28 October 2012

A Quote from L.E.J. Brouwer

"Life is a magic garden. With miraculously soft shining flowers, but amidst the flowers the little people walk, that I am so afraid of, they stand on their heads, and the worst is, that they cry out to me that I must also stand on my head, now and then I try it, and I burn with shame; but sometimes the little people then shout that I do it very well, and that I am after all a real gnome too. But under no circumstances are they going to make me believe that."

 From a letter to Carel Adama van Scheltema, August 7, 1906. Cited here.

28 September 2012

Blanking on Rödl

From today's NDPR review of "The Twenty-Five Years of Philosophy":

Although this seems on its surface to suggest a possible link between Goethe's idea, at least generally taken, and the more recent work by Michael Thompson and Sebastian Rödl on how species terms work, Förster does not explore that link. On the other hand, one can't do everything.
What work by Rödl does Pinkard have in mind? I thought Rödl just pointed to "The Representation of Life" when he needed to talk about species terms; am I just forgetting somewhere that Rödl does the work for himself? Or is Pinkard mistaken in thinking that Rödl is relevant on just this point? (His work is clearly something that should be sat next to Förster's book as a whole, so I'm glad he got mentioned in the review. But I don't see why he got mentioned just here.)

On Facebook, Ben Wolfson pointed to chapter six of "Categories of Temporality", but that doesn't satisfy me: Rödl doesn't talk about animal species as such very much there, and in any case he points to Thompson a few times in that book (all three parts of "Life and Action" are in his bibliography), so Pinkard's sentence still feels weird.

Another possibility that occurs to me is that Pinkard meant to point to Rödl's discussion of "species" in the logical sense (the things under a genus), in which case chapter six of "Categories of Temporality" is clearly relevant. But then mentioning Thompson seems odd: I can't think of any work of his which is that general, as opposed to work on "species" as a type of life-form.

I feel like I'm just forgetting something Rödl's written.

21 September 2012


I needed to write some things; I have checked none of my quotations (and give no citations because of it), and am too lazy to italicize where it needs doing etc.; anyone who reads this is advised that they do so only under their own judgement, and I foreswear all responsibility for such actions.

"Only in the context of a proposition has a word really a meaning" Frege tells us; this is the stronger formulation used in the middle of the Grundlagen, after his initial, more cautious warning "Never to ask for the meaning of a word except in the context of a proposition", for fear that what we will confuse with the meaning is an "idea", a subjective Vorstellung which comes to mind when a word is heard but is orthogonal to any question of meaning.

The author of the Tractatus tells us much the same: "Only in the context of a proposition has a name meaning"; only in a proposition can there be a symbol. Outside of the context of a proposition, we have only things which we can confuse with signs: but as a sign is "the perceptible aspect of a symbol", a blot of ink or a noise which is not presently symbolizing is not even a sign. To see the symbol in a sign, we must consider the context of significant use: this means that if we are considering a putative sign in such a way that we can think of it just as we are without its having a context of significant use, then we are not thinking of even a sign: we have only ink or noise, and these have no innate connection to any symbols (for signification is arbitrary).

So, if there is a context in which we are supposed to refer to a sign in a way that is independent of that sign being used, we in fact refer to no sign: we mention only ink or noise, or something else which may (or may not) be arbitrarily connected with a meaning in some further use of it as a symbol. Such a thing cannot have any meaning.

There are many ways to use a symbol: this is demanded by what the author of the Tractatus thinks of as the "bipolarity" of a proposition, its ability to be true or false. If we cannot use the same symbols to say both a true thing and a false thing (with the aid of a sign for negation, or by denying where someone has affirmed) then we lose this bipolarity: the same symbols need to be able to function in both affirmation and denial in the same ways for a given thought to be held as true and held as false. So logic demands that there be ways to modify the force of a proposition, to use Frege's terminology.

Perhaps the same point, perhaps a better one than I just made: "Thaetetus" must be the same symbol in "Thaetetus sits" and in "Thaetetus flies" for the inferences in which these propositions are involved to be intelligible. So there arises the illusion that we can speak of the meaning of "Thaetetus" in these propositions on its own, so that we can after all speak of the meaning of a word outside of the context of a proposition. It seems we have just done so, by putting "Thaetetus" in quotation marks: by doing this we are now talking about the symbol which is combined with other symbols in propositions, but without its being combined in any particular proposition.

I think this must be seeing things wrong.

Rather than saying that in ""Thaetetus" refers to Thaetetus" we refer to a name (or that in the longer quoted expression I just used we refer to a sentence), we might say that we use "Thaeteus" with a modified force: where normally "Thaeteus" symbolizes only in some such proposition as "Thaeteus sits" or "Thaetetus flies", the quotation marks around ""Thaetetus"" cancel the force of the rest of the proposition, for all of the propositions in which "Thaeteus" has a use: thus we do not use quotation marks to refer to something which might exist before any proposition, but to refer to something which exists only in abstraction from propositions. Not: A name has a reference, and can be combined with other words to form a sentences, but: A sentence has names in it, which can be picked out in it and seen in other sentences. The use of quotation marks around an expression thus depend on that expression already having a use in the language, to use them in the way they are ordinarily used in logic and semantics. So this way of using "Thaeteus" is not using it outside of the context of a proposition, but it using it in the context of propositions which are bracketed out: not outside of a context of significant use, but in a different context of significant use which is parasitic on those contexts. "Thaeteus" is not something we can mention which has a meaning by itself, but is something we can mention as having its meaning in this-and-that proposition which we leave unstated (but could state examples of).

This is contrary to the manner in which artificial languages are constructed (as in Carnap), where we distinguish between the introduction of atomic signs and the rules for formation of sentences from the combination of atomic signs (and from other sentences). This gives the appearance that we can have something logical in view before the final proposition-in-a-context-of-significant-use is given, that we can build up one of these out of some things understandable antecedently.

Carnap is one of the inventors of metalogic; he reads into the Tractatus a notion of "a language" which is at home in his own work on metalogic, where a "language" is something we can have in view without presently using it (as its use is external to it: a formal language is in itself a system of manipulable marks, and can be manipulated or not as we please). The Tractatus has no such notion: its author is not teaching us about a formal language, but about a method of rewriting the propositions of ordinary language, which is for its author "the only language I can understand". (Thus we do not need to saddle this author with the view that every language has the same expressive power, that all languages are intertranslatable: his Begriffschrift is not meant to be a language which has the powers of all languages, but to be a style of notation which can serve to rewrite any language. The notation itself does not need to have expressive powers in the way that the languages it is used to rewrite do: anyone who wants to rewrite something in the notation of the Tractatus can make use of whatever sorts of (e.g.) names his own language gives him, and doesn't need a Begriffschrift to supply him with any.)

When working with a formal language which resembled ordinary language, we can mistake a sentence of the formal language (which exists only according to the arbitrary dictates of the formal system in which it is produced) with a sentence of ordinary language which superficially resembles it: we can then imagine that our ordinary language is what this formal language has created, forgetting that the formal language is a free creation of a particular subject and no ordinary language can be this. ("The only language which I understand" cannot be something I produce by a free act, for I must already understand it to formulate any such end for myself.) "Formal language" and "ordinary language" have only a sign in common, and the author of the Tractatus reminds us that this is of no logical import.

(It is probably important that Davidson rejects Tarski's theory of quotation marks in the Warheitsbegriff as an error, and has to replace it to apply Tarski's definition of truth to natural languages; I would have to look at Tarski again to remember what his view actually was.)

This way of thinking goes along with thinking that the rules of "logical syntax" are constitutive of thought, not normative for it: we cannot violate them. Thus there cannot be an impermissible combination of signs, for to speak of "permission" makes no sense here. In not being able to violate these rules, we are not prohibited from thinking anything; outside of the limits of thought there is simply nonsense: not something which we are prohibited from thinking. (I am not happy with any formulation of this I can think of. This is perhaps an important point about the constitutive-normative distinction in these areas, that formulations of either sort of view can be taken as formulations of the other.)

In logic we can never do something we shouldn't do, but only misunderstand what we are doing. We can only mistake something other than logic for logic, as Frege warned us about; but Frege's rule to always sharply distinguish the logical and the psychological does not go far enough, for there are other troubles than psychologism to worry about. (Frege perhaps falls into a confusion of logic and language when he looks for the referents of concept-expressions, as both names and concept-expressions are written in words.) Or perhaps: we all too easily underestimate what it is that is "psychological" as opposed to logical: not just the subjective play of Vorstellungen is opposed to the logical. "Logical" is perhaps not a term that wears the pants, as Austin said of "real".

I have no idea if I'm going anywhere (with this?). I want to say: I am a mass of errors, and can do nothing but err. Is there a context of significant use in which such "philosophy" as I produce has a sense, or is this too nothing but confusion? (That there is not is suggested by the fact that this question strikes me as sophistry: but I feel it forced upon me by my own thinking, which is also tarred as sophistry by this association, and so the question seems to have force: and on in circles I go.)

16 September 2012

Sellars Society Interview

The Sellars Society has started an interview series; it's off to a good start.

Aside: As I expected, this semester has me too busy to blog; I get to start grading midterms tomorrow. It's been an unrewarding grind so far, and thinking for fun hasn't seemed like much fun because of it. Hopefully the spring is better.

10 September 2012

Hooray for C.I. Lewis!

This post is nothing but cheering for the guy I like winning a thing.

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.

28 July 2012

Geach's "Mental Acts" and the dualism of the conceptual and the sensible

I have been reading through "Mental Acts" over the past few days. It's long been on my short list of things to read, but I'd never picked the book up until this week. (Literally: if I had seen for myself how short it was, I would've gotten it read years ago.)

It's mainly good, in the way that everything I've read by Geach has been mainly good.

I am making a post about it largely as a reminder to myself: Chapter 15, "Judgements About Sensible Particulars [Reference to Particulars]" is striking, from a Kantian perspective. But spelling out what I find so striking about it is probably of more general interest.

Geach's puzzle is about how we can judge about particulars, given that judgements are acts of our conceptual capacities, and our conceptual capacities are always universal (as they are capable of repeated use independently of what might be presently sensed).

The judgement he considers is "That flash was before this bang", uttered on different occasions and referring to different flashes and bangs. Of this he says "there is no difference to be found on the side of the judgement itself [on these two occasions]. What we may call the intelligible content of the judgement is the same in all judgements expressible as "that flash was before this bang", regardless of which flash and bang are in question." (ps.63-64) So, given that judgements are always capable of being formed regardless of occasion, how can any judgement have reference to an occasion?

Geach's answer: "How could the utterance "flash before bang" be taken to refer to a particular flash and bang? The answer is obvious[!]; the utterance can be, and probably will be, so understood in a sensory context in which the hearer notices a flash and a bang. Similarly, the utterance "some cats, white" could be taken to refer to particular cats if its hearer was looking attentively in the right direction. The content of the judgement is always intelligible and conceptual -- acquaintance with a particular sensible thing is no part of the judgement itself -- but an act of judgement performed in a particular sensory context may thereby be referred to particular sensible things." (p.64)

The most striking fact about this answer is that Geach tries to answer the question of how judgement can have reference to particulars by referring to what a hearer would take an utterance to refer to, in a given context. He seems to want to answer the question of how thought can be about the world by noting that others take it to be so: but this is patently Munchhausenianism, with empirical content being pulled up by its own bootstraps. Unless the hearer can already judge concerning particulars, then she can't take an utterance to refer to particulars: so it does no good for Geach to appeal to her judgements on the matter.

But this may be unfair: he seems to not notice what he has said, and thinks of all the work in his picture as being done by "the context" of a judgement. How to spell this out, he is unsure of: "It is clear, indeed, that the act of judgement must bear a closer relation than mere simultaneity to the context of sense-perception that gives it its special reference to these particular sensible things; I am not prepared to characterize this special relation it must bear to its context.... But I do not think this throws any doubt on what I have said; although more remains to be said." (p.64)

It is "clear" to Geach that context must be able to do this work, for we do in fact judge about particulars, and he doesn't see anything else that can make inherently-universal judgements latch onto sensible things. He is aware that "mere" simultaneity between an act of judgement and a thing will not suffice, but I hear in this the suggestion that something more than "mere" simultaneity will do the work: Judgement + Thing + Simultaneity + Y = Judgement is about Thing; future philosophy can solve for Y.

I begin here a long aside:

I find this sort of buck-passing in philosophy disagreeable, setting aside the particular problem Geach lays out for working on: it is too easy for everyone to only think through a problem so far, because "others" can always do the rest of the work. I encountered a particular egregious version of this in a seminar recently: several rival positions on a topic in the metaphysics of social groups were compared, and a criticism against one of them (I believe it was Searle's) was rejected on the grounds that if it worked, it would work for all of the positions on offer: "And if it's everybody's problem, then it's also nobody's problem", it was said with a grin. This sort of "metaphysics" struck me as nothing but intellectual masturbation: it was an intentionally restricted way of thinking, and could never bear fruit. The sort of thing people made fun of scholasticism for.

Immediately after the last Geach quote, he continues: "The problem I have just been discussing -- how we judge about sensible particulars -- was much agitated in the Middle Ages; and in my solution of it I believe I am following Aquinas. Aquinas's expression for the relation of the 'intellectual' act of judgement to the context of sense-perception that gives it a particular reference was "conversio ad phantasmata", "turning round towards the sense-appearances". [I don't know why Geach gives a gloss on this; the book is peppered with untranslated Latin phrases.] This metaphorical term is obviously a mere label, with negligible explanatory value;  but it does not pretend to be more than a label. Aquinas has, in my opinion, at least rightly located the problem; the problem is not how we advance from judgements like this is before that to more general judgements, but contrariwise how a judgement inherently general can be tied down to referring to particular things (Ia q. 86 art. 1)" (p.65)

What do we find, if we follow Geach's pointer to Thomas? Here we read that "Our intellect cannot know the singular in material things directly and primarily.... But indirectly, and as it were by a kind of reflection, it can know the singular, because, as we have said above (Question 85, Article 7), even after abstracting the intelligible species, the intellect, in order to understand, needs to turn to the phantasms in which it understands the species, as is said De Anima iii, 7. Therefore it understands the universal directly through the intelligible species, and indirectly the singular represented by the phantasm."

So in the passage Geach cites, Thomas points a few pages earlier in his book. I believe there is an error in the online edition here; Question 85, Article 7 seems irrelevant, but Question 84, Article 7 is about precisely this question: "Whether the intellect can actually understand through the intelligible species of which it is possessed, without turning to the phantasms?" Thomas's sed contra is that "The Philosopher says (De Anima iii, 7) that "the soul understands nothing without a phantasm."" -- so even in following Geach's pointer to Aquinas through Aquina's pointer to Aquinas through an incorrect citation to Aquinas we find: a pointer to Aristotle. (In fairness to Aquinas, he had given the same reference in the first place Geach pointed to.)

But Thomas does add some argumentation in support of Aristotle's view, in his replies in the same article. He states the view he is defending thusly: "In the present state of life in which the soul is united to a passible body, it is impossible for our intellect to understand anything actually, except by turning to the phantasms." -- But now it emerges that Thomism cannot help Geach here, for Thomas is concerned with a narrower problem than the one Geach has. Geach needs an answer for how judgement can be about particulars, but Thomas is concerned only with how our, human, intellect has need of "turning to the phantasms". So in his replies, he appeals to psychological facts about our minds (even appealing that "anyone can experience this of himself") to ground the need for "turning to the phantasms". But Geach's problem is a logical one: how can it be so much as possible that "inherently general" judgements can be "tied down to referring to particular things?" It is no help to note that, in fact, our judgements are so tied down, and human minds cannot but be so tied down: Thomas's investigations enter too late to be of use.

(I won't trouble with looking at De Anima III 7; I remember the passage in question, and looking at it will not help make Geach's puzzle clearer. From what I could see, Aristotle was merely marking a psychological fact with his "no thought without an image" remark: there are always things fluttering about "before the eye of the mind" while we think. But merely noting this does not make thinking less mysterious.)

I end here my long aside.

--So, Geach thinks he can tell that there must be a Y such that Judgement + Thing + Simultaneity + Y = Judgement is about Thing.

Geach faces the same problem in his next chapter, "Judgements Involving Identifications [Judgements of Identification]", which involves judgements that contain proper names. It appeared that perhaps "This flash" could be made to pick out the right flash by demonstrative ostension; proper names do not appear handleable this way, as "Smith" can be Smith's name even if Smith is not within my ostensible reach. Geach closes out his discussion of this problem with a simile: "The problem how you call Smith, the right Smith, to mind is like the problem how you call him ([Philosophical Investigations], Part I, ss691). Although lots of people are called "Smith", the summons "Smith!" may be quite effective to fetch the Smith I want if he is the only man of that name within earshot; and similarly, a judgement that might in principle relate to many men may yet in a particular real-life context be relatable to just one." (p. 73)

Here again we see the pattern of
1. There is a problem for my view of judgement.
2. In "real-life" this problem does not arise.
.'. 3. Context must supply what is lacking in my view.

At no point does Geach consider that our conceptual capacities might inherently refer to particulars, just as he knows they are inherently general. He sees that empiricism asks a bad question when it tries to solve hour we can judge of general matters, given that we can judge of particular ones; but he thinks their error was that the real question is how we can judge of particular matters, given that we can judge of general ones. There is a dualism of the conceptual and the sensible in Geach, just as there is in the empiricists he spends so much time attacking. And if he is right about the medievals, Thomas errs on his side while many Thomists and other scholastics err with the empiricists, with Aristotle claimed by all parties. If nothing else, reading Geach has been good for helping me see that Kant's problems are not new -- or at least they can be seen to have caused trouble, beneath the surface, further back than Kant traces his histories.

On a final note (and this was actually what I originally found interesting enough to post on, before I got caught up in providing context for it), Geach notes that "Quite similar considerations apply to judgements involving tense. The difference between judgements to the effect that a hydrogen bomb will be exploded and that a hydrogen bomb has been exploded is an intelligible or conceptual difference -- a specifically different exercise of concepts is involved. But there is no conceptual difference between judgements formed in different years to the effect that a hydrogen bomb has been exploded, although such a judgement formed in 1940 would have been false and one formed in 1956 would be true." (p.65) When I first read it, I was surprised by how closely connected Geach's claim about tense was to his claims about judgements of particulars: they are treated of in the same section, are said to have "similar considerations" applying to them, and I thought that perhaps the same Kantian solution was what he had overlooked. I had hopes that perhaps here I could finally find a compelling argument for why time is the form of all intuition, what the connection is between reference to particulars and reference to temporal entities. But thinking on it more, I think Geach is just mistaken about how tenses work in language (in thought): it is the same conceptual capacity at work when I judged yesterday that I would be up all night and when I judge today that I was up all night; what has changed is not the judgement, but the context in which it is considered. There is an indexical element to judgements involving tense, just as with judgements involving the concept "now", and changes of index are not changes of indexical. (Ironically, I take this to be something I learned from reading Anscombe on the first person.)

But if this is where Geach went wrong, then the connection between reference to particulars and time boils down to the connection between reference to particulars and the indexicals "here" and "now". And it strikes me as hopeless to try to establish why space and time must be forms of intuition from the fact that (as it happens) we have spatial and temporal indexicals in our language; for if there are other possible forms of intuition, presumably the minds which intuit by them have their own indexicals. So again Kant is proving damnably right: I cannot show why space and time are (our, the) forms of intuition, though it seems clear that they are. So for now I am no better than Geach; I daydream about "others" solving that problem, and think it must have a solution!

21 July 2012

A Link Post

Robert Stern was interviewed in 3:AM magazine; it is a good read.

In the wake of Förster's book, I have been reading more about Schelling and Goethe. Robert Richards's work has been very helpful here; "Did Goethe and Schelling Endorse Species Evolution?" (PDF) was particularly stimulating.

Richards gave a seminar on "The Origin of Species" while I was at Chicago; I only sat in on the first couple of classes at the time, since I was busy and it was being recorded for posting online. Sadly, the video and podcast links are dead now, but I had most of the podcasts downloaded. (For some reason I didn't download week 2's podcast; ironically, that is the one class I am sure I was present at. The slides for that week of the course are still posted (PDF), and are worth looking at just for the cartoon of Professor Icthyosaurus on page 13. (The context for that cartoon was a cyclical theory of evolution, where extinct species were supposed to arise again once catastrophic floods had changed the character of the Earth so that humans were no longer viable, but e.g. ichthyosaurs were again. I just really like the design on the whole thing.)

Edit: This is a great sentence: "This kind of metaphysics enticed Goethe the way several of his women friends did at this time: with great allure and seduction, with the poet giving way even while recognizing the impropriety of his indulgence." (Source, PDF)

17 July 2012

Förster's "Twenty Five Years": an overview.

It seems worthwhile to outline the story of German Idealism, as Förster presents it in "The Twenty Five Years of Philosophy". I suspect my previous post on Förster's book is unreadable, and so unread.

Kant begins with the realization that philosophy before him has taken for granted that our thoughts can get things right or wrong -- that they have "objective validity", in his later terminology, or objective purport as McDowell says it -- and that metaphysics is building on sand so long as it is unsettled whether metaphysical thinking can so much as get things wrong. So in the first Critique, Kant tries to settle the question of how and when thinking can have objective purport. The answer he arrives at is that thinking has objective purport by standing in a relation to sensibility: the receptive aspect of our cognition provides us with a kind of cognition which is dependent on the objects it purports to be about, and so the question of objective purport does not arise for it; the other aspects of our cognition (the categories and the ideas) are explicated as structuring and guiding this receptive aspect of our cognition. As time and space are the forms of our sensibility, this means that thinking has objective purport only in relation to objects in time and space: as the traditional objects of metaphysics are extraspatiotemporal, traditional metaphysics thus shows itself as confused.

But a new sort of metaphysics stands primed to take its place: in establishing how it is that our (empirical, spatiotemporal) thinking can have objective purport, Kant has also established that certain principles govern such thinking. That they in fact do this is a condition on the possibility of thought, as thought must be (able to be made) self-conscious. It is the task of the new metaphysics to establish these principles, and lay out what follows from them.

Förster notes that Kant subtly changes the question he is answering after the A-edition of the first Critique: where before he was asking "How can thinking have objective purport?", starting with the Prolegomena he is asking "How are synthetic a priori judgements possible?" In the case of theoretical synthetic a priori judgements, this question is what the new metaphysics confronts and answers. This shift in Kant's question is both a narrowing of his original question, as he is no longer questioning how empirical judgements are possible as such (though this will in fact still be a topic he addresses in the B-edition of the first Critique), and a broadening of it: for there are judgements which do not depend on a relation to an object for their validity, but which are connected with synthetic a priori principles. These are practical judgements. In the first Critique, Kant had left moral questions underscrutinized, and he had explicitly denied that practical philosophy was connected with transcendental philosophy. But now practical and theoretical philosophy are both the concerns of the transcendental philosopher.

Förster thinks that Kant's attempt at his project fails at several points. For one, Kant's construction of matter in "Metaphysical Foundations of Natural Science" is circular, as Kant and Schelling both notice; Förster notes that Kant was still working on this problem in the Opus Postumum, and that he still did not solve it there. Förster thinks that this is a significant problem, because he thinks the Metaphysical Foundations was trying to complete something the first Critique had accidentally ignored: a spatial schematism of the categories to parallel the temporal one given in the first Critique's Analytic. Whether Kant needed such a thing is controversial in the literature. (My judgement is that Kant didn't think he needed one, and that by his own standards he was right -- but that these standards were too low, and he in fact did need one if he wasn't to take the spatial form of our intuition as simply Given. I'm not sure that his failure to construct the concept of dense matter matters for this, though.)

This is related to a second place where Förster thinks Kant failed: he simply takes the fact that space and time are the forms of our receptivity as given, and he does the same with the table of general logical forms. Förster spends less time on this complaint, but I think it's the most important one he brings up.

Very shortly after the first Critique, Reinhold will try to present Kant's philosophy in a more systematic form than Kant had managed (following up on hints from Kant that such a system should be possible, that the transcendental unity of apperception really is the ground of all synthetic a priori judgements). The form this takes in Reinhold is an attempt to derive all of the Critical Philosophy from what he calls "the principle of consciousness": "In consciousness representation is distinguished though the subject from both object and subject and is related to both". Reinhold held this to be an analytic judgement, and from it tried to prove via a "short argument" that we can never know the thing-in-itself (because we know representations only, which are distinguished from the object) or the subject-in-itself (because we know representations only, which are distinguished from the subject), but that our representations have objective purport (because they are related through the subject to the object). (I know Reinhold only second-hand, through Karl Ameriks's "The Fate of Autonomy", but the prospects for his project strike me as dim.)

In "Aenesidemus" Schulze criticized Reinhold's attempt to found all of the Critical Philosophy on this one analytic principle. He claimed that Reinhold was tacitly appealing to many other principles in his derivations from it, for instance to the logical principle of noncontradiction, and so the appearance of systematicity was merely apparent. It was his reading of "Aenesidemus" that first startled Fichte out of his dogmatic attraction to Reinhold's philosophy; Schulze did not convince him that the whole project was hopeless, but rather spurred Fichte to try to fill the gaps and genuinely establish all of the Critical Philosophy on a single self-evident principle (from which he hoped to derive the "principle of consciousness", and therefrom use Reinhold's efforts to derive the bulk of Kant's philosophy).

Telling this part of the story occupies several chapter of Förster's book, and for my money this is the most interesting and successful part of the work. I found the accounts of how Fichte and (his very Fichtean) Hegel tried to systematize Kant's philosophy intriguing and energizing, even when I did not find them convincing as presented. The general idea is that Kant simply did not go far enough in trying to establish the conditions under which self-consciousness is possible, and that he mischaracterized the nature of self-consciousness. Where Kant still (sometimes) seems to think of self-consciousness as receptive, as relying on an "inner sense" which relates consciousness to a (noumenal) self which is not dependent on the thought of it, Fichte resolutely treats the self as nothing but its apperceptive unity. This residual empiricism in Kant's conception of the self has vanished in Fichte, and the results which are claimed as proved will be considerably more impressive, but the very general argumentative strategy of the Wissenschaftslehre is Kant's: What must be the case, given that I am aware of myself as a self?

There is a third area where Förster thinks Kant failed where I found his criticisms less clear, and the responses on the part of German Idealists seemed less on-point. This is the question of the unity of practical and theoretical reason hinted at in the third Critique, where the regulative principle of the purposiveness of nature is used to guide inquiry (as it already was in the appendix to the Dialectic of the first Critique), and also to somehow aid moral faith (by suggesting that since both the order demanded by the moral law and the order demanded by the purposiveness of nature are demands put by reason to nature, seeing one fulfilled (in scientific empirical inquiry and in beauty) is an aid to believing that the other is fulfilled, that the world is morally structured).

As I recall, Förster's complaint is largely focused on Kant's skepticism regarding whether we can know there to be purposes in the world. He presents Schelling as presenting as an empirical hypothesis that the world is so structured, and as taking contemporary developments in physics as confirming it. Förster is generally skeptical of Schelling's whole approach here (and he presents Hegel as likewise skeptical of it, after the break with Schelling in his Jena period). Förster's positive remedy to Kant's skepticism here comes from Goethe's botanical and optical writings: Goethe claimed that he could "see ideas", and Förster endorses this, and presents it as the way forward for philosophy.

Now, it is easy to see that Kant's skepticism has to be wrong somehow: we do know that there are purposes in nature, for we know that there are living things in nature, and living things are purposes. A horse does things for the sake of maintaining itself and reproducing its kind; it is not merely mechanically explicable, and in fact cannot be understood as a horse if approached mechanically. Human action is the action of a living being, and so likewise is purposive: so if we are not to be skeptical of whether there is human action in nature, of whether freedom is at work in the world, we must not be skeptical of whether we can know nature to have purposes in it.

But Schelling seems to want to prove more than this: not merely that there are purposes in the world, or that the world is purposive to the extent that morality requires (that virtue and happiness will coincide), but that nature as such is purposive. Schelling wants to derive the general structure of nature from what he calls an "intellectual intuition", but it is not at all clear how he can have such a thing. Kant used the term "intellectual intuition" to characterize how God knows the world (supposing he does): he knows it by creating it. Fichte follows Kant in this: the I knows itself in its act of self-positing, and in its act of self-positing knows itself. Schelling explicitly does *not* mean this: his "intellectual intuition" is not creating the world, for the world is already there before Schelling's Naturphilosophie. Fichte's intellectual intuition of the I was used to work out the Wissenschaftslehre, and it appears that this is the usage Schelling is following: his "intellectual intuition" is the foundational principle for his Naturphilosophie. It's unclear how he can establish it, and Förster seems to be of the view that he simply can't: Schelling built on sand.

Förster opposes Schelling and Goethe on this score. Where Schelling ultimately appeals to an intellectual intuition (which is hopeless), Goethe appeals to something else: an intuitive intellectual apprehension of an idea, which Förster also refers to by the Spinozan title scientia intuitiva. Goethean scientia intuitiva is supposed to establish what Schelling could not, and what Fichte left only as an incompletable task: that the world and the mind are both structured by the mind, that nature and reason are both rational, that the purposiveness demanded by freedom is the end of the world itself.

I said some things about why I don't think the scientia intuitiva stuff works in my previous post about Förster's book, but I think the real problems show up in his examples (the film, the book, etc.). Looking at those is probably something I need to devote a post to, because this one is already feeling too dense to be read. So I stop here.

tl;dr: Kant is insufficiently systematic; Fichte is sufficiently systematic, but does not establish all that he needs; Goethe establishes limited results about colors and plants; Hegel uses Goethe's methods to establish all that Fichte had not, to supplement what Fichte had genuinely established, and in this way brings Kant's program to a successful close. Schelling was an enthusiastic blind alley.

The future of philosophy, as I see Förster presenting it: Hegel's own post-Phenomenology work is doing a better job presenting what was already contained in nuce in his Jena-period work. Where there are problems in Hegel's system, they are to be resolved by doing Hegel's job better than he managed it himself -- but Hegel has effectively established what it is that should be done. The Absolute Idea was presented in Jena; what is left to us later philosophers is the seeing of subordinate ideas, such as Goethe saw in his optical and botanical works. (Presumably philosophers can also just do something else, not directly related to the history of metaphysics that Kant is working in: Kierkegaard and Nietzsche simply wrote books which are not trying to do what German Idealism is trying to do, and their work neither contributes to nor (directly) challenges what was going on in "the twenty five years of philosophy". But I suspect that people like Russell and Heidegger would figure as mere epigones to Fichte, on Förster's view.)