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.