"Purity" in Morals

Here is a claim I think is obviously true, but which I'm not sure I've ever seen anyone state clearly, and which in any case doesn't seem to be as significant to people as I think it should be: Decision theory is the pure doctrine of prudence, in Kant's sense: it is the parallel of what Kant does in the first two parts of the "Groundwork for the Metaphysic of Morals". This claim I mean strictly and rigorously; Kantian ethicists who mock decision theory are as misguided as utilitarians who denigrate the Moral Law itself.

Here is why I think people miss this obvious truth: Decision theory is not "pure", in Kant's sense, because it is not independent of psychology; it is not entirely unempirical, despite being largely mathematized. But Kant's own work is also not independent of psychology, as anyone who has taught Kant's own examples from the second section of the "Groundwork" is well aware: Kant helps himself to just a little bit of psychology, to the claim that (as Plato had already said in the second book of the "Republic") each human has many desires, and no one can satisfy these desires without assistance from others. Kant doesn't realize how much of a cheat this is, and so keeps up the artificial attempt to build ethics on this thin of an account of the human -- it is thus no accident that the full "Metaphysic of Morals" has so much rubbish in it, as Kant was building on sand. Hegel's ethics is free of this artificial limitation that Kant had laid down for ethics, but still shows all the limitations of Hegel's own parochialisms (sexism, racism, nostalgia for guilds and wariness of mass suffrage). So the obvious lack of "purity" in decision theory is not a barrier to granting it status parallel to Kant's own (hypothetical) derivation of the Moral Law in the first two sections of the "Groundwork": that work is itself not really pure, once it has been properly understood. By Kant's own standards, nothing is really "pure": and so what is reasonably called "pure" is not going to meet Kant's strictures.

That there is still something to the "pure"/"empirical" distinction I think is clearly shown by the case of decision theory: decision theory is not like the mass of information that is involved in making actual decisions; avoidance of dutch books in decision theory is clearly akin to crafting reductio proofs, as anyone who has played a little with both must realize. There's some sort of categorical difference between keeping a dutch book and simply making an unwise choice: this is what I think the "pure"/"empirical" distinction should aim to make clear. But even the terms used in labelling the distinction make this difficult. Hence much becomes muddled when thinking about practical philosophy.

Unrelated: I wrote a dissertation, you can find it open-access here.

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.

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.

"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.)

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

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

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


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

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

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

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

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

and my favorite one

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

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

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

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

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

Martin's article ends shortly after this; if anyone can point me towards discussions of Fichte's later views on general logic, I'd appreciate it.

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

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

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

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

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

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

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

i has an m.a.

I officially graduated last weekend. Finished my thesis in late November; I haven't been blogging because whenever I would get the urge to blog (or would begin a post), I would think "Shouldn't I really be working on my thesis instead?", and that killed the fun of it. And then after finishing my thesis, I had to get PhD applications done. Finished those of earlier this week. I am now free of any academical-type obligations, for the first time in quite a while. (It feels strange, like I must owe someone a paper, and just can't figure out who.)

So, now I can blog freely again.

Because it seems like a thing to do, here's a brief recounting of my year at Chicago:

Fall quarter was when I had to take the MAPH "core" course, which was about Theory. I was reminded of the "Theory's Empire" book-event from The Valve often. I did not enjoy this course, and was glad when it ended. I really can't say I got anything from this course, except some painful and awkward introductions to Freud, Lacan, and Adorno (and some other guys I would've been happy to never encounter). It wasn't even good for writing practice; the longest paper I had to write was five pages or something like that. And that paper was about Lauren Berlant and some movie I've never seen based on a book I've never read. Just a mess of a class.

There was an "introduction to analytic philosophy"-type course that was only open to MAPH students; I figured it was a good thing to take. There were issues that lead to the class being taught by a PhD student, Tom Lockhart, but he did a good job of it I thought. I enjoyed the class, and it was a pretty gentle way to get back into the swing of things after having a semester off (and before that, a semester of law school). I wrote a paper on the second part of "Mental Events" for it (and a shorter one on "Naming and Necessity", which was much easier to lay out than the second part of "Mental Events").

Haugeland's Heidegger's "Being and Time" was a good excuse to read the rest of division one of "Being and Time". I fell a day behind in the reading at one point, and caught up by skipping a section I'd read before: the bit about the broken hammer. It turns out that if you read all of division one except that bit, the "present at hand" sounds like a philosopher's fiction: nothing is ever actually given to Dasein like that. It's always something richer, like the ready-to-hand, the living, Daseins, etc.; the "present-at-hand" is paradigmatically what is presented to a res cogitans (i.e., it is nothing but something confused philosophers dreamed up). Now, in the broken hammer passage, this is clearly not Heidegger's view. We can see the broken hammer, and he says we see it as just something present-at-hand. So I spent a lot of this quarter misreading "Being and Time". I like my misreading a lot more than Heidegger's actual view, though, and I think that my misreading makes sense for pretty much all of the rest of division one (especially section 21, "Hermeneutic Discussion of the Cartesian Ontology of the 'World'"). Incidentally, this is the class that taught me how the quarter system works: I suddenly had to scramble for a paper topic when I realized the course was almost over, and ended up having to get an extension for the paper (by a week or two). I ended up writing something about Dreyfus's Heidegger and "Telling" that I don't think really came together, but was kinda fun to work on.

Winter quarter was very cold and dark.

I sat in on Ford's "Action and Practical Knowledge" seminar, which gave me an excuse to read Anscombe's "Intention" and Thompson's "Naive Action Theory", along with some more of Davidson's old action papers. This also got me up to speed on philosophy of action well enough to know some of what was going on at the Anscombe Conference in the early spring. Definitely glad I didn't take this for credit, though; I'm still mulling a lot of it over, and I'm not sure I really get what's so important about Thompson. (I've read the rest of "Life and Action" now, and still don't see it. Though he did say some stuff about gold and Kripke-Putnam essentialism in the third part that lead me to suspect I in fact do not want to get on board with his broader program. I should probably look at that passage again, and post on it.)

I also sat in on Irad Kimhi's "Active Thoughts" seminar. It was utter madness from beginning to end and I couldn't get enough of it. I couldn't tell you what the class was about, but there was a lot of interesting stuff crammed in there. Sitting in on it also gave me an excuse to read more Frege ("The Thought" and "Negation" especially), and some other fun logic-y stuff.

For credit, I took "Intermediate Logic", "Modern Moral Philosophy", and Pippin's "Kant's Critical Philosophy". Logic did not require me to write a paper, or to read very much; this made it an excellent course for the winter quarter. It was also fun to do more logic homework, though some of the completeness proofs were annoying.

"Modern Moral Philosophy" was taught by a visiting professor from Rome, Piergiorgio Donatelli. We read a little Bernard Williams, several Iris Murdoch pieces, two chapters from "The Claim of Reason", a McDowell essay I hadn't read yet, and then a lot of Cora Diamond's stuff. And Donatelli brought up dozens of other figures in the lectures. It was a heady mix of stuff; my lecture notes are a mess (though not as bad as the notes for "Active Thoughts"). I read an article of Diamond's that wasn't assigned for class (her piece in the "Cambridge Companion to Wittgenstein") that bothered me in ways I couldn't quite get a handle on; I wanted to write on that, but wasn't getting a grip on it, so instead I wrote about something Diamond said about McDowell, and somehow a quarter of the essay ended up being about Davidson.

I read several Diamond pieces about Truth and Tarski-type approaches to it for this paper; I did not like them very much. She seemed to go after Rorty for the wrong reasons (as Conant did, in much greater length, in his article about Rorty and Orwell), and she seemed unhappy with Davidson's take on truth for no reason I could figure out. (If I recall correctly, it had something to do with there being "many ways something could be true"; I couldn't see how this was a problem for Davidson, since any difference between e.g. moral facts and chemical facts would be paralleled in the relevant T-sentences: they would say that the different sorts of sentences are true IFF different sorts of things are the case. Diamond didn't flesh any of this out so much as say we needed to pay attention to it. I can't tell what exactly I'm supposed to notice, so I don't see why Diamond-on-ethics-and-truth is so great.)

For Pippin's class I wrote a paper on the Transcendental Aesthetic. It was straightforward: Kant says that the transcendental ideality of space and time are established here; what are his arguments, and do they work? I defended the venerable "neglected option" objection, more or less. It was pretty easy to write, which was good because the rest of the quarter had me pretty frayed.

The Anscombe Conference was in the early spring. Thompson is a lot of fun to watch, and McDowell is surprisingly frail and birdlike in person; he looked like he might break if someone ran into him. I made it to most of the papers; most of them were good. McDowell had a paper on Anscombe-on-sensations that was pretty much the paper you would expect him to write on that topic. I will need to find my notes to say much about the rest of the speakers, but I do remember this: Thompson is a genius.

I was supposed to have a draft of my thesis done early in the spring; difficulties finding a workable topic lead to that not happening. I ended up writing about McDowell's criticisms of Davidson in "Gadamer and Davidson on Understanding and Relativism"; most of the paper was devoted to setting the stage, since "Epitaphs" is a tricky paper to get right. I'm pretty happy with how it turned out, though Kremer (my advisor) remains unconvinced. One section of the paper ended up getting cut before it was even to the draft stage, what I was trying to articulate in the comments here, because a) I realized that spelling things out would take another paper to do well and b) I'm not at all sure that McDowell makes this argument against "Epitaphs" (and I'm suspicious that he doesn't make it because he knows it's not a good objection; certainly the closest he comes to making it explicitly is very hand-wavey stuff, and he could've made it very straightforwardly. I think Dummett does make it, for instance.). This paragraph probably makes sense to nobody except me, since only three or so people on the planet have read my thesis, but I refuse to cut it! Blogging is for vanity's sake.

Bridges taught a course on "Rationality" and a seminar on "Contextualism" in the spring; I considered both, but ended up taking neither. (I didn't know anyone in the seminar and it felt awkward; the "Rationality" course was not exciting in the first few courses, and was overfull -- I dropped it so someone else could have my slot.) Stephen Nadler (a visiting prof from U Wisconsin-Madison) had a course on Spinoza's "Ethics" which was simply phenomenal; I'd planned on just sitting in on it (and asking some questions about Hegel and Spinoza), but by the end of the second class I knew I had to take this course. Nadler did an amazing job leading the class: we got through the entire book, and discussion was always lively and unforced. I wrote a paper on Spinoza and anomalous monism, which I thought turned out very well, and it was the third Davidson-y paper I'd written in as many quarters. (When I asked Nadler about the topic, I assumed it was probably too banal to write on, and was going to ask for suggestions as to what in specific to focus on in the area; turns out it's not all that well-represented in the Spinoza literature, though Della Rocca does defend the connection, so I got to write a paper that came very easily.) Hands-down the best course I took for credit at Chicago.

Another (regularly) visiting professor, Jocelyn Benoist, was teaching a seminar titled "Intentional Objects: An Inquiry into the Common Origins of Analytic Philosophy and Phenomenology"; about half of the course name shows up on my transcript. Benoist lectured about a lot of interesting people I'd had only superficial knowledge of before, like Bolzano and Brentano and Meinong, and some I had never heard of (mostly Polish philosophers, who were all interesting to read). All of it was shiny and new, and Benoist covered a lot of material very quickly. The guiding thread through most of the class was what to do about terms with sense without reference (if Meinong is wrong and there are any), and what lead into that question getting asked in that way. I wrote a paper about Frege and Evans's account of him in chapter one of "The Varieties of Reference", basically just trying to make sense of how Frege could be so cavalier in saying that "Odysseus" has the same sense whether or not Odysseus ever existed. (One nice point Benoist stressed was that Frege's example was not random; this was around the time when Troy was discovered by archaeologists, after having been considered as mythical for centuries.) I read a lot of Frege (and a fair bit of Evans) in preparation for this paper, but something just didn't quite come together in the end; I'm happy with what I have in the paper, but feel like I didn't really finish it. I don't know what I failed to write, but I definitely did not write something that needed writ.

It was a fun year.

And randomly: these conference papers are pretty good listenin'. And the "Coherentisme" paper is actually delivered in English. Hours of Sellarsian fun.

Boyle's paper on Kant's logic is terrific

I am sick as a dog at the moment, but I managed to haul myself to the Modern Philosophy Workshop this morning. The paper was "Kant on Logic and the Laws of the Understanding", and it was very illuminating. Boyle's presenting a paper on sortals at the Contemporary Philosophy Workshop on monday; that also looks good, though I haven't read the paper for it yet.

Conant was at the workshop this morning, which was nice; he mentioned that the paper seems to slide between two sorts of oppositions: Kant's view of logic vs. Frege's view of logic and Kant's view of logic vs. the "post-Hilbertian" view of logic that Conant actually thinks is what you most commonly come across nowadays (he specifically mentioned Brandom, Belnap, and some other guy at Pitt that Boyle studied under). Boyle conceded the point, modulating the claim of his paper to the claim that Frege's view is an illuminating waystation between Kant's view of logic and the post-Hilbertian view which is not regnant.

I found the notion of a "post-Hilbertian" view of logic very agreeable, and the term is apt. The idea is that logic is a "purely prescriptive" science; you have the various axiom systems etc. and the question of whether a given system has anything to do with things like "truth" or "reason" or "inference" is a concern which is outside of the purview of logic. The parallel is of course to Hilbert's view about geometry: You have the various geometries that geometers study, and the question of which (if any) describe a physical space is not something geometry is concerned with. (I recall hearing that Frege wrote a letter to Hilbert complaining about this, and Hilbert basically rolled his eyes in response.)

I took a good deal of other notes, but I mainly wanted to just throw a post up before I forgot, and in case the paper isn't online forever. Easily the best paper on Kant and logic that I can recall coming across.

edit: Note the strikethroughs.On a jarringly unrelated note, newly-hired U Chicago professor Ben Callard is terminally ill. Cancer. He just found out, apparently; he held class on monday, and didn't seem that sick to me then. (He'd said he had a doctor's appointment right after class; he wasn't sure if he was going to end class early or what, since he really felt terrible. He did not end class early, and the general consensus was that the class was starting to take form and looked like it would be fun -- I know of at least three people who weren't enrolled in the class who were planning on continuing to sit in, just because the discussions were good -- including me. Callard was doing a good job leading the discussion, keeping it going interesting places, etc.) But, apparently he has inoperable lung cancer, and not very long to live. (The longest I heard was "less than a year". I won't repeat some of the things I heard, but I heard nothing good on this front. edit: Practically everything I heard on friday was groundless. See above post.) The Callards had their second child this August. Cute lil' guy. Suffice to say, today's news was horrifying, is horrifying, on all sorts of levels.

Friday was an eventful day.