15 August 2012

Förster's examples of Idea, transitions, and individuals

Following on from where my previous post left off, here is Förster, in "The Twenty Five Years of Philosophy":

First example: Let's suppose we are watching a modern, 'experimental' film in which the scenes follow each other in a seemingly random, unconnected way: Times, places, and actors are constantly changing with no indication of how they are connected. It seems as if every scene constituted an independent and self-contained episode. Then comes the final scene, and suddenly everything that came before is illuminated in a flash. This final scene provides the key to understanding the film and allows us to recognize the idea that the director wanted to present. Now we might perhaps wish to see the film for a second time, and then something decisive occurs: Although we see exactly the same scenes again, this time we see every scene differently. When we watch the film again, the last scene or rather our knowledge of the film's underlying idea is now present in every single scene. And it now makes clear how the scenes which formerly appeared to be unconnected are in fact internally linked.
In this example we are at first, i.e., after seeing the film for the first time, given all the parts (scenes) of a whole as well as the underlying idea, but we are not yet given the internal link, the 'transitions' between the scenes. With the aid of the idea, however, we can produce or reconstruct these transitions for ourselves after a second viewing. This suggests that if a whole consists of these three elements and two of them are given, then I can infer the third element from them. We could put this to the test if for example, differently than in the case of the film, we imagine a case in which the idea and the transitions are given, but the parts still have to be found....(p.258-259)
Two things to immediately note about this example: Förster is explicit that whether a whole consists of an Idea and a series of individuals with Ideal transitions between them is posited, a mere "if", and not a given. And in the particular example, we are merely told that we "recognize the idea that the director wanted to present", which implies there was one in this case. It seems questionable whether even every "modern, 'experimental' film" has an Idea, a single "thing" which could illuminate every transition between scenes, and very doubtful that all films do. (What is the Idea manifested in Return of the Jedi?)

Now, even granting to Förster that the film he asks us to imagine does have an Idea present in it, his presentation seems optional. He needs us to think of the process as follows:

1. I first see each scene in sequence, and do not understand them.
2. I see the final scene, and now grasp the Idea of the film.
3. I watch the film again.
4. While doing this, I see each scene along with the transitions between it and its surrounding scenes, according to its Idea.

But why should we think of it that way, rather than as follows:

1. I first see each scene in sequence, and do not understand them.
2. I see the final scene, and now, in recollection, understand the scenes that preceded it.
3. I watch the film again.
4. While doing this, I confirm that my recollection was faithful to the film: the final scene did in fact allow me to understand how the earlier scenes hung together.

This seems to me more faithful to how watching that sort of movie actually works: the understanding of the whole comes in a flash, as Förster says -- but in his explication of this, he divides the "flash" into an initial moment of "grasping an Idea" and then later "understanding the transitions between scenes". Förster's own characterization betrays the artificiality of this divide: as he notes, "we might perhaps wish to see the film a second time", which makes sense if the second viewing is merely confirmatory.

To concretize this a bit: Memento seems like a decent example of the sort of film Förster has in mind. Although it's not as apparently incoherent as the film he describes, it is a film which is really understood only once its final scenes have been seen: before then, the viewer has a wildly false idea of the reality of the film. But I didn't need to see the film twice to get this effect: the correction of my view of the reality of the film came alongside the viewing of the final scenes themselves. It seems false, "phenomenologically", to say that my grasping of "the Idea of Memento" and my seeing how the earlier scenes hung together were two distinct acts of the mind. So I can't grant that this example shows what Förster wants it to show, that if two elements (of Idea/sequence/transitions) are given, I can "infer" the third. The example doesn't seem to have the sort of division he needs it to have between elements two and three, the Idea and the transitions.

And now on to the
Second example: A psychiatrist interested in philosophy delves ever more deeply into the intellectual world of Nietzsche. Because of his profession, he take a special interest in Nietzsche's insanity and its causes. Time and again he wonders how it might have been if Nietzsche could have undergone psychoanalysis. Since his illness took place in the period in which psychoanalysis was first developed, the thought is not unrealistic. It gradually grows into the idea for a novel: 'Nietzsche in Therapy'. However: everything we know about Nietzsche indicates that he himself would never have agreed to undergo therapy. How, then, is the idea to be realized? Our author conceives the following plan: In the story, Nietzsche, who was very proud of his deep psychological insights, has to be convinced that it is he himself who has to give therapy to someone since only he, Nietzsche, can help that person, whereas in reality and without Nietzsche's being aware of the fact, the 'patient' is the psychiatrist and Nietzsche himself is the object of the therapy. To this end, one of Nietzsche's friends (Lou Salome), who is deeply worried about his mental health, persuades a doctor with whom she is acquainted (Josef Breuer, Freud's mentor), to take part in the scheme and present himself as the 'patient'. With this a narrative framework is in place which connects the beginning, middle and end of the story and become a central thread, making transitions possible between the individual scenes. The only thing still missing are the scenes themselves -- the different parts of the narrative in which the idea is to be realized. But now they can be 'found' in light of what is already given: they have to be realistic scenes in the sense that they are not only to reflect the locality and the Viennese milieu in the period when psychoanalysis was originally developed, but also to draw on Nietzche's biography in such a way that a fictional narrative about Nietzsche comes about and not about someone who would bear no resemblance to the philosopher.
Whereas in the film example the parts and the idea were given and the transitions were to be discovered on their basis, in this second example the idea and the transitions (the 'central thread') are given and it is the parts which have to be found. Can we then also imagine a third case in which the parts and the transitions are given and the idea is to be discovered on their basis? Here I no longer need to construct an example, for this is exactly the case that Goethe seeks to solve with the help of his morphological method: all the parts ('the complete series') and the attentive observation of the transitions between them are to provide a basis for studying the idea underlying the whole. Here, too, I require two elements in order to find the third. (p.259-260)
Förster notes that this premise of the bestseller "When Nietzsche Wept", by Irvin Yalom.

This example I find implausible on its face. Förster needs this example to work as follows:

1. Yalom has the Idea of a novel about Nietzsche undergoing psychoanalysis.
2. Yalom thinks of the "central thread" of the novel, which connects the novel's beginning, middle, and end.
3. These suffice to provide Yalom with the individual scenes depicted in the novel.

But 3 is simply implausible: After one has an idea for a novel, and even has a fairly detailed idea about how the plot will go and what gets the reader from the beginning through the middle to the end, actually writing the novel is a lot of additional work. The scare-quotes Förster puts around "'found'" cannot be removed; there really is not a finding of the words, as they must be created. If the process was as simple as Förster here implies, there would be no need for drafting and editing this novel: the Idea and the transitions ("the guiding thread") were had before a single word was put on paper, and they are supposed to suffice for the finished product, so how can the composition itself be more than a mechanical affair? So I can't grant Förster that this example shows that you can go from the two elements of "Idea" and "transitions" to the sequence in which the Idea is manifested.

For such a transition to be plausible at all in this example, the "central thread" of the novel which is supposed to be in Yalom's mind before it is written would have to be so detailed as to lay out exactly how to write the novel, in a way sufficient to issue in a publishable result. But then Förster's point would still not follow, for then it would appear that the transitions and the scenes themselves were already had, and there is no transition from two elements to a third. More problematically, it would appear here that the transitions and the scenes meld into one another, as in the first example the transitions and the Idea melded into one another: to make the example realistic, the three elements dissolve into two.

So, neither of Förster's examples seems to me to show what he needs, that one can transition between two of the elements Idea/transitions/sequence to the third. Either the transition is impossible, or there is no real transition from two to three.

Extending these complaints to his third example (which he doesn't need to produce an example for), I find myself with the following suspicion/complaint: Rather than a transition from a sequence and the transitions between its members to knowledge of an Idea, Goethe presents us only with either

1) a man who surveys the members of a sequence as transitioning between moments of an Idea; or
2) a man who surveys members of a sequence and notes connections between them, and then (groundlessly) posits an Idea underlying them; or (most charitably)
3) a man who surveys members of a sequence and notes connections between them (rhapsodically, as it were), and then begins to survey them as transitioning between the moments of an Idea.

In the first case, Goethe is no help to we who wish to acquire scientia intuitiva: we are only assured that he has it, and are not helped to gain it by this assurance.

In the second case, the very possibility of scientia intuitiva is left doubtful, and Goethe's example is no help.

In the third case, we are given a model we can imitate (unlike the first), and which leads to scientia intuitiva (unlike the second), but not in sufficient detail to know how. Against Förster's desires, there is no transition from two elements to a third: there is a transition from two elements, not seen as elements of a triple, to seeing three elements as elements of a triple. What is needed for the transition is not the elements themselves, but the elements grasped correctly: and this is done only with all of the elements available for viewing.

So, regarding the question of the reality of the (absolute) Idea, I see no help for Förster in his examples.

On an unrelated note: My semester is starting again, so blogging will probably dry up for a while again. But at least this time I posted all I had meant to post on Förster's book -- which I still think very highly of, and recommend to all my readers.

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.

01 August 2012

Some remarks of Fichte's about general logic, with an aside about Schopenhauer and math

From a letter to Reinhard, January 15 1794:
"But isn't it true that philosophy, unlike geometry and mathematics, is quite unable to construct its concepts in intuition? Yes, this is quite true; it would be unfortunate if philosophy were able to do this, for then we would have no philosophy, but only mathematics. But philosophy can and should employ thinking in order to deduce its concepts from one single first principle which has to be granted by everyone. The form of deduction is the same as in mathematics, that is, it is the form prescribed by general logic." (p.793 in Early Philosophical Writings, tr. Dan Breazeale)

From a letter to Reinhold, March 1 1794:
"I have been avidly awaiting the second part of your Contributions. I particularly look forward to the explanation of how you derive the categories. (To derive them from the logical forms of judgement presupposes that logic provides the rules for philosophy, and this I cannot accept.)" (p.376, ibid)

Fichte apparently changed his mind about the relationship of general logic to philosophy during these months, while he was first working on the Wissenschaftslehre, after Schulze's "Aenesidemus" gave him such a shock.

The first quotation surprised me: I am used to Fichte affirming the paradoxical aim of establishing logic through the Wissenschaftslehre, or else of it being its own distinct "science" apart from philosophy. I didn't know he had at one point affirmed that what he was trying to do was find a first principle "which has to be granted by everyone" and then get all of the rest of his philosophy out of it analytically. Though I suppose that's not too big of a surprise, since this was how Reinhold viewed his own philosophy, and Fichte at this point was still self-consciously a Reinholdian. (It's insane to think you can get anything interesting out of a principle like "I=I" analytically, but I think the error is more understandable if you imagine that Fichte's first principle was something longer, and in prose, like Reinhold's "Principle of Consciousness" was.)

The first quotation is also interesting for Fichte's remark that deduction in mathematics proceeds according to "the form prescribed by general logic". This might seem tautological (what other sort of deduction could a proof have?), but it's not obviously a Kantian way to think about mathematical proof. Schopenhauer, for instance, says things like this:

"In mathematics, according to Euclid's treatment, the axioms are the only indemonstrable first principles, and  all demonstrations are in gradation strictly subordinate to them. This method of treatment, however, is not essential to mathematics, and in fact every proposition again begins a new spatial construction. In itself, this is independent of the previous constructions, and can actually be known from itself, quite independently of them, in the pure intuition of space, in which even the most complicated construction is just as directly evident as the axiom is." (WWR I, p.63)

"Now if with our conviction that intuition is the first source of all evidence, that immediate or mediate reference to this alone is absolute truth, and further that the shortest way to this is always the surest, as every mediation through concepts exposes us to many deceptions; if, I say, we now turn with this conviction to mathematics, as it was laid down in the form of a science by Euclid, and has on the whole remained down to  the present day, we cannot help finding the path followed by it strange and even perverted. We demand the reduction of every logical proof to one of perception. Mathematics, on the contrary, is at great pains deliberately to reject the evidence of perception peculiar to it and everywhere at hand, in order to substitute for it logical evidence." (WWR I, p.69)

and my favorite one

"Therefore, I knew of nothing to take away from the theories of the Transcendental Aesthetic, but only of something to add to them. Kant did not pursue his thought to the very end, especially in not rejecting the whole of the Euclidean method of demonstration, even after he had said on p.87(V, 120) that all geometrical knowledge has direct evidence from perception. It is most remarkable that even one of his opponents, in fact the cleverest of them, G. E. Schulze (Kritik der theoretischen Philosophie, ii, 241), draws the conclusion that an entirely different treatment of geometry from what is actually in use would result from Kant's teaching. He thus imagines that he is bringing an apagogical argument against Kant, but as a matter of fact, without knowing it, he is beginning a war against the Euclidean method." (WWR I, p.438, my emphasis)

Now, Kant's actual views on geometry and arithmetic are obscure, even by Kant's standards; there is not much in the way of consensus in the secondary literature on any point related to it. But I think Schopenhauer actually latched onto an interesting way to read Kant here: if Kant is really serious about all our synthetic knowledge standing under the principle of the conditions of a synthetic unity of intuition in a possible experience, and if mathematics is synthetic, then it looks like mathematics should depend on a relation to possible experience in a way that it hasn't traditionally. In Euclid, it looks like what we are given is some self-evident axioms, and then logic is supposed to carry us from those to all of the proofs (if this is not true of Euclid himself, then consider how the more geometrico ends up appearing in the hands of a Descartes or Spinoza). Euclid-style mathematics looks an awful lot like rationalist metaphysics, Schopenhauer thinks. Kant himself had drawn the moral that philosophy can't try to imitate mathematics; Schopenhauer draws a further moral that mathematics can't try to imitate mathematics: the procedure the rationalists tried to follow isn't just illegitimately extended by the rationalists, it's rotten in and for itself. Brouwer's intuitionistic mathematics self-consciously follows Schopenhauer on this.

Fichte's view is much less revisionary, in this respect: he seems to think that math relies on intuition somewhere along the line, but that mathematical proofs are just logical ones; the rules for what follows from what in geometry are the same sort of rules that govern syllogistic. FWIW, I think this was Kant's own position; but it is hard to fit to the text of the Critique: there Kant says odd things about mathematics and geometry, and their supposed relation to pure intuitions of time and space. Schopenhauer is able to make those odd things look intelligible, at least, even if the position he endorses looks crazy. (Or maybe it's not! I don't want to pick any fights with intuitionists if I don't have to.)

Now, it's possible that Fichte's views on mathematics changed after 1793; I have read literally nothing on Fichte's philosophy of mathematics. But I think he probably had to change them, given that he certainly changed his views on general logic. In the letter to Reinhold above, he's already refusing to put logic before philosophy; later on, he gets even harsher. So far in my Fichte studies, I've ignored anything that happened after 1800, just because the Jena-period work is what influenced Hegel & co. But I recently read the short article "Nothing More or Less than Logic: General Logic, Transcendental Logic, and Kant's Repudiation of Fichte's Wissenschaftslehre" by Wayne Martin, and it has this startling bit:

In his earlier discussions of the relationship of logic and philosophy, Fichte had been concerned only to mark the difference between the two disciplines, content to leave the doctrines of general logic well enough alone. But he now calls for a thorough-going critique of logic itself. He explicitly marks this as a shortcoming of Kant’s philosophy, complaining that Kant “was not so disinclined as he ought to have been [toward general logic]”; that he “had not recognized that his own philosophy requires that general logic be destroyed to its very foundation” – a destruction Fichte now vows to undertake “in Kant’s name” (SW IX, 111–112). As the lecture course unfolds we find that the scorn previously reserved for the so-called “dogmatists” is now directed against “die Logiker” instead. Their account of concept-formation is said to be “durchaus falsch” (SW IX, 317); their accounts of judgment and of the syllogism are said to be in need of “total reform” (SW IX, 367); and the “spirit” of their enquiry is said to be “the same as that of all untrue philosophy – that is, of all philosophy that is not idealistic (SW IX, 407)" (p.35-36)
Martin's article ends shortly after this; if anyone can point me towards discussions of Fichte's later views on general logic, I'd appreciate it.

But there are a few things Martin does note about Fichte's critique here. One is that Kant's discussion of concept-formation in the Jasche logic looks like it's literally the same as Locke's account of how we get general ideas: it's an unreconstructed abstractionism. But if Kant endorses Locke here, it can only be out of mental inertia; Kant simply can't have taken on such a central part of empiricist epistemology, given how much of it he (rightly) rejected entirely.

There are more than a few reasons Kant couldn't have consistently been a Lockean abstractionist about concepts, but Fichte latches onto an interesting one: "If the logicians had indeed realized all this they would have realized that the concept, in this case, of a horse, only occurs in the grasping of something as a horse – that is, in the judgment that something is a horse. (SW IX, 331)" (quoted on p.37 of Martin's article).

As Kant had already said, the understanding can make no use of concepts except to judge by means of them; Fichte puts this even more forcefully, and has concepts simply being nothing but capacities to make certain sorts of judgements. So one reason abstractionism is false is because it tries to explain how we first derive concepts from our experience, and then combine them in judgements -- but there can be no gap here, for deriving concepts is nothing but coming to be able to make certain sorts of judgements: Fichte thus prefigures Geach's main objection to abstractionism in "Mental Acts": Possession of a concept is the capacity to make certain sorts of judgements; it is not primarily a recognitional capacity. But abstractionism tries to explain how we acquire certain recognitional capacities, not the capacity to make certain sorts of judgements. Hence abstractionism does not explain how any of our concepts are acquired.

Fichte is then already seeing what's wrong with much work that is done even today on concepts: read a random article on "Whether animals have concepts?" and you are almost certain to be told that they do, because e.g. a dog can recognize when his name is called, or a dolphin can recognize its image in a mirror. It will often then swiftly be granted that we have more concepts than dolphins and dogs, for e.g. they do not have a concept of a logical copula (or at least this is rarely claimed), and that sort of thing is supposed to explain the difference between the minds of brutes and the minds of rational beings. But it's just Kant's insight that the concepts which are employed in the logical forms of judgements are needed to bring objects under concepts at all: no logical form, no judgement; no judgement, no relation of intuition and concept; no relation of intuition and concept, no representation with objective purport, and hence no concept.

Fichte's complaint about Kant here can then be put thus: Kant knows that abstractionism is deeply wrong, and that we can't form judgements by putting together logical forms which we "already have" with concepts which we "get via abstraction"; the concepts and the logical forms are nothing outside our capacity to judge, which requires both to be the capacity it is. But it looks like his procedure regarding general logic, for instance in the "Metaphysical Deduction" in the first Critique, is just the abstractionist one: he regards the logical forms as being something over against the concepts which are supplied to them ab extra for combination, in Lockean fashion. Kant seems to introduce judgement by first having in view the table of logical forms of judgement; what is needed is to arrive at the logical forms of judgement (the topic of general logic) only by first having judgement itself in view. And if it is transcendental logic that shows us what our capacity for judgement is in its full actuality, then general logic will need to be preceded by transcendental logic, and not be followed by it.

Something I find exciting here: Fichte is here presenting the problem of the Metaphysical Deduction and the question of general logic in Kant as tied to (what is later called) the problem of the unity of the proposition. Fichte's objections to Kant's views on general logic thus look similar to the author of the Tractatus's objections to Russell: Kant/Russell take logical forms as "given" in some peculiar way (Kant is silent about it, but implies the understanding simply has them; Russell appeals to "acquaintance" with these strange "objects"); nothing "given" in this way can do the work of a logical form (Fichte's objection about the primacy of judgement; Wittgenstein's objection about it being impossible to judge a nonsense); hence "general logic" is in need of rethinking from the ground up, and any attempt to establish a substantial truth on a logical basis (such as deriving Kant's categories from general logical forms) or to make a logical proposition itself appear substantial (as Russell and Frege did) must be shown to be confused.

But if that is the point I reach, then I now can say to myself: "Well! Then I will have the problematic status of general logic in Kant cleared up as soon as I clear up what's right and wrong about the role of logic in the Tractatus." I am reminded of something Locke says somewhere (I cannot locate the passage) about being able to move around piles of dirt, but never being able to actually clean the room.