Logical and Spiritual REFLECTIONS
Book 2. A Short Critique of Kant’s Unreason
Chapter 5. Kant’s “categories”
Kant proposed a list of twelve “categories” as corresponding to the “forms of the understanding” that he considered the foundations of our conceptual knowledge. Aristotle had long before proposed a list of ten “categories” that remained essentially unchallenged till Kant. Kant did not modify Aristotle’s list, but replaced it with another.
Aristotle’s categories were concepts averred to be the highest possible in a classification of all things, i.e. the summa genera of existence. Actually, he conceived them and presented them as all the kinds of things that would be subjects or predicates of propositions (by which he here meant categorical propositions of the simplest predicative form ‘X is Y’). It was a natural continuation of Aristotle’s formal logic to ask what contents one might expect in the propositions under study. Although this research project was essentially justifiable and interesting, Aristotle made many methodological mistakes in its pursuit.
Aristotle’s list of categories included: substance, quantity, quality, relation, place, time, action, passion, position, and state. Aristotle developed this list empirically, i.e. by considering numerous propositions, and noting what the subject and predicate were about. It was not a systematic division and arrangement proceeding from some theoretical considerations, but a random collection of disparate items based on observation.
Briefly put, substance refers to subjects like Socrates (a particular, or primary substance) or Man (a universal, or secondary substance). The other categories refer to possible predicates. These may be quantitative (e.g. is big), qualitative (e.g. is red), or relational (e.g. is louder than so and so), they may indicate place or time (e.g. yesterday, at the market), they may describe some action of the subject (e.g. he hammers the nail in), or resulting position of it/his (e.g. he is tired out), or some passion of the subject (e.g. the page was blown away by the wind), or resulting state of it/his (e.g. it is lost).
Note that a particular cannot be a predicate of a universal subject, but a universal can be a predicate of a particular subject (e.g. Man can be predicated of Socrates) – so substance is also a predicable. Also note that other categories can be subjects if we intend them as substances, ‘as such’ (e.g. big size, redness, hammering, etc.).
Now, some of these categories seem artificial to me, i.e. I am not sure they can be cast in the role of predicates without forcing them. Take, for instance, the category of “relation”. In truth, every proposition is relational. The copula ‘is’ in the proposition ‘X is Y’ is, note well, a specific relation between the terms X and Y.
A proposition like ‘X is bigger than Y’ might be called more specifically comparative, with regard to size (in this case). I would not regard ‘bigger than Y’ as a predicate. We can formally permute such a proposition, i.e. fit it into the basic ‘X is Y’ format, by saying ‘X is [something bigger than Y]’. But note that in such event the new predicate is not ‘bigger than Y’ but ‘something bigger than Y’ – and this new predicate is not a “relation” but a “substance”!
It is more accurate to view ‘is bigger than’ as the relational aspect of the proposition (i.e. as the ‘copula’, in an expanded sense not limited to ‘is’), and X and Y as its terms (which are called subject and object in such relational contexts). Moreover, such a comparative copula can concern some of the other categories (in the sense that ‘bigger’ concerns quantity, ‘redder’ concerns quality, ‘further’ concerns place, ‘later’ concerns time, etc.).
Again, take “place” and “time”. They are not directly predicated, but are terms (the objects, Y) of distinct relational propositions: ‘X is in this place and is at that time’. In such cases, the copula (relation) involved is not really ‘is’, but ‘is in’ or ‘is at’. As regards to time, it can be tied to the copula in the way of its tense, as in ‘X was, is or will be Y’, indicating past, present or future predication. In the case of prediction, i.e. future predication, complications are involved – regarding whether the projected event is inevitable, or dependent on both human volition and natural events, or dependent on human volition alone.
Now, consider “action” and “passion”. We are somewhat justified in distinguishing them, because this allows us to convert the one to the other; for example, ‘X sings Y’ to ‘Y is sung by X’, or vice versa. Apart from that, their formal properties are usually little different, but great care must be exercised in syllogistic reasoning to make sure the putative middle term is indeed one and the same in both premises. Additionally, each such copula has its own rules of inference; for instance, causative propositions (‘X causes Y’, ‘Y is caused by X’, and the like) constitute by themselves a whole field of logic, and cannot be treated as mere cases of action or passion.
On the other hand, it is hard to see why “position” and “state”, which are presented as the end-results of some “action” or “passion” respectively, are distinguished from each other and from other categories like quantity or quality. Their formal properties are surely the same, and the only way we manage to distinguish them is with reference to another proposition – one stating: “this predicate emerged after that action or passion”. So, in truth, position and state have no intrinsic justification as distinct categories, but are at best subcategories of other categories.
At a deeper level, the distinction between “action” and “passion” (and their end-results) is not truly as widely applicable as it may seem at first glance. If we consider aetiological issues, they are seen to refer specifically to volitional contexts, i.e. to action in the sense of change through one’s will and to passion in the sense of change against one’s will. For examples, crushing is action and being crushed is passion. In this more limited sense, even a static event involving restraint of willpower, such as a man just sitting (rather than doing anything else), is an action.
In this perspective, all so-called actions of things devoid of the power of will, i.e. functioning exclusively under determinism, or even spontaneity, such as stones or machines, or subatomic particles – are really passions in a large sense. This means that the terms action and passion as initially apparently used are confused and equivocal.
Thus, Aristotle’s proposed categories are not all on the same level of abstraction, and many of them fudge many meanings. Some are not clearly mutually exclusive though they should be, and some ought to include others but do not do so. There are many ambiguities and unanswered questions in this list. Moreover, how can we be sure the proposed list is comprehensive – why not leave the list open-ended, allowing for new discoveries and insights?
Most important, Aristotle’s listing is flawed from its very conception, because it effectively presupposes that all propositions (or more precisely, all categorical propositions, and by extension the categorical-looking antecedents and consequents of hypothetical propositions) are ‘predicative’ (i.e. truly ‘X is Y’) in form. But, though all (or maybe just most) propositions can be recast in the form of predications by judicious permutations (as in the example above given), it does not follow that their full meaning is conserved in such a logical operation.
The non-predicative forms are not to be dispensed with or glossed over by logicians; they are interesting and important in their own right. Permutation is an artifice, which we find convenient in some situations, but it must not be overestimated. Because of the silly presupposition that “is” is the only ultimately significant copula, Aristotle prevented future logicians from seriously studying categorical propositions other than the standard classificatory form.
Moreover, Aristotle naturally pursued this idea by trying to force all terms into the corresponding subject-predicate format in his doctrine of the categories. To do so, he had to artificially merge part of the copula with the object in many cases. To top it all, he overconfidently declared the search for categories closed at the round number of ten. Even if his categories were individually worth formulating, he had no right to assume them together exhaustive and thus to arbitrarily arrest further research.
It is only in modern times that this Aristotelian scheme began to be challenged. Kant was the first (or one of the first) to challenge it, though what he offered in exchange was not entirely satisfactory either.
The important things to note here are the following: Aristotle’s search for the top genera, a list of concepts that include all other concepts, is not per se illegitimate; nor is his empirical method of pursuing this goal to be fundamentally criticized. His methodological sins here were rather: that he wrongly assumed all propositions were fully reducible to the ‘X is Y’ form, and that he artificially stopped his empirical search at ten categories. These two mistakes caused him to try and force all things to fit into his scheme, turning it from a scientific endeavor to a dogma.
The lesson to learn is the following: we ought indeed to be attentive to all levels of conceptualization, and we should do this in an open-minded way rather than by applying some rational prejudice. Logicians must seek out every existing form of proposition, rather than assume there is one significant form only and search for all its possible subjects and predicates (as Aristotle did). We should investigate the logic of each and every form (including the variety of contents it may house). We should at no time assume our list of forms is complete, but remain open to new discoveries and inventions.
Kant rightly abandoned Aristotle’s list, in view of the haphazard way it was accumulated and its lack of a “guiding principle” (other than its declared mission to exhaust all contents of predication). Actually, as we shall see, Kant’s proposed list, though in many respects an improvement on Aristotle’s, suffered from similar imperfections in other respects. It was less haphazard, but also less empirical. It was more systematically conceived, but also forced things into a preconceived arbitrary scheme.
The following is Kant’s list of twelve “categories”, made up of four groups (called “moments”) of three categories each, with some explanatory and critical comments by me:
Ø Quality = reality, negation, limitation. I would refer to this group as Polarity, and to its first two members as respectively presence and absence (of some specified thing, entity, character or event); these are contradictories, of course. To use the word “reality” here would not be accurate, since we are in fact on a phenomenological level of consideration. Regarding limitation, this could be defined as “X is present till Y and absent beyond Y” (where X is some thing and Y is some point in space and time). Thus, limitation is effectively a compound of presence and absence; and it involves a notion of space and/or time, subdividing a whole into parts. The categories of Quality play a role in those of inherence and subsistence.
Ø Quantity = unity, plurality, totality. Quantity, here, means Number (or Scope). Unity refers to this one, i.e. some indicated single (thing); plurality refers to an unspecified number of units, i.e. many, more than one (thing); and totality to all (things of a certain group). Note that totality (all) may be taken as a special case of plurality (some unspecified number), or as contrary to plurality (if the latter is read as ‘only some’). Totality also presupposes that we have already delimited some group of things. Thus, the categories of Quantity ought to be related to the category of community, if we understand the latter as referring to classification (see below).
Ø Modality = existence, possibility, necessity. Modality is aptly named, but existence here should more accurately be called actuality; it means this indicated fact, here and now or there and then (a precise space and time position is specified). Possibility may mean some conditions or only some conditions; the latter is called contingency, the former includes necessity as an alternative to contingency. Necessity refers to something that occurs under all conditions. Comparing modality to quantity, we see that the three modalities are special cases of the three quantities, applicable specifically to numbers of conditions. Modality is also closely related with Causation.
Ø Relation = inherence and subsistence, causality and dependence, community. I suppose that Kant had in mind here categorical, conditional and disjunctive propositions; thus, by Relation he meant the Copula of categorical propositions, or more broadly the Forms of conditional (if-then-) or disjunctive (either-or-) ones. Note that his three categories are defined through five subcategories, here, breaking the desired symmetry somewhat. The first pair of relations is based on the formal notions of subject and predicate; it is thus usually interpreted as referring to ‘substance and accident’, i.e. to entities and their properties. The second pair is interpreted as ‘cause and effect’; but note that though causation (the kind of causality here apparently intended) is a compound of conditional propositions, it does not follow that these forms are equivalent; moreover, volition and natural spontaneity do not seem to have been given a place in this scheme. With regard to the last category, ‘community’, more will be said further on.
Various additional comments are in order.
a. In sum, Kant here seems to have tried to list the ontological assumptions or implications apparently underlying the various already known logical features of propositions (or “judgments”, in his terminology). That is to say, starting from our known forms of discourse, he infers a corresponding list of what they seem to intend, presume or imply out there in the apparent object. He consciously interprets logical features, to bring out their ontological significances.
It is therefore surprising that he goes on, after drawing up this list, to overturn its ontological moment, changing it into a sort of mental reformatting of data inputs. The transition seems arbitrary, without intrinsic logic. I refer here to Kant’s interpretation these twelve categories as the “forms of the understanding”, i.e. as “pure (a priori, non-empirical) concepts” on which our knowledge is based. This requires explanation.
Kant characterized (with typical grandiosity) the above-mentioned transition from features of propositions to facts of reality as “metaphysical deduction”. It is important to dwell on this phrase, because it tells us a lot about his thinking. Kant here takes the various logical distinctions developed by Aristotle as his givens, and “deduces” from them corresponding facts of reality (referred to by the adjective “metaphysical”).
This is, of course, topsy-turvy. Kant can maybe do that, because he has Aristotle’s work behind him. But Aristotle had to go the other way, and derive the logic from the reality; he had no doctrinal givens. That is, in truth, no deduction is involved in relating formal logic to reality, but an induction. And I would suggest that even Kant and ourselves, coming after Aristotle, need induction to understand all this; we cannot do so by mere deductive means.
Thus, Kant was essentially thinking in the way of a passive, conventional-minded student, whereas Aristotle had to proceed in the way of a creative, original researcher. So it is not surprising that Kant conceived a reverse epistemology, in which the effect becomes the cause and vice versa. That is, it was to be expected that Kant would present the logical categories as determining the metaphysical categories, rather than the reverse. He was just describing his own rather deductive thought process; but this was not a universally applicable description, since it ignored the more inductive thought processes Aristotle had used before him.
b. We should of course also note that, though Kant’s list is prima facie more intellectually interesting and satisfying than Aristotle’s, it is not a list of the same things. Albeit some similarities in terminology (viz. the use of the words “categories”, “quality”, “quantity”, “relation”, “substance”), this list obviously essentially refers to something essentially different. Aristotle’s list could be said (forcing it a little) to have concerned, in Kantian terms, only the subdivisions called inherence (subjects) and subsistence (predicates).
Aristotle’s list was meant to clarify the possible contents of propositions, i.e. the kinds of things we may and do think about. Kant’s list, on the other hand, was intended as a collection of the possible logical properties of propositions, i.e. the various formal features of our thoughts. These various factors were not unknown to Aristotle – in fact, it was he who originally discovered and discussed most of them. Thus, Kant was not discovering new ideas, but merely drawing attention in a new way to certain already existing ideas.
So, whereas Aristotle had assembled a list of categories of content, Kant proposed a list of categories of form. Kant (wisely, I think) considered the latter list more worthy of philosophical study; his doctrine was novel only in the emphasis he gave to already known formal characteristics.
We could also say that whereas Aristotle sought to identify what we think about, Kant sought to identify how we think about them. That is, while Aristotle’s list may be regarded as ontological information, Kant’s list has a more epistemological significance (although he misjudged precisely what that was).
Moreover, whereas Aristotle’s categories are acquired possessions of ours (albeit almost inevitably acquired, by virtue of their ubiquity), Kant’s are averred forces innate in us. While Aristotle drew up his list in the way of an empiricist observation of objective phenomena, Kant drew his up in the way of a rationalist prediction of subjective phenomena; i.e. he effectively claimed his categories to be instincts, which somehow control our thoughts, out of our control, and he claimed to know this about them by purely “deductive” means.
c. Note well the above-mentioned interrelations between the three categories under each heading, and those between the headings. The interrelations in each group are clearly not symmetrical in all respects. The trouble with system building is that it almost inevitably involves oversimplifications; the natural diversity involved is obscured and accuracy is sacrificed. Kant’s attempt to force his list in a numerically symmetrical scheme is a case in point.
(i) Consider first the polarities. In Aristotle’s logic, there are two mutually exclusive and exhaustive polarities, the positive and the negative. Limitation is not in his list. Kant seems to have introduced this third category for the sake of symmetry.
If we consider his proposal, it seems to refer to a quantification of the predicate. When we say X is Y, we mean that X is Y in some respect, without excluding that it might be other than Y in other respects. For example, “Roses are red” does not exclude these same roses from having green leaves or from being wet, soft, etc. One predication does not exclude others. On the other hand, when we say X is not Y, we mean that X is not at all Y in any respect. For this reason, affirmation and denial are mutually exclusive and exhaustive.
To insert limitation here suggests that a third possibility exists, viz. X is partly Y and partly not Y. This possibility does indeed exist, but it is already tacitly covered by the proposition X is Y, as just explained. To insert limitation seems to imply that X is Y means X is wholly Y – which is never true of anything, except perhaps X is X (provided “is” is here understood as “equals”). Moreover, if we insert limitation, logic requires we insert its opposite, infinity; and if we do that, we must consider infinity both on the positive side and on the negative side. But clearly, all this no longer has anything to do with the polarities of ordinary predication. It is just an attempted analogy gone berserk.
If we were to insist on having a triad, I would suggest as our third category that of problemacy, which could be characterized as limitation of certainty. This would allow us to refer to problematic propositions, those involving an uncertainty as to whether X is Y or not Y, or a probability rating favoring the one over the other. When presence and absence is predicated without qualification, certainty is tacitly implied; this is appropriate to a deductive system of logic. But when we consider inductive issues, we need the in-between concept of problemacy (implying intermediate degrees between truth or falsehood, or knowledge of them), as against settled (known) truth or falsehood. Without such a tool, our discourse would be stuck.
However, it might be asked whether this is the appropriate place to mention certainty and problemacy. They are, after all, logical or epistemic (de dicta) modalities; so, they should be included under the heading of modality. In that case, the heading of polarity should only have two categories. On the other hand, if we look upon the heading of modality as essentially concerned with the de re modes of modality (the spatial, temporal, natural, and extensional modes), then it would be reasonable to place problemacy here. In either event, Kant’s category of limitation should be abandoned. It has more to do with quantity (scope of application) than with quality (i.e. polarity).
(ii) Consider now the quantities and modalities. They are very analogous sets – not fortuitously, but because quantity is a mode of modality! Quantity refers to extensional modality. Alternatively, quantity is used to define the other modes of modalities. Therefore, the heading of modality in Kant’s list should be taken to refer to the natural mode of modality, and eventually the spatial and temporal ones, too; that is, to the remaining de re modes. However, it is clear from Kant’s references in this context to assertoric, problematic and apodictic propositions that he rather has in mind de dicta modality.
In adopting this position, Kant is somewhat influenced by Aristotle, who in his work on modal logic generally refers to de dicta modalities. However, in his work on ontology, Aristotle examines de re modalities in great detail. Kant does not apparently take these important modes of modality into consideration here. If this is indeed Kant’s intention, then he is clearly in error here. This error of his would explain why Kant essentially followed Hume’s denial of natural necessity. When Kant speaks of necessary vs. contingent propositions in the context of the analytic-synthetic dichotomy, he is apparently referring to de dicta modalities. At least, mainly so; but perhaps, not exclusively so. It seems that he did not have a distinctive notion of the de re modalities.
Another critique of Kant’s list of the quantities and modalities is its one-sidedness. Unity, plurality and totality are the positive side of judgments: this one, some (indefinite) plurality of, and all X are Y. But there are the corresponding judgments this X is not Y, some X are not Y, and No X is Y to consider. Similarly, Actuality, possibility and necessity are the positive modalities. But there are parallel negative ones, namely: actuality, possibility and necessity of negation. It is, admittedly, legitimate to consider the negative cases as special applications of the positive ones, since the polarity is attached to the copula rather than to the quantity or modality.
However, it is also true that some people (notably, Hume) do not realize the logical connection between impossibility and necessity, and seek to appeal to the former while denying the latter. Moreover, we need to mention that possibility (the negation of impossibility) and possibility-not (the negation of necessity) can be conjoined, yielding the modal category of contingency. Similarly with regard to quantity. It is therefore justified to consider Kant’s lists of quantities and modalities as consisting of three pairs of categories each. This destroys the symmetry somewhat, but after all his heading of relations comprises three sets of two categories, so this is no big deal.
One more comment regarding symmetry – it could be argued that the positive and negative polarities (“qualities”) are included in the quantitative category of unity and the modal category of actuality. In other words, the set of categories called polarity could be viewed as redundant; or alternatively, the negative quantity and modality categories could be viewed as applications of the polarities to the quantities and modalities. In either case, the symmetry Kant sought is again broken. All this is said to point out the artificiality of his list.
(iii) With regard to the heading of relations, now. It is not at all obvious that this list is complete. Kant is influenced by Aristotle in thinking that the predicative form “X is Y” suffices to express all categorical relations. Aristotle built his list of categories by glossing over important formal differences (because his main goal was to develop his syllogistic theory), and Kant follows his lead in assuming a very limited bestiary.
For instance, just where in Kant’s list should positioning in space and time be classified? Aristotle treats place and time as predicates; so perhaps Kant thinks so too (although “is in” and “is at” are rather, in my view, relational copulas). Again, where is the process of comparison mentioned in Kant? Nowhere, yet comparative propositions like “X is more Z than Y” are crucial to distinguishing and classifying. Another set of categorical propositions crucial to human knowledge is that dealing with change of various kinds. I mean forms like “X gets to be Y” (alteration), “X becomes Y” (radical change), and “X evolves to Y” (evolution). Such propositions are not reducible to predicative ones, or at least not directly. Again, Kant does not classify volition and natural spontaneity in this context.
Clearly, categorical propositions are in fact a broad class (or genus) of many different kinds of propositions. The predicative form “X is Y” is just one species of categorical proposition. In fact, there are many more, and we would be hard put to list them all. Kant follows Aristotle in treating the class as ultimately homogeneous; but we cannot really reduce all other categorical forms to this simplest of categorical forms without important losses of meaning.
Kant makes the same mistake with regard to hypothetical propositions. He does not realize that each of the de dicta and de re modes of modality has its own set of hypothetical forms. He thinks of hypotheticals as solely if–then (logical) propositions, but some are distinctively different in intent: “in cases that–then” (extensional), “when–then” (natural), “at times when–then” (temporal) or “in places where–there” (spatial). These different modes cannot be reduced to each other, but must be treated separately if we are to truly reflect human thought. To each corresponds a mode or type of causation.
Moreover, Kant’s apparent ontological interpretation of disjunction as “community” seems forced to me. Some commentators explain this as “reciprocity of agent and patient”, but I fail to see what that has to do with disjunctive judgment. I would rather see in it the logical ground for classification (in the sense that a class is a disjunctive collection of members). Alternatively, disjunction is much used in inductive thinking, to list alternative theories or directions. Kant interpreted disjunction the way he did, simply because he could think of no other interpretation.
d. As we have shown, Kant’s errors of enumeration were mostly based on Aristotle’s errors of classification. Also, by insisting on a fixed number of twelve categories, Kant was making the same mistake Aristotle had made when insisting on precisely ten categories. He exacerbated this artificial difficulty by his scheme of four groups of three. He painted himself into a corner, making difficult any further development of his list, by himself as well as others. It would have been wiser for him to declare this heading forever open, allowing mankind to invent or discover new relations.
For if we consider what Kant was trying to do in drawing up this list of categories, it is clear that he missed out on a fifth heading, namely: Logical processes, comprised of Deductive arguments, Inductive arguments, and (if we insist on a third category for the sake of symmetry) Fallacies, i.e. arbitrary or irrational arguments.
Granting that Kant’s list of categories was an attempt, however gauche, to summarize the most basic tools of logic, his list is clearly too short. He has given attention to various static features of judgment (polarities, quantities and modalities), but has simply ignored the all-important dynamics of judgment, through which we rightly or wrongly justify our beliefs or infer new beliefs from them. I refer here to processes like syllogism, generalization, and the fallacy of accident, to give some obvious examples.
Thus, Kant ought to have listed fifteen rather than twelve categories. Note however that deduction and induction are not exactly mutually exclusive, though both refer to valid argument as against the invalid logical processes labeled fallacious. Induction may be viewed as the essence of the human method of knowledge; and in that case, deduction should be viewed as one of the tools in the wide array of inductive processes. Alternatively, deduction could be viewed as the essence of logic; and in that case, what distinguishes induction from it is that inductive reasoning yields two or more alternative conclusions, whereas deductive reasoning yields only one conclusion. Thus, these categories are closely related to each other.
It should be added that when I say that induction and deduction are all the means of knowledge available to mankind, I do not mean to exclude at the outset more mystical ways of knowledge, such as prophecy or meditative enlightenment. I do not, either, mean to include them, but only to keep an open mind. The point made here is that since induction includes all possible experiences, as well as use of logic, then if one has such mystical experiences, they would be accepted as new, additional data to be taken into consideration, and to be assimilated as well as one can by logic. There is no conflict in principle between the empirical-rational method and out of the ordinary experiences.
Note also that induction and deduction are the very means through which we validate induction and deduction and invalidate fallacious arguments. There is no circularity in saying so, if we keep in mind that these two methodologies are based on both the laws of thought and experience.
The science of logic as a whole, which attempts to list and justify all the arguments in these two branches, is not validated by an axiomatic system of any sort (the more geometrico) but built up from successive experiences and logical insights (i.e. particular instances of the laws of thought). To seek to call upon some other justifications than those is to fail to ask where those in turn would come from, ad infinitum. And one cannot reject logic because of that implied infinity, because this would mean one regards that rejection of infinity as a supreme principle not itself needing justification – which is self-contradictory. Thus, logic is solidly grounded and in no fear of reproof.
 The failure to understand this simple fact has led to much confusion in modern logic. Thus, Frege’s arbitrary analysis of ‘X is Y’ into two components: [X] and [is Y] – instead of into three components: [X], [is] and [Y] – led to the Russell Paradox (see my Future Logic, chapter 45). We see here that Aristotle’s inadequate theory of the categories was partly responsible for this confusion.
 Actually, two of the three categories in the last group are not named, but subdivided into two subcategories each.
 This is comparable to Descartes’ cogito ergo sum (deducing of “I am” from “I think”), or to the St. Anselm’s ontological argument (deducing the existence of God from the very idea of Him). Kant no doubt had these examples in mind when he concocted this deduction from the logical to the ontological.
 Kant’s theory of the categories involves further complications, such as the “transcendental deduction”, the “schemata”, and other intricate notions and arguments designed to justify his Copernican revolution. But I will not examine such details further here, other than to say these were attempts at rationalization of unreasonable proposals rather than credible justifications.
 I say “the” various contents or features, here, because both Aristotle and Kant considered their lists complete; but I do not wish to imply that I agree with them (i.e. I would prefer to drop the word “the”).
 Some (namely, Lesniewski and Carnap) have already noted this difference, calling Aristotle’s categories semantic and Kant’s categories syntactic.
 Note that “more”, “less” and “as much” are essentially both relational and quantitative, and they are not part of the predicate.
 As I have already mentioned, the relation of ‘causality’ here seems to more specifically intend causation, in view of its implicit reference to conditional propositions.
 I think it is wise to include fallacies as the third category under this heading, because people do not only reason correctly, in the way of induction and deduction, but also very commonly incorrectly. Such erroneous logical processes, or paralogisms, are sometimes intentional perversions of thought, to be sure; but very often they are expressions of ignorance of logic. Under the heading of fallacies I would include any failure to apply any of the laws of inductive or deductive logic.