09 August 2012

Problems with scientia intuitiva and the Absolute Idea

I have mentioned a few times that I should write a post discussing Förster's examples from "The Methodology of the Intuitive Understanding", chapter 11 of "The Twenty-Five Years of Philosophy".

First, it's probably best to look at what Spinoza tells us about scientia intuitiva, what he calls in his Ethics "the third kind of knowledge". There's surprisingly little telling us what this actually is in the Ethics; the only clear treatment of all three "kinds of knowledge" comes at EIIP40S2:

From all that has been said above it is clear, that we, in many cases, perceive and form our general notions:--(1.) From particular things represented to our intellect fragmentarily, confusedly, and without order through our senses (II. xxix. Coroll.); I have settled to call such perceptions by the name of knowledge from the mere suggestions of experience. (2.) From symbols, e.g., from the fact of having read or heard certain words we remember things and form certain ideas concerning them, similar to those through which we imagine things (II. xviii. note). I shall call both these ways of regarding things knowledge of the first kind, opinion, or imagination. (3.) From the fact that we have notions common to all men, and adequate ideas of the properties of things (II. xxxviii. Coroll., xxxix. and Coroll. and xl.); this I call reason and knowledge of the second kind. Besides these two kinds of knowledge, there is, as I will hereafter show, a third kind of knowledge, which we will call intuition [scientia intuitiva]. This kind of knowledge proceeds from an adequate idea of the absolute essence of certain attributes of God to the adequate knowledge of the essence of things. I will illustrate all three kinds of knowledge by a single example. Three numbers are given for finding a fourth, which shall be to the third as the second is to the first. Tradesmen without hesitation multiply the second by the third, and divide the product by the first; either because they have not forgotten the rule which they received from a master without any proof, or because they have often made trial of it with simple numbers, or by virtue of the proof of the nineteenth proposition of the seventh book of Euclid, namely, in virtue of the general property of proportionals.

But with very simple numbers there is no need of this. For instance, one, two, three, being given, everyone can see that the fourth proportional is six; and this is much clearer, because we infer the fourth number from an intuitive grasping of the ratio, which the first bears to the second.
Now, it is famously unclear how to understand this example, but as Spinoza exegesis is not Förster's concern, I can ignore those questions. One thing worth noting is that Spinoza also characterizes scientia intuitiva as proceeding from knowledge of the essence of a thing to knowledge of its properties; I am too lazy to look up that quote, but I believe it's in Treatise on the Emendation of the Intellect. But I am mainly interested here in Spinoza's example itself: We are given three numbers in a series, 1, 2, 3, and told to find the fourth. The answer Spinoza is looking for is '6', which is (3*2)/1, as 6/3=2/1.

I remember when I first read this passage, I didn't pay any attention to the math-talk and was surprised when the number after 1, 2, 3 was not '4'. This nicely illustrates an important point: being given a series of numbers does not always uniquely determine "what number comes next" in the series.

More strongly, the following is true: No finite series of numbers uniquely determines a function. Trivially, a finite series of numbers that fit a function will also fit an infinite number of piecewise functions which are defined for the given elements in the same way as that function, but in some other way for elements not given in the series. (I'm not sure if the same holds for infinite series, since my math skills are inadequate, but I only need the weaker claim for discussing Förster's examples).

A point related to this is one Leibniz spends some time discussing (somewhere): given a series of points, there is no line which uniquely fits those points. (I believe this is equivalent to proving the stronger claim I was hesitant about in the previous paragraph, since an infinite series of elements can be treated as a list of ordered pairs, which will equate to points on a graph, and if no line is determined by them then neither can they determine a function, since if they determined a function you could draw the line the function displayed and it would uniquely fit the points. Yes, I have now convinced myself of this. But again, I don't need that stronger claim.)

Now, here is Goethe, in "The Experiment as Mediator Between Object and Subject", quoted by Förster on page 256:
In the first two installments of my optical contributions I sought to conduct such a series of experiments which border on and immediately touch upon each other, and which indeed, once one has become thoroughly familiar with them and contemplates them as a whole, constitute but one single experience seen from the most various vantage points. -- An experience of this kind, consisting as it does in a series of experiments, is manifestly of a higher kind. It represents the formula in which countless individual problems of arithmetic are expressed. To work towards such experiences is, I believe, the highest duty of the natural scientist.
Förster then reminds the reader of the historical context: Goethe had believed that he could "see" the Idea of color by doing all possible experiments with the way light shines through a prism onto boundaries between light and dark surfaces, and then his "seeing" of this Idea would allow him to articulate a correct theory of color. Lichtenberg had pointed out that the theory of color Goethe put forward on this basis didn't explain why I see green dots if I stare at red dots and then turn quickly to look at a white surface. The moral Förster draws from this is general: Goethe believed that if he looked at enough individuals of a certain kind, he could grasp the Idea which manifested itself in these various individuals (the Idea of color which made all colors colors, the Urpflanze which made all of the various plants plants). But the (merely empirical) fact that his early theory of color fails to explain the empirical phenomena of "couleurs accidentelles" revealed a logical problem with his methodology: given what an Idea is supposed to be, one cannot grasp an Idea by simply seeing individuals which manifest it; some further logical element is needed.

Here it is probably helpful to remember the Kantian context for this problem: Goethe's strange efforts with colors and trying to see the "Idea of color" are akin to trying to see a cow as a cow. Kant believed that we cannot know whether there are genuine purposes in nature (such as organisms), and that the idea of such things was of only regulative use. Here is a passage from section 77 of the Critique of Judgement, AK 5:407:
Our understanding, namely, has the property that in its cognition, e.g., of the cause of a product, it must go from the analytical universal (of concepts) to the particular (of the given empirical intuition), in which it determines nothing with regard to the manifoldness of the latter, but must expect this determination for the power of judgement from the subsumption of the empirical intuition (when the object is a product of nature) under the concept. Now, however, we can also conceive of an understanding which, since it is not discursive like ours but is intuitive, goes from the synthetically universal (of the intuition of a whole as such) to the particular, i.e., from the whole to the parts, in which, therefore, and in whose representation of the whole, there is no contingency in the combination of the parts, in order to make possible a determinate form of the whole, which is needed by our understanding, which must progress from the parts, as universally conceived grounds, to the different possible forms, as consequences, that can be subsumed under it. In accordance with the construction of our understanding, by contrast, a real whole of nature is to be regarded only as the effect of the concurrent moving forces of the parts. Thus if we would not represent the possibility of the whole as depending upon the parts, as is appropriate for our discursive understanding, but would rather, after the model of the intuitive (archetypal) understanding, represent the possibility of the parts (as far as both their constitution and their combination is concerned) as depending upon the whole, then, given the very same special characteristic of our understanding, this cannot come about by the whole being the ground of the possibility of the connection of the parts (which would be a contradiction in the discursive kind of cognition), but only by the representation of a whole containing the ground of the possibility of its form and of the connection of parts that belong to that. But now since the whole would in that case be an effect (product) the representation of which would be regarded as the cause of its possibility, but the product of a cause whose determining ground is merely the representation of its effect is called an end, it follows that it is merely a consequence of the particular constitution of our understanding that we represent products of nature as possible only in accordance with another kind of causality than that of natural laws of matter, namely only in accordance with that of ends and final causes, and that this principle does not pertain to the possibility of things themselves (even considered as phenomena) in accordance with this sort of generation, but pertains only to the judging of them that is possible for our understanding.
This passage is where Goethe (and Förster) get the idea of an "intuitive intellect", of an intellect which can see "a whole as a whole" rather than having to see a whole only by seeing its parts (and then concluding that these are parts of a whole, in a separate act of the mind). Kant has earlier argued (to the satisfaction of all of the German idealists, and Goethe) that knowing a particular object in nature as an organism requires knowing it as a whole in which the parts are reciprocally the cause and effect of the whole: seeing a cow as a cow requires seeing its parts as being there because they are organs of a cow, and of seeing the cow as there because of the functioning of its organs. Now, Kant thinks that the peculiar nature of our "discursive" understanding prevents us from having this sort of knowledge. As he puts it in this passage, a discursive understanding has only "analytical universals" as concepts, it has concepts which do not determine any of the content which is given in intuition. In seeing a metal sphere lying on an incline, the concepts which I bring the intuition of that sphere under ("metal", "sphere", "substance", "solid") do not determine what will be given to me in intuition. If what is next given to me is this sphere rolling up the incline instead of down it, then this shows that I was wrong in bringing it under some of the concepts I brought it under (it must not be made of metal, or at least must not be solidly metal). However the sphere behaves, I require further intuition to know it: thus there is a contingency between my representation of the sphere as solid metal and its being given to me in future intuitions as behaving like I expect a solid metal sphere to behave. In contrast to this, suppose I see a cow as a cow: then in bringing it under the concept of "cow" I determine that it must have four legs, chew cud, give birth to calves after mating with bulls, etc. I do not require future intuitions to know that it does this: if it does not do these things, then it has failed as a cow, and I did not fail in bringing it under the concept "cow". Future intuitions of the cow living as a cow lives can only confirm what I already knew about it when I saw it as a cow, and are not required for me to know this. Thus there is not a contingency between my representing the cow as a cow and its being given to me in future intuitions as behaving in the way I expect a cow to behave. I also know that it must have a stomach with four components, a liver, kidneys, lungs, etc., for these are among the organs proper to a cow: if a particular cow lacks any of them, then it is deficient as a cow. And so I do not require future intuitions to know that the cow has them: I require new information to tell me ways in which an animal is unhealthy, not to tell me how it is healthy.

Because of Kant's overextension of a particular picture of how concept and intuition are united in cognition, he denies that we can have empirical knowledge of organisms. Goethe makes a modus tollens out of Kant's modus ponens: because we do have knowledge of organisms, we must have intuitive intellects (and not merely discursive ones).

So, Goethe's problem is this: How can it be possible to see "a whole as such", as opposed to only ever seeing a whole by progressing from the parts to the whole?

His initial, flawed, answer, is that we can see "a whole as such" by seeing individuals which are instances of that kind of whole. But I cannot learn what a cow is simply by seeing many cattle; for to know what a cow is, I need to know things about the ways a cow's organs interrelate with one another, and the way that various actions of a cow function in the life-cycle of a cow. But if I only ever look at particular cow organs on their own, and particular cow actions in isolation from one another, then I will never learn from this how these organs and these actions are organically united in the life of the cow.

Returning to Förster, and Goethe:
What is the problem here? Let us consider once again Goethe's characterization of what he calls an experience of a higher kind: It comprises a number of different experiences and "represents the formula in which countless individual problems of arithmetic are expressed." Like a mathematical formula, the experience of a higher kind is meant to provide a means for deriving the individual phenomena from it. Is this the case? If for example I have the formula y=2x+1, I can express it in countless instances: 1, 3, 5, 7, 9, 11... This does not represent any problem. However, our task is still to discover the formula corresponding to the idea! Instead of generating the series on the basis of the formula, we have to derive the formula on the basis of the series. Thus to begin with all I have is (say) the series 1, 1, 2, 3, 5, 8, 13, 21... What is the formula on which the series is based? What would be the next number, after 21?
And here we see: Just as little as the arithmetic series as such provides the formula that generates it, neither does the 'systematic variation of every single experiment' in a complete series reveal the underlying idea.... When assembling the materials that comprise an experience of a higher kind, we must also take care not to leave out a single step if the underlying regularity is to be determined. However, the mere fact of having discovered all the parts (properties) is not in itself equivalent to having derived them from a single origin (idea).
...Something crucial is still missing, but what is it? Goethe's own path, the one that in the end actually lead him to the solution of his problem, left hardly any traces in his writings. Even so, the mathematical example from above gives us a clue what to look for. What must I do in order to find the appropriate formula for the series 1,1,2,3,5,8,13,21? Apparently I have to investigate the transitions between the numbers in order to see how one arises from the other and whether the intervals between them are based on some regularity. However I end up achieving this, there is no doubt that the path from the series to the formula lies in studying the transitions.[Footnote: An intellectual re-presentation of the transitions between 1,1,2,3,5,8,13,21, is necessary in order to realize that, from the third element in the series onward, every number is the sum of the two preceding numbers; hence the next number must be 34, and we are dealing here with the formula for the Fibonacci series.] (ps.256-7)
So to put the case in parallel with Kant (and my example of the cow):

1. I am given a series of numbers/intuitions of parts of a cow.
2. I want to know the formula which produces the series/to intuit the cow as a whole.
3. I cannot proceed from the mere series to the formula/discursive intellection cannot provide me with an intuition of the cow as a whole.
-- but here there is a further parallel, which Förster gives too little time to --
4. I cannot know if there is a formula for the series/we cannot know that there exist organisms in nature by discursive intellection.

Now, consider the following sequence of numbers: 3, 12, 10, 7, 10, 19.... To know the formula behind this series, Förster says, I must "intellectually re-present" "the transitions" between them. Well, here is how that series was generated: I rolled a d20 several times, and recorded my rolls. The transitions between the items were my picking up the die and throwing it again. So even if there is a simple function that fits my rolls (as there would be if I had rolled 1, 2, 3, 4, 5, 6), this would tell you nothing about that series: the next element in the series will always be a random number between 1 and 20. There is a fact of the matter about what the next number in the series was (it was a 4), but no formula would have been able to tell you it. So if "the formula" being looked for is something that will both tell you what numbers are in the series and what future numbers will be added to the series, there simply is no such formula to be found: the relation between the present list of elements and any future elements in the series is contingent. This is how Kant thinks of our knowledge of (what we heuristically imagine to be) organisms: the "whole" imagined serves merely a regulative function in judgement, and doesn't allow us to know the object intuited. And there are areas where Kant's picture of our understanding is correct, just as there are serieses of numbers which are not determinations of a formula: sometimes there is no "whole" to be grasped, but a mere conglomeration of contingently related items. So there is a real possibility that the sort of "higher experience" Goethe wanted in a particular case will just not be available, because the items he is looking at are not manifestations of a (single) Idea. Even if Förster/Goethe are granted a great deal about "Ideas" and our cognitive capacities for apprehending them, it remains open that there simply will not be an Idea where one is looked for. It might be that the concept being sought after in the phenomena is simply discursive, and not an Idea at all.

But Förster/Goethe want to avoid Kant's skeptical result, and at least in some cases it is clearly right to resist it. So let us look again at the mathematical example and the cow in parallel, without Kant's skeptical item 4:
4a. If there is a formula for the series, it determines how to proceed from one element in the series to the next/If the cow is an organic whole, then its being an organism determines how the parts of the cow relate to one another.
5. If I can proceed from one element in the series to the next while knowing that this is what I am doing (and not merely by a prior knowledge of which numbers are in the series), then I have a practical knowledge of the formula (This is something like Spinoza's second kind of knowledge.)/If I can see the particular parts of the cow as working in such a way that they cannot work without one another, or the various actions of the cow as actions that could not be done by something which did not do all of those sorts of actions, then I have a practical recognition that the object I am apprehending is an organism.
6. If I can see the elements in the series as following from one another with necessity simply by following the series along, this is what Spinoza called scientia intuiva/If I can see the individual parts or actions of the cow in such a way that I could not see them without seeing them as done by a cow (here considered as an organism, a natural end), then I have an intuitive intellect and intuit by means of what Kant called a "synthetic universal": what I see is already determined by the concept, and does not depend on future intuitions to give me knowledge of its future states.

Förster identifies three elements in "the methodology of the intuitive understanding" he finds in Goethe: there is a series of elements, there are transitions between those elements, and there is the Idea which makes itself manifest in the elements. He argues that if we are given any two of these, we can infer the third: "if a whole consists of these three elements and two of them are given, then I can infer the third from them." (p.259)

He gives two examples to try to show we can go from Idea and elements to transitions and from Idea and transitions to elements; the movement from elements and transitions to Idea is then left as what Goethe and Hegel accomplished.

I think that neither of his examples shows what he wants to. But as this post is getting long (and feels already impossibly dense), I think I will again put off looking at those two; I have at least done all the ground-clearing for looking at them now. The bigger problem is one I believe I mentioned in my first post on Förster's book, but which I can now put with more clarity: Förster does not take seriously enough his own italicized "if".

Again, here is Förster: "if a whole consists of these three elements and two of them are given, then I can infer the third from them" (p.259) -- a few pages later, this is taken as haven been proved: "In summary, then, we can say that if an idea lies at the basis of a set of phenomena and is operative in all its parts, then that fact can only be recognized by the method described here. Whether or not an idea in this sense lies at the foundation of a set of phenomena can also only be determined in this way." (p.264) -- So, by Förster's own lights, whether or not an Idea lies at the basis of phenomena is a question that is not immediately answerable, but rather is answered only by "the methodology of intuitive understanding": knowing that there is an Idea underlying phenomena does not come before actually grasping that Idea, and seeing how it guides the transitions between the individuals in which it manifests itself.

Now, look at Förster's treatment of "the classical and continually recurring objection" to the claim "that Hegel's description of the path of philosophical consciousness to the standpoint of science is in principle correct" (p.372) as it has "sublated the subject-object dichotomy that previously constituted it, thereby giving birth to a new kind of thought distinct from the discursive thought which had been appropriate within the dichotomy that previously laid claim to (almost) exclusive validity" (p.371-2). (Another way he puts this central claim is that Hegel had succeeded at demonstrating "the actuality of the (absolute) idea" (p.367).) The objection to this claim is that "the steps in Hegel's argumentation are lacking in necessity; that the historical shapes that he discerns do not exhaust the alternatives; that, on the contrary, many new alternatives have emerged since Hegel's time in science, art, and so on." (p.376)

Förster's reply is as follows, in four parts:
(1) As we saw at the beginning of Chapter 13, Hegel is not concerned in the Phenomenology with 'historical shapes' -- these are ultimately no more than examples and could be replaced by equally serviceable 'alternatives'. Rather, Hegel is interested in the 'method of the passing over of one form into another and the emergence of the one form out of the other'. But then the question is not whether there are alternatives to Hegel's examples, to the historical shapes chosen by him, but whether there are alternatives to the transitions between them.
Förster is clearly right about this, and I'm always astonished when people can't recognize this. The idea that in the first few chapters of the Phenomenology Hegel is concerned with the transition from Russellian "knowledge by acquaintance" to Platonic forms to Newtonianism to the instiution of slavery to Stoicism/Skepticism/Roman Catholicism is simply wacky: how could that grab-bag assortment of historical phenomena, in their weird non-temporal order, be something that has a logical progression? [It is worth noting here that Förster is chiefly concerned with roughly the first half of the Phenomenology, up through the section on "Spirit"; he convincingly argues that this is what Hegel had originally planned to have as the "introduction" to the Science of Logic, and these sections do in fact seem to function as the "Positions of Thought" chapters in the opening of the Encyclopedia Logic do.]
(2) And here again, the question is not whether we today, with the conceptual means placed at our disposal by the current level of development, might be able to imagine different transitions, but whether a different transition would be possible for the observed consciousness on its level. What we can imagine is therefore irrelevant to answering this question.
(3) If this is conceded, then the objection ought rather to be formulated this way: it is not convincing that a specific transition is supposed to be necessary for consciousness at its given level. And such an objection may, in any given case, in fact be justified. Then the question becomes: Is the transition itself not necessary, or has its necessity simply not been convincingly presented? As long as we find that some of the other transitions are necessary, we can always be sure that the problem is one of presentation. That is the crucial point! **If** a whole makes its parts possible and gives them their shape, then it must be active in all the parts and in all their transitions, not only in some. If that activity (necessity) has been recognized in some of the transitions but not in others, all this implies is that the latter have not yet been adequately grasped and presented.
(4) Hegel's project could therefore only be said to have 'failed' if no necessity whatsoever was to be found in the 'science of the experience of consciousness' [the Phenomenology's original title, which corresponds to the parts through "Spirit"], and if instead the transitions between shapes were contingent and thus might have happened differently. But that assumption is unwarranted, as I hope to have shown in Chapter 13 despite the undeniable imperfections in my presentation.
Förster's (2) is unobjectionable, and I accept that he has in fact shown in his chapter 13 that at least some of the transitions between the "shapes of spirit" happen with necessity. But his (3) is problematic: he grants that many of Hegel's transitions, as written, are unconvincing. But he tries to argue that this can only be a problem of presentation, for all of these transitions must in fact be there to be described. (In this he follows Fichte's views of the "deductions" in the published version of the Wissenschaftslehre, which Förster argues Hegel took as a guide for his project in the Phenomenology; Fichte thought his published "deductions" were largely awful, but that this was always a flaw merely in the presentation and not in the Wissenschaftslehre itself.)

The problem is the "if" which I added emphasis on, and which Förster had (previously in the book) always italicized: it is a real question whether an Idea lies behind a group of phenomena. Some wholes are mere aggregates, and not organically structured: in that case the "if" fails, and the whole does not make the parts possible or give them shape, and is not active in them or their transitions. (Indeed, whether there are "transitions" between them seems doubtful; it appears there are only "transitions" between our apprehensions of them, as there is nothing uniting them beyond our having united them.) And given what I thought I understood about "the metholodogy of the intuitive intellect", we cannot know whether an Idea lies behind phenomena without knowing that all of this is true: so Förster here argues in a circle, asserting that there is an (absolute) Idea because of the transitions and that there are transitions because there is an (absolute) Idea.

This is related to a puzzling paragraph in the concluding chapter of the book. Förster notes that Goethe's Ideas are multiple and various, as the Idea of color and the Urpflanze are very different sorts of Ideas. This is in distinction from Hegel, who speaks of the Idea, the Absolute Idea, and not of various "Ideas" in the plural. But Förster thinks this reflects only a difference of attention, and that the two approaches complement one another:
Nor, of course, does a multiplicity of ideas contradict the fact of a single, unified reality. Just as a concept (the manifestation of the idea in the subject) is impossible in isolation from the broader conceptual network, and just as an isolated Urphaenomen is an impossibility, neither is it conceivable that there could be ideas existing apart from any connection with other ideas. They too must be moments of an internally differentiated whole; they must stand to each other in relations of greater or lesser affinity, mutually conditioning, facilitating, impeding, or excluding one another, and hence they must be hierarchically ordered and subordinated to a highest (absolute) idea constituting the internal nexus of the whole. Goethe remarks in this connection...(p.370)
and then he gives two Goethe quotations which are not arguments in support of these claims. I don't see what support he can give for them. I am well acquainted with arguments to the effect that concepts only come in groups, and an Urphaenomen that doesn't make itself manifest in individuals is clearly not doing the work of an Urphaenomen. But why do Ideas require other Ideas? And why do they have to stand in an orderly hierarchy with regards to one another? (That's not true of concepts, since not all concepts are "the manifestation of the idea in the subject": some are merely discursive representations. It was with good reason that Kant only urged as a task that our concepts should be organized in a single Porphyrian tree, and did not claim that they already are so organized.)

As far as I can see, the actuality of the absolute idea is left as an assumption in Förster's book. Which is rather problematic, since that's what the whole thing is trying to demonstrate.

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