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.
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Loving the recent posts on German philosophy! You should check out the review of Wood's Mathesis of the Mind: A Study of Fichte's Wissenschaftslehre and Geometry published on NDPR today:
http://ndpr.nd.edu/news/32285-mathesis-of-the-mind-a-study-of-fichte-s-wissenschaftslehre-and-geometry/
Glad you're enjoying them.
Thanks for the NDPR pointer; the review is an interesting read. Like I said, I have read absolutely nothing about Fichte's philosophy of math (aside from this book review, now).
I think that Fichte may be closer to Kant than he imagines here, at least if his position follows the general outline that you have drawn. I want to comment on two points: (i) Kant's views about concept formation; (ii) Kant's views on the relation between general and transcendental logic. I'll be honest right from the start and point out that my views about this topic are not really "mine", but actually Longuenesse's, as expounded in her incredible work on Kant.
Anyway, in regards to the first topic, I think that Kant's views only approach Locke if you read the account in the Jäsche Logic in isolation from the rest of his views. Specifically, I think it's impossible to consider it a purely abstractionist view once one considers the primacy that Kant accords to judgment and also his transcendental idealism.
In relation the former, his position is much closer to Fichte than to Locke; concepts are not a matter given prior to judgment, and which we would only have to compare in order to establish the truth or falsity of a judgment. One the contrary, staying true to his motto that the form always precede the matter, for Kant the form of judgment -- as the four moments of the table (quantity, quality, relation, and modality) -- actually presides over concept formation, essentially determining its outcome. Hence, concept formation is not an activity independent of the power of judgment, but is actually guided since the beginning by it. Analysis of experience, with an aim to form concepts, thus consists, for Kant, in the formation of "silent judgments" (the comparison, reflection, and abstraction that he mentions in the Jäsche Logic, which are all judgments, and not original operations of the mind), which are made explicit in the concept of the object in question.
To be more specific, and following the example of the Jäsche Logic, I acquire the concept of a tree only after I compare the objects that shall fall under it (i.e., a spruce, a willow, a linden, comparison according to quantity), compare the marks that will constitute this concept (i.e., 'has branches', 'has a trunk', comparison according to quality), think through the external or internal conditions that follow from this concept (i.e., 'if it's winter, a tree loses its leaves', 'a tree has a trunk', comparison according to relation), and, finally, am able to use this in a system of inferences ('if it's winter, a tree loses its leaves; it's winter; so, this x, which is a tree, will loses its leaves', comparison according to modality). Obviously, such an activity of comparison may not be explicit at first, so that I may only have an obscure awareness of the concept in question. Nevertheless, what is important is that, by reflecting on such "silent judgments" that make up this activity of comparison, I can finally acquire the concept of a tree.
One interesting thing to note regarding this process is that, at least as I see it, Kant does not consider that concepts emerge "once and for all" from this activity. Quite some time ago, we discussed, in relation to Kant's notion of analytic and synthetic judgments, a passage from the KrV that I wish to return to now, since I think it's an important passage regarding his thoughts about concepts. It starts in A727/B755 and continues until A730/B758, and it's the place where Kant discusses the respective roles of definitions in philosophy and mathematics. There, he remarks that, since an empirical concept can never be exhausted, it is always imperfectly defined, in such a way that further refinements, be it by experience or experiments, are always possible. I think this is important because it shows that, for Kant, concept formation is not an activity which produces a definite result, but is rather a never ending process of refinement. This has as a consequence that concept acquisition is not merely a matter of abstracting a concept from the empirically given matter, but rather a process of comparison that is always taken further up in a network of inferences which in a certain way determines its result. In other words, we never simply abstract a concept from given sensations, but rather produce one in the context of experience, understood here as a system of interconnected perceptions. It is this system that enables me, in order to produce a certain concept, to privilege certain marks and abstract from others, guiding my activity of comparison.
Which brings me to my next point, namely, Kant's transcendental idealism. I think this is a point connected to your reproach of Geach, that he is unable to consider the possibility that our conceptual capacities may inherently refer to particulars, all the while being inherently general. This is because, in Kant's views, the rules that are made explicit in a concept are also rules which are immanent to the object in question, albeit in a still indeterminate fashion. As Kant puts it in a note (quoted by Longuenesse): "This community of representations under one mark presupposes a comparison, not of perceptions, but of our apprehension, insofar as it contains the presentation of of an as yet undetermined concept, and is universal in itself" (R 2883, 1776-8?, Ak XVI, 558). This turn of phrase is very reminiscent (at least to me) of McDowell's considerations in "Avoiding", and I think further reflection on them might gives us more coherent conception about how Kant views concept formation.
As for the relations between general and transcendental logic, well, this is a notable complex matter, but I think Longuenesse (and others, such as Michael Wolff, whose work, because of linguistic barriers, is unfortunately unaccessible to me) has made it clear that the relation of dependence is not as simple as some have thought. In particular, while it's true that Kant used the Table of Judgments in order to establish his parallel Table of Categories, it's not true that this makes transcendental philosophy dependent on general logic; in fact, the specificity of Kant's table, which is very different from similar ones from his time in important respects, already shows that this table was not established independent of any transcendental consideration. On the contrary, it's transcendental philosophy which establishes the precise function of judgment (as per §19 of the Transcendental Deduction) and its relation to thought in general (as per §10, the [in]famous Metaphysical Deduction), thus establishing the basis on which the forms of judgment will be considered. Once these forms of judgment have been established, then the categories can be derived. In other words, the relations between transcendental and general logic are far more organic than previously assumed, specially by Hegel and other idealists...
Incidentally, I would like to, once again, thank you for maintaining this very good blog. As always, your posts provide me with great food for thought, which is not something I can often say. In this sense, I hope this reply can come as a way of furthering the inquire in a friendly manner, and not as confrontational!
I have read long stretches of Longuenesse's "Capacity to Judge" book several times, when people have pointed me to it; I never seem to see what gets people excited about it. Allen Wood likes it a lot, too. (FWIW, I took a lot away from her Hegel book. So I don't think it's an issue of her writing style, or anything like that.)
"Anyway, in regards to the first topic, I think that Kant's views only approach Locke if you read the account in the Jäsche Logic in isolation from the rest of his views. Specifically, I think it's impossible to consider it a purely abstractionist view once one considers the primacy that Kant accords to judgment and also his transcendental idealism. "
Well, the issue then is to give a reading of the Jasche passage such that it is coherent with these other Kantian views. It certainly looks like Locke. And it certainly looks like Kant giving an account of where we get empirical concepts, which he is otherwise oddly silent on in his published works.
"staying true to his motto that the form always precede the matter"
Where does Kant state this "motto"? I would've thought his view was a more Aristotelian one: what is primary are form-matter composites, and neither "pure form" nor "pure matter" is given. You can arrive at either only by abstraction (in thought), not by extraction (which would give you just a form or just a matter).
"Analysis of experience, with an aim to form concepts, thus consists, for Kant, in the formation of "silent judgments" (the comparison, reflection, and abstraction that he mentions in the Jäsche Logic..."
I don't see how this solves the problem. How can I form "silent judgements" to the effect of "Disregarding the leaves and trunk, there is something these substances have in common..." (or however the "silent judgement" is supposed to run), without already having empirical concepts like "leaves" and "trunk"? According to the view you present (Longuenesse's), it looks like I have to already have empirical concepts to form empirical concepts. Or else "marks" have to be something which are not empirical concepts, and which present things which can be "noticed" in experience without the use of empirical concepts, but which seem to do just the work that empirical concepts do. And then (what Longuenesse calls) "empirical concepts" are just the coming-to-full-awareness of these things, which look like they were always already everything that empirical concepts were supposed to be. So the real issues are just pushed back a step: now the question is how I can have the relevant capacities to apprehend the marks which I (silently, unconsciously) make use of in forming empirical concepts, given that it looks like these capacities are nothing but (empirical) conceptual capacities.
FWIW, this is not the reading of the Jasche passage Allen Wood gave when I asked him about it. He suggested that in the Jasche Logic Kant is concerned not with saying how we do form empirical concepts, but with how we *should* form them: we should form them by a process of comparing, reflecting, and abstracting, so that we will end up with concepts which stand in clear hierarchical relations to one another etc. And then when I asked him what Kant's actual theory of empirical concept formation was, he could only point me to Longuenesse. Who seems to me to not grasp the real problem.
(cont.)
(I also think it's doubtful that Kant was trying to give a merely normative account in the Jasche Logic, because I don't think Kant has a normative view of logic at all: logic tells us what it is to think, not what it is to think *well*. If we violate a "norm" of logic, we simply cease thinking; we don't do something that could stand in need of correction by cleaving to a norm. Clinton Tolley's "Kant on the Nature of Logical Laws" finally convinced me that this is in fact Kant's view of the matter, with ample textual evidence. But Tolley also has to face many passages where it looks like Kant *does* have a normative conception of logic, which he has convincingly showed Kant cannot have. Tolley's final judgement is that Kant likely slipped into thinking of logic in the way others had before him, normatively, out of habit. I see Fichte making the same objection re: empirical concept formation: Kant simply cannot have coherently been an abstractionist, but he endorsed abstractionism out of inertia -- and this inertia also kept him from seeing that he simply had no account on offer of empirical concept formation.)
"I think this is important because it shows that, for Kant, concept formation is not an activity which produces a definite result, but is rather a never ending process of refinement. "
This is ambiguous. In one sense it is correct: Kant doesn't believe we can reach a "final" set of empirical concepts (since the ideal of such a thing is merely regulative), so in that sense the process does not produce a definite result.
But in another sense it is false: Kant does think we have empirical concepts, and so we must have produced them in some way. The concepts we use in such judgements are up for replacement: As Kant says, what use would a definition of "water" be? Any such concept we have is merely used to direct our attention to certain further experiments, whose results might lead us to discard the old concept of "water" and form a new one, with different characteristics. But for a given empirical concept to be up for replacement, we have to *have* it: the endless process of empirical concept formation is not uniformly smooth, but has us forming concepts, using them, and then forming new concepts (by piecemeal revision of our old ones, usually). The section on definitions you pointed to is only about these latter stages, not the original process in which we first are able to form empirical concepts.
(cont.)
"In other words, we never simply abstract a concept from given sensations, but rather produce one in the context of experience, understood here as a system of interconnected perceptions. It is this system that enables me, in order to produce a certain concept, to privilege certain marks and abstract from others, guiding my activity of comparison."
It is clear that Kant wants part of his picture to work in the following way: I do not form empirical concepts by "copying" a form that is present in the items presented to me, which I then use as a component in judgements. Rather, I only go through the process of comparison/reflection/abstraction once I am already presented with some determinate individuals, and the way that I compare/reflect/abstract is up to me (and nature does not tell me how to do it). But I think this is exactly how Locke thinks of it. After all, Locke's abstractionism is an attempt to explain how we arrive at *general* ideas, not how we arrive at ideas at all; like Kant, he presumes we are already presented with determinate individuals, and can compare and reflect and abstract in different ways. As you are (Longuenesse is) spelling Kant's theory out, the Jasche Logic passage seems to line up very closely with Locke's account in Essay III.iii.7, which is just as Fichte accused. The problem is just *how* experience can enable me to "privilege certain marks and abstract from others" unless I already possess (empirical) concepts which I can bring to bear to articulate what it is that is given to me in experience. In Locke's case we have a paradigm instance of the Myth of the Given; as you present it, I don't see how Kant (Longuenesse) fares any better.
You'll have to spell out what you see the Remark you quote in the final paragraph of your second comment as coming to. I remember Longueness talking about this sort of thing, and finding it terribly obscure how any of it was supposed to help her view out.
I don't think Kant can have McDowell's views on empirical concepts, because McDowell is explicit that we arrive at some of our empirical concepts by being "trained up" in language: they aren't all derived from experience (in the way he discusses in "Avoiding"), even though they're the sort of concept which could have been. So McDowell doesn't face the problem I (and Fichte) see Kant facing: he is already taking on board the idea that some of any particular individual's empirical concepts were not formed by that individual in the way that she can go on to form further empirical concepts, but were formed in the original process that lead to that individual becoming a thinker at all. There's no space in McDowell's picture for an abstractionist account of how those concepts were formed, of either Locke's or Longuenesse's sort: it just so happens that in coming to be the thinker I am, I became empirically aware of e.g. mama and kitties, because I first learned to talk (to think) by being trained to reliably respond in disinct ways to mama and kitties in the way that leads infant humans to become minded. All of my judging/thinking/speaking begins from some such store of empirical concepts. The social origins of mentality are thus important, as it is this original context which provides a thinker with empirical concepts: they are equiprimordial with his being a thinker at all. Kant still has a Cartesian tendency to think of an individuals's mental capacities as explicable purely on their own basis, which I think blinds him to this. But I think McDowell's views actually fit better with Kant's views in the section on definitions you quoted than Kant's own: if Kant denies there is any final end to empirical concept formation (except as an ideal), why should there be any definite starting point for empirical concept formation? Why not embrace the idea that with empirical concepts, we are never otherwise than in medias res, revising the empirical concepts we find ourself with?
I don't see how transcendental idealism can help Kant out here.
"On the contrary, it's transcendental philosophy which establishes the precise function of judgment (as per §19 of the Transcendental Deduction) and its relation to thought in general (as per §10, the [in]famous Metaphysical Deduction), thus establishing the basis on which the forms of judgment will be considered. Once these forms of judgment have been established, then the categories can be derived."
I think Kant sees himself as establishing less than he would need to produce the Table of Judgements, and that Fichte and Hegel are correct in seeing this as a gap. By Kant's own lights, we are "incapable of further explaining... why we have just these and no other forms of judgement" (B145/6, close of §21), and it is just this that is complained about. You are correct that Kant thinks it is part of transcendental philosophy to say what judgement qua judgement is, what it is to have a "logical form": this is what he accuses previous logicians as not addressing, in §19. But Kant's own answer is very general, and does not suffice for deriving even the four headings Quality/Quantity/Relation/Modality, to say nothing of the four moments that fall under them. Kant's principle of logical form (bringing concepts to the objective unity of apperception) does not suffice for deriving the table of (general) logical forms -- and he asserts dogmatically that no principle can do better, even though he somehow has arrived at just these forms, and never doubts that he has listed all of them. This is just what the post-Kantians complain about, and try to remedy.
"Incidentally, I would like to, once again, thank you for maintaining this very good blog. As always, your posts provide me with great food for thought, which is not something I can often say. In this sense, I hope this reply can come as a way of furthering the inquire in a friendly manner, and not as confrontational! "
I am glad you like it.
Thanks for continuing to comment; getting spurred into rethinking things and having to find clearer ways to present my thoughts are just what I want out of blogging. I have of course taken your comments in the fashion you wished; but even if they were meant to be confrontational, then so long as they genuinely served to further inquiry my pragmatist heart could not say "no" to them.
I will note, though, that my semester is about to begin: blogging will probably become sparse again soon. So if it takes me a while to reply to comments, that is probably why. (It would also help if I didn't always write such long multi-part comments, but I don't think that can change.)
With regards to Tolley's essay, first of all, thanks for the pointer. I hadn't read that essay yet (though I had read others from the same volume), and, although I'm not entirely convinced by Tolley's argumentation, he does build a very interesting case against what he calls "the normative interpretation". In the very least, it raises important questions that should be addressed. I'll have to return to it in the near future, in order to better clarify my own views on the topic.
As for Longuenesse, this may be my own particular view, but I think her book is best read as a whole. One of her most impressive feats, in my opinion, is to display very vividly the organic unity of Kant's Critique. She shows, in a convincing manner, how Kant builds one intricate argument throughout the Analytic, in which each part of the argument is progressively clarified as the argument develops. I personally found it a very beautiful exposition, extremely powerful. I think the only other Kantian commentary which caused a similar impact on me was Strawson's, but for different reasons.
Anyway, moving on to Kant's Table of Judgments. You claim, in your reply, that, although it's true that transcendental philosophy can provide us with a more adequate explanation of judgment, this explanation by itself is not sufficient to derive Kant's Table of Judgments. Moreover, you also claim that this insufficiency is actually buttressed by Kant's own statements to the effect that we are "incapable of further explaining... why we have just these and no other forms of judgment" (B145-6). Well, I (obviously!) disagree, in both accounts. Starting with Kant's statement, I am here in agreement with Allison (who appears to be agreeing with Michael Wolff), when he emphasizes that the important element in that sentence is "further", i.e. we are incapable of further explaining...", that is, of giving an explanation in addition to the the one already given, namely, the unity of apperception. In other words, as Allison highlights, Kant is not saying that no ground can be given, only that no further ground can be given. If this is so, however, the next question is: how is this derivation possible, then?
Well, to offer a thorough explanation would be rather laborious, but I think the basics of it are easy to grasp (for a more detailed treatment, check out Allison's own summary of Wolff's treatment of the topic, in his Kant's Transcendental Idealism, 2 ed., pp. 133-151; the argument for the completeness proper is found in pp. 135-146; check out also chapter 4 of Longuenesse's Kant and the Capacity to Judge). Kant defines judgments, in §19, as "nothing other than the way to bring given cognitions to the objective unity of apperception" (B141). This definition is of utmost importance, I think, for it provides the precise function of judgments: to reflect the synthesis of the manifold (the given cognitions) in a higher synthesis (judgment itself) which relates those cognitions to an object. This definition is highly significant, as it makes objectivity (in the sense of a purporting to be about objects) an intrinsic feature of judgment, as well as a norm that govern its employment. How, however, is this objectifying function achieved?
With regards to Tolley's essay, first of all, thanks for the pointer. I hadn't read that essay yet (though I had read others from the same volume), and, although I'm not entirely convinced by Tolley's argumentation, he does build a very interesting case against what he calls "the normative interpretation". In the very least, it raises important questions that should be addressed. I'll have to return to it in the near future, in order to better clarify my own views on the topic.
As for Longuenesse, this may be my own particular view, but I think her book is best read as a whole. One of her most impressive feats, in my opinion, is to display very vividly the organic unity of Kant's Critique. She shows, in a convincing manner, how Kant builds one intricate argument throughout the Analytic, in which each part of the argument is progressively clarified as the argument develops. I personally found it a very beautiful exposition, extremely powerful. I think the only other Kantian commentary which caused a similar impact on me was Strawson's, but for different reasons.
Anyway, moving on to Kant's Table of Judgments. You claim, in your reply, that, although it's true that transcendental philosophy can provide us with a more adequate explanation of judgment, this explanation by itself is not sufficient to derive Kant's Table of Judgments. Moreover, you also claim that this insufficiency is actually buttressed by Kant's own statements to the effect that we are "incapable of further explaining... why we have just these and no other forms of judgment" (B145-6). Well, I (obviously!) disagree, in both accounts. Starting with Kant's statement, I am here in agreement with Allison (who appears to be agreeing with Michael Wolff), when he emphasizes that the important element in that sentence is "further", i.e. we are incapable of further explaining...", that is, of giving an explanation in addition to the the one already given, namely, the unity of apperception. In other words, as Allison highlights, Kant is not saying that no ground can be given, only that no further ground can be given. If this is so, however, the next question is: how is this derivation possible, then?
Well, to offer a thorough explanation would be rather laborious, but I think the basics of it are easy to grasp (for a more detailed treatment, check out Allison's own summary of Wolff's treatment of the topic, in his Kant's Transcendental Idealism, 2 ed., pp. 133-151; the argument for the completeness proper is found in pp. 135-146; check out also chapter 4 of Longuenesse's Kant and the Capacity to Judge). Kant defines judgments, in §19, as "nothing other than the way to bring given cognitions to the objective unity of apperception" (B141). This definition is of utmost importance, I think, for it provides the precise function of judgments: to reflect the synthesis of the manifold (the given cognitions) in a higher synthesis (judgment itself) which relates those cognitions to an object. This definition is highly significant, as it makes objectivity (in the sense of a purporting to be about objects) an intrinsic feature of judgment, as well as a norm that govern its employment. How, however, is this objectifying function achieved?
Kant's answer, which he had expounded in the Metaphysical Deduction, is "by means of an analytic unity" (B105). I agree with Longuenesse here that we should follow Klaus Reich lead (see especially chap. 3 of The Completeness of Kant's Table of Judgments) and identify this "analytic unity" with the analytic unity of consciousness, as explained by Kant in §16 of the Deduction, in particular B133-4 and the footnote appended to this passage. There, Kant explains that this analytic unity, as "the identity of the consciousness in these representations" ("these representations", namely the manifold of representations given to me), is the unity that attaches to all concepts qua concepts. This explanation, in turn, needs to be read in light of what Kant said previously in the beginning of the Clue Chapter (A68-9/B93-4), where we find a very concise explanation of the function of judgment. This makes clear that judgment achieves its function (of relating representations to objects) by means of concept subordination. As Kant himself explains (this passage is, I think, worthy quoting in full):
"In every judgment there is a concept that holds of many, and that among this many also comprehends a given representation, which is then related immediately to the object. So in the judgment, e.g., 'All bodies are divisible', the concept of the divisible is related to various other concepts; among these, however, it is here particularly related to the concept of body, and this in turn is related to certain appearances that come before us. These objects are therefore mediately represented by the concept of divisibility. All judgments are accordingly functions of unity among our representations, since instead of an immediate representation a higher one, which comprehends this and and other representations under itself [namely, analytic unity -- D. N.] , is used for the cognition of the object, and many possible cognitions are thereby drawn together into one ['drawn together', i.e. synthesized -- D.N.]." (A68-9/B93-4)
Hence, a judgment such a "All bodies are divisible" can actually be developed as "To every x, to which the concept 'body' belongs, belongs also the concept 'divisible'" (Following Kant's lead in the Jäsche Logic, §36). In other words, as the reference to appearances in the above quotation makes clear, in a judgment, not only are the marks of a given concept attributed to another concept, but the extension of a concept is also thought under the extension of the other (that's why Kant says that "These objects [i.e. the appearances] are therefore mediately represented by the concept of divisibility"]). Thus, it's possible to already derive two of the Titles: Quantity and Quality. That is, if one considers that the function of judgment is to relate given cognitions to an object by means of an act of concept subordination, in which the extensions of the concepts in play are also taken into account, then, as the above consideration shows, one must take into account the quantity of the extension of the concepts (are we dealing with all or some of the objects that fall under the concept?), as well as the quality of the logical subordination that is established (are we subsuming the extension of one concept under another, or, on the contrary, are we excluding one from the other?). It's possible then to see how Quantity and Quality are so many moments which determine this original act of concept subordination.
But that's not all. Merely concept subordination is still insufficient to relate given cognitions to the objective unity of apperception, since conceptual unity, as such, does not yet refer to objects (i.e. a concept is not true or false). So, as Reich argues (in pp. 49-51 of the aforementioned study), for a judgment to take place, there is need of "an additional given condition of its [viz. a given concept] employment for the cognition of an object" (p. 50, original emphasis). In other words, reference to truth is intrinsic to the function of judgment as such; it's what distinguishes a judgment (e.g. "All bodies are extended") from a mere conceptual unity (e.g. "extended body"). If this analysis is correct, then reference to the truth conditions are also essential to a judgment. To put it another way, judgment is not merely an act of concept subordination, but is also an assertion under a condition. Hence, a judgment must also make reference to the relation between an assertion and its condition. This relation can be an internal relation, in which the subject is considered as a sufficient reason for the assertion of the predicate (contra Brandt, who inverts the direction of the determination), or an external relation, in which the predicate is asserted of the subject under some added condition. The first relation gives us categorical judgments, the second hypothetical judgments.
Incidentally, it's important not to confuse this logical considerations with ontological considerations. That is, the determination of the relation between an assertion and its condition is an act of thought, and thus specifies essentially different, non-reducible logical forms. To incur into this confusion is precisely the mistake made, first by Wolff, and later by Eberhard, when he assimilated Kant's distinction between analytic and synthetic judgments to Wolff's distinction between predications with and without added conditions.
As an aside, if the analysis presented so far is correct, it has some interesting consequences. First, it corroborates Manley Thompson's interesting suggestions (in "Singular terms and intuition in Kant's epistemology") to the effect that "had Kant known quantificational logic, he would have recognized 'Fx' as a representing the form of predication and would have seen that the corresponding relation in his transcendental logic (epistemology) is that of a concept to an object" (p. 334). I think this is correct as far as it goes, except for being expressed as a counterfactual. True, Kant didn't know quantificational logic. Nevertheless, as it is clear from the above, he already had the resources to capture the relations Thompson thinks he should have captured. This, in turn, supports Thompson's claim that concepts, for Kant, should be regarded as open sentences, with their different uses (Thompson is here thinking of their different uses in universal, particular, or singular judgments) corresponding to different quantifications of open sentences (cf. p. 323). I would also add, following Longuenesse, that a judgment for Kant always involves a conditional, so that the appropriate formalization of a categorical judgment (say, "All bodies are divisible") would be "(x) (Bx --> Dx), whereas the appropriate formalization of an hypothetical judgment (say, "if bodies are composite, then they are divisible") would be "(x)[(Bx & Cx) --> Dx]", where the "Cx" represents precisely the added condition to be fulfilled. As she concludes: "This presentation of Kant's categorical and hypothetical judgments shows that the formal difference between them is merely a difference in the complexity of the relation of condition to conditioned. The two thoughts considered here under the heading of relation can both be formalized as uses of the conditional connective, combined with conjunction in one case and not in the other." (p. 103n53)
Interestingly, the above analysis also buttresses Kant's claim that all acts of the understanding are contained in his Table of Judgments. This is because Kant's notion of condition, together with his extensional theory of concept subordination, ties his account of judgment very nicely with his syllogistic doctrine. Roughly put, his extensional account of concept subordination means that every judgment is a potential major premise in a syllogism that attributes the predicate-concept to the objects (or marks) that fall under the subject-concept. To use Kant's example, when one judges that "All bodies are divisible", this furnishes us with the major premise of a syllogism such as "All bodies are divisible; now, this x is a body; therefore, this x is divisible". Or, again, "All bodies are divisible; now, every metal is a body; therefore, every metal is divisible". This means that every judgment can be located in a potential syllogistic chain, which is precisely what is captured by Kant's concept of condition. The concept of "metal", for example, is the condition in the judgment "Every metal is divisible", insofar as it's subsumable under the concept "body"; on the other hand, this means that the concept "body" is also the "ultimate" reason for that judgment, as it is what "ultimately" provides the reason for attributing to the subject the mark "divisible" (I put "ultimate" between scare quotes to indicate the relative function of this term, for the syllogistic chain may be pursued further, i.e. one can say that the condition for the attribution of the concept of divisibility to the concept of a body is composition, such as in the judgment "All bodies are composite"). In other words, the condition of a judgment is a condition only because of its relation to a further condition, which also derives its function from another condition, and so on, thus locating every judgment in a syllogistic chain that may be extended in both directions (cf. Longuenesse, pp. 90-93).
This connection of judgment with syllogism also shows how organically connected is Kant's philosophy. If every judgment is a potential major premise in a syllogistic inference, and this is derived precisely from the notion of its condition, then we can expect to find the syllogistic doctrine "encased", as it were, in the Table of Judgments. And, lo and behold, that's precisely what we find: the three moments of Relation, namely, categorical, hypothetical, and disjunctive judgments, are also what define the three main types of syllogism in Kant's doctrine (which, in this respect, doesn't depart much from the logical tradition of his time), namely, categorical, hypothetical, and disjunctive syllogisms.
Anyway, let's recap what we have seen so far. I claimed, following Longuenesse, that Kant's Table of Judgment could be given a derivation taking it's clue from the precise definition of judgment that Kant gives in §19 of the Critique, that is, "a judgment is nothing other than the way to bring given cognitions to the objective unity of apperception." We saw how this could be developed into the idea that a judgment is a subordination of concepts (which gave us the titles of quantity and quality ) under a determinate condition (which gave us the title of relation). My analysis, however, privileged the first two moments under each heading, leaving out the third moment (respectively, singular, infinite, and disjunctive judgments), as well as the title of modality. As Kant himself remarks, these are "special" cases, and must thus be dealt with separately (that's why he devotes separate explanations to each of them; cf. the passages that immediately follow the Table of Judgments, A71-6/B96-101).
I think those cases are special precisely because of their relation to transcendental logic (here, Brandt has interesting suggestions: cf. his The Table of Judgments, p. 78). Following Longuenesse's wording (in chap. 4 of her Kant on the Human Standpoint, p. 99), singular judgment is a form that "allows special consideration of individual objects", while infinite judgment considers "their relation to a conceptual space that is indefinitely determinable", where this conceptual space is specified by the relations of subordination between concepts, thus allowing for their systematization under the form of disjunctive judgments. Finally, they're also inferentially articulated with other judgments, resulting in the fourth heading, that of Modality: as Kant explains (cf. explanation number 4 of the ones referred to above), a judgment derives its modal status from its place in an inference. Problematic judgments are those, e.g., that function as components judgments in hypothetical and disjunctive judgments; assertoric judgments are taken as minor premises of a syllogism; and its conclusion is apodeitically determined (relative to its conditions, obviously). (Kant also connects Modality with Method, but I admit that this connection is not entirely clear to me. About this, again, Brandt has some interesting remarks: cf. the aforementioned book, pp. 82-3)
On a final note, one may ask, is it a coincidence that, under each heading, we find a trichotomous division of moments? Here, Allison, following Wolff, points to an interesting passage by Kant, in the Introduction to the Critique of the Power of Judgment, in which he answers in the negative:
"It has been thought suspicious that my divisions in pure philosophy almost always turn out to be threefold. But that is in the nature of the matter. If a division is to be made a priori, then it will either be analytic, in accordance with the principle of contradiction, and then it is always twofold (quodlibet ens est aut A aut non A). Or it is synthetic; and if in this case it is to be derived from concepts a priori (not, as in mathematics, from the a priori intuition corresponding to the concept), then, in accordance with what is requisite for synthetic unity in general, namely (1) a condition, (2) something conditioned, (3) the concept that arises from the unification of the conditioned with its condition, the division must necessarily be a trichotomy." (KU, 5:197n)
I'm not going, however, to develop the application of these to the case at hand, Kant's Table of Judgment. Some interesting suggestions to this effect are found in Allison, op. cit., pp.145-6, who apparently bases his account upon Wolff's treatment of the same topic.
In any case, what this whole development leads us to is that there is, in fact, a principle that organizes Kant's exposition of the Table of Judgments. This principle is his account of judgment, together with additional assumptions about "what is requisite for a synthetic unity in general". Hence, I think it's fair to say that Kant's procedure is very far from the empirical "borrowing" that Hegel accuses him of (cf. Hegel's Science of Logic, p. 541). This is in partial agreement with your assessment: since it's only transcendental critique that can tell us what judgment is, the immediate consequence is that general logic is in part dependent on transcendental logic. But this does not mean that the structure of dependencies is a simple one; rather, I think Longuenesse is correct when she claims that Kant viewed both general and transcendental logic as mutually interdependent. This makes more sense of Kant's views of a system as an organic whole, I think, and also results in a much more defensible view of the Metaphysical Deduction, which, otherwise, is rendered almost incomprehensible. (For the relation between general and transcendental logic, see her very interesting introduction to part 2 of her KCJ, pp. 73-80)
(Aside: about Hegel's critique of Kant on this precise point, I think matters are a bit more complicated. I don't see Hegel as pointing out a "gap" in Kant's exposition; rather, I see him as completely reversing Kant's position, a reversal that includes the relation between logic and ontology and, thus, it's not by chance that Kant's exposition of the forms that govern our thinking also comes under fire. This is shown, I think, by Hegel's own appropriation of Kant's table. After all, as Longuenesse highlights in her "Hegel on Kant on Judgment", for all his criticism of it, Hegel expounds his own Table of Judgments in the section on Judgment in the Science of Logic by taken his cue from Kant's own table, preserving its moments (though not its titles) in a basically unaltered form. In spite of this adherence to Kant's exposition, he nevertheless gives it a very different interpretation, taking it as exhibiting a dynamic progression of thought's own determinations from a simple, positive determination to its development in a more appropriate syllogistic inference.
In other words, while Kant tried to display, through his table, an analysis of the rules which constitute every judgment as such (hence the adequateness of the tabular form, as Kant himself stresses), Hegel, on his part, is exhibiting the development of though itself. I think this is highly significant. It shows precisely how Hegel's criticism of Kant is more profound than a simple complaint about Kant's own exposition; it is a complaint directed at his method. Hence why I think it's unfair, both to Kant and Hegel, to see the latter as merely filling in a gap in the former's exposition. Kant's exposition, by his lights, is complete. There's no need to "complete" it by other, further considerations. Which, of course, does not impede us of preferring other expositions than his.)
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