1. Introduction
In the Critique of Pure Reason Kant claims that Aristotle’s logic is complete (‘completeness claim’).Footnote 1 This claim has been largely cast in a negative light. By some accounts, Kant assumes but has no way to prove the completeness of Aristotelian formal logic.Footnote 2 Maimon, for instance, argues that Kant is unable to produce such a proof due to his treatment of formal logic as prior to transcendental philosophy, when in fact logical forms can be neither correctly classified nor completely enumerated ‘without a prior [transcendental] critique’ (Maimon Reference Maimon1794: 408). Fries, in contrast, traces Kant’s failure to his viewing logic as absolutely independent of psychology (and anthropology) (Fries Reference Fries1837: 5).Footnote 3 If these remarks suggest that Kant has failed to supply the proper grounding for (formal) logic that would have ensured its completeness, Husserl reproaches Kant for failing to ask any transcendental question about the ground of formal logic – that is, to investigate how it is possible as science.Footnote 4
Husserl’s inquiry about the ground of formal logic may, according to Haaparanta, be seen as prompted by two conditions: a ‘foundational crisis’, which occurs when the received framework of logic is threatened, and the fact of ‘various confrontations within logic and philosophy of logic’ (Haaparanta Reference Haaparanta2009: 149). Notably, Kant was in a similar situation.Footnote 5 On the one hand, as Windelband puts it, the so-called Aristotelian logic had become ‘the object of most violent polemic’. The doctrine of syllogism, for instance, was to be ‘driven from its commanding situation’ – for being ‘incapable of yielding anything new’ and hence being ‘an unfruitful form of thought’ (Windelband Reference Windelband1958: 360).Footnote 6 On the other hand, a survey of the developments in logic from humanism to Kant reveals profound disagreements over similar philosophical questions about logic that will confront Husserl (as well as many other post-Kantian philosophers). For example, is logic theoretical or practical? How is it related to other sciences such as metaphysics and psychology? Is it concerned merely with the form or also with the matter of knowledge (Husserl Reference Husserl1970: 56; see Capozzi and Roncaglia Reference Capozzi and Roncaglia2009)?
In such a context, Kant could not avoid querying the foundation of logic – particularly that of purely formal logic. If it is correct to say that – with the introduction of a transcendental viewpoint – he entirely changed the situation of logic (Windelband Reference Windelband1961: 1), the change lies not only in his adding a transcendental logic alongside formal logic, but also in his recognition that even the latter logic needed a new foundation in order to be a proper science. Thus, contrary to Husserl’s complaint, Kant was in fact concerned about how formal logic is possible as science. Only, as Jäsche points out in the editorial preface to the Logic, it would take Kant the transcendental philosopher not Kant the logician to address the question (Log, 9: 9).
Indeed, when we examine Kant’s defence of the completeness claim in the Critique in conjunction with his remarks about logic throughout his logic corpus,Footnote 7 we shall see him being mindful of the necessity to establish formal logic on a firm ground – in a way that Aristotle supposedly failed to do. In the final analysis, it will be no exaggeration to say that the completeness claim encapsulates the key reformative aspects of Kant’s philosophy of logic, and that his defence of the claim reveals more disagreement with than allegiance to Aristotle’s approach to logic.
In the following, I explicate these points by reconstructing and analysing Kant’s proof of the completeness of what he takes to be the Aristotelian formal logic. I shall pay special attention to how he perceives and addresses the foundational crisis facing logic in his time.
2. What it Means to say Aristotle’s Logic is Complete
2.1 The History of Logic from Kant’s Standpoint
Logic underwent significant developments during the seventeenth and eighteenth centuries. These developments involved at least three topics that would eventually become Kant’s central concerns. First, the nature of logic: is it a ‘science’ (doctrine, theory) or an ‘art’ (instrument)? Second, the subject matter of logic: is it about the purely formal rules of thinking or the natural operations of the mind? Third, the basis of logical investigation: should it be founded on empirical observations about the human mind?Footnote 8 Aristotle’s logic (Organon) – the syllogistic perceived to be at its core – was the main target of contention.Footnote 9
Such contention was manifest in the disagreements between Locke and Leibniz about logic. Locke argued that syllogisms are of little use to the attainment of new knowledge and unnecessary for the proper use of our reason, given that many people in fact think well without ever being taught syllogisms (Locke Reference Locke1975: 668–79).Footnote 10 Meanwhile, Locke took himself to have introduced ‘another sort of logic’, which is ‘the doctrine of signs [i.e. ideas and words]’ and which is one of the three sciences that ‘fall within the compass of Human understanding’, the other two being natural philosophy and ethics (Locke Reference Locke1975: 720–1).Footnote 11 In response, Leibniz defended the syllogistic as ‘a kind of universal mathematics’, an invention that ‘is one of the finest, and indeed one of the most important, to have been made by the human mind’ (Leibniz Reference Leibniz1996: 478). He contended that (formal) logic could not be proved useless, as Locke thought it had been so proven, by the empirical observation that ‘the common run of men know nothing about logic as an art, and that they nevertheless reason as well as – and sometimes better than – people who are practiced in logic’ (Leibniz Reference Leibniz1996: 482). Furthermore, Leibniz rejected Locke’s classification of logic as a separate science, regarding it instead as one of the various ‘ways of organizing the totality of doctrinal truths’ and ‘the art of reasoning’ or ‘the art of using the understanding not only to judge proposed truth but also to discover hidden truth’ (Leibniz Reference Leibniz1996: 524; Reference Leibniz1956: 755).
That Kant was familiar with such developments is clear from his frequent comments on the history of logic. To begin, consider these remarks about Aristotle’s logic:
History of logic. Aristotle: merely objective laws, form of reason. (Refl 1629, 16: 48)
Aristotle erred by including in logic a division of general concepts by means of which one can think objects; this belongs to metaphysics. Logic has to do with concepts whatever they might be, and deals only with their relation. (Refl 4450, 17: 556)
Aristotle can be regarded as the father of logic. But his logic is too scholastic, full of subtleties, and fundamentally has not been of much value to the human understanding. It is a dialectic and an organon for the art of disputation. … Still, the principal ideas from it have been preserved, and this is because logic is not occupied with any object and hence it can be quickly exhausted. (V-Lo/Wiener, 24: 796)
From Aristotle’s time on, logic has not gained much in content, by the way, nor can it by its nature do so. But it can surely gain in regard to exactness, determinateness, and distinctness. … Aristotle had not omitted any moment of the understanding; we are only more exact, methodical, and orderly in this. (Log, 9: 20)
We have no one who has exceeded Aristotle or enlarged his <pure> logic (which is in itself fundamentally impossible) just as no mathematician has exceeded Euclid. (V-Lo/Dohna, 24: 700)
These remarks deliver a nuanced assessment of Aristotle’s logic. In terms of content, (1) this logic includes a presentation of the objective, formal rules of reason and the understanding, thereby giving names to all the moments (or forms) of thinking,Footnote 12 but (2) it also includes, erroneously, ‘a division of general concepts by means of which one can think objects’. (This complaint refers to Aristotle’s Categories.) That logic since Aristotle cannot gain much in content is due to (1). Meanwhile, regarding its manner of presentation, Aristotle’s logic still needs improvement – to be more ‘exact’, ‘determinate’ and ‘distinct’.
This call to improve Aristotle’s logic in manner of presentation does not come from a mere interest in style. Rather, it indicates a concern about the status of logic as science. This concern becomes clear in light of how Kant regards Wolffian logic.
Among the moderns, Leibniz and Wolff are to be noted. The logic of Wolffius is the best to be found. It was subsequently condensed by Baumgarten, and the latter was again extended by Meier. (V-Lo/Wiener 24: 796; and see Log, 9: 21; V-Lo/Pölitz 24: 509)Footnote 13
Kant praises Wolffian logic not so much for its specific content as for its formal features – for being ‘demonstrative’, ‘distinct’ and ‘orderly’ (Refl 1629, 16: 48; Refl 1641, 16: 62; V-Lo/Philippi, 24: 337–8). Notably, he uses similar terms in the Critique to describe ‘the strict method of the famous Wolff … who gave us the first example … of the way in which the secure course of a science is to be taken’ (Bxxxvi). The Wolffian method in question, as Kant interprets it, will turn out to be the method of systematic demonstration that is supposedly essential to accounting for the possibility of logic as science and to proving a given logical system (e.g. the Aristotelian one) as complete. I shall return to this point in §2.2.
Kant’s comments on other developments in modern logic are also informative, albeit largely negative.
Locke: origin of concepts. … Modern: not pure, but mixed logic with psychology. Crusius: fanatic logic. Lambert: an organon of mathematics and physics. (Refl 1629, 16: 48)
After [Aristotle and Peter Ramus] come Malebranche and Locke. This last wrote a treatise de intellectu humano. But both writings deal not only with the form of the understanding but with content.Footnote 14 They are preparatory exercises for metaphysics. … The logic of Crusius is crammed full of things that are drawn from other sciences, and it contains metaphysical and theological principles. Lambert wrote an organon of pure reason. (V-Lo/Wiener, 24: 796; and see Log, 9: 21; V-Lo/Philippi, 24: 337–8; V-Lo/Dohna, 24: 701; V-Lo/Hechsel, LV, 2: 288–90)
These remarks touch upon two philosophical questions about logic that greatly interested Kant. The first is how logic relates to empirical psychology. This question, as I shall explain later, is ultimately about the ground of logic as science. The second question is what belongs to logic as a science that sharply differs from other sciences like metaphysics. For Kant, a strictly scientific logic deals with nothing other than the form of thinking, in abstraction from all relation (Beziehung) to the object – that is, from all content (Inhalt) of thought (A55/B79). This notion of logic underlay Kant’s earlier complaint that Aristotle’s logic wrongly included a division of the concepts by which to think objects. It is now also his basis for charging Locke with mixing in logic a metaphysical topic, namely the origin of concepts,Footnote 15 and Lambert with making logic an instrument or ‘organon’ of substantive knowledge.
This overview of Kant’s comments on the history of logic provides a crucial background for interpreting his appeal to the work of past logicians. Take for instance his claim that apropos judging – as the act of the understanding that is the basis for discovering all categories – he had before him
already finished though not yet wholly free of defects, the work of the logicians, through which I was put in the position to present a complete table of pure functions of the understanding, which were however undetermined with respect to every object. Finally, I related these functions of judging to objects in general … and there arose pure concepts of the understanding [i.e. categories]. (Prol, 4: 323–4)
By ‘the work of the logicians’ is likely meant whatever logic texts retained the part of Aristotle’s logic that supposedly belongs to logic proper, which should contain all the ‘pure functions of the understanding’ listed in Kant’s Table of Judgements (A70/B95), although the logicians themselves might not recognize them as such. If so, Kant must explain his decision to privilege such work and deem it ‘already finished’. After all, given his awareness of the anti-Aristotelian developments in logic, he could not simply take the Aristotelian texts for granted. To the contrary, absent any consensus among the previous philosophers about the nature, subject matter and proper content of logic, Kant would need a great deal of philosophical manoeuvre to get himself ‘in the position’ to extract a list of all the logical functions of judging from the purported work of the logicians. Moreover, as will become clear next, Kant would be compelled by some of his own philosophical commitments to reconstruct the Aristotelian logic on an independent ground before he could help himself with those functions of judging in a deduction of categories.
2.2 Completeness and Kant’s Notion of Logic as Science
Kant takes Aristotle’s logic to be complete in the quantitative sense, in having not omitted anything that ought to be included in logic proper.Footnote 16 Thus the completeness of Aristotle’s logic essentially concerns the nature of logic. This point was implied in Kant’s previously cited comments on Aristotle’s logic, the gist of which can be recapitulated as follows. Logic deals solely with the form of thinking; as such, its content is quickly exhaustible, as it includes nothing other than the formal rules of thinking in general;Footnote 17 Aristotle’s logic has not left out any of those rules, to which extent it is complete.
Kant makes the same point in the second preface to the Critique, which opens with the topic of whether ‘the treatment of the cognitions that belong to the business of reason travels the secure course of a science’ (Bvii). Logic has allegedly travelled such a course in that, since Aristotle, it ‘has not had to retrace any step (keinen Schritt rückwärts hat tun dürfen)’ and ‘has also been unable to take any step forward (keinen Schritt vorwärts hat tun können)’ – and therefore seems complete (Bviii). Note Kant’s use of modal language: his claim is not just that logic has not taken any step backward or forward since Aristotle, but that it has ‘not had to’ or has been ‘unable to’ do so. What has happened to logic is history. What has to or can happen concerns its nature. This focus on the nature of logic is again manifest in how Kant dismisses the attempts of ‘some moderns’ to expand logic by interpolating psychological, metaphysical or anthropological chapters: these attempts betrayed ‘ignorance about the peculiar nature of this science’, as ‘a science that exhaustively presents and strictly proves nothing but the formal rules of all thinking’ (Bviii–ix). Thus, if logic has been able to take the secure path of a science to the extent of allowing no possible expansion, it is thanks to its essential ‘restriction (Eingeschränktheit)’ to the mere form of the understanding (Bix).
The nature of logic, however, at best explains how a system of logic, whatever it may be, can be complete in the quantitative sense specified above. It does not show that Aristotle’s logic is indeed complete in that sense. Especially, it is far from proving that the specific logical forms of thinking (or judging) named by Aristotle – i.e. the ones listed in Kant’s Table of Judgements – are what ought to be included in logic proper. To invalidate any attempt at expanding logic beyond the Aristotelian system and do so without begging the question, Kant needs to do more than just delineate the boundaries of logic. He must find a way to prove that exactly such and such logical forms must be included therein.
To see how the requisite proof might go, it will be instructive to consider Kant’s view on what makes us certain about the completeness of a science. As he puts it in the Critique, for a given science, ‘a full guarantee (Gewährleistung) for the completeness … of all the components that comprise [its] edifice’ can only come from its ‘idea’, whereby its entire plan is outlined ‘architectonically, i.e., from principles (Principien)’ (A13/B27).Footnote 18 If the certainty about the completeness of a science has thus to do with its grounding ‘principles’, Kant appeals to the same connection while comparing how he and Aristotle, respectively, arrived at the categories. On Kant’s part,
[the Table of Categories] is systematically generated from a common principle (aus einem gemeinschaftlichen Princip … erzeugt), namely the faculty for judging (which is the same as the faculty for thinking), and has not arisen rhapsodically from a haphazard search for pure concepts, of the completeness of which one could never be certain (gewiß). (A80–1/B106–7)
By contrast, Aristotle ‘had no principle (Principium)’ in his search for categories, but ‘rounded them up as he stumbled on them’ (A81/B107). The point of this contrast is straightforward: one arrives at categories either by systematically generating them from a principle or by searching for them without any such principle, as Aristotle allegedly did; one can be certain about having completely presented them in the former but not the latter case.
Mutatis mutandis, Kant would make the same point about Aristotle’s presentation of the formal rules of thinking. If Aristotle got the credit for having named all those rules, Kant never saw him as having derived them in accordance with a principle. If Aristotle’s logic contains things that do not belong to logic proper, Kant would trace this problem to a failure to build logic from the idea of such a science, which would have marked its precise boundaries vis-à-vis other sciences. Kant might be alluding to such an idea when he exalted Wolff’s logic for being ‘demonstrative’, ‘distinct’ and ‘orderly’ but suggested that Aristotle’s lacked those qualities. Meanwhile, if a presentation of logic fails to exhibit those qualities, it lacks the proper form of science – and so one cannot yet be certain about its completeness.Footnote 19 Such is the situation of logic as Aristotle handed it down.
Accordingly, Kant’s first step toward proving Aristotle’s logic as complete is to articulate the idea of a scientific logic. This idea is implied in Kant’s notion of pure logic.
In general logic the part that is to constitute the pure doctrine of reason … alone is properly science, although brief and dry, as the scholastically correct (schulgerecht) presentation of a doctrine of the elements of the understanding requires. … As pure logic it … is a proven doctrine (eine demonstrierte Doktrin), and everything in it must be completely a priori. (A53–4/B78)
‘Scholastically correct presentation’ is part of what puts a system of cognitions (e.g. metaphysics) on the secure path of a strict science (Bxxxvi).Footnote 20 A strict science on Kant’s account has three key features: it is systematic, as ‘a whole of cognition ordered according to principles’; it ‘treats its object wholly according to a priori principles’; and it is apodictically certain (MAN, 4: 467–8). If logic is to be strictly scientific, then, its content must be cognized entirely a priori, i.e. derived from a priori principles. Logic in this sense is a ‘demonstrated science’, which ‘rests on’ and ‘can be taught from principia a priori’ (V-Lo/Wiener, 24: 793; and see: V-Lo/Blomberg, 24: 13; V-Lo/Dohna, 24: 694; V-Lo/Pölitz, 24: 505–6; Log, 9: 14–15). In these terms, Kant’s assessment of Aristotle’s logic may be rephrased as follows: although it includes all the items belonging to logic proper, namely the formal rules of thinking, it lacks the form of a strict science, insofar as those rules have not been systematically derived from a priori principia. Hence, to prove Aristotle’s logic as complete, Kant must begin by identifying the requisite principle(s).
3. Rendering Aristotle’s Logic Scientific and Proving its Completeness
3.1 The principium of a Scientific Logic
To sort out Kant’s view regarding the principium or ground on which a scientific logic rests, I shall examine two groups of texts: those in which he directly states what the ground of true logic is, and those in which he discusses the nature of logic and thereby explains why its ground must be so construed.
To begin, consider this remark: ‘Locke’s book de intellectu humano is the ground of all true logica’ (V-Lo/Blomberg, 24: 37). Kant is referring to An Essay Concerning Human Understanding. It might seem puzzling that he should hold the Essay in such a high regard, given that he repeatedly criticized Locke for including in logic topics that belong, say, to metaphysics. The remark makes sense, however, when we take into account its broader context, where Kant contrasts two ways of philosophizing – the critical versus the dogmatic (V-Lo/Blomberg, 24: 37). Kant takes dogmatic philosophizing, as Leibniz and Wolff have allegedly practised it, to be ‘quite mistaken’ and to have ‘so much in it that is deceptive that it is in fact necessary to suspend the whole procedure’. Meanwhile Locke, by ‘[seeking] to analyze the human understanding’, has supposedly ‘set in motion another, the method of critical philosophizing, which consists in investigating the procedure of reason itself, in analyzing the whole human faculty of cognition and examining how far its limits may go’ (Log, 9: 32; and see: V-Lo/Wiener, 24: 804; V-Lo/Hechsel, LV, 2: 301). In terms of this contrast, Kant’s claim that Locke’s Essay is ‘the ground of true logica’ marks his recognition that logic must be preceded by and grounded in an analysis of human understanding.
Kant disagrees, however, with Locke over the exact nature of the needed analysis. The disagreement is telling. From Kant’s perspective, the Lockean analysis is physiological, as it considers the actual operations of our mind under empirical conditions – and therefore amounts to an empirical psychology (Refl 4866, 16: 14; Refl 4893, 18: 21; Refl 4951, 18: 10). A strictly scientific logic cannot build on empirical psychology, but must be grounded on a true critique, which ‘separates 1. the pure from the empirical faculty of cognition, 2. sensibility from the understanding’ (Refl 4951, 18: 9). This contrast between the Lockean analysis and a true critique of human understanding underlies Kant’s distinction between pure and applied logics. If applied logic ‘is directed to the rules of the use of the understanding under the subjective empirical conditions that psychology teaches us’, pure logic ‘has strictly to do with a priori principles’ and therefore ‘draws nothing from psychology’ (A53–5/B77–8). More specifically,
[in pure logic] we abstract from all empirical conditions under which our understanding is exercised, e.g., from the influence of the senses … indeed in general from all causes from which certain cognitions arise or may be supposed to arise, because these merely concern the understanding under certain circumstances of its application, and experience is required in order to know these. (A53/B77)
Applied logic, to the contrary, is ‘a representation of the understanding and the rules of its necessary use in concreto, namely under the contingent conditions of the subject, which can hinder or promote this use, and which can all be given only empirically’ (A54/B78–9). This logic cannot be a ‘true and proven science’ (A55/B79) – for a truly scientific logic must treat its object (i.e. the faculty of thinking) entirely a priori, no matter how it operates under empirical conditions.
Apart from the demand of the strict notion of science, Kant has another reason to think that true logic must have an a priori ground. This reason concerns the nature of logical rules as the ‘universal rules of the use of understanding in general’ (Refl 1620, 16: 41) and as what are ‘necessary … and essential to thinking in general’ (Refl 1628, 16: 44). The universality of the rules entails their necessity: logic, as a ‘universal theory of understanding’, ‘puts forward only the necessary rules of thinking … hence only the form of thinking in general and the rules without which nothing could be thought at all’ (Refl 1620, 16: 40). The necessity of the rules in turn requires that they be ‘derived a priori’ (V-Lo/Wiener, 24: 792). This connection among the universality, necessity and apriority of logical rules echoes Kant’s account of ‘strict universality’ in the Critique, which is characteristic of a rule to which ‘no exception at all is allowed to be possible’. (By contrast, a rule has merely ‘comparative universality’ if ‘as far as we have yet perceived, there is no exception’ to it.) To be strictly universal, then, a rule must be derived independently of experience. This requirement ‘points to a special source of cognition (Erkenntnisquell) for it, namely a faculty (Vermögen) of a priori cognition’ (B3–4). Similarly, if logical rules need ‘a ground from which they are derived’ as the conditions without which no thought would be possible, the derivation must establish them as ‘universal according to reason’, reason being the faculty for cognizing them a priori (V-Lo/Dohna, 24: 694).
A further feature of logic holds the clue to the specific a priori ground from which logical rules are to be cognized: logic is a ‘self-cognition of the understanding and of reason’, in that the understanding (in the broad sense), which cognizes logical rules, is also the very object of logic (Log, 9: 14; and see: V-Lo/Blomberg, 24: 24–5; V-Philippi, 24: 315; V-Lo/Dohna, 24: 695; V-Lo/Wiener, 24: 792; V-Lo/Bauch, LV, 1: 10, 13–14; V-Lo/Hechsel, LV, 2: 278, 280).Footnote 21 More precisely, since logic deals only with the necessary rules of thinking, it must proceed from an analysis of the understanding as the faculty of thinking – ‘logica will thus have no other grounds or sources than the nature of human understanding’ (V-Lo/Blomberg, 24: 25). Accordingly, the a priori cognition of logical rules is to proceed in roughly these steps: it starts with a reflection on the understanding merely as regards its capacity to think; on that basis, a set of rules are derived as what determine the possibility of thinking (as regards its form).
Before we turn to Kant’s logic corpus for more details about such a procedure, it is important to bear in mind a distinction between two kinds of ‘principle’ pertaining to logic. On the one hand, Kant takes logic to present ‘principles of all logical assessment (Beurtheilung) of our cognition’ (A60/B84) – namely principles for evaluating a given cognition as regards its formal correctness (Log, 9: 15; V-Lo/Dohna, 24: 696). Among these evaluative principles is the law of contradiction, which is the most general albeit merely negative principle of all our cognition – if it is to be true – in that whatever violates the law is false (A150–1/B189–90). On the other hand, when Kant inquires about the principle of logic as science, he is seeking to uncover the ground or source of a properly scientific cognition of the rules of thinking in general. This inquiry should not be confused with a project of reducing all logical rules, in an axiomatic-deductive manner, to a self-evident principle like the law of contradiction.Footnote 22
Moreover, there are two kinds of logical rules according to Kant. There are generative rules, which specify the logical functions of the understanding whereby any thought – a concept, a judgement, or an inference – may be generated as to form. Then come truth rules, which include the law of contradiction among others and which constitute the formal conditions of the truth of a given thought.Footnote 23 When Kant takes Aristotle’s logic to be complete in having not omitted any ‘moment’ or ‘form’ or ‘function’ of thinking, he is referring to the first kind of rules. These rules are my focus in this paper.
3.2 From the Nature of the Understanding to Logical Rules
In the Critique, Kant introduces the notion of logic against the backdrop of a contrast between sensibility and the understanding. Sensibility is ‘the receptivity of our mind to receive representations insofar as it is affected in some way’. The understanding is the faculty of spontaneity, namely ‘the faculty for bringing forth representations itself’ or the capacity to think in a way that can transform received representations into a thought of something, a thought that is essentially conceptual. Although these two faculties must work together to produce cognition in the strict sense, their roles are distinct and must be investigated independently of each other. Thus arise two sciences – aesthetic, ‘the science of the rules of sensibility in general’, and logic, ‘the science of the rules of the understanding in general’ (A51–2/B75–6). Logic, so construed, ‘abstracts … from all content of cognition, i.e. from any relation of it to the object, and considers only the logical form in the relation of cognitions to one another, i.e. the form of thinking in general’ (A55/B79). This indicates that logic, as a scientific cognition of the formal rules of all thinking, must build on an account of the form of thinking.
We can find such an account in the ‘Prolegomena’ to most of the extant transcripts of Kant’s logic lectures, as well as in the ‘Introduction’ of the Logic edited by Jäsche.Footnote 24 It centres on an analysis of the understanding as the faculty of thinking. Briefly, it revolves around the following theses (besides the aforementioned conception of the understanding as a faculty of spontaneity).
(i) Thinking is the act (Handlung) of the understanding and, as such, is governed by rules.
Everything in nature … takes place according to rules … The exercise of our powers (Kräfte) also takes place according to certain rules … Like all our powers, the understanding in particular is bound in its acts (Handlungen) to rules, which we can investigate. (Log, 9: 11; and see V-Lo/Philippi, 24: 311; V-Lo/Pölitz, 24: 502; V-Lo/Dohna, 24: 693; V-Lo/Wiener, 24: 790; V-Lo/Bauch, LV, 1: 3–6; V-Lo/Hechsel, LV, 2: 271–2; V-Lo/Warschauer, LV, 2: 505)Footnote 25
(ii) Thinking has both matter and form. Specific sciences differ as to matter.Footnote 26 They nevertheless have one thing in common, namely the ‘use of the understanding in accordance with rules of which one is conscious’.Footnote 27 Logical rules, as what pertain to the mere form of thinking, are presupposed by all sciences.
In all thought there is matter and form. Matter concerns the object and form the mode of treatment.
Our understanding has various objects of cognition and of science, such as history, mathematics – but universal logic abstracts from all this content, from all variety of cognition, and considers in everything only the form of concepts, judgements, and inferences. In short, it is one of the sciences that prepare us for others. (V-Lo/Wiener, 24: 791; and see V-Lo/Dohna, 24: 693; V-Lo/Warschauer, LV, 2: 506; Log, 9: 12–13; A52/B67; Refl 1603, 16: 33; 1620, 16: 40; 1628, 16: 43–4)
(iii) There are rules for how we think and there are rules for how we ought to think. The latter rules are those without which no thought would be possible.
We can divide the laws of our understanding in the following way[:]
1. Rules for how we think.
2. Rules for how we ought to think.
… Logic teaches us this last, namely, how to use the objective rules of our understanding. … the universal rules are the sole condition of our thought [as to form]. (V-Lo/Wiener, 24: 791–2; and see V-Lo/Pölitz, 24: 502; V-Lo/Dohna, 24: 694; Log, 9: 14; also Refl 1579, 16: 18, 20–1; 1599, 16: 30; 3939, 17: 356)
(iv) Three kinds of cognition, as to form, originate through the act of thinking (as the spontaneous act of bringing forth representations).
Logically, all origins (Anfänge) in thought are divided thus:
1. The cognition is a simple cognition, a concept.Footnote 28
2. The cognitions are combined in a judgement.
3. That judgements are combined and that inferences arise therefrom. (V-Lo/Wiener, 24: 904; and see V-Lo/Pölitz, 24: 565; V-Lo/Hechsel, LV, 2: 389)Footnote 29
These theses together suggest that logical rules first include the ones that determine the acts of the understanding whereby concepts, judgements and inferences are to be generated. To specify these rules, one begins with an analysis of the nature or ‘form’ of concept, judgement and inference, respectively.Footnote 30 This procedure is most clearly manifested in Part I of the Logic (‘Universal doctrine of elements’), which comprises three sections (‘Of concepts’, ‘Of judgements’, ‘Of inferences’), although the same procedure can also be recovered from many transcripts of Kant’s lectures.Footnote 31
For a brief illustration of this procedure, we start with concepts. Every concept has the form of a ‘universal representation, or a representation of what is common to several objects’ (Log, 9: 91; and see V-Lo/Pölitz, 24: 567–8; V-Lo/Wiener, 24: 904, 908; V-Lo/Bauch, LV, 1: 151–2; V-Lo/Hechsel, LV, 2: 390, 395; V-Lo/Warschauer, LV, 2: 609). As such, a concept is ‘always made (gemacht)’ (Log, 9: 93). Accordingly, there are rules that determine how the representations that are ‘given to [the understanding] from elsewhere, whatever this may be’, may be ‘transform[ed] … into concepts’ (A76/B102; and see Log, 9: 93; V-Lo/Pölitz, 24: 566; V-Lo/Wiener, 24: 907). These rules specify the ‘logical actus of the understanding’ – i.e. comparison, reflection and abstraction – that constitute ‘the essential and universal conditions for generation of every concept whatsoever’ (Log, 9: 94; and see V-Lo/Wiener, 24: 907–10; V-Lo/Hechsel, LV, 2: 393–5; V-Lo/Warschauer, LV, 2: 609–10).
Next, an analysis of the nature of judgement serves as the basis to derive the formal rules for generating all possible judgements. Briefly, a judgement relates a multitude of cognitions in the unity of one representation. Different forms of judgement are just different ways in which such a unified relation may be effected (Log, 9: 101; V-Lo/Pölitz, 24: 577; V-Lo/Wiener, 24: 928–9; V-Lo/Hechsel, LV, 2: 422; V-Lo/Warschauer, LV, 2: 623). Relating multiple cognitions in one is an act of the understanding, which is to manifest itself in twelve forms under four titles – quantity (singular, universal, particular), quality (affirmative, negative, infinite), relation (categorical, hypothetical, disjunctive), and modality (problematic, assertoric, apodictic).Footnote 32 These are precisely the twelve moments of ‘the function of thinking’ listed in Kant’s Table of Judgements (A70/B95). It is not surprising, then, that he occasionally introduces logical forms of judgement simply as the various ‘acts of the understanding (Verstandeshandlungen) that appear in a judgement’ (V-Lo/Wiener, 24: 929; and see V-Lo/Pölitz, 24: 577; V-Lo/Hechsel, LV, 2: 423; V-Lo/Warschauer, LV, 2: 623–4).
Finally, the derivation of the rules for generating (syllogistic) inferences likewise proceeds from a general analysis of inference (Log, 9: 114–30; V-Lo/Pölitz, 24: 583–93; V-Lo/Bauch, LV, 1: 181–203; V-Lo/Hechsel, LV, 2: 439–73; V-Lo/Warschauer, LV, 2: 632–47).Footnote 33
By this sketch of Kant’s procedure for deriving logical rules, my intention is to clarify what kind of proof he would give for the claim that Aristotle’s logic is complete, without dwelling on how exactly each one of those rules is supposed to be derived. In short, if Kant had the aforementioned rules in mind when he claimed that Aristotle exhaustively named all the formal rules of thinking, the claim is justified – by the Kantian standard – insofar as those rules can be systematically derived from a common principle or ground in the way described above. Philosophically speaking, I submit, what is important here is not whether the proof is convincing in its details, but what it has revealed about Kant’s theory of logic – especially in connection with some of the pre-Kantian developments in logic.
One would be missing Kant’s point, then, to read his completeness claim as a mark of uncritical adherence to the Aristotelian logical tradition. Kemp Smith writes: ‘however many provisos [Kant] made and defects he acknowledged, they were to him merely minor matters, and he accepted its teaching as complete and final’ – for, since Aristotle’s logic ‘has stood the test of 2000 years, and remains practically unchanged to the present day, its results can be … employed without question in all further inquiries’. No wonder Kemp Smith is frustrated when observing that ‘Kant recasts, extends, or alters [its doctrines] to suit his own purposes’ in the Critique (Kemp Smith Reference Kemp Smith1918: 184–5). This frustration is self-inflicted in a way: Kemp Smith is looking at the wrong thing. The completeness claim, as Mosser puts it, in fact ‘tells us much more about Kant’s conception of logic … than it does about what he thinks of Aristotle’ (Mosser Reference Mosser2007: 131). Given that the need for Kant to prove the claim is rooted in his idea of a strictly scientific logic, the proof amounts to deducing and reconstructing Aristotle’s logic – or, more precisely, the part of this logic that contains all the formal rules of thinking – from an a priori ground and thereby transforming it into a true science. It is this reformed Aristotelian logic that Kant feels assured to use in the Critique. The assurance is not from Aristotle’s authority as the father of logic or from any time-tested prevalence of the Aristotelian tradition. (Moreover, as we saw, the Aristotelian logic no longer enjoyed uncontested prevalence during Kant’s time.) It is rather founded on Kant’s own philosophical convictions about logic as a proper science.
4. The Above Proof as Part of a Larger Reform
The proof of the completeness of Aristotle’s logic sketched above helps to answer another question that concerns the critical Kant: what is the legitimate use of logical rules? This brings us back to the Wolffian approach to logic. Earlier I explained that Kant extols Wolff’s logic as what, among the available logical systems, best satisfies the formal conditions of a proper science. I also mentioned, however, that Kant rejects the dogmatic philosophizing practiced by Wolff among others, which proceeds without a prior critique of human understanding.Footnote 34 Now, given that Kant views logic as a pure cognition a priori, he would worry about the danger of dogmatism in this case as well: reason might be tempted to employ logical rules for purposes they cannot serve. Meanwhile, by grounding pure logic in a philosophical analysis of the understanding, Kant has also signalled a remedy for the said temptation. I shall briefly explain these points, as they show how Kant’s proof of the completeness of Aristotle’s logic fits with his overall reformative project regarding logic.
To appreciate Kant’s worry about the danger of approaching logic dogmatically, note his following caution against a certain misuse of (general) logic.
[G]eneral logic, which is merely a canon for assessment (Beurtheilung), has been used as if it were an organon for the actual production of at least the semblance of objective assertions, and thus in fact it has thereby been misused. (A61/B85)
To say that logic is ‘a canon for assessment’ is to say that it is an a priori proven ‘doctrine of the elements of the understanding’ (A54/B78) that ‘subsequently serves for critique, i.e., as the principle for the assessment of all use of the understanding in general’ (Log, 9: 15; and see V-Lo/Dohna, 24: 696; V-Lo/Wiener, 24: 793; Refl 1601, 16: 32). Now logic is a canon of the understanding ‘only in regard to what is formal in [its] use, be the content what it may’ (A53/B77). Thus it can only serve for assessing cognitions with respect to their form, without providing us with any resources for judging about their material truth.
General logic analyzes the entire formal business of the understanding and reason into its elements, and presents these as principles of all logical assessment of our cognition. … But since the mere form of cognition, however well it may agree with logical laws, is far from sufficing to constitute the material (objective) truth of the cognition, nobody can dare to judge of objects and to assert anything about them merely with logic without having drawn on antecedently well-founded information about them from outside of logic[.] (A60/B84–5; and see Log, 9: 15; V-Lo/Dohna, 24: 694, 696)
It is therefore ‘nothing but idle chatter’ to use logic – which teaches us only the formal conditions of the use of the understanding – ‘as a tool (organon) for an expansion and extension of its information (Kenntnisse)’ (A61–2/B86).Footnote 35
Nevertheless, Kant recognizes that ‘there is something so seductive in the possession of an apparent art (scheinbaren Kunst) for giving all of our cognitions the form of understanding’ that logic has been mistaken as an organon for obtaining material cognitions (A60/B85). Tellingly, this recognition echoes Kant’s diagnosis of the surreptitious move that reason makes in using conceptual analysis – which can afford only formal (analytic) truths – to make material (synthetic) claims.
Now since this [analysis of concepts] does yield a real a priori cognition, which makes secure and useful progress, reason, without itself noticing it, under these pretenses surreptitiously makes (erschleicht) assertions of quite another sort, in which it adds something entirely alien to given concepts and indeed does so a priori, without one knowing how it was able to do this and without such a question even being allowed to come to mind. (A5–6/B9–10)
Note that reason would make the surreptitious move ‘without itself noticing it’. Hence, to forestall the move, reason must first examine the nature and possibility of analytic and synthetic cognitions respectively (A6/B10). Likewise, to prevent any unintended misuse of logical rules, reason must first reflect on the nature and possibility of logic as science and, on that basis, specify what counts as the valid use of its rules.Footnote 36 Once it is clarified that logic – as a strictly scientific cognition of the necessary rules of thinking in general – concerns the mere form of thought, one can see that logic is only a ‘propaedeutic … to the sciences’ and that ‘when it comes to information (Kenntnissen) … its acquisition must be sought in the sciences properly and objectively so called’ (Bix). Only this reflective understanding of the limited function of logic can prevent its misuse as a tool for extending material cognitions.
By this analysis, the misuse of logical rules that Kant wishes to counter is a result of reason being unknowingly tempted by the deceptive appearance of logic as an art for acquiring new cognitions, which is in turn rooted in a failure to examine the true ground of logic. So construed, the misuse is a symptom of dogmatic philosophizing and can be treated only through the adoption of a critical method. To paraphrase Kant’s earlier contrast of the two methods, there are so many deceptive elements in a dogmatic philosophy that the whole thing must be suspended. In the case of logic, reason must start all over again, beginning with an inquiry about its ground.
The fact that the same inquiry was pivotal to Kant’s proof of the completeness of Aristotle’s logic suggests that, if Kant would indeed prove Aristotle’s logic as complete by systematically deducing the formal rules of thinking named therein from an a priori ground, such deduction would be an integral part of his overall critical reform concerning logic. The reform, as I have portrayed it, involves a complex response to two inspiring pre-Kantian developments in logic, each of which has in its own way exceeded Aristotle’s original treatment of logic. On the one hand, Kant agrees with Locke that logic is an independent science with its own subject matter and that it is important to ground logic in an analysis of human understanding, but rejects Locke’s empiricist treatment of such a ground. On the other hand, if Kant models the scientific form of pure logic after the Wolffian philosophy, he also recognizes how Wolff’s dogmatic procedure could lead reason to misuse logic as an organon for the material extension of cognition. Thus Kant’s insistence on constructing pure logic from an a priori analysis of the understanding amounts to a serious engagement with some of the major developments in logic during the seventeenth and eighteenth centuries – in an attempt both to establish logic as a proper science and to specify the valid use of its rules. For Kant, an effective and fruitful engagement with those developments – and with Aristotle’s logic in its original shape – must centre on a true critique of human understanding.
Only if this [critique] is one’s ground does one have a secure touchstone for appraising the philosophical content of old and new works in this specialty; otherwise the unqualified historian and judge assesses the groundless assertions of others through his own, which are equally groundless. (A13/B27)
As far as the philosophical evaluation of his intellectual heritage goes, then, Kant is taking nothing for granted. Logic is no exception.
5. Conclusion
In this paper, I have read Kant’s inquiry about the ground of (formal) logic in connection with certain developments in logic during the seventeenth and eighteenth centuries. On this reading, Kant has to prove the Aristotelian formal logic as complete not merely to justify its role in his critical philosophy, but also because the previous developments in logic have presented him with new philosophical questions – especially about the ground, subject matter, scope and legitimate use of logic. Kant’s proof of the completeness claim, as I have reconstructed it, serves to bring together his answers to all these questions.
By giving a historically informed reconstruction of the said proof, my goal is not to show that it was successful. (Assessing the success or failure of the proof would require a careful explication of the relevant success criteria, which I have not provided.Footnote 37) Nor do I deny that Kant’s inheritance of the Aristotelian tradition marks his fundamental limitations when it comes to logic. These limitations are not however unique to Kant. In a sense, the chief players in logic during his era all started with the Aristotelian logic, asking, among other things, whether it can serve as an effective instrument for the discovery of truths and whether it constitutes the universal standard for the proper use of our cognitive faculties. When innovative steps were taken, they fell on either side of such questions. Even Leibniz, who may be seen as having sparked the most exciting developments in formal logic through his vision of a universal logical calculus, made special efforts to defend the Aristotelian syllogistic as an indispensable part of the universal logic (see §2.1).Footnote 38 As for Kant, he did not mean to be an innovator in logic per se, but rather focused on the philosophical issues raised by the sundry developments in logic that faced him. He had a good reason to be so focused: without sorting out those issues, all the innovative attempts in logic would be blind if not a total waste of time.
In this connection, it is important to add, the philosophical questions Kant addressed while defending the completeness of Aristotle’s formal logic are not limited to that logic, but can be raised with respect to any purported formal-logical system. Hence, if the logic Kant inherited has, as Paton puts it, ‘suffered serious, and perhaps shattering, blows’ (Paton Reference Paton1936: 188), the reformative elements of his philosophy of logic – as are manifested in his attempt to defend that logic – nevertheless remain as historically significant insights.Footnote 39
