Series Index

1. Introductions and the Introduction
2. Transcendental Aesthetic and Introduction to Transcendental Logic
3. Transcendental Synthesis
4. Transcendental Analytic, Part I

We now begin (at long last – summer is a time of uncertain schedules) Book II of CPR: The Analytic of Principles as the heading reads, having completed the section on the Analytic of Concepts that Nathan and I have divided between us in our reading.

Introduction

In the present section, Kant begins a discussion of the rules for judgment – the principles of understanding – as he designates them at A132/B171. The introduction to this section is interesting – in it, Kant argues that the abilities of the power of judgment (the ability properly to apply the rules that he will be outlining in this book) is not something that can be taught. He makes, in a footnote, a rather memorable statement to this effect, saying “A lack in power of judgment is in fact what we call stupidity, and for such a handicap there is no remedy.” (B173) He argues – not without a bit of crass bluntness – that if the power of judgment is present in an individual, then that person may be equipped through learning – but if that gift of judgment is lacking, there is little one can do to for that person. It is an interesting point, if put in a less than gracious way, but something which I think we all can agree is characteristic of people. Knowledge of facts, and even rules, as Kant discusses, is within the purview of virtually everyone – but such knowledge is quite different than what we might in modern educational parlance designate abilities in critical thinking.

In exploring this concept of the power of judgment, Kant argues for the power of transcendental, rather than general logic (which largely relies upon examples to teach the rules of judgment (A135/B174), since examples rarely give insight into the rules themselves, which insight is really necessary to strengthen one’s grasp on the tools necessary to develop new ideas and think most critically. The power of transcendental logic lies in the fact that (A136/B175) its approach involves reference to objects a priori – and because the approach is free of a posteriori references to specific objects, it is most broadly applicable, and objective. Kant’s discussion that follows concerns this transcendental doctrine of judgment, and is divided into two chapters, which I’ll treat in this post. The first considers the conditions in which pure concepts of understanding may be used – while the second – which is considerably longer than the first – discusses the principles of synthetic judgments which may be obtained under these conditions.

Chapter I : on the Schematism of the Pure Concepts of Understanding

At the outset of this chapter, Kant makes the important point (A137/B176) that objects must be homogeneous with the concepts under which they are subsumed, or categorized. Empirical concepts – such as that of a plate – are homogeneous with the pure mathematical concept of a circle or disk. He states this to distinguish pure concepts from empirical ones – and asks the question that naturally arises from this consideration: if pure concepts are heterogeneous from empirical intuitions (as he has demonstrated in prior discussions) then how can they be categorized (i.e. subsumed under categories – categories which apply to appearances) and thus be useful for application to real experience? Kant notes the importance of this question as he has before, and then reminds the reader that it is this very question that requires a transcendental doctrine.

In order to bridge the gap between pure concepts of understanding and appearances of objects to which these concepts should be applied, Kant posits transcendental schemata which are sufficiently homogeneous to both the pure concept and the appearances given to the understanding by the senses. These schemata are absolutely necessary in Kant’s thinking – and are not necessarily complicated ideas – rather they are simple, universal procedures which the imagination may use for providing concepts with images. He gives a very helpful illustration of one such schema (A140-141 / B179-180) : the schema of magnitude (or quantity) which he applies to the particular concept of a sequence of dots on a page. A sequence of five dots, he says, would be an image of the number five. One could also construct a similar set of 100 dots – or 1000, which he argues might hardly be surveyed (counted) to compare with the concept of 1000. (I note here that it seems Kant has little faith in his counting ability – let us say 10 billion instead, if we could make that many dots in our lifetime. Hint: we couldn’t, at least manually. Five dots a second for 60 years would be required to make 10 billion dots).

His point with this rather silly example (that I’ve made sillier) is that one can think any number of numbers – of immense magnitude – and constructively use them in further synthetic thinking. All of them can be subsumed under a universal schema – or procedure – connected to magnitude or quantity.

Such schemata as these – and he lists at the end of this chapter several – give a basis for pure sensible concepts. Individual images, or appearances, of things like particular triangles, or particular dogs, are inadequate to the universal concept of triangle- or dog-ness. The universal a priori concept is much broader than individual examples or instances. Our minds are powerful enough, though, to construct such universal empirical concepts that subsume all such particulars. Again as I think over these concepts, I am reminded of Platonic forms – though I think it’s probably dangerous to identify Kant’s ideas with those of Plato too closely.

Kant closes the chapter with a discussion of particular schemata which will illustrate this idea better than what he warns would be a “dry and tedious discussion of what is required for transcendental schemata of pure concepts of understanding as such.” (A 141-142 / B 181-182). These schemata are the schema of magnitude (as already discussed); of reality (quantity of something existing in time); of substance (the permanent essence of the real existing in time); of causality (the concept of one event following necessarily upon another); of community, or interaction (simultaneous existence of two objects or events); of actuality (the existence within a determinate time interval); and of necessity (the existence at all times). These schemata will be reflected in the topics taken up in Kant’s discussion of the Synthetic Principles of understanding which can be found at the end of Chapter II.

Chapter II – System of All Principles of Pure Understanding

In this chapter, Kant seeks to demonstrate the principles of pure understanding in sequence. If we recall the consideration that began the discussion in CPR, Kant is concerned to demonstrate the possibilty of synthetic a priori judgments. Again, for the sake of refreshing the idea, Kant made the point that nobody would dispute the possibility of analytic judgments a priori – or synthetic judgments grounded in experience/empirical observation, a posteriori. Again, analytic judgments are those in which one concept is derived from another – in some sense the second is contained in the first, as Kant argues in book I. Synthetic judgments are those in which two cognitions are linked – and the resulting concept is contained in neither of the prior cognitions. The question on his mind is that of synthetic judgments made a priori (pure concepts, disconnected from empirical observation, yet synthetic and not analytic), since synthesis of empirical concepts is rather straightforward to understand.

In this chapter, he reminds us of this distinction in the first two sections, wherein he establishes a key principle for analytic and one for synthetic judgments – before further elucidating the nature of synthetic thought. In carrying out this discussion, as Kant indicates in the introduction to the chapter, he will only make reference to principles referring to the categories of pure understanding (discussed in Book I, Section III).

Section I and II: Supreme Principles of Analytic and Synthetic Judgments

In these two brief sections, Kant establishes simple principles which underlie all Analytic and Synthetic Judgments.

The key principle that Kant specifies as underlying all analytic judgments is the law of non-contradiction, which he ably describes in this section. A and not A cannot possibly be true of an object simultaneously. A wet blanket cannot be simultaneously dry. An empty box cannot simultaneously contain 385 Froot Loops. The nature of this principle concerns analytic judgments because of this requirement of simultaneity in the definition Kant gives – We are considering one concept and its contradiction. The original concept and the secondary are thus interrelated – the one is contained in the negation of the other.

In section II, Kant names the key principle for synthetic judgments – the necessity of the possibility of experience. As Kant puts it, “Every object is subject to the conditions necessary for synthetic unity of the manifold of intuition in a possible experience.” (A158/B197) He is in other words stating the requirement of objective reality – and the principle is that such is only possible if it is possible to experience the objects of our thought.

Section III: Systematic Presentation of All the Synthetic Principles of Pure Understanding

Kant’s interest as noted above is to explicate the synthetic principles of pure understanding that underlie a priori synthesis. His presentation centers around (as is his wont) a four-fold division that is often arranged in a diamond shaped diagram: Axioms of Intuition, Anticipations of Perception, Analogies of Experience, and Postulates of Empirical Thought as Such. The rest of this chapter – this section and the fourth – is consumed by Kant’s discussion of these principles. The first two of these principles: Axioms of Intuition and Anticipations of Perception are treated relatively briefly.

The Axioms of Intuition

In the first, Kant deals with mathematical categories – the categories of quantity, whether of extension in space, duration in time, which involve concepts of unity, plurality, and “allness”, as described in Book I. His unifying principle for these concepts is that “All intuitions are extensive magnitudes” (A160/B200). The related idea here is that all intuitions – as he noted in Book I – must be thought in terms of a synthesis of space and time. The modifier “extensive” refers to the fact that presentations of parts make possible the presentation of the whole which is made up of the parts.

One of the interesting distinctions Kant makes in this section is that between axioms (universally applicable propositions) and procedural rules. He argues that a proposition such as 5+7=12 is, while synthetic, not axiomatic – it is a specific case. On the other hand, a proposition such as the following – that a figure constructed by joining two line segments with a third, such that the sum of the lengths of the first to is greater than the length of the third, one will produce a triangle – is an axiom. An innumerable multitude of specifically observable triangles might be produced according to that axiomatic principle.

This first principle makes possible the connection between intuition and real external appearances – and thus connects pure concepts to reality (which as we’ve noted is critical).

The Anticipations of Perception

Here Kant deals with the categories of quality (as opposed to quantity): reality, negation, and limitation. He argues here (A166/B208) that “in all appearances the real that is the object of sensation has intensive magnitude”. What he means here is that magnitude is a measure of degree – degree of the sensation received. A red light is perceived – the appearance that our eyes receive – in degrees. We may fully perceive its light – or for various reasons our minds might be provided with only a partial perception of the fulness of its red intensity… or we might simply imagine its red intensity (i.e. the presentation may be purely intuitive). The range of the appearance runs from “full reality” as it were to “negation”. He seems here to be arguing (it’s not completely clear to me that I have this down correctly) that appearances may be built up – from zero to some maximum degree – step by step (just as the parts of an object – or the parts of a concept – maybe synthesized into a whole).

Related to this idea, Kant claims that because the degree of receptivity by sensation of any object may be reduced to zero, one cannot – on the basis of appearances – conclude that (for instance) empty space can exist. He’s taking on here the ideas of Newton, Boyle, and others, of the absolute reality of empty space – though I’m not sure he’s entirely on the right track. I’ll have to mull this one over a bit more.

The Analogies of Experience

By far the longest part of this section is devoted to what Kant terms Analogies of Experience. Here he deals with the category of relation. He argues here that “Experience is possible only through the presentation of a necessary connection of perceptions.” In discussing experience, Kant continues to assert the fact that objects, perceived and presented to our minds, require the a priori concept of time in order to link them together in any meaningful way. At the outset of this section, he describes the MODES of time: permanence, succession, and simultaneity. All of these are a priori concepts, necessary for us to even begin to perceive and conceive of objects as being in time.

A side note – it would certainly be interesting to hear how Kant would react to modern physics – where ideas of simultaneity are broken: NOT universals. I would have to think a little bit about what that reaction might be – the reaction to special relativity as it is actually conceived, not the sci-fi version of it… might be worth another blog post at some other time. Stay tuned.

First, Kant treats what he denotes the Permanence of Substance. His claim here is that the reality of an object – its essence – it’s substance – is neither created nor destroyed, but may be changed. It is in this sense permanent despite the changes one might observe. An apple, he would argue, when it rots, does not disappear – only its form changes. The MATTER is not gone, only its form is different. This sounds an awful lot like LaVoisier’s principle of the conservation of mass, which was codified first at the eve of the French Revolution (another interesting side note – go check out what happened to LaVoisier – the father of modern chemistry – because of his sympathies and activities at the time of the Reign of Terror). While it is similar in nature, LaVoisier didn’t publish his theory of the conservation of mass (matter) until two years after the second edition of CPR… would be interesting, though, to explore connections between the two, or common progenitors in the matter of matter.

Interestingly Kant treats this as an a priori concept. In a note scrawled in his working copy of manuscript A (the 1781 edition), Kant asks concerning one who argues for the permanence of substance, “From where does he know that? Not from experience.” Very interesting indeed – since LaVoisier’s work in fact was exactly concerned with the empirical proof of the permanence of matter in chemical reactions.
Second, Kant deals with Succession – here, more plainly, we might call this principle the Law of Cause and Effect. “All changes occur according to the law of the connection of cause and effect.” Here again he is dealing with changes of state – just as he was in the first part. Now, however, he seems to argue that changes do not occur out of the blue (so much for the randomness associated with quantum mechanical processes, which empirically cannot be connected to anything by way of causal relation) but that all changes are initiated due to a prior cause (familiar ideas, Aristotle?). He seems certainly to argue here for a broad determinism – whether this is characteristic of his thought I do not know, and will have to bow to the Kant scholars out there (or to Nathan, whose experience with Kant far outstrips mine). Certainly he argues this for our own empirical presentations – whether or not he argues it in terms of the reality of things.

Finally, Kant discusses the third analogy: Simultaneity according to the Law of Interaction, or Community. His principle is stated in this way : “All substances, insofar as they can be perceived in space as simultaneous, are in thoroughgoing interaction.” On the face of it this is a rather broad and sweeping claim – but it is nuanced. He discusses the possibility of substances being isolated – so that one cannot influence the other – but in a sense then, he argues, they cannot empirically be presented as existing simultaneously. I’m interested in exactly what he means by that – but it needs more processing time. I wonder if I, as the observer, in perceiving each of the objects in question, am in Kant’s mind the means of interaction between the two? Can he mean, really, that in the absence of anyone observing two objects that do not influence on another are still to be thought of as being in interaction, if they are to be deemed as existing simultaneously? This seems odd to me.

*The historian of Physics Max Jammer has, in fact, written an entire volume on the ideas of simultaneity (http://www.amazon.com/Concepts-Simultaneity-Antiquity-Einstein-Beyond/dp/0801884225) wherein Kant looms large. Reminder to self: check out this book.

Analogies of Experience: Summary

These analogies of experience, Kant says, are principles for the determination of the existence of appearances in time – relations in terms of magnitude (duration), succession (as sequential), and in relation to each other (simultaneity). Without these principles, he argues, empirical determination of objects as in time would be impossible or have no validity – we would have no way of connecting our intution to real objects.

The Postulates of Empircal Thought as Such

We come now to the final section of this rather lengthy chapter. Here, Kant treats the principle connected to his fourth set of categories from Book I – that of modality. He is concerned here with the possible, the actual, and the necessary. His three postulates state that what is in agreement with formal conditions (previously outlined) of experience is possible; that which coheres with the material conditions of experience (sensation) is actual; and that whose coherence with the actual is determined according to universal conditions of experience is necessary. (B266) These, as Kant notes, don’t add anything new, per se, concerning the determination of objects, but rather simply explicate the use of concepts of possibility, actuality, and necessity in terms of empirical judgment. (B267).

When we speak of possibility, actuality, and necessity here – again – we should be careful to evaluate what Kant is in fact saying, and what he is not saying.

With regard to possibility, Kant here is engaging in hypotheticals only – the possibility of objects as conceived of using pure concepts, not empiricism (for the establishment of the possibility of an object can be empirically determined by observation, and none of the principles of pure understanding are relevant). Kant actually makes this point at B271. Example: the possibility of a triangle can easily be established by the physical construction of an example. However, it is possible also to establish the possibility of the concept of triangle simply using pure intuition.

In speaking of the determination of actuality of an object, here clearly sensation is required – the actual existence of an object, as Kant notes at A225, certainly requires perception of the object.

In his discussion of necessity – surely the most complex of these subjects. Again, since actual existence is required for an object to be determined to be necessary, we again are dealing only with objects which are perceived (or could be). As he writes, “the necessity of existence can never be cognized from concepts, but always only from the connection with what is perceived, and according to universal laws of experience.” (A227) He goes on to argue that that which is deemed necessary must follows according to the laws of causality which he outlined previously.

At the tail end of this discussion, Kant closes with several generally applicable transcendent principles: (A 228-A229) 1) Nothing arises through blind randomness. 2) No necessity in nature is a blind necessity. 3) There are no leaps in the series of changes an appearance undergoes. 4) There is no gap between two appearances.

I really need to noodle on these four ideas for a bit here. These four ideas follow from the discussion Kant has given us concerning the analogies and the postulates here presented at the end of this section. What exactly is he claiming? First it certainly seems that he would argue against the modern physical notion of the random nature of things like radioactive decay or spontaneous mutations. He is wedded sufficiently to a cause and effect model that the probabilistic nature of decays or of mutations, which empirically seem to have no cause whatsoever, that I think he would argue that we who accept a probabilistic model at the quantum level are missing some hidden variable (this was tried in the 50s and 60s and found wanting by David Bohm) that dictates such decays. Our perceptions would simply be insufficient, in Kant’s eyes, to detect the cause which must be there. Interestingly in points 3 and 4 above he argues for a distinct gradualism (something like that which geologists of his day were arguing for contrary to the catastrophism that ruled the day in geology. In light of the lateness of my posting this contribution, I think I’ll hold off in musing out loud about these four points for now… but certainly what Kant is thinking of here has direct application to the science of the 19th and 20th centuries which followed…. fascinating!

Until next time,

Todd