I have a published article now!

In case anyone still has this blog in their RSS aggregator: My first published paper, "Hegel's 'Idea of Life' and Natural Purposiveness", is now available in preprint: https://www.journals.uchicago.edu/doi/abs/10.1086/698659

It's lacking final pagination, but that's it. It has a DOI number that can be cited to for now.

See the Dancing Bear

http://www.xavier.edu/philosophy/Contemporary-Debates-in-German-Idealism-Conference.cfm

My poor blog; neglected for so long my imageshack links have all died. Alas!

Relative Identity in Heidegger

Poor neglected blog; even my images are dead now. Ah well, mourning is for the dead.

I have noted before that Heidegger had read some Frege; this isn't a huge surprise, given that he was a student of Husserl, but it's easy to forget from our current "analytic/continental" vantage point. I just stumbled across a place that reminded me of this, and where better to make a note of it than on a dead blog?

In section 44 of "Being and Time", Heidegger is concerned with picking apart the view of truth as adequatio intellectus et rei. His point in doing this isn't to deny the view so much as to complain that it obscures what is significant about truth: if we try to have a "thing" and a "mind" already in view, and then want to add "truth" (and falsity) on top of those as a certain kind of relation between the two ("agreement", "correspondence", or the lack of this), then we have gone badly awry: instead we need to first have Dasein's openness to the world in view, and then the "mind" and "thing" which are supposed to "agree" will all show up as abstractions from a more important phenomena which originally makes claiming possible at all.

One of the ways Heidegger tries to do this is by poking at the "adequatio" relation, which Heidegger translates as "Übereinstimmung": "Was meint überhaupt der Terminus »Übereinstimmung«?", what does one in general mean by the term "agreement"? It has to be some sort of relation, it has to be a bringing-together of two things, but clearly not just any relation will do: we need to get a sort of "agreement" which relates a "thought" and a "thing" just in that the one agrees with the other with regards to truth: and this is obscure. Plausibly, the only way to pick out the right sort of relation is by already having an understanding of truth: A true thought agrees with its object just in that the thought says that things are thus-and-so with the object, and the object is thus-and-so -- and cashing out this "says that" talk already will involve a notion of truth, for saying that things are thus-and-so is just to put forward "things are thus-and-so" as true. (And so adequatio intellectus et rei is empty as a definition of truth; it moves in a circle.)

But that is not what interests me -- I want instead to point to a moment in Heidegger's discussion of relations of "agreement":

Die Zahl 6 stimmt überein mit 16 - 10. Die Zahlen stimmen überein, sie sind gleich im Hinblick auf das Wieviel. Gleichheit ist eine Weise der Übereinstimmung. Zu dieser gehört strukturmäßig so etwas wie ein »Hinblick auf«. Was ist das, im Hinblick worauf das in der adaequatio Bezogene übereinstimmt?

Auf Englisch: The number '6' agrees with "16-10". The numbers agree, they are equal in regard to "how many". Equality is one way of agreeing. To this belongs structurally something like a "regards to". What is that in regards to which the terms related by "adequatio" agree? [This is my own translation; someone please let me know if I've fouled it up too much.]

Heidegger here mentions numerical equality as one form of "agreement", and says that "agreement" always takes a complement: Two things agree in some particular respect, with regards to something: For example, '6' and "16-10" agree in coming to the same number, but not in being the same arithmetical formula.

Heidegger here puts forward (as unproblematic and not in need of argument) a view of equality as distinct from identity; equality is only sameness of number, not "sameness" as such. This is Frege's early view, in Begriffschrift; I believe he changes to his more familiar view (that equality simply is identity) in "Sense and Reference", when he settles on truth-values as the referents of sentences -- that move lets him consolidate a fair bit of his notation. (I would check this if I were not too lazy to do so.)

More interestingly (if you are me), Heidegger also puts forward as unproblematic a view of the genus of which numerical equality is a species, a view of what I think we analytics usually call "identity", as needing a complement: "Wieviel", "How much?" specifies the sense in which '6' and "16-10" are identical, they are the same number. Without some such question as this, no species of "agreement" is specified: The question "Do they agree, are they identical?" does not itself have a sense, unless the context makes clear in what respect agreement is being asked about. (It may be that the context makes clear that every respect is meant, and any dissimilarity will be an absolute lack of agreement between the one and the other.)

If I am reading Heidegger correctly here, then he agrees with Geach against Frege (and against the vast majority of analytic philosophers) in holding that "identity is relative": that to say that A and B are identical is, in the primary case, to say that they are the same in some definite respect, such as being the same color or the same make of shoe. To say that they are absolutely identical, which Frege had taken as the more primordial notion, Geach claims is only to say that they are the same in every respect: they are the same color, the same make of shoe, occupy the same location in space, etc. -- Geach uses Leibniz's Law to introduce the notion of "absolute" or "simple" identity as a defined term in logic.

To remind the reader of the opposing view: Many have held that to say that A and B are the same color is, when put in a logically regimented way, to say that

There is an X and a Y such that X is the color of A, and Y is the color of B, and that X is (absolutely) identical to Y, and that there is no Z such that Z is the color of A or Z is the color of B and Z is not (absolutely) identical to X (and to Y).

This way of rewriting "A is the same color as B" carries with it an ontological commitment to colors; Quine and Davidson take this commitment along happily (Davidson a little more happily than Quine), and so see a sort of Platonism as an unexciting logical consequence of some ordinary claims: There are colors, and there are shapes, because there are true claims on the order of "X and Y are the same shape", and writing those out in a logically acceptable way involves committing oneself to the truth of "There is a W such that W is a shape".

Geach is able to avoid these commitments: he treats "A is the same color as B" as a primitive equivalence relation in the language, and so does not need to quantify over colors to write "A is the same color as B" in ordinary first-order logical notation; it just comes out as looking like "aRb". By a neat trick, Geach notes that he can (in a sense) keep his ideology conservative as well: Quine's way of writing "A is the same color as B" requires a way to say "A has a color", which he writes as "There is an X such that X is the color of A"; Geach writes "A has a color" as "A has the same color as A", as anything which lacks a color cannot be the same color as anything: he is able to use his primitive equivalence relations to do the work of coloredness-predicates, and so doesn't need the latter as primitive terms in his language. This trick works in general for turning predicates into equivalence relations. So Geach doesn't need to include more predicates in his language than Quine did, but is able to reduce his ontological commitments. And since Geach is able to introduce a sign for "absolute" identity in his language by means of Leibniz's Law, the resulting calculus is just Quine's beloved first-order predicate calculus with identity; Geach disagrees with Quine not over a matter of regimented logical notation, but of how to rewrite ordinary language claims in that regimented form.

There are a few other wrinkles to Geach's account of relative identity, but hopefully the above is clear enough to get it in view. One aspect of his view which Geach finds remarkable is that he, unlike Frege, is able to treat statements of sameness and statements of number along the same lines: where Frege insisted that "How many?" required a complement, that statements of number were assertions about concepts, he had also insisted that "Are A and B identical?" required no complement, and that this identity was a logically peculiar notion which everyone immediately grasps in a special way. Geach thinks this was quite odd of Frege; Frege had demolished the idea that "oneness" is a special property of every object, and had left "self-identity" as a special property of every object: but in English and German both we have the phrase "one and the same" "ein und dasselbe", which Geach thinks should have already suggested to Frege that sameness and oneness ought to be handled along the same lines. I think that Heidegger had (without having much affection for logical notation) done just this: he requires an im Hinblick auf before questions of sameness are answerable. It would be interesting to see if Heidegger was consistent in this; rejecting "absolute" in favor of "relative" identity has a fair number of consequences in metaphysics, as Geach was well aware -- puzzles about whether a statue is identical with its clay fall to the ground, for example -- and Heidegger is not uninterested in a number of these metaphysical puzzles.

Peregrin on "Logic and Reasoning"

I just finished listening to this talk; I quite liked it. Peregrin defends the view that logic is "constitutive" of rationality, and not merely normative for it: the laws of logic make the game of giving and asking for reasons possible, not what tells you which moves within the game are good ones or bad ones to make. This isn't a new idea, but I very much liked seeing someone defend it without leaning on the fact that they are also trying to exposit Kant's views on general logic, or the views of the author of the Tractatus.

There is one bit that struck me as odd, though, which is why I'm writing this post: at one point Peregrin is concerned to show that his view can still claim that logic is "a supreme arbiter of rationality" despite not allowing the laws of logic to be violated (in general -- he allows occasional violations by single members of linguistic communities, but says very little about the details of how even this could happen given that the laws violated constitute the act which is supposed to defy them). His reply seems odd, though: He says that being rational may be "having implications, negations, etc., not using them in an appropriate way."

This seems wrong for at least two reasons. One is that minutes earlier he'd allowed that there might be linguistic communities which don't have implication (a group in Siberia studied by a Soviet scientist is discussed as a possible example), and so don't have modus ponens because of this. So, what he put on his slide seems to contradict his own commentary on it, unless he wants those linguistic communities to fail to be rational (which is obviously undesirable). The other is a generalization of the point Peregrin made when he allowed for a linguistic community to lack "implication": Why should the material conditional, classical negation, exclusive disjunction, etc. be so important for being rational as such? They seem to be of fairly recent invention, and sit uneasily next to the ordinary-language terms often used to characterize them (as anyone who has ever had to teach undergraduates well knows). How could having them in one's language be so important as to constitute the game of giving and asking for reasons?

The remedy to this, I think, is just what Sebastian Rödl talks about in the first chapter of "Categories of the Temporal": we should retain the idea that logic is constitutive of thought as such, but not identify this logic with a calculus (and so in particular not with classical logic and its material conditional etc.): the possession of any particular logical calculus is an optional tool in reasoning, not constitutive of it. The kind of logic which is constitutive of thought as such is transcendental logic, not general logic: it essentially involves reference to thought's relationship to its objects (and so refers to inquiry, the process by which those objects are known). Being rational cannot plausibly be "having implications, negations, etc." but it is (at least plausibly) having distinctions of truth and falsity, of oneself as an inquirer who can err and be corrected by others or correct oneself, of the objects of inquiry as being capable (at least in many cases) of settling questions about them when some are in error or ignorant of them, etc. It is hard to see how one can be a rational subject without such notions; it is the task of a transcendental logic to outline them and give their laws, without which thought as such is impossible.

I think this sort of view also helps to make sense of so-called disagreements in logic (as between classical and intuitionist logicians, or dialetheists and everyone else): they are not expressing conflicting views on "the" logic constitutive of thought as such (which would have to be a transcendental logic), but expressing views which disagree with one another on which calculus captures the laws of thought as such (or which are normatively correct in describing how one should proceed if one wishes to think rationally, as they tend to think of it). Accepting or rejecting the law of excluded middle, or rejecting (and not merely accepting) the law of noncontradiction can then be seen not as doing the impossible (if laws of logic are constitutive of thought as such), but as advancing rival views on a distinct question -- one which the transcendental logician may reject as relying on a false assumption, that the logic of thought as such is the logic of a calculus, is general and not transcendental logic. So long as it is not among the laws of transcendental logic that one has a particular view of transcendental logic (which would be a surprising result), the disagreements in logic do not need to be seen as violating laws which are constitutive of thought as such, and can be regarded as genuine disagreements without overturning the view of logical laws as constitutive.

It might be thought that the existence of dialetheists still posed a problem: Didn't I say that a distinction between truth and falsity was (plausibly) involved in the laws of transcendental logic, and isn't this just what the dialetheists want to argue about? Are they not still seemingly violating the laws which are supposed to be constitutive of thought as such?

I think not: Even in the extreme case of Graham Priest's acceptance of every version of the denial of the law of noncontradiction he is presented with, one can find him affirming (in "Doubt Truth to Be a Liar") that one cannot both affirm and deny a proposition simultaneously. He views this as a psychological claim, and his ultimate evidence for it is phenomenological, but he recognizes that he needs something of this sort to make his own views so much as stateable: if he has access to no such distinction as this, then he can't intelligibly say that even dialetheists believe that there are monaletheias (propositions which are only true or false, and not both): without something in his system to keep two truth-values apart in the end, there is nothing to keep his opponent from asking "Yes, yes, you accept that P is true and not false, and is a monoletheia -- but how do I know you don't also hold it to be false and not true, and a dialetheia?" (The context in which Priest invokes an absolute psychological-phenomenological distinction between affirmation and denial is one in which he has rehearsed the many "revenge" Liars that a dialetheistical treatment of the Liar leads to; Priest needs some way to handle "This sentence is false and is a monoletheia", which on his treatment is both true and false and has both one and two truth-values, without undermining his own view that dialetheism is compatible with classical monoletheic logic "mostly" holding in everyday reasoning. I would look at my copy of the book to confirm this and find references, but I am lazy and as far as I know I'm the only person who feels a need both to defend the constitutive view of the laws of logic and to make sense of Graham Priest.) So I think that Priest can be seen as still abiding by (and affirming and not denying) the distinction between truth and falsity at the level of generality at which transcendental logic needs to deal with such truth-values: he just has peculiar views about how truth-predicates should be used in formal languages, etc. When it comes to knowing that when a question has been settled in inquiry it is not also still open, or that we can err when we hold that a question has been settled or not and might need reopening, Priest (and I think any other dialetheist who considers the issue) says nothing but what the transcendental logician says we all know qua rational beings: what is, is, and what is not, is not.

Rödl on Kant's First Analogy of Experience

Here's how Kant states the First Analogy in the A-edition of KRV, where it is labelled the "Principle of Permanence": "All appearances contain the permanent (substance) as the object itself, and the transitory as its mere determination, that is, as a way in which the object exists." (A182)

In the B-edition of KRV, Kant adds a paragraph to the beginning of this section. In "Logical Form as a Relation to the Object", Sebastian Rödl goes through this paragraph sentence-by-sentence (omitting some parenthetical remarks of Kant's and the final sentence). As Rödl presents it, Kant argues as follows (following the Kemp Smith translation, B224-5; each of these is a single sentence of Kant's German):

1) All appearances are in time; and in it alone, as substratum [...], can either coexistence or succession be represented.

2) Thus the time in which all change of appearances has to be thought, remains and does not change. For it is that in which, and as determinations of which, succession or coexistence can alone be represented.

3) Now time cannot by itself be perceived.

4) Consequently there must be found in the objects of perception, that is, in the appearances, the substratum which represents time in general; and all change or coexistence must, in being apprehended, be perceived in this substratum, and through relation of the appearances to it.

5) But the substratum of all that is real [...] is substance; and all that belongs to existence can be thought only as a determination of substance.

Claim 1) is established by the Transcendental Aesthetic. See II.ss4.1, the first paragraph of the Metaphysical Exposition of the Concept of Time, for the argument; the idea is that we can't build up to a representation of time by first perceiving items as simultaneous or sequential and then abstracting "time" out of those perceptions, since perceiving them in that way requires already seeing them as in time: so the representation of time is a priori, as it is only against the background of time that we can represent things as simultaneous or sequential.

2) follows from 1): if we need to use time as a background against which to represent things as happening simultaneously or sequentially, then representing anything as changing will also require this (as changes are sequential: there is something changed from and something changed to). The background against which change is represented is not itself represented as changing, but is what makes the change intelligible as a change. As this background is time, time must be represented as remaining without change. Rödl here notes that it seems that the way to represent the logical form of thoughts of items in time is as "determinations of time", as Kant says: something like "A exists at t1", with the time "t#" being part of what the thought determines. Simultaneity would then be existence at the same t#, succession would be existence at a later or earlier t#.

3) I am sure Kant argues for somewhere, but I'm not finding a reference at the moment. That time is not itself an empirical intuition follows from the argument for 1), but I don't see where Kant actually makes that inference explicit. But it's a trivial enough point that he hardly needs to: once a distinction is noted between perceiving objects in time and perceiving time itself, it is easy to grant that we do the former and not the latter. (There's a reason we need clocks.) Rödl notes that this simple point poses a problem for the idea that the way to represent an item in time is "A exists at t1": we are trying to articulate the logical form of an appearance of something in time. So if the logical form of an item with a temporal position (simultaneous with, earlier than, or later than some other item) is "A exists at t#", then we cannot be given any items with temporal positions in perception, as perception does not provide us with a time to put for the schematic "t#".

4) From this Kant concludes that "there must be found in the objects of perception [...] the substratum which represents time in general": Rödl puts the point thusly: "what is given in intuition—appearances—as such contain something that represents time in the sense that something is conceived as a determination of time in virtue of being apprehended as a determination of it. Apprehending A and B as determinations of this thing, we apprehend A and B as succeeding, or as simultaneous with, one another." (p.365) The problem with thinking that "A exists at t1" could represent the logical form of a thought of an appearance having a temporal position was that nothing was given which could stand in for a "t#": the solution is to see A as a determination of time (as having a temporal position determined in the thinking of it) in virtue of it being represented as a determination of something which is given in perception, and which functions as a substratum against which simultaneity and succession can be represented.

5) And here Kant draws the conclusion of the Principle of Permanence: All appearances are in time, as the Transcendental Aesthetic established; this entails that they are given to us as simultaneous with one another or earlier or later than one another. To be represented in this way (which they must be to be given to us as appearances in time), there must be found in these appearances something which is grasped as a substratum against which temporal positions can be apprehended, and the various temporal positions must be represented against the background of such a substratum. But such a substratum in appearance is just what the Principle of Permanence calls "substance": there is in all appearances in time a distinction that can be made between substance and "mere determination", which Rödl calls "state". Rödl puts it this way: "We perceive that A succeeds or is simultaneous with B, as we apprehend A and B as determinations of time [by perceiving them thus]. And we apprehend A and B as determinations of time, not by predicating A and B of a time as in “[A exists at t1 and B exists at t2] ”, but by predicating A and B of a substance as in “S was A and is B” . Temporal thought bears a predicative structure. It is not articulated into a time and what is at this time, but rather into a substance and its states. It is in virtue of being thus articulated that a thought distinguishes a time from what is at this time and thus represents its object as temporal. This completes the proof." (p.365) "S was A and is B" represents a substance, 'S', which can be in different states at different times (is now B, was previously A) while remaining the same substance. Thoughts which represent substances as substances exhibit this form: the substance thought of is known as something which can bear contrary predicates at different times, as Aristotle put it; it is a perceptible item which can be seen to change or remain the same at different times. Being able to perceive such items is what enables us to have appearances which have a temporally order internal to how they are given to us: thinking thoughts of the form "S was/is F" is how we can represent some appearances as coming before, after, or alongside others. A Hume-style skeptic about substance needs to make this intelligible by thinking thoughts of the form "A exists at t1" and "B exists at t2", and this cannot be done, as time is not perceptible. Thus the proof against this sort of skepticism is complete: in all appearances substances are given, as the substrate of changeable states.

Rödl continues on to note a few things from the later pages of the Analogy, but the impression given is that the rest is a mop-up operation: the important work is already done in that first five sentences. There is a small puzzle about this, given that these sentences were added in the B-edition, and replaced a short section that doesn't contain this argument. But I think it's plausible that the argument Kant puts more clearly in those five sentences can be found in the first few paragraphs of the A-version Analogy, spread out more widely and unclearly.

There are two more puzzling things about Rödl's handling of the First Analogy. One is that it might seem that Rödl's way of handling perception of time-positions can't handle the relative positions of states of distinct substances. I will handle this indirectly, by first looking at something Rödl points out. It might be thought that one advantage of representing temporal thought by "A exists at t#" is that the various numbers which slot in for '#' will all line up of themselves: t1 is before t2, which is before t3, etc. But this is an illusion: "the things to which “t1” and “t2” refer, and the unity of these, cannot be perceived. Here nothing satisfies “the condition of the empirical unity of time” (A 188/B 231). By contrast, in “S was A and now is B”, there is no need to connect two things determined by A and B respectively, for there is only one thing, the substance, determined by both. Its unity represents the unity of time. In this way is the “condition of the empirical unity of time” satisfied." (p.366) That is, the attempt to represent temporal thought by "A exists at t1" and "B exists at t2" etc. fails to satisfy a demand established by the Transcendental Aesthetic: there is only one time, and all times are limitations of it. There is nothing in the representation of temporal appearances by "A exists at t#" which guarantees that everything which stands in for "t#" will be part of a single time. Rödl's way does meet this demand: If S was A and is now B, this can only happen in a single time through which S persists, as is represented by the single symbol 'S' in the notation.

Now, what does that have to do with the following worry: Rödl's way can't handle "S is A" and "P is B" being simultaneous, since those two thoughts don't share a substance? Here I think I see why Rödl talks of "states" and not "properties" or "determinations": it is tempting to think that there is something special about monadic properties or determinations, but it is much less tempting to think this about states. The 'A' in "S is A" can perfectly well be "near the P which is B"; this is a state a substance can be in, and the thought of it includes the time-determination of the other substance, and represents the empirical unity of the times in which these substances exist. Here I am speculating as to how Rödl handles this question; it seems like something he should address, but I haven't read anything where he takes it up. But I don't see any reason my way wouldn't do fine for him: relational states are perfectly good states, and an appearance of multiple substances in relational states will satisfy Kant's demand to respect the empirical unity of time. (The Transcendental Aesthetic can, I think, already be taken to have shown that all appearances will be related in a single time; it will thus not be necessary to further guarantee that all states of substances will be so related, as these are merely a species of the genus "appearance". That is to say, I do not need to establish that all substances will stand in relational states to one another which determine their time-relations; the Aesthetic does the needed work. What is needed is only to provide a way of presenting substances in thought which does not violate the condition of the empirical unity of time, as "A exists at t#" did. Provided that substances are in fact related to one another in time, polyadic state-variables represent them as in a single time.)

There is another puzzling thing about Rödl's way of handling the First Analogy. The five-sentence proof from Kant he looks at is only in the B-edition, but he only presents the A-edition's statement of the Principle of Permanence. Related to this, he does not discuss the last sentence of the paragraph added to the B-edition: "And as it is thus unchangeable in its existence, its quantity in nature can be neither increased nor diminished." This sentence goes along with the B-edition statement of the (slightly renamed) "Principle of Permanence of Substance", which says "In all change of appearances substance is permanent; its quantum in nature is neither increased nor diminished."

Rödl mentions this sentence only in a footnote: "We disregard the last sentence of the proof (“Da diese also im Dasein nicht wechseln kann, so kann ihr Quantum in der Natur auch weder vermehrt noch vermindert werden.”), which does not pertain to anything stated in the First Analogy in the A-edition. It is a further thought, with its own difficulties, which lie beyond the scope of this essay." (p.369)

Now, it is curious that Kant changes the statements of the principles of the Analogies in the B-edition. But he leaves so much of the argumentation unchanged in these sections that it seems hard to deny that he thought he merely reworded them, and left their substance unchanged. But I think Rödl is simply right about this much: Nothing in the First Analogy in the A-edition supports the claim that the quantity of substance in nature is constant. Substances are things which can change in various ways while remaining the same substances; Kant tells us nothing here about why "quantity in nature" is something unchangeable. More problematically, I don't think Kant has given a sense to "quantum" here: Does he mean that substance in nature does not change in total mass, or in total energy, or in total extension, or in some other quantity measured in some other way? There are many quantities of substance in nature which do change: the number of dinosaurs is a quantity in nature. As far as I've been able to tell, at this point in the Transcendental Logic Kant has no grounds whatsoever for speaking of a single quantity of any sort which is constant for all substance at all times: the Principle of Permanence is entirely compatible with an Aristotelian world of many finite substances with different natures and different ways of being. (The only thing I can find which can even pretend to be an argument otherwise is the Anticipations of Perception, with its talk of intensive magnitudes of reality -- but this section also does not establish that there is a single scale of reality-magnitude, but only that any reality given in sensation is given in a scaleable way.)

Here I suspect Kant changed the B-edition of KRV to make it line up more smoothly with his physics, which he had in the meantime laid a groundwork for in "Metaphysical Foundations of Natural Science". But this sort of move is illicit, by Kant's own standards: principles of a special science such as physics are not established before the System of Principles of the Pure Understanding, as these pure principles are used in determining the principles of the special sciences (which are partly empirical: in MFoNS Kant relies on experience for the claim that bodies have weight, if memory serves). If Kant hasn't established that the sort of substance which must be found in the appearances to make experience possible is the kind his preferred empirical science talks about, he shouldn't pretend otherwise: and viewed from our later vantage-point, we should feel welcome to jettison the supposed necessity of Kant's Newtonianish physics, and feel no compulsion at all to read it back into the Analogies -- even if Kant himself did this while revising the B-edition. It is only Kantian for us to attempt to understand the philosopher better than he understood himself.

"Kantian Humility"

I read about half of Rae Langton's "Kantian Humility"; I skimmed the chapters between the one on phenomenal substance and the one on primary/secondary qualities. Here are some thoughts I had.

She latches on to some passages that I find fairly opaque, and is able to give a sense to them (the stuff about matter being constituted by "mere relations"), but I felt like her overall interpretation was severely hindered by her unwillingness to discuss core arguments of the Transcendental Analytic. For instance, she doesn't commit herself to any view as to how the argument for the First Analogy is supposed to work. But, she's committed to reading "phenomenal substance" as akin to "wax duck": phenomenal substances just aren't substances (and in her defense, she shows that this is how Wolff used the phrase); the schematized category of substance is not a species of the pure category for her, and on her reading Kant denies that we are ever given anything in experience which "can only be thought as subject, not as predicate". She puts a lot of weight on Kant's remark that we can make anything a "logical subject" in a judgement without that saying anything about whether or not it's a substance ("Love is abiding" and "Yellow is pale" don't make love or yellow into metaphysical substances), and holds that this shows that treating "matter" as a substance is only done by Kant in a "comparative sense": that it is a logical subject relative to empirical predicates of matter, not that it can't be thought of as a predicate of the thing-in-itself. And in fact she holds that this is how it is: the only substances for her Kant are things-in-themselves, which can't be thought as predicates of anything. (She assumes this throughout, without any argument that I saw. I don't know why someone like Spinoza wouldn't deny it, and claim that these monadic "substances" are in fact mere predicates of God; I've never been clear on how Leibniz prevents his monads from collapsing into God in this way, though it's clear he wants them not to.) All of this means that, in fact, no knowledge of substance can play any part at all in the First Analogy: the subsistent in time is only a permanent predicate, not something which can only be thought as subject. This strikes me as ruling out any plausible interpretation of the First Analogy, as it makes the relationship between its principle and the category associated with it essentially null.

She constantly turns to Kant's physics when discussing what Kant means by "matter", and reads his dynamical theory of matter as providing argumentative support for large swathes of the critical philosophy. (How this doesn't render the entire project circular is a problem I don't think she ever addresses: From what I recall of the Metaphysical Foundations of Nature, Kant uses the Analogies to argue for his force-theory. So he can't presume that this is how matter works when arguing for the Analogies themselves.) But if the permanent in experience is the matter explicated by Kant's physics, then it's not something we are consciously aware of as such: attractive and repulsive forces are not something we can sense directly. She takes a very radical move here, and severs the connection between the senses and intuition: she reads the Third Analogy's principle as committing Kant to the view that all matter affects us at all times, and that it is only because most of these effects are too small ("lacking in reality") to be brought to consciousness that prevents us from being aware of all objects at all times. This puts Kant's view of experience very close to Leibniz's: every subject represents the entire world at all times. In her defense, she quotes Kant saying things that seem close to this radical a view in his reply to Eberhard in "On a New Discovery etc.", which I haven't read. (I remembered reading Allison's introduction to it years ago, and then skimming the text to confirm that it was how Allison had said it was. But all of the details are now lost to me.)

But if this sort of neo-Leibnizian view is Kant's, then it seems simply incoherent: if external bodies are given to us only by means of attractive/repulsive forces, then the fact that forces sum means that external bodies are not given to us individually: two forces of velocity X and one force of velocity 2X are not distinguishable, and so all of those remote objects which Langton's Kant has making "subconscious" effects on us are not distinguishable (in principle) from a single external object making a single impression on us whose force is the sum of those effects. It might seem that her Kant also faces the problem of how to distinguish between proximal and distal causes of the effects on us, but I think that's actually not a problem for her Kant if the issue of forces summing isn't: since Newtonian forces act instantaneously at a distance, a proximal and a distal stimuli simply produce distinct forces on us, and so if these forces can be distinguished then so can the proximal and distal stimuli.

I don't think Leibniz's view has these problem, because Leibniz thinks that forces, which are relational properties of bodies, are "well-founded phenomena" which reduce down to simple properties of monads: so the representation in a single monad of some particular lump sum of force is analyzable (by God, not by us finite provers) into non-relational properties of monads, and it is only by means of these non-relational properties that Leibniz has each monad representing the entire world. But Kant is adamant about relations not being reducible to non-relational properties, as Langton shows at length, so I don't see how her Kant can go from the forces to anything which represents the world -- even setting aside that Kant has independent arguments against Leibniz in these quarters (such as Leibniz presuming the identity of indiscernibles, which is needed to make his monads "represent" individual objects by means of non-relational descriptions of them). I don't know how her Kant is supposed to be able to represent individual objects merely by having forces impinging upon it at all, but she is explicit that this sort of physical interactionism is what drives Kant's thoughts about thought's receptivity.

I found the book disappointing overall, but if Langton's not right about what "matter being constituted by mere relations" means, I don't know what those passages in Kant mean. (Langton can here apply Modus Tollens; I apply Modus Ponens.) So the book is worth looking at just to see how she handles the passages her view handles well; it is a desideratum for any alternative view of Kant's matter-doctrine to be able to handle them as smoothly, but without sacrificing so much of the rest of Kantianism.

McDowell on Cognitive Science and Epistemology

University College Dublin has put online two lectures (and an interview) McDowell gave there recently; kudos to them for doing this. It is all the to better that more talks are going online these days, so that it's easier for those who want to hear them to do so.

I just finished listening to the first one, "Can cognitive science determine epistemology?" Its topic is familiar for anyone who's read McDowell very much, and its content replicates some material available elsewhere recently: McDowell is here replying to Burge's recent attacks on him, just as he was in a talk he gave when visiting IU three years ago.

It's actually interesting to listen to McDowell's views on cognitive science while at IU: he is sanguine throughout on the current state of representationalist cognitive science, and explicitly doesn't want to make any waves or raise complaints against it. This is not exactly the attitude one finds most often at IU. (B.F. Skinner was at IU for nine years, and reportedly designed the psychology building; his influence is still felt here.) It's especially surprising to hear him speak of "representations" so blithely, though I suppose this is in accord with the "representations without representationalism" slogan he urged on Rorty back in "Rehabilitating Objectivity".

But I think that, even if he does harbor secret doubts about the current state of the science (which I have no reason to believe he does, but which I think is the horse he should bet on), it makes sense to be ameliorist in a lecture like this: there's no reason to fan the flames of people who, like Burge, see self-standing epistemology as just an armchair form of psychology by running together such a self-standing epistemology with a rival vision of psychology. This is especially true because of the claim he concludes his talk with, which I think might represent a genuine shift in his thinking: he claims that cognitive science needs epistemology (as a self-standing enterprise) to be able to identify contentful states in the way that it does.

I know McDowell has long claimed that alternative accounts of perceptual knowledge make the very idea of perceptual knowledge unintelligible (this is a central claim of "Knowledge and the Internal", and is tied to the central arguments against Davidson in "Mind and World"), but I can't think of another place where he so straightforwardly says that an empirical science (as opposed to a (discardable) alternative account in philosophy) relies on something that his sort of account of perceptual knowledge provides. I think that's a stronger claim than anything he made up through the 90s, at least; I would need to reread the exchange with Dreyfus to see if there's a similar claim made there, given how Dreyfus views his own relation to psychology. If this sort of thing is true, then philosophy can't be a purely therapeutic enterprise: the sciences need it to do something else in addition to showing flies the ways out of flybottles, in order that they may be sciences. A certain sort of constructive work (in some sense of the term "constructive") is needed from philosophy to allow a properly empirical science to proceed. I don't think that McDowell would have been willing (or happy, at least) to say this at all points in his career, but he seems to have said it explicitly here. I have to wonder whether he thinks claims of this sort generalize beyond the field of representationalist cognitive psychology -- might physics rest on principles like the analogies of experience, or biology on a logical account of the lifeform? If there are some dependencies between empirical sciences and accounts of rational self-consciousness, how deep (far?) do these dependencies go? (This way lies Naturphilosophie, which is worrying and at least a little heady.)

Side-note: Michael Friedman argues for something like the claim McDowell made in his "The Dynamics of Reason", that philosophy needs to provide (and has, in the past, provided) the sciences with something they need in transitions between paradigms during periods of revolutionary science. I was unconvinced that Friedman had shown anything stronger than the claim that, in fact, work done in philosophy was instrumental in making turn-of-the-century revolutions in physics possible; I'm not sure how strong of a case can be made for the usefulness of philosophy in the other scientific revolutions he briefly discusses, and am skeptical of a general claim he argues for, that philosophy in general provides the connections between mathematics and mathematical physics that physics needs. He clearly wants to put forward a vision of scientists and philosophers working in tandem in a certain way, but I came away from the book with the impression that he's too weak to a nostalgia for logical positivism in its heyday. I couldn't see a future for that sort of thing, because I couldn't see how his account generalized beyond the weird combination of Neokantianism and crises in physics that lead to the syntheses he spent so much time looking at. On the authority of Einstein, work in philosophy really was important in certain reformulations of physics -- but it's in the nature of revolutionary science that we can't tell in advance what sorts of reformulating will be called for, and so I don't see how philosophers could intentionally try to provide it. It was just a happy accident that it did in that case, it seems to me. But it was a fun little book regardless.

Dummett's Frege and Rödl

I have not been good at blogging recently; I have neglected comments for about a year, and have written nothing. Apologies to those who I did not respond to (which by my records include Daniel Nagase, N.N., Charles Wolverton, Evan Kuehn, and Duck; I could make excuses for this bad behavior, but they would be of merely psychological importance, and that's a poor way to start a Frege post).

But if I cannot manage to blog well, then I should at least blog badly more often; here then are things I typed to try to get clear to myself on what Rödl is getting from the Dummett essay he leans on in the first chapter of "Categories of Temporality".

In "The Context Principle: Centre of Frege's Philosophy" Dummett claims that Frege tried to use the context principle to justify his "realism", his treatment of numbers as objects, while simultaneously using it to answer the question of how numbers can be given to us ("epistemologically", in Dummett's term). Dummett's idea is that Frege tried to answer this question (and establish his realism) by fixing the truth-values of every sentence in which a number-word appeared; in the Grundgesetze, this is fixing the truth-value of every sentence in which a term for a value-range appears.

The line of thought seems to be this:
1. Frege can fix the truth-values of sentences by (in part) stipulation, going through each possible combination of a value-range term with a primitive concept-term and assuring that it has a truth-value.
2. For Frege truth-values are the Bedeutungen of sentences.
3. The context principle: the Bedeutung of a subsentential term is determined only by the way it contributes to the Bedeutungen of the sentences it appears in.
Which gives Dummett's Frege the conclusion that by stipulating truth-values for each (atomic) sentence in which a value-range term appears, he has also settled what the Bedeutungen of value-range terms are.

Dummett contrasts this to a way of providing terms with Bedeutungen which would go against the context principle: first establish the domain over which the variables of the language can range, and then determine for each term of the language which needs a Bedeutung which of the items from that domain is to be its Bedeutung. As this initial domain-determination requires a grasp of the possible values of variables anterior to the securing of Bedeutungen to the sentences of the language in which those variables appear, it violates Dummett's version of the context principle.

Dummett spends some time on the objection that one might ascend to a metalanguage to avoid this violation of the context principle: if the domain-determination for the object language takes place in sentences of another language, then the context principle is not sinned against. But Dummett argues that Frege did not mean to be giving Bedeutungen to the terms of Begriffschrift which were already understood by anyone who could read his German: this would make some of Frege's prose a necessary element of his logic, which Frege clearly wants to avoid. The Begriffschrift is supposed to stand on its own, with the German prose serving only as a propaedeutic to its understanding; in particular, if the question of whether numbers are objects or how they may be given to us is to be solved by the Grundgesetze project, then it cannot rely on the German-reader's already knowing these objects and including them in the domains over which Begriffschrift variables are allowed to range.

Dummett's objection to Frege here is put rather tersely, and I am writing this post because I need to do some work to unpack it for myself: "The fallacy appeared at the very first step. The stipulations governing the primitive functors [what I called concept-words, above], including the criterion of identity for value-ranges embodied in Axiom V, could be determinate only if the domain, consisting wholly or largely of value-ranges, was determinate; but the domain was in the process of being determined by fixing the Bedeutungen of the value-range terms, and so the procedure went round in a circle." (p.18)

The circle seems to be this: Frege tries to establish that among the objects are value-ranges (the Bedeutungen of value-range terms) by stipulating truth-values for each atomic sentence which results from combining a value-range term and a primitive function of Begriffschrift. But the sentences which are here stipulated to have truth-values can only have truth-values if the domains over which their variables range is determinate; an indeterminacy in the domain means an indeterminacy in what can count as the sentence being true or false, and Frege's stipulations do not settle this question about domains. In fact, Frege wants to settle questions about domains by securing Bedeutungen for his primitive terms, so that he can settle the question of whether numbers are objects, and how numbers can be given to us, by making clear how sentences featuring number-words function in inference. So he both needs to settle the domain issue prior to his procedure and only by means of it, which is contradictory. This is why he is able to think he has given Bedeutungen to all of his Begriffschrift expressions such that all of his Basic Laws are true, when in fact they are jointly inconsistent (because of Basic Law V, whose Bedeutung was supposed to be settled by the procedure of securing Bedeutungen for value-range terms).

Dummett's verdict here is despair. His closing paragraph:
"The realist interpretation could be jettisoned without abandoning the context principle itself, but only if that principle, as here understood, can be shown to be coherent; and this remains in grave doubt. And yet it is hard to see how it can be abandoned, so strong is the motivation for it. The alternative is an apprehension of objects, including abstract objects, underlying, but anterior to, an understanding of reference to them, or, indeed, a grasp of thought about them; and this is a form of [what Putnam calls] external realism too coarse to be entertained. I am therefore forced to conclude without either endorsing the central feature of Frege's philosophy or rejecting it; I can do no more than to say lamely that the issue if one whose resolution is of prime importance to philosophy." (p.19)

This is where Rödl intervenes: he claims that the context principle can be saved (and should be saved), but only by rejecting the idea that a logic such as the Begriffschrift can be said to present us with the form of thought as such. As Dummett argued, a coherent version of Frege requires something other than Begriffschrift to settle the question of what objects Begriffschrift is about; Begriffschrift cannot take care of itself, but needs the "pinch of salt" Frege infamously asks his readers for. The distinguishing characteristic of Begriffschrift Rödl picks out for blame here is that Begriffschrift expressions are characterized only by their inferential structure: a Begriffschrift expression is to have its meaning fixed solely by determining how it figures in lines of a Begriffschrift proof. This is what Frege really fixes by his procedures: how Begriffschrift expressions are to be used in constructing Begriffschrift proofs. But Rödl claims that this fails to settle the question of how Begriffschrift expressions relate to their objects, for the reasons Dummett gave: and this is why Frege fails to notice that his logic cannot take care of itself, as part of what determines the thoughts expressible in Begriffschrift is the relation of these thoughts to their objects, and not merely the relations of these thoughts to each other, and this is why Frege fails to determine thoughts expressible in Begriffschrift in the way he believed he had. So the form of thought as such cannot simply be an inferential order, but must already determine the relation of thoughts to their objects in a way that Frege's logic did not.

The option Dummett's despair overlooks is that of determining the truth-values of sentences not in a way anterior to their relatedness to their objects, but only by already having in view these sentences' relatedness to their objects. Dummett's Frege erred in trying to secure relatedness to objects only indirectly, by means of securing the inferential functions of thoughts, and Dummett as sees the only alternative to secure the relatedness to objects of thoughts to be that of grasping thoughts and objects independently and then bringing them together (in some medium other than thought, which yet stands in need of relatedness to objects). Rödl's excluded third alternative is to promote a logic which determines thoughts only as already related to objects which are given by these thoughts: such a logic is what Kant called "transcendental logic". Kant distinguished this from the sort of logic he infamously claimed to have been settled since Aristotle, which he characterized as a "general logic" that abstracts from all objects of thought and deals with modes of inference independently of the relatedness of thoughts to any objects (which is why for Kant general logic can lead to transcendent metaphysical thoughts by means of fallacious inferences, but transcendental logic does not give any "Sinn oder Bedeutung" to the "thoughts" of transcendent metaphysics).

To present a transcendental logic is to present a logic which includes within it an account of the objects which can be given to thought; non-transcendental logic can omit this only because it treats of thoughts without inquiring into their relatedness to objects. If a logic is not to leave the question of the relatedness of thougts to their objects outside of itself (as a topic for something other than logic), i.e. if a logic is to take care of itself, to be able to present the form of thought as such, then the objects which are given in thoughts must be treated of by logic itself: thus transcendental logic must be metaphysics. This is just what we find in Kant: the Transcendental Logic is just where Kant establishes the principles of his "metaphysics which is to come forth as a science", that all appearances are substances undergoing lawful changes in mutual interaction etc. As general logic determines the forms of thoughts which are capable of figuring into inference, so transcendental logic determines the forms of thoughts of objects: and so it determines the ways in which objects may be given to us, the way in which objects which can be given to us may (or must) be. And unless there is a distinction made between objects which can be given to thought and objects which can be given to our thought, transcendental logic will not have as a consequence transcendental idealism: if the metaphysics of transcendental logic determines how objects must be to be given to thought, then to speak of objects which are not (or might not be) thus is to speak of something contradictory, or to put forward a thought which has no relation to any object: thus it cannot have as its object any "thing in itself" which is unknowable by thought. Kant's transcendental idealism arises because of his accounting our form of sensibility as not the only logically possible one: hence his transcendental logic does not present the form of objects which can be given to thought, but only the form of objects which can be given to spatiotemporally-formed thinkers; the "thing in itself" thus remains as something which (as far as logic allows) might be given to thought, but cannot be given to our thought, and so is for us unknowable and undetermined by Kant's metaphysics. If Kant's forms of sensibility can be shown to be the only logically possible ones, to be demanded by transcendental logic and not merely an addition from a "transcendental aesthetic", or if Kant can be shown to have erred in his claiming that the (logically contingent) forms of space and time are the forms of our sensibility, then Kant's transcendental idealism can be excised from his system. This is part of Rödl's project, in line with earlier German Idealists such as Ficthe and Hegel: to carry out transcendental logic without an independent transcendental aesthetic, so as to avoid transcendental idealism and the "thing in itself". They do not reject the division between transcendental logic and transcendental aesthetic because of ignorance of the importance of a transcendental aesthetic, of an account of the form of objects which can be given to thought, but because they seek to have transcendental logic alone provide for it, as it should be able to if transcendental logic is a logic which can take care of itself.

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.

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.

"Thinking"

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.)

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.

Hooray for C.I. Lewis!

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

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.

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.