by Badiou as mere hermeneutics, hence mere theology)–i.e., undecidable within mathematics itself. Cantor (and Godel) were quite clear that these swerving infinities had a theological import for them; but my guess is that Badiou’s atheist math, if I may put it so, is every bit as ‘consistent’. Godel showed that the continuum hypothesis is unprovable but consistent with the rest of set theory, and my guess and gamble is that the same is true of “the God of the philosophers.” I am not saying Maimon held precisely this, but he does claim to be able to reconcile theism and atheism. As you know, Harman reclaims a version of occasionalism in his account of causality; he tends to reference the Muslim philosophers and also Suarez, but I think he’s close to Malebranche.

    Now you might have been thinking of the temporal dimension in Descartes, (i.e., the ontological constitution of the res cogitans), rather than the argumentative dimension (i.e., the epistemological guarantee that I haven’t made a mistake in my inferences), but I think the question of continuity is more or less isomorphic between these two cases.

    Hope any of that makes sense. As you can see, I tend to think in scatter-shot.

  10. I’m not sure about this reclamation of occasionalism, of course, as you know – not because I find the argument for such a reclamation to be weak, but because I don’t find any argument there at all, but the usual posturing (“People will tell you occasionalism is stupid, but what if it isn’t it?” – superbly parodied in the character of Eli Cash: “Well, everyone knows Custer died at Little Bighorn. What this book presupposes is… maybe he didn’t?”).

    What is the value of occasionalism in this sense? I mean philosophical value? Certainly the problem of causality can easily be labeled the problem of seventeenth (and then eighteenth) century, right? In this sense, Kant, in reconciling rationalism and empiricism is still working on solving it – to suggest that we simply need to go “back” and rediscover occasionalism makes me think why we should only go back as Malebranche (or whichever Islamic scholars Harman wants to revive in order to be “Harman who revived our interest in X”)? Why not go all the way to some totemic or animist version of reality in which it is clear to everyone that the rabbit did it…

  11. Ah, Mikhail, you have stolen my thunder. My entire project is precisely the reclamation of the rabbit. Or is it the duck?


    In any case, I was just following up your point re. Cartesian concern with continuity (say fast five times, please) and Maimon.

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