Lectures on Kant’s CRITIQUE OF PURE REASON

These notes (which I have divided into lectures for ease of reference) are intended to offer a reading of the Critique of Pure Reason, which dwells upon the main themes of Kant’s metaphysical and epistemological thought. The content of each lecture is largely provisional and far from complete due to the fact that Kant’s text presents very condensed arguments nearly in every single page. Nevertheless, I hope these lectures will be of use for students who approach Kant’s thought for the first time. There are some gaps here and there that need to be filled. I’ll add Lecture 10 as soon as possible.

My preferred translation of Kant’s Critique is Guyer-Wood’ edited by Cambridge. I strongly recommend it. However, since I refer to the text using the standard numeration of original Critique editions (1781 and 1787, A and B respectively, followed by page number), it is possible to opt for other translations such as those of Pluhar (edited by Hackett) or Kemp Smith (edited by Cambridge). I do not recommend any other translation.

Introductory works

Burnham D., Young H., Kant’s Critique of Pure Reason. An Edinburg Philosophical Guide, (Edinburg, 2007)

Buroker J.V., Kant’s Critique of Pure Reason. An introduction, (Oxford, 2006)

Gardner S., Kant and the Critique of Pure Reason, (London, 1999)

Advanced works (for who is interested in looking at certain topics in more depth)

Allison H., Kant’s Transcendental Idealism. An Interpretation and Defense (Yale, 2004)

Bird G., The Revolutionary Kant. A Commentary on the Critique of Pure Reason, (Chicago, 2006)

Guyer P. (ed), The Cambridge Companion to Kant’s Critique of Pure Reason, (Cambridge, 2010)

Schedule

Lecture 1, Preface A/B and Introduction B. Reading: A vii-xxii; B vii-xliv; B 1-30.

Lecture 2, Aesthetic. Reading: B 33-73.

Lecture 3, Analytic of Concepts I. Metaphysical Deduction of the Categories. Reading: B 74-116.

Lecture 4, Analytic of Concepts II. Transcendental Deduction B. Reading: B 116-168.

Lecture 5, Analytic of Principles I: Schematism (ch.1); Axioms and Anticipations (ch.2a). Reading: B 169-218;

Lecture 6, Analytic of Principles II: Analogies and Postulates (ch.2b). Reading: B 218- 273;

Lecture 7, Analytic of Principles III: Phenomena & Noumena (ch.3). Reading: B 274-315;

Lecture 8, Dialectic I: Introduction (book 1), Paralogisms (book 2, chapter 1). Reading: B 396-432;

Lecture 9, Dialectic II: Antinomies (book 2, chapter 2). Reading: B 432-488;

Lecture 10, Dialectic III: the Ideal of Pure Reason (book 2, chapter 3). Reading:

LECTURE 1: Preface A/B and Introduction B. (A vii-xxii; B vii-xliv; B 1-30)

Even if Preface A emphasizes the character of metaphysics that render it a “battlefield”, both prefaces share the same structure in turning on the same chief question: how a knowledge independent from all experience can be possible.

Let’s start with Preface A. Here Kant famously argues for the dramatic situation of metaphysical knowledge caused by endless battles between dogmatists and skeptics. This continuous state of war between opposite factions leads to dissatisfaction, or in Kant’s own words “indifferentism”, typical of the present popular philosophy.

That situation might be seen as a dramatic one, and it is. However, Kant points out a positive aspect in the idea that extreme skepticism might be a mark of maturity of the time, that “our age is an age of criticism” (A xi note) and only signals the “power of judgment” (A xi)…

“…which demands that reason should take on anew the most difficult of all its tasks, namely, that of self-knowledge, and to institute a court of justice, by which reason may secure its rightful claims while dismissing all its groundless pretensions, and this not by mere decrees but according to its own eternal and unchangeable laws; and this court is none other than the critique of pure reason itself” (A xi-xii).

But what is “critique”? what does it mean? What is it concerned about? In Preface A Kant delivers a couple of definitions:

1. Court of justice that wants to establish the “rightful claims” of reason;2. A critique of the faculty of reason itself which has to do with cognitions independent of all

experience;

“…but a critique of the faculty of reason in general, in respect of all the cognition after which reason might strive independently of all experience, and hence the decision about the possibility or impossibility of its source, as well as its extent and boundaries, all, however, from principles” (A xii)

3. “An inventory of all we possess through pure reason” (A xx); (self-knowledge of reason itself);4. It must lead to the “decision about the possibility and impossibility of a metaphysics in general”;

The clearer statement on the matter is the following: “What and how much can understand and reason cognize free of all experience?” (which is opposed to the rather different one “How is the faculty of thinking itself possible?” A xvii). Notice that the independence from experience clearly refers to the a-priori character of cognition which Kant associates in this text to “certainty”, “absolute necessity” or “apodictic certainty” of cognitions (see A xv).

Now consider Preface B.

- starting point is “the secure course of a science”; Kant gives here more emphasis to the development of sciences.

- what is science or scientific cognition? Science is a priori cognition as opposed to empirical one. Some examples: logic, mathematics, natural sciences. Is metaphysics following the same “secure course” of other sciences? Of course not (remember metaphysics is a “battlefield”, the typical metaphysical movement is “groping”).

- Baconian inspiration 1. Remember that Kant takes his motto from Bacon, a partisan of the cause of modern science. What Bacon’s Instauratio Magna merely anticipated (a general renewal of thought), Kant actually accomplishes with regard to metaphysics.

- Baconian inspiration 2. Let’s try an experiment: “Copernican Revolution” (“this experiment succeeds…” B xviii). This experiment has consequences, some are positive, others negative.

Positive: it allows us to justify a priori knowledge (and hence science) within reason;

Negative: it restrict the use of theoretical reason within the boundaries of (sensible) possible experience (end of B xix)

Look at some other effects of the experiment:

The problem of the “unconditioned” takes now a rather different shape: the “metaphysical contradictions” traditionally attached to it disappear but we must admit the notion of “things in themselves” (B xx e xxvi).

Traditional metaphysical problems, such as the existence of God, freedom and the soul, can’t be resolved on the ground of theoretical reason (which is limited to possible experience), but solely in the practical domain (primacy of the practical, in opposition to the risks of dogmatism, see B xxv e xxviii-xxix, xxx etc.).

- return to the question of Preface A: what is critique? A positive effect of Copernican Revolution is related to the definition of Kant’s enterprise. “Critique” is the self-knowledge of reason, “a treatise on the method” (B xxii), a “catalog” (B xxiii), the critique of reason must remain “within reason” (see further comments section below).

Introduction B

The basic question of the Introduction are two: what are experience? What are synthetic a priori judgments?

- Kant’s “metaphysics” or “critique” is a theory of experience: “to work up the raw materials…” (B1, see also the definition of experience in A1). To anticipate, experience will turn out to be a structured process involving both sensibility and understanding, each of which has different roles.

- Kant employs some conceptual distinctions all referred to cognition and its ground, i.e. judgment: pure/empirical, a priori/a posteriori, analytic/synthetic (plus some new metaphysical distinctions appearances/things in themselves, transcendental/real).

- a priori / a posteriori is a distinction concerned with the source of our knowledge, independent or dependent upon experience. It derives from medieval commentaries on Aristotle’s Posterior Analytic (see Ockham, Summa Logicae III; 2, 17).

- analytic / synthetic judgments: is concerned with the legitimation and potential expansion of knowledge.

Judgment in the logical sense is an assertion or proposition that connects a two representations, the subject S and the predicate P through the copula, is/are, in a unity, “S is P”. so, for example, “body” and “heavy” are combined in “All bodies are heavy”.

In the case of analytic judgments, the ground of the connection lies in the subject in which the predicate is already, sometime “covertly”, contained (B 10). So for example we can derive by analysis from the concept of “body” those of “extension”, “impenetrability”, “figure”, and so on. (B

12). Notice that the truth of such assertions is decided by the semantic rule of language not by experience. Think for example another case: “a triangle is a figure with three angle” is a true judgment or proposition, but its true does not require an inspection of experience.

Synthetic judgments are ampliative in the sense that they go beyond the knowledge already contained in the subject. “Judgments of experience, as such, are all synthetic” (B 11)

A priori analytic (necessity, universality) explication merely logical truths RATIONALISM

A posteriori synthetic (contingency) amplification empirical judgments EMPIRICISM

If this scheme were exhaustive, science would be impossible. But we know that at least logic, math and physics are actually “sciences”, they “are actually given” (B 20), while metaphysics is not (see the general problem B 19). So, a new kind of judgment must be possible: synthetic a priori judgment.

A priori analytic (necessity and universality) clarification

A posteriori synthetic (contingency) amplification (but without certainty)

A priori synthetic (necessity and universality) amplification (with certainty) = SCIENCE

How are synthetic a priori judgments possible? Is the core question of the entire Critique. If they are possible, then, are they also valid in the metaphysical domain?

Famous examples of synthetic a priori judgments by Kant: “Everything that happens has its cause” (B 13) and “7+5=12” (B 15), “in all alterations of the corporeal world the quantity of matter remains unaltered” and “in all communication of motion effect and counter-effect must always be equal.” (B 17).

- transcendental: is one of the most terms of the entire Kant’s Critique, one that can be easily misconceived. “Transcendental” (a term coming from medieval tradition, Wolff and Baumgarten) has nothing to do with a world beyond the senses. We can distinguish at least two main senses of the word:

1) the first is connected with the concept of the synthetic a priori: “I call all cognition transcendental that is occupied not so much with objects but rather with our mode of cognition of objects insofar as this is to be possible a priori” (B 25).

2) according to the second, the critique of knowledge has two parts (that we will encounter both in Aesthetic, Analytic and Dialectic), a metaphysical part and a transcendental part more properly.

Metaphysical: shows THAT certain elements have non-empirical origin

Transcendental: explains HOW these elements can relate a priori to object of experience

through that twofold examination, elements receive a proper justification or “deduction” (we find a deduction not only in the Analytic, i.e. the famous deduction of the categories, but also in the Aesthetic and Dialectic; in the Aesthetic it is called “exposition”).

- at the end of the introduction Kant sets out the “division of the transcendental philosophy”. He relies on “two stems of human cognition” (B 29), sensibility and understanding, which in turn will constitute the subject matter of Aesthetic and Logic (Analytics and Dialectics).

Further comments on Kant’s critical project

- Baconian inspiration 3: Kant shares Bacon’s view that the sciences:

have been characterized by countless disputes but very few achievements;

achievements can only lie in the genuine progress of knowledge;

we must seek out an entirely new method;

human mind must be liberated from previous errors;

we must cease to disparage the role and evidence of the senses.

This means, according to Kant, making an experiment of reason itself and acknowledging that we possess two faculties, understanding and sensibility, and therefore we need to seek a middle path between empiricism and rationalism. Bacon’s reproaches against universities for marrying “the mind of man” to “vain notions and blind experiments” (Works, VIII: 125) is echoed by Kant’s motto “thoughts without content are empty and intuitions without concepts are blind” (B 75).

Vocabulary Note. The origins of Kantian terminology.

perception, intuition, pure = in Locke’s Essay and Leibniz’s Nouveaux Essais;

category, transcendental, analytic, dialectic = Aristotelian tradition of German philosophy;

idea = Plato

amphiboly, antinomy, paralogism = handbooks of the time (e.g Meyer and Zeller)

critique = ars critica of Cicero (a central theme of Enlightenment, served to designate the capacity to distinguish between true and false). Kant’s derives the image of “tribunal of truth” or “trial” from the article “Critique” in the Encyclopédie (IV: 494): “appeler au tribunal de la verité”.

It is worth considering the meaning of “critique” in more detail.

- Kant’s critique is directed upon “pure reason”, i.e. reason itself (we already noticed that). Reason assumes here five different (self-referring) roles: 1) it is the accused, 2) the prosecution 3) the defense 4) the judge 5) and who enacts the law, at the same time.

- the judicial critique of the higher human faculty breaks down in two main part: I) it secures the justified claims of reason in view of a legitimation of scientific knowledge (Aesthetic, Analytic); II) it repudiates the groundless assumptions of reason by unmasking the errors of traditional metaphysics (Dialectic). (For a more comprehensive general partition of the Critique see the chart attached).

AestheticAnalytic (logic of truth)

Preliminary examination of traditional metaphysical disputes.In opposition to empiricism, it is discovered conceptual foundations, independent of experience, which demonstrate, against skepticism, that objective knowledge is possible.In opposition to rationalism, that knowledge is restricted to the realm of possible experience.

Dialectic (logic of illusion) It pursued the trial of metaphysics: in transgressing its proper limits, reason loses itself in fallacies, antinomies and failed demonstrations of the existence of God. Reason has no access to objects that transcend experience and is incapable of

acquiring any knowledge in this regard (Good, freedom, soul)

Doctrine of Method Philosophy is said to be “the science of the relation of all knowledge to the essential interests of reason” (B 867). It emphasizes the practical interest of the enterprise (e.g. cosmopolitism, moral interest, overcoming of skepticism and relativism, etc.)

- What is then philosophy according to Kant? We can point out four levels of philosophical enquiry:

1) is concerned with the basic pure a priori elements of experience (theory of human experience): SPACE, TIME, CATEGORIES of understanding (remember the definition of “critique” as “inventory” or “catalog”)

2) new transcendental theory of science which exhibits the a priori conditions of possibility of science itself (the aforementioned elements)

3) confronts with the typical metaphysical objects (soul, God, freedom) in a critical way, and supplements the theory of experience with the “regulative employment” of IDEAS.

4) reflects upon the limits of philosophical work stated in points 1, 2 and 3 (meta-philosophy).

LECTURE 2: Transcendental Aesthetic (B 33-73)

Transcendental Aesthetic is the study (science) of the a priori condition (principles) of sensibility (B 35). Kant starts with some definitions which contribute to set the stage of following arguments.

Sensibility = receptivity, “the capacity to acquire representations through the way in which we are affected by objects” (B 33), “objects are given to us by means of sensibility” (B 33). It is the name of a faculty generally conceived.

Intuition = the way in which a cognition “relate immediately to objects” (B 33). It entails “intentionality” or directedness toward the “singular”.

Sensation = “the effect of an object on the capacity for representation, insofar as we are affected by it..” (B 34). It corresponds to matter and is indeterminate.

- Kant points out a crucial distinction between empirical intuition, which is related to sensation, and pure intuition which is not and is independent from experience. Appearances are constituted by two elements:

Matter = that which corresponds to sensation;

Form = “which allows the manifold of appearances to be ordered in certain relations” (B 34). Even if, we’ll see, this ordering of the manifold in the case of sensibility is not yet conceptual.

According to Kant, the former is given to us a posteriori, while the latter is already in the mind a priori. He gives an argument for this distinction:

“Since that within which the sensations can alone be ordered and placed in a certain form cannot itself be in turn sensation…” (B 34)

This means that even sensation or perception are structured experiences, composed by a posteriori and a priori elements, which in principles may be considered separately (and studied separately). Notice that all intuitions are empirical (because they are all related to objects) but they all have an a posteriori element (matter) and an a priori element (form).

So, there is a pure form of intuition that has to be kept distinct from the matter of intuition that is always known or given to us a posteriori. Kant gives another argument for that distinction:

“So if I separate from the representation of a body that which the understanding thinks about it, such as substance, force, divisibility, etc., as well as that which belongs to sensation, such as impenetrability, hardness, color, etc., something from this empirical intuition is still left for me, namely extension and form. These belongs to the pure intuition, which occurs a priori, even without an actual object of the senses or sensation, as a mere form of sensibility in the mind.” (B 35)

Transcendental Aesthetic is the study of what remains after having discarded understanding (and then it remains empirical intuitions) and the matter of sensation (and then it remains pure forms of intuition). Pure forms of intuition are SPACE and TIME (B 36).

The Aesthetic is dedicated to SPACE and TIME. The crucial question here is: granted that space and time cannot be intuited directly (B 37), what are they?

- the exposition follows the distinction between “metaphysical exposition” and “transcendental exposition” (see the previous lecture for some comments on this distinction). The former is intended to show “that which exhibits the concept as given a priori” (B 38), while the latter contains “the explanation of a concept

as a principle from which insight into the possibility of other synthetic a priori cognitions can be gained.” (B 40).

- the two metaphysical expositions of space and time state that SPACE and TIME:

1) are not empirical concepts drawn from experience, but are a priori presuppositions of experience;

They cannot be derived from abstraction from experience because they “already underlie” all outer or inner sensations (B 38, cf. B 46).

If I perceive a chair, for example, as external to me besides the table, I employ the concepts of “chair” “myself” and “table” together with the representation of something “outside” me (SPACE) within which me, the chair and the table can entertain relations: “In space their form, magnitude, and relation to one another is determined” (B 37). “Outside me” means “being in a different place from myself”. The same for TIME in reference with the concept of succession.

2) are necessary a priori representations that ground a) outer intuitions (space is the outer sense), b) all intuitions, respectively (time is the inner sense that is presupposed by all intuitions; see for the primacy of time B 50);

“One can never represent that there is no space, although one can very well think that there are no objects to be encountered in it” (B 38f). “In regard to appearances in general one cannot remove time, though one can very well take the appearances away from time” (B 46).

If we think away every objects that is actually present from space and time, we remain with a medium, a pure form of intuition, an antecedent unity.

3) are not discursive, or general concept of relations of things, but pure intuitions;

SPACE and TIME furnish certain unity to multiplicity, but not a conceptual one. The unity of SPACE and TIME is not a universal in relation to a particular, but a whole in relation to its part. For example, a segment is not a particular case of the universal concept “segment”, but is a part of the SPACE as a whole.

4) are both represented as infinite magnitudes, but are both unique (there are not many spaces or many dimensions of time), hence are intuitive in character. They do not contain an infinite number of representations under them, but an infinite number of objects within them.

- the two transcendental expositions state that:

1) SPACE, as a priori form of outer intuition (contiguity), grounds the possibility of Geometry;

2) TIME, as a priori form of inner intuition (succession, simultaneity), grounds the possibility of the concept of alteration or motion, and so the possibility of Arithmetic.

- all these statements serve as a basis of the discussion of a central assertion related with Kant’s Transcendental Idealism:

SPACE and TIME have empirical reality and, at the same time, transcendental ideality.

Further comments on the Aesthetic.

- the rehabilitation of sensibility. “without sensibility no object is given to us” (B 75), “at which all thought as a means is directed as an end, is intuition” (B 33). “Without sensibility no object would be given to us, without understanding no object would be thought. Thoughts without content are empty, intuitions without concepts are blind” (B 75).

Sensibility is no longer conceived as an obscure and deficient source of knowledge (in Leibniz-Wolffian tradition sensibility is a kind of indistinct form of knowledge in opposition to intellect which gives us distinctness), but is an independent and indispensable source of knowledge (B 61f). Kant’s here challenges the arrogance of the conceptual.

Sensibility in no longer subordinated to intellectual cognition, in fact, it is through sensuous intuition that cognition relates immediately to objects: “all thought as a means is directed” (B 33).

Such a rehabilitation serves to overcome the opposition between empiricism and rationalism (B 327):

1) The raw material of sensuous experience in not independently produce by the subjects.2) Sensuous intuition does not suffice to produce cognition. It is necessary the

intervention of the formative and unity-bestowing activity of the subject. Nonetheless, the indeterminacy of sensation is apt to receive determination from the understanding.

3) AGAINST RATIONALIMS: indispensability of sensibility / cognition is always intrinsically bound to empirical sensibility / mathematics is coordinated with sensibility.

4) AGAINST EMPIRICISM: senses provides only raw materials that are in need of the determination provided by the understanding / a priori elements are even in sensibility not only on the part of understanding / the character of mathematics is independent of experience. “Without sensibility no object would be given to us, without understanding no object would be thought. Thoughts without content are empty, intuitions without concepts are blind” (B 75).

5) It restricts the validity of cognition to possible experience, i.e. to appearances (phenomenal character of all human cognition).

- the Aesthetic is the first decisive step in the path of the Copernican Revolution; it is intended to prove the viability of the experiment presented before as a hypothesis (B xix).

The Copernican Turn is presented as a hypothesis in the Preface B, in the Aesthetic (and subsequently in the Analytic) as a confirmed thesis; then it is used as a premise for the arguments deployed in the Antinomies.

- the alleged priority of TIME over space. Since the subject is aware of every representation of outer sense, the latter is simultaneously a representation of inner sense as well (B 50f).

However, Kant does not subordinate space to time. In fact, consider two related affirmation: 1) outer intuitions will turn out to be required for the objective reality of the categories (B 291); 2) merely inner consciousness cannot ground self-knowledge (B 293f).

In addition, SPACE fulfils five important tasks:

1) is required for the external shape and extension of things;

2) is required for the individuation of things (remember that intuition provides objects as singulars)

3) is required for objectivity of knowledge (it furnishes the proper material for inner intuition B 67)

4) even for self-knowledge

5) we can represent temporal order to ourselves on analogy with spatial sequence: “under the image of a line, which we draw” (B 156)

- transcendental idealism clarified.

It represent a “revolution in the way of thinking” (B xi), “we can cognize of things a priori only what we ourselves have put into them” (B xviii). Metaphysics turns out to be a theory of cognitive subjectivity instead of a theory of supersensible entities.

Objectivity derives from the knowing subject, not from the different particular features of empirical subjects, but from pre-empirical elements that belong to theoretical subjectivity in general.

This brings us again to the distinction between appearances and things in themselves.

APPEARANCES- are objects dependent on the knowing subject

1) we can acquire knowledge by means of certain subjective pre-empirical accomplishments.2) subjectivity is dependent upon the sensuously given (understanding alone is not sufficient to provide knowledge)

THINGS IN THEMSELVES- are independent of the subject- can be thought, but not known

1) precede the threshold of sensation –the unknown impact that gives rise to sensation.2) stand beyond the understanding and its merely conceived objects (soul, freedom, God)

Lecture 3: Transcendental Analytic I. Metaphysical Deduction of the Categories (B 74-116)

- Logic occupies the central, and most ample, part of the Critique. “Logic” is for Kant a sort of theory of thought, not a general theory of formal inferences as is conceived today. Kant understands logic as the analysis of the understanding and its content, which has to reveal the criterion for determining the possibility of all knowledge and its respective limits.

It is worth remarking that Kant’s logic is not an ORGANON of sciences, that is, the logic as Kant conceives of it, cannot be an art of scientific discovery, but only a CANON for the correct use of the understanding.

- the articulation of logic follows the German tradition of Aristotelian thought (e.g. J.H. Lambert, in his Organon [1764] and Architektonik [1771] already stated all of the types of judgments distinguished by Kant in his table of judgments): the understanding, the power of judgment, reason and their corresponding logical objects: concepts, judgments and inferences (B 169).

Analytic: doctrine of pure concepts of the understanding and synthetic a priori judgments

Dialectic: doctrine of ideas and rational inferences

- Logic as the pure analysis of the understanding and its content, pure concepts, mediates between rationalism and empiricism. While rationalism considered concepts as innate and already completed collection of powers, and empiricism as simply acquired, Kant treats concepts as dispositions or potentials.

- Kant’s articulation of logic is divided in two main parts: GENERAL logic and PARTICULAR logic (B 76-79):

GENERAL logic = contains “absolutely necessary rules of thinking”, it “abstract from all content of cognition”, “it has to do with the mere form of thinking”

PARTICULAR = “rules for thinking about a certain kind of objects”

GENERAL logic divides in PURE and APPLIED:

PURE = it “abstract from all empirical condition under which our understanding is exercised” (from the influences of the senses, from the play of imagination, the laws of memory, etc.)

APPLIED = “it is directed to the rules of the use of the understanding under the subjective empirical conditions that psychology teaches us”; “it deals with attention, its hindrance and consequences, the cause of error, the condition of doubt, of reservation, of conviction, etc.”; “and general and pure logic is related to it as pure morality […] is related to the doctrine of virtue proper..”.

Then Kant introduces a third type of logic, TRANSCENDENTAL = is a material logic, is concerned with content, but only with the a priori condition of it. “It would therefore concern the origin of our cognition of objects insofar as that cannot be ascribed to the objects;”, “a science of pure understanding and of the pure cognition of reason, by means of which we think objects completely a priori. Such a science, which would determine the origin, the domain, and the objective validity of such cognitions..”. (B 81)

Notice the important remark on “transcendental cognition”: not all a priori cognition are transcendental, but only those “by means of which we cognize THAT and HOW certain representations (intuitions and concepts) are applied entirely a priori, or are possible (i.e. the possibility of cognition or its use a priori)” (B 80-81, my emphasis). This passage marks the distinction between the THAT and the HOW of critical project, namely, between “metaphysical” and “transcendental” deduction (as we’ll see in short).

So, we might say that TRANSCENDENTAL LOGIC is an investigation in the field of transcendental cognition with reference to the conditions of the possibility of conceptual knowledge, that is, the conditions of the possibility of scientific use of understanding.

We now have a twofold partition of transcendental logic based on two distinct tasks:

(i) expounding the elements of conceptual pure cognition belonging to the understanding along with the principles without which no object can be thought: TRANSCENDENTAL ANALYTIC (logic of truth)

(ii) criticizing the misuse of the understanding (dialectical use, a material use of the merely formal principles) when it is counted as the organon of a general and unrestricted use or cognition (beyond experience): TRANSCENDENTAL DIALECTIC (logic of illusion).

Then, what is the content of understanding that is to be analyzed? Kant says: concepts.

- the understanding and its content. Two passages are of the greatest interest: B 74-76 and B 93-94. In these four paragraphs Kant lays out a general picture of the content and function of the understanding in sharp contrast with sensibility.

SENSIBILITY UNDERSTANDINGReceptivity: the capacity “to receive representations”.

“Without sensibility no object would be given to us...“Thoughts without content are empty,…

INTUITIONS (space and time)- always sensible in character- rest on affections- provide content or raw material of cognition

- refer to the object immediately

Spontaneity: “the faculty for bringing forth representations”.

..and without understanding none would be thought”.…intuitions without concepts are blind.”

CONCEPTS (pure and empirical)- discursive in character- rest on functions, are rules- provide unity and determinacy to the manifold of intuition (empirical concepts) or to the manifold of concept (pure concepts or CATEGORIES)- refer to objects by judging, i.e., a mediate cognition of an object

Example: To illustrate the difference between referring to objects through intuition or through concepts (and so understanding why Kant thinks that conceptual cognition is a sort of mediation), let’s think of the desk in front of us. If I refer to it immediately I can see its color, shape, extension, etc. (remember that space and time are forms of intuition). Then, if I say, “this desk is suitable for writing and cooking”, I connect the sensible aspect of intuition with other concepts: “desk”, “suitable”, “writing”, “cooking”; so, my knowledge of the desk is mediated by the relation of the concept “desk” with other relevant concepts through the copula “is”. But “this desk is suitable for writing and cooking” is a JUDGMENT, which connects a subject (the desk) with one or more predicates in a proposition. Thinking, then, means judging, that is, connecting concepts, and is to keep distinct from SENSING. Insofar as we have cognition of objects, judging and sensing cannot be separated. “Thinking is cognition trough concepts” (B 94)

Kant’s example: “All bodies are divisible” (B 93).

Concepts can be empirical or pure. “Desk” is an empirical concept because it arises from experience and is connected with sensations, whereas pure concepts or CATEGORIES confer unity and determinacy on a

manifold of concepts and arise from the understanding itself (are the proper content of pure understanding).

Aristotelian categories = elementary meaningful expressions which are capable of signify something. They identity the most general classes of possible assertions.

Kant’s CATEGORIES = second-level rules of unity and determinacy. They prescribe a certain order to the first level of experience. Provide rules for the composition of thoughts. Grammar of thought.

Against empiricism: relevant concepts are not derived from experience, but rather make it possible in the first place: whenever the manifold of sensory impressions is brought into an objective unity grounded in the objects themselves, we are always dealing with a categorical unity.

Against rationalism: the understanding always requires a corresponding intuition, which implies that there can be no knowledge beyond the limits of possible experience. Objectivity only comes about through the contribution of certain subjective achievements, which implies that things in themselves remain unknowable.

- argumentative strategy

- isolating thought from intuition

- isolating the pure from the empirical moment of thought

- METAPHYSICAL DEDUCTION: expounding the full list of categories. Quid facti: What are the elementary concepts of the pure understanding? (remember the THAT-part of transcendental cognition).

- TRANSCENDENTAL DEDUCTION: justifying the relevant categories as subjective yet indispensable for the constitution of things as objective appearances. Quid iuri question. (the HOW-part of transcendental cognition).

Metaphysical Deduction of the Categories

Kant shows that the pure understanding possesses a content of its own (we already seen this above), systematically derives the categories from a common principle, which forms the “clue to the discovery of all pure concepts of the understanding”, and finally employs this clue to furnish the systematic, complete and internally organized presentation of the categories. We can isolate three main steps:

1) we identify judging, independent of experience, by abstracting from all content and concentrating on the form of judging itself. The connecting that is indispensable for experience is thus discovered in the pure forms of judgment. These in turn depend upon the corresponding faculty, the pure understanding. “The functions of the understanding can therefore all be found together if one can exhaustively exhibit the functions of unity of judgments.” (B 94)

2) the principle of the metaphysical deduction is the table of the pure forms of the understanding, the table of judgments. “If we abstract from all content of a judgment in general, and attend only to the mere form of the understanding in it, we find that the functions of thinking in that can be brought under four titles, each of which contains under itself three moments.” (B 95).

3) Kant coordinates each form of judgment with the corresponding category.

Table of judgments. Table of Categories.

Most of the concepts can already be found in the traditional ontology of Wolff and Baumgarten. The originality of Kant lies in the derivation of the categories and the elucidation of their function.

Lecture 4: Analytic of Concepts II. Transcendental Deduction B. (B 116-168)

The transcendental Deduction of the categories is one of the most difficult pieces of the entire philosophy, and it cost to Kant the greatest effort. I shall begin providing an overall scheme of the central argumentation. After discussing the main achievements of it, we’ll focus on other more particular themes. In the second edition of the Critique, Kant introduced numbered paragraphs, for simplicity I’ll refer to them in my reconstruction.

Brief overview of the argument

1. INTRODUCTION. Sections (§13) e (§14) specifies the aim of the argument, one which corresponds to Kant’s general epistemic revolution in seeking the origin of the categories in the subject rather than in the object of experience.

2. MAIN BODY I (§§15-21). First part of the central argument is divided in three subsidiary steps:

a. Kant begins by explicating transcendental self-consciousness as the origin of all objective unification of experience: (§15) the activity of connection that is required for all knowledge can only be “performed by the subject itself”, (§16) and this corresponds to transcendental self-consciousness (I-think), (§17) which in turn forms the “highest principle of all employment of the understanding”.

b. These sections qualify transcendental self-consciousness as objective unity (§18), and present the categories, without explicitly mentioning the term, as the necessary conditions of such unity (§19).

c. After an initial summary of the argument (§20), Kant goes on to show how all sensuous intuitions can only be made into objective cognition through the transcendental self-consciousness and the categories (§21). Kant has hitherto proved that pure concepts of the understanding are necessary for experience. It has not yet been demonstrated that these concepts apply to experience as a whole and to nothing but the field of experience.

3. MAIN BODY II (§§22-26). Part two of the central argument explicitly takes up this remaining task and therefore represents an independent proof step in its own right There are four problem cases or objections considered by Kant, whose discussion restricts the application of the categories to the objects of possible experience, and explains how the categories are valid, within possible experience, for all objects, and particularly for mathematics:

a. The first case is that of mathematics (§22);

b. The second concerns the possibility of non-sensuous intuition and is thus simply eliminated (§23);

c. The third, concerning transcendental self-consciousness, reveals that the latter does not represent any kind of self-knowledge (§§24-25);

d. The fourth problem, concerning the connection process of perception in which experience consists, can only be fully through careful interpretation (§26);

4. (§27) CONCLUSION. It summarizes the result of the preceding argument.

- Notice that the argument mentions “categoriality” in general, not individual categories, so is not concerned with the deduction of individual categories. The range for the application of each individual category, along with the justification of this application, will be undertake in the Schematism and Analytic of Principle (B 167). There Kant will show that the synthesis accomplished by transcendental self-consciousness with respect to the manifold of intuition consists in extensive magnitude (Axioms of Intuitions), with respect to perception consists in intensive magnitude (Anticipations of Perception), and with respect to experience consists in the necessary connection of perceptions (Analogies and Postulates).

- The argument emphasizes the distinction between the two sources of knowledge, sensibility and understanding (B 146), together with the opposition between empiricism and rationalism.

In fact, the first part, demonstrates, against empiricism, that the manifold of intuition can be the object of cognition through the categories, and hence it ascribes them objective and constitutive validity for our knowledge.

The second part emphasizes the contrast with rationalism by restraining the application of the categories within the boundaries of possible experience (B 149). The footnote to the section 27 refers implicitly to the following discussion in “Phaenomena & Noumena” (distinction between logical, transcendental and transcendent use of the categories).

- the argument is meant to offer a solution to the “Copernican” experiment by answering three questions:

i) how is that concepts which arise solely from the subject itself can still properly apply to the objective world?

ii) how is that elements which belong to the non-sensible faculty of the understanding can nonetheless be valid for objects of the sensuous world?

iii) how can elements independent of experience nevertheless constitute experience itself?

- the range of the argument: no objective relations to the world is possible without the categories and no legitimate application of the categories is possible without an objective relation to the world.

Enlarged overview with comments

§§15-16-17

§15. The “I-think” as the origin of all combination of the manifold. If we remove everything that is incapable of effecting combination we remain with the understanding and its pure activity.

In a sense I-think, as synthesis of the combination, is self-activity of the understanding: “is not given through objects but can be executed only by the subject itself” (B 130).

“it must be originally be unique and equally valid for all combinations” (B 130) and consists in “the ground of the unity of different concepts in judgments” (B 131).

Even analysis presupposes an activity of combination since “where the understanding has not previously combined anything, neither can it dissolve anything” (B 130).

Synthesis enjoys epistemological pre-eminence over the kinds of possible analysis and combinations of the manifold (both of the intuitions and of the concepts). It occupies a logical “higher level” (B 131), must be a priori and independent from the category of unity itself. It is the ultimate ground of unity.

§16. What “I-think” does not mean: empirical consciousness of this or that feeling, mind state, or subjective ascription of mind state. Kant is here concerned with the pre-empirical condition of the unity of experience (even of inner or psychological experience).

“I-think” is a synthetic unity of self-consciousness insofar as it accomplishes combination…

Is an originally unity of SC insofar as it essentially precedes all combination

Is a non-empirical unity of SC insofar as it is presupposed in all empirical cognition, including empirical cognition of self-consciousness.

§17. “Synthetic unity of apperception” (or “transcendental self-consciousness” or “I-think”, have all the same meaning) is the “highest point to which one must affix all use of the understanding, even the whole of logic and, after it, transcendental philosophy” (B 134 footnote).

Threefold definition of understanding as (i) faculty complementary to sensibility, (ii) faculty of judging and (iii) faculty of all cognition (B 137).

1) the manifold of sensations is brought into the unity of a concept (body, or weight, etc.)

2) concepts are combined by means of the categories into the unity of an objective judgment: “the body is heavy”.

3) the knowledge of the object, with its potential reference to the self, comes to the unity of transcendental self-consciousness

§§18-19

§18. It contrasts objective unity with the subjective, empirical and contingent unity of consciousness which determines inner sense in accordance with the laws of association, and which is accomplished by the reproductive imagination.

§19. In the case of objective unity the judging subject is present in the background as the accompanying “I-think”. It defines the judgment as “nothing other than the way to bring given cognitions to the objective unity of the apperception” (B 141). This means that objectivity is due to the connection of the categories. In addition to transcendental-SC, categories are the conditions of all objectivity.

§§20-21,

These sections draw the relevant conclusion: “Thus the manifold in a given intuition also necessary stands under categories” (B 143).

§§22-26

The second part of the main argument supports the above conclusion in two respect, by showing (i) that the categories can be employed for the construction of objective reality as a whole, and (ii) that they can indeed only be employed for this purpose. This interpretation is consistent with Kant’s emphasis on the theme of the two sources of knowledge and his war on empiricism and rationalism (as we had seen above).

In order to contrast rationalism, Kant faces 4 problem cases or objections.

I. (§22) Pure mathematics seems to yield “categorial” cognition of object independent from experience (Descartes e Leibniz). Kant replies that Geometry is not possible through the intuitions of space and time alone, but also through the intuitive representation, which implies a synthesis of the manifold mediated by categories. This means that categories apply also in the field of mathematics.

For example, “The sum of the angles of a triangle is 180” is certainly a tenet of Euclidean Geometry; however, is nonetheless a judgment in which categories are employed (universal of quantity, affirmative of quality, categorical of relation, etc.).

Naturally, without intuition mathematics would yield solely a formal type of knowledge (B 147, on this see B 229, First Analogy), which is nonetheless objective as far as is granted by categories (a weaker form of objectivity indeed, because it cannot be supplemented by sensible intuition).

II. (§23) as far as a possible non-sensible object of experience, like the soul, Kant submits that we can provide only negative statement which do not represent genuine knowledge (B 149).

III. (§§24-25) against Descartes, who believes that self-consciousness implies self-knowledge, Kant maintains that transcendental apperception, or transcendental self-consciousness, contains only conscience of the fact that “I am”, but never the knowledge of “what” I am. I-think is a form that deploys concepts, whereas the real self is an object of empirical introspection, knowable through the internal experience made possible by intuitions and categories (but this experience can have access only to self’s affections not to the self in itself). The subject never appears as things in itself, it has a purely phenomenal character (B 152sgg).

IV. (§26) with reference to perception, categories are capable of prescribing laws to nature (B 159), and are the conditions of the possibility of the cognition of sensible objects (e.g. house and freezing water, B 162). It arises the problem if cognition does pre-form all perceptions, or if there could be a non-conceptual kind of perception (B 161). In B 164-165 Kant submits that categories are conditions of all possible perceptions.

(B 164-165). The transcendental I-think is at once the unity of self-consciousness and the unity of nature, subjectivity and objectivity in one.

(§27) the conclusion of the argument consists in two statements referring to the twofold parts of the argument itself: “We cannot think any object except through categories; we cannot cognize any object that is thought except through intuitions that corresponds to those concepts.” (B 165). Kant underlines the Copernican meaning of that conclusion (B 166).”

Lecture 5: Schematism (B 169-187), Analytic of Principle I: introduction (B 187-202), Axioms and Anticipations (B 202-218).

Schematism

- What’s the meaning of this section? After the deduction, Kant introduces a third faulty of cognition, the power of judgment, which purports to mediate between sensibility and understanding by means of “transcendental schemata”.

This is a crucial point with reference both to the prosecution of the Critique’s argument (in particular the second chapter of the Analytic of Principle develops the judgments which the understanding makes a priori under the presuppositions of the transcendental schemata) and to its general theoretical achievement (in particular with reference to the third chapter of the Analytic of Principle, titled Phenomena and Noumena B 186).

One may wonder what the aim of this part really is. Many scholars have found this chapter rather obscure, confused and superfluous. This is not the case. The reason why this part is necessary is that Kant does not finish the deduction, he does not entirely accomplish the transcendental task of demonstrating the objectivity of the pure elements of cognition in regard to the understanding. The previous deduction has certainly shown that what we have called “categoriality” is indispensable. But it has not yet demonstrated this specifically either for the individual categories or for natural science (“pure natural science” B 20). Remember that until now, Kant has demonstrated that mathematics includes a synthetic a priori dimension, but there is also another science (physics) which has not even been discussed yet.

Kant has stated how categories relates to the synthesis of the I-think, but how the categories can be applied to the domain of sensibility is a rather different concern. This question explicitly recognize the heterogeneity of sensibility and understanding. And this is precisely why the schemata are required: filling the gap between the two. The schema is a “third thing, which must stand in homogeneity with the category on the one hand and the appearances on the other, and makes possible the application of the former to the latter” B 177).

- the argument can be broken down in three parts:

a) isolating the pure power of judgment

b) seeking in the chapter on the schematism to identify it’s a priori elements

c) developing the principles which follow a priori from the pure concepts of the understanding (the task that Kant will take up in the second chapter of the Analytic of Principles).

- what is the new faculty? The power of judgment “is the faculty of subsuming under rules” (B 171).

In this respect is distinct from understanding: knowing that the rules are such an such, does not coincide with the “know how” that is required to apply them properly. Hence the importance of the examples (B 173).

It is subsidiary to the understanding, and not to sensibility as well.

It requires schemata, a representation that exhibits both an intuitive and conceptual character.

- There are schemata for empirical concepts, sensible concepts (e.g. a triangle), and pure concepts. The latter are significantly the most difficult to handle and are called “transcendental schemata”. Transcendental schemata are to be kept distinct from images or concepts (B 179): see example of the five points “…..” (B 179): “On the contrary, if I only think a number in general, which could be five or a hundred,

this thinking is more the representation of a method for representing a multitude (e.g. a thousand) in an image in accordance with a certain concept than the image itself..” (B 179). The schema is thus “a representation of a general procedure of the imagination for providing a concept with its image” (B 180). So, the schema is a method which allow us to elaborate upon the individual case and to decide which empirical concept we should employ with respect to which sensible intuition. The schema is a method for judging. See Kant’s examples: “the triangle”, and “the dog” (B 180).

- The justification of the temporal aspect of transcendental schemata goes like this:

They mediate in relation to the pure understanding

The categories relate to sensibility through schematization: “Without schemata, therefore, the categories are only functions of the understanding for concepts, but do not represent any object” (B 187).

To be pure, they must refer to pure intuition.

The pure unity required by the category can be provided by inner sense (B 181): “is a transcendental product of the imagination, which concerns the determination of the inner sense in general…” (B 181)

Transcendental schemata are determinations of time in accordance with a priori rules.

As determination of time they accord with intuition, as governed by a priori rules, they accord with concepts. This doubled accordance furnishes the criteria for applying categories to sensible impressions. The function of a schema is to realize the category as well as restricting its use (legitimation and limitation). Kant establishes that human experience has a transcendental temporal structure.

- Then, Kant goes on presenting a taxonomy of schemata in accordance with the four classes of categories: quantity, quality, relation and modality.

Quantity: schema of magnitude = time series (the concept of number “is a representation that summarizes the successive addition of one homogeneous unit to another” (B 182).

Quality: schema of filled or empty time = content of time.

Relation: order of time. Schema of substance = permanence (duration); schema of the cause = temporal sequence (succession); schema of community = simultaneity.

Modality: sum total of time. The scope of time, the circumstance that an object exists…schema of possibility (at some time), schema of actuality 8at a particular time), schema of necessity (at all time).

Example: the street becoming wet. We have to recognize the street in its both states, dry and wet as the same subject that underlines the process, as the substance that undergoes an alteration of “accidents”. The recognition of a subject presupposes a duration through time. The relevant schema is the permanence of the real in time “which endures while everything else changes” (B 183). We cannot perceive time but we can perceive a substance’s changes that come about within it.

Example: “it rains, the street becomes wet”. We must assert a causal succession, not only a succession of events in general, but a succession which must be grounded in the objective situation. This is possible only if events elapse in accordance with a precise rule: causality.

Analytic of Principles I, introduction

The task of this part (the second chapter of the Analytic of Principles) “is to exhibit in systematic combination the judgments that the understanding actually brings about a priori” (B 187). The method consists, again, in following the table of the categories: “for which our table of the categories must doubtless give us natural and secure guidance”. The overall intent is to furnish a general philosophical theory of science independent of any theological foundation.

Kant specifies that the principles with which he is concerned about are principles related with the categories, hence principles of mathematics are excluded.

The principle of contradiction receives a rather careful discussion, not only in view of a theoretical completeness but also because Kant can take side against the use rationalists have made of it. That principle has two basic functions according to Kant:

A merely formal-logical function (in contrast with rationalists like Wolff and Leibniz who attributed to it a substantive role);

The discussion of it is able to clarify Kant’s own enterprise

- Principles (Grundsätze), grounding propositions. In this section, Kant has to deal with the fundamental universal laws of nature which make our experience of nature passible in the first place. They are the rules for the objective employment of the categories through the mediation of the schemata. For this reason they can be derived from the table of the categories.

Four level of knowledge: intuition, perception, experience and empirical thought.

Four kinds of a priori certainty: axioms, anticipations, analogies and postulates.

In analogy with the table of the categories, the first group is defined as “mathematical” while the second “dynamical”. The former has a “constitutive” significance, while the second only with a “regulative” one 8due to the fact that they try to establish a necessary relation between events which are contingent; e.g. they are directed toward relation of substance and accidents, causal relations, etc.).

Kant discusses, as he did before with schemata, one example for each of the mathematical principles, and three examples for each of the dynamical ones.

Note that here Kant is not dealing with the principles in themselves, but with their a priori conditions. Kant analysis is therefore transcendental (a second level, or meta-level inquiry). This means that principles may not be accurate or truly synthetic a priori from a contemporary point of view, but Kant’s analysis may nonetheless be sound.

Axioms of Intuition

The overall meaning of this proof is the justification of mathematics as the science of magnitude. Kant wants to prove that mathematics, as a science of magnitude, is fundamental for the knowledge of nature. Since nature is “magnitude” mathematics turns out to be constitutive for nature (Kant’s main transcendental thesis).

The second step is to refine the concept of “magnitude” that is relevant here. Mathematics is concerned with “determined” magnitudes, that is, magnitudes capable of mathematisation (precise quantities). All nature turns out to be a sum of mathematically determinable quantities (in the spirit of Galileo and modern physics).

The proof goes like this:

1a. space and time underline all appearances;

1b. determination of space and time rest upon the synthesis of the homogeneous (main acquisition of the deduction of the categories);

2. the consciousness of the homogeneous manifold of the intuition is the concept of “magnitude” (it identifies the consciousness of the homogeneous with the concept of magnitude);

3. all appearances are “magnitudes”, more precisely, “extensive magnitudes”;

Extension is thus represented as a whole composed of parts which can be composed in a sequence of composing processes. Kant says that all intuitions are perceived as “aggregates” (B 204) and this in turn bring us to mathematics: “On this successive synthesis of the productive imagination, in the generation of shapes, is grounded the mathematics of extension with its axioms” (B 204).

But here Kant is concerned with the transcendental aspect of the story, that is, “the conditions of sensible intuition a priori”. So, he is not properly concerned with axioms per se but with meta-axiom which expresses their a priori conditions: nature is intuitively given / so spatio-temporally extended /then objectivity is bound to quantity /and quantity is bound to extensive magnitudes. In conclusion, every single appearance is a case of applied mathematics (the science of quantity and extension).

Example: numerical formulas vs. axioms.

Anticipations of perceptions

Perception is a representation accompanied by sensation (empirical consciousness). Sensation gives the material, the stuff, “for some object in general” (B 207). This is continuous with what Kant have said before. The problem now is this: how can we represent the objectivity of perceptions? Is there any such objectivity or should we believe that perception is always a subjective process?

Kant states that even perception has an objective character because is bound to an a priori pre-condition: anticipation. Anticipation means a type of sensation that underlies the different individual sensations. Anticipation is a kind of pre-empirical moment, an intensive magnitude (so a magnitude again) that exerts a “degree” of influence on the senses. This means that every sensation has a strength, a degree, and can be located on a scale. Kant speaks of “anticipations” in the plural, because that strength depends on the type of object and sensory qualities.

Kant connects to the principle two thesis:

A. sensations are strengthened or weakened in a continuous fashion;

Sensations possess a defined degree of strength. This is crucial for the justification of the objectivity of sensations. Only if my sensation has an objective degree I can compare it with other sensations, and I can compare my sensations with those of other people (with reference to the same object).

B. they never entirely vanish;

Kant here reject a space, or a consciousness, devoid of sensation. Absence of sensations corresponds to absolute emptiness. But absolute emptiness is impossible given the character of sensation: we always perceive something, we never perceive the nothing (perceiving nothing is not perceiving at all). So, there could not be an object of perception without sensory intensity.

Again mathematics is important here. In this case, mathematics deals with “intensive” magnitude, that is, non-extended phenomena. We may think of some intensive magnitude in physics, for example, density of energy, pressure, heat, temperature, etc.

Example: 13 dollars.

Lecture 6, Analytic of Principles II: Analogies and Postulates. B 218- 273;

Analogies of Experience

- Kant starts to elucidate dynamical principles of the understanding. As is made clear by the table below, the Analytic of Principle develops a sort of internal climax with regard to knowledge. There are four different, and increasingly complex, levels of knowledge: intuition, perception, experience and empirical thinking.

Intuition = offers spatio-temporal magnitudes (without furnishing any reality per se)

Perception = sensory contents which furnish substantive realities of a certain kinds

Experience = those realities are then connected with one another according to some a priori rules

Empirical thinking = and finally constitute proper cognition

Now is quite clear why Kant’s whole enterprise could be read as a metaphysics of experience. It turns out that to experience something is to connect perceptions in some relevant ways, that is, following certain rules given by the understanding (through the mediation of schemata in accordance with the categories of relation). So, experience is a product of understanding not of perception or sensory faculty alone.

- In this section, Kant demonstrates that our experience is not a “juxtaposition” of manifold of perception (B 219), but is a structured whole capable of objectivity. This is a crucial step in Kant’s argument, because allows him to speak of nature as an interconnected single whole.

- “Analogy” means “relationship of equivalence” and has its origin in mathematics. So, here Kant is concerned with connections and relations, not with individual objects (which were indeed the subject of the previous section). This in part explains why Kant thinks that dynamical principles have only a “regulative” status with regard to experience (B 222): individual objects are objectively given through perception, but experience begins when these perceptions are properly connected with one another. So, dynamical principles cannot “constitute” objects (even if we might say that they constitute experience as a whole, see B 692), but only regulate the relations between intuitions.

- We can represent an analogy as an equation: a : b = b : c, or a : b = c : d. Given the value of the elements, we can discover the missing one. For example, 2 : 4 = 4 : x, x = 8. In the field of experience, we can discover an event if we know the events to which it is related. The primary conditions for the objectivity of a sequence of events is certainly time (the unifying apperception of I-think). But since time cannot be perceived, the objective connection can only be ascertained through rules governing connection itself. So, we have, according to Kant, three rules, or “analogies”, in accordance with three modes of time: persistence, causal succession and reciprocity in simultaneity.

The order in which the three principles are presented is also meaningful:

1. requires us to recognize alterations in a permanent substance,

2. which is the condition for grasping sequences as causal effects (e.g. a stone heated by the sun),

3. which in turn makes possible to recognize reciprocal and coexisting causal relations.

Summary table of the Pure Principles of the Understanding

Axioms od Intuition All intuitions are extensive magnitude

Anticipations of Perceptions In all appearances the real, which is an object of the sensation, has intensive magnitude, i.e., a degree.

Analogies of Experience Experience is possible only through the representation of a necessary connection of perceptions.

1. Principle of the persistence of substance.

[In all change of appearances substance persists, and its quantum is neither increased nor diminished in nature]

2. Principle of temporal sequence according to the law of causality.

[All alterations occur in accordance with the law of the connection of cause and effect]

3. Principle of simultaneity, according to the law of interaction, or community

[All substances, insofar as they can be perceived in space as simultaneous, are thoroughgoing interaction]

Postulates of Empirical Thinking in general

1. Whatever agrees with the formal conditions of experience (in accordance with intuition and concepts) is possible.

2. That which is connected with the material conditions of experience (of sensations) is actual.

3. That whose connection with the actual is determined in accordance with general conditions of experience is (exists) necessarily.

First Analogy

The argument stated by the “Proof” (first paragraph of the text added in B) goes roughly like this:

a. that things change is a matter of fact, we experience changes,

b. without a fixed and unchangeable background (substratum) there is no hope to establish objective knowledge of the change,

c. TIME is the condition of the representation of all change (bringing all manifolds to the unity through the synthesis of the apperception or I-think) because id the “persistent form of inner intuition” (B 224),

d. but TIME cannot be perceived

e. so, the substratum cannot be TIME in sé,

f. we must search that substratum in the objects of perception,

g. what do not change in the objects of perception, and is therefore persistent, is substance,

h. that substance underlies all change in appearances and turns out to be the necessary condition of bringing a multiplicity of perceptions into the unified form of experience.

The persistence of substance, which “gives general expression to time as the constant correlate of all existence of appearances, all change..” (B 226), is the condition of possibility of the perceptions of a change in things, and so it makes possible to perceive relations of succession and simultaneity. The underlying substance of things makes possible to speak of duration of things in existence.

This conclusion permits to clarify the concept of change itself. Change means only alteration with respect to the determinations or accidents of substances that are permanent. Change is not a passage from non-being to being (B 230).

The point is particularly relevant with regard to the distinction between appearances and things in themselves. We experience change in appearances not in things in themselves. Kant links his discussion of permanence with the major principle of transcendental idealism. If change would be applicable to things in themselves, we should infer that any new alteration correspond to a creation of an entirely new thing in the world. The creation of things in time would destroy the unity of time itself, and so, the unity of our sensible experience (B 229). With this remark, Kant simply denies that we can ground knowledge on a theological principle (God’s creation of things), and indirectly supports his Copernican Turn.

Second Analogy

- Hume’s conception of causality: we acquire causal relations from experience. Experience, according to Hume, contains only a sequence of events without necessary connection. All that we might say is that there are some regularities. Such a stable connection, as implied by the concept of a cause related to an effect, is a product of imagination which leads us, through customary association, to expect regularities. So, causality is a product of habit. The conclusion is that we have only subjective experience and we can ascribe to events only a certain degree of probability, never necessity or certainty. (to be expanded with references to Hume’s works).

- Kant wants to demonstrate that the regularities we experience in nature are objective and are grounded in reason (in pure understanding). In order to do that, Kant has to prove that necessary causal relations rests on objective, pre-empirical and a priori aspects of intellectual knowledge.

- the subject of this analogy is again change but conceived in terms of a sequence of events determined by force. That kind of sequence has to show determinable regularities in order to be objectively grounded (and in order to provide physics with a solid bedrock). That regularities, or order of succession in time, has to be grounded in the object (B 236). Regularity here could not be based solely on subjective apprehension, because subjective apprehension is fundamentally arbitrary.

Kant confronts the case of the house with that of the ship (B 237-238). In the first case, that of an house, the subjects are free to change their perspective and so the order of perceptions (for example, deciding to concentrate on the roof and only then on the doors and basement), while in the second case, that of a ship sailing downstream, perceptions present themselves to the subjects in an objective and unchangeable order (we can’t help but perceive first the ship at the top and only then at the bottom of the river in the

precise order stated by the stream which is the cause of the event). This phenomenological argument is mounted against Hume and proves that causal relations is a sequence of successive and non-reversible perceptions. This kind of knowledge of objective relations between causes and effect is grounded on the pre-empirical contribution of the understanding which furnishes the category of relation and the relative schema of causality.

- this conclusion affects the way we understand the principle of sufficient reason: it now appears to be a rule for the unity of nature and the ground of all possible experience. (B 246) Every objective alteration implies a connection of cause and effect.

- the causal principle according to Kant:

Ontological: refers to events as objective within nature

Epistemological: binds the objectivity of a series of events to an intrinsic causal connections ascribed to appearances, so grounded in transcendental subjectivity.

Methodological: invites us to investigate the specific character of causes and effects.

We can draw three related distinctions:

Relational necessity of causal laws concerns the irreversibility of sequences of events

Kant does not claim that nature is determined solely by one type of causal laws (discovering different types of causation is part of the empirical project).

Transcendental principle of causality is the condition of cognizing series of events as objective, and explains both why sciences (physics) seek to discover causes in nature and why scientific research is empirical in its very essence (we cannot derive a single causal law from the causal principle itself).

Empirical Thinking

The Postulates deal with nature as a whole and apply to three specific levels or modalities of reality: possibility, actuality and necessity. These modalities are conditions of experience, so have epistemological significance (and also methodological), not metaphysical.

1. POSSIBILITY = we have to add to the formal principle of contradiction, the principle of sensible intuition. If an event does not contradict the former and satisfy the latter, then it is an empirically possible object of experience.

2. ACTUALITY = the mark of the reality of an object or event is perception (even in cases such that of magnetism, electricity and gravitation we can perceive their effects)

3. NECESSITY = the connections of our experience is necessary when it is determined in accordance with the universal conditions of experience itself.

Lecture 7. The Refutation of Idealism, Phenomena and Noumena (B 274-294; B 294-315)

The Refutation of Idealism

- One may wonder why Kant inserts here a rather complicated argument against the skepticism concerning the external world. Kant is hitherto going on to saying that external world, that is, the world of outer sense, is perceived through sensible intuition. Why then he did not discuss this issue in its proper place, that is, in the Aesthetic? The reply to this question is simple enough: Kant regards the doctrine developed after the Aesthetic, namely the doctrine of categories and schemata in the Analytic, has a necessary step toward a sound argument against skepticism. In other words, Kant thinks that a proper refutation of skepticism about the external world cannot be furnish by reference to sensibility alone.

- The main targets of Kant’s criticism are Descartes’ “problematic idealism” and Berkeley’s “dogmatic idealism”. With respect to both, is essential to bear in mind the overall meaning of Kant’s Copernican Turn. (1) What is relevant here is that the external world can only be grasped as appearances rather than as things in themselves.

As a consequence of that, (2) external world is given to us through outer sense, space, but space is merely a form of intuition which is need of completion of a material content offered by sensations.

- Given these assumptions, (1) and (2), Kant challenges Descartes’ claim that inner experience is indubitable while the outer can in principle be doubted.

The starting point of Kant’s argumentation is the empirical consciousness of our existence (without any reference, as we found in Descartes, to a non-deceiving God);

This consciousness experience is “determined in time”.

But determinateness in time implies something “permanent” (as we have seen in the First Analogy) in perception.

This “permanent” cannot be the I-think or time (neither can be perceived or show any reference to perception), neither empirical self-consciousness that is reached through perception.

So, Kant’s conclusion is that “even our inner experience, undoubted by Descartes, is possible only under the presupposition of outer experience” (B 275). The existence of myself, indubitably identified through inner sense, presupposes something permanent outside me, and thus the existence of external things which are not merely imagined but actual.

To achieve this is crucial the cooperation of outer sense with the understanding (outer experience).

- Kant thinks that Berkeley’s idealism presupposes space as a thing in itself, so the general argument of Aesthetic is sufficient to repudiate it.

- note that the section on “The Refutation of Idealism” finds its completion in a section at the end of the Third Antinomy, in the Dialectic, in which Kant explains how the objectivity of nature is grounded in the recognition that nature, or the external world, forms a connected whole in accordance with empirical laws. In a sense, the laws of nature, elucidated by the Principles of the Empirical Thinking, are constitutive for outer experience. Only the cooperation of spatio-temporal intuitions and understanding can ground the unity of experience and permits us to describe what is represented in accordance with empirical laws as an actual rather than merely imagined object.

On the ground of the distinction of all objects in general into Phenomena and Noumena

The following section, Phenomena and Noumena, was in part emended for the second edition. It consolidates the conclusion reached in the Aesthetic: that all the knowledge we might have is knowledge of appearances, and it goes on to precise further the limitation in the application of the categories.

The main thesis is that there is only one legitimate use of the categories: the empirical use. The transcendental use of the categories is illegitimate.

The distinction bears emphasis on a negative result with respect to metaphysics, contesting the presumption of ontology to furnish synthetic a priori knowledge of things (B 303).

Knowledge of things in themselves is impossible even with respect to mathematics and Euclidean geometry (as for theoretical astronomy).

The distinction again enforced Kant’s polemic with rationalism and empiricism. Against the former, Kant says that concepts of the understanding cannot furnish knowledge without reference to empirical sensibility, while against the latter he reaffirms that there are concepts of the understanding that are independent from sensibility.

The concepts of a thing in itself is to be considered from an epistemological point of view:

In a first sense, the concept of a thing in itself expresses a LIMITING CONDITION on the scope of our knowledge. Things in themselves are not ontological objects: since our knowledge depends on sensible intuition, there cannot be knowable objects in a super-sensible world as correlate of an intellectual faculty of intuition (against rationalism). Noumena are things utterly unknown to us.

In contrast to empiricism, however, we should recognize that the concept of a thing in itself is not self-contradictory, because sensibility is directed toward appearance.

Things in themselves do not have any POSITIVE SIGNIFICANCE. They do not express a further or second level of reality. Nevertheless, they do have reality in the moral domain, and have an interesting EURISTHIC meaning in the theory of scientific research.

- Along with the empirical use of the categories, which constitutes the basis of the possibility of experience and meaningfulness of scientific discourse, there is a third use: LOGICAL or TRANSCENDENTAL SIGNIFICANCE (B 305, as opposed to “transcendental use” beyond experience). Categories cannot be employed without any reference to sensibility. They have “meaning” (empirical content) when (1) they can be referred to the forms of judgment (and hence schemata), (2) to be determinate, they must be referred to something coming from sensible experience.

Provided all this, we might say that Kant is not a verificationist. Pure concepts have their own “transcendental” or “logical” meaning even if they do not are applied to sensible contents. When all material from sensibility is simply lacking, pure concepts have a cognitive but not a semantic deficit.

In that context, finds its meaning the issue of the dialectical illusion. Categories, by their very nature, prompt to go beyond experience (at least in their transcendental and logical significance; see B 186-187). That supposed extension of their employment has two consequences: (1) they allow us to think, by means of the imagination, our sensible experience beyond its actual realization; on the other hand, (2) they press us toward the discovery or knowledge, entirely illusory, of the things in themselves.

We may draw these conclusions:

a) we have no knowledge of noumena, and have knowledge only of phenomena or appearances.

b) we are sometimes tempted, by virtue of our conceptual capacities, to think that knowledge of noumena is attainable; this temptation can be explained and diagnosed by distinguishing the semantic and the cognitive scope of concepts (B 186-187).

c) Those temptations, and their explanation and correction, are distinctively philosophical matters (B 296-297). The transcendental distinction between “things as they appear” and “things as they are” is not our ordinary empirical distinction between the way objects may appear to us and the way they actually are (B 3)13).

d) Despite (a) we can take it for granted that this things beyond our cognitive powers may very well exist (B 309). We cannot know such things, but by the same token we do not know that they do not exist and cannot rationally deny their existence (B 344). The concept of a noumenon is for us acceptable only in that negative sense as a “problematic”, not “assertoric”, concept (B 308-9, 310-11, 342-44).

e) In the negative, problematic sense, the concept of a noumenon is not an “arbitrary invention” but something we are bound to conceive as a correlate of “appearance”, which functions only as a “limiting” concept (B xxvi-xxvii, B 310-311).

Lecture 8, Dialectic I, Introduction (First book, B 349-396); Paralogisms (Second Book, B 396-432).

The Dialectic is the most critical part of the Critique with respect to the traditional metaphysics. Traditional or special metaphysics (God, soul, freedom or theology, psychology, cosmology) becomes in the last section of the Dialectic, a general theory of scientific investigation and a preparation for a new approach to moral demands. The task of the Dialectic is to limiting the pretension of knowledge with respect to the faculty of reason. The result is that there isn’t knowledge of intelligible objects or objects of reason such as God, soul, freedom, and the world as a totality.

- Let’s confront Analytic and Dialectic. In a certain sense, the Dialectic keeps up Analytics’ general approach to metaphysics. The Analytic has reduced the function of general metaphysics into a mere analytic of the pure understanding. Dialectic engages in a detailed exploration of the origins of our belief in illusory knowledge, provides a careful analysis of the features common to all special metaphysical projects. By discovering that all our metaphysical knowledge is illusory, it confirms the results of the Analytic.

There is another way to state the continuity between Analytic and Dialectic. Analytic is a grammar of thought; Dialectic shows that this grammar is oriented, internally and necessarily, to a theory of the unconditioned, and thus to special metaphysics, but it remains nonetheless a grammar of thought, not a knowledge of thought.

The Dialectic develops a transcendental logic which is required to explain both why metaphysics is necessary and why it necessarily produces illusions of truth.

- the structure of the Dialectic resembles that of the Analytic:

Metaphysical deduction = Book I, discovery of the central elements of reason (ideas)

Transcendental deduction = Book II, justification of the use of ideas

But since ideas provide only apparent and illusionary knowledge, the “discovery” and the “explanation” have to do principally with the dialectical illusion, not with the possibility of their application to intuition (so we don’t have a proper justification here). In other words, Kant need not to prove that ideas are pure a priori elements of reason since that character intrinsically belong to them, and don’t need to justify their application to experience since they are “not congruent” with anything belonging to experience. What Kant has to do is solely to expound a system of them.

- Kant’s relation with Plato and Aristotle. The discussion of the meaning of the term “idea” in the Dialectic, with reference to its origin in the philosophy of Plato, represents a lyrical attempt to capture the spirit of Plato’s moral and political enterprise, with particular reference to the Republic. While Kant refuses to accept the speculative meaning Plato has attached to ideas, he certainly embraces the spirit of the moral and political significance of Plato’s project. Analytic follows Aristotle in naming “categories” the pure concepts of the understanding (B 105). Kant shows a great deal of respect with regard to Plato and Aristotle.

- reason is the faculty of the unconditioned, it has a natural interest in searching for a supreme and comprehensive unity in all our knowledge. While concepts bring unity to the manifold of intuition under judgments, reason brings unity to the manifold of judgment under principles by drawing “inferences” (B 366). Ideas are concepts that are obtained through inference.

As there are three kinds of judgment of relation, so there are three kinds of inference which corresponds to three ideas, that is, three way of interpreting the relation between the conditioned and the unconditioned.

Categorical j. = concerns the relation of the predicate to the subject. The unconditioned is to be find in a subject which is no longer itself a predicate; the idea of a subject as such, the soul or absolute unity of the thinking subject (rational psychology).

Hypothetical j. = concerns the relation between ground and consequent. The unconditioned consists in the ultimate and final term of a series; a presupposition that does not presuppose nothing, the idea of a totality of things, with its related topic of freedom (transcendental cosmology).

Disjunctive j. = concerns the relations of parts within a system. The unconditioned consists in the absolute unity of all beings in a single subject, the idea of GOD (natural theology).

The corresponding fallacies (remember that in the Dialectic Kant deals with the logic of illusion not with the logic of truth, so here inferences become fallacies) are also three:

Para-logism = infers from the transcendental subject to the absolute unity of the subject as real.

Anti-nomies = infer from the totality of all think to contradictory conclusions which struggles to establish the correctness of their own view.

Ideal = infers from the totality of conditions under which all objects are thought, to the actual existence of this reality (God as absolute highest being).

Note that the title of the last chapter, “The Ideal of Pure Reason” is not meant to refer to a fallacy, but is focused on the positive aspect of the idea of a totality of knowledge.

- Kant critic of ideology. The three fallacies violates the a priori conditions of knowledge and thus represent a case of transcendental illusion, rather than merely sophistical. In this respect, Dialectic performs a radical critique of ideology. As such, is directed against “the monopoly of the Schools” (B xxxii). The task of the Dialectic, in this respect, is to fully expound the theory of experience so that reason can be liberated from illusion.

The Kantian attempts has two related positive aspect:

1) ideas can serve to correct both rationalism and empiricism. In contrast with rationalism, ideas forfeited all cognitive content, and, in contrast with empiricism, they keep a regulative function, that is, to order the fragments of reality into a whole. In this way, ideas give the goal of a constantly advancing process of scientific investigation whose end functions like an horizon.

2) ideas carry a peculiar moral character. Since the existence of God and freedom cannot be dispelled, we can counter the opposing positions (materialism, atheism, superstition, etc, B xxxiv f.). Remember the Preface B xxxi. The positions Kant alludes in the Preface B corresponds to the three main fallacies (materialism and free-thinking correspond to paralogism, fatalism and fanaticism to the antinomies, atheism and superstition to the ideal).

In so doing, Kant clears the way for a good metaphysics that concerns itself with the theoretical clarification of scientific investigation and with practical demands of morality in a proper way (a new metaphysics of freedom).

Paralogisms

- I will not take up the overall significance of Kant’s theory of mind; more modestly, I’m going to offer a reading of the Paralogisms’ chapter as it figures in B edition of the Critique.

Some preliminary notes, which are necessary to fully appreciate Kant’s task and might clarify the overall meaning of the section:

Sensibility and understanding are complementary sources of knowledge, the first is receptive, the second active.

The forms of intuition and understanding have pre-empirical validity.

Our sensory impressions are subject to various level of elaboration and unification.

We can only know appearances not things in themselves.

These preliminary points, already discussed above, should bring us to consider the difference between the “I think” as the transcendental unity of self-consciousness, along with its functional and transcendental role of vehicle of categories, from the empirical assertion “I exist as a thinking being”. The “I think” cannot be cognize and, for that reason, it is not a distinct substance. Clarifying that distinction is the main task of Kant’s Paralogisms.

- Kant introduces the first class of sophistical syllogisms in B398. He describes that kind of syllogisms as unavoidable inferences of reason which give objective reality to something “of which we have no concept” (B397). In particular, a paralogism, is a syllogism which infers from the formal unity of the subject to the real existence of it.

As such, paralogisms contain a fourfold fallacy, derived from the mistaken application of the table of the category to the “I think”: according to substance “The soul is a substance”. According to quality “The soul is in its quality simple”. According to quantity “The soul retains unity over time as numerically identical”. According to relation “The soul is an immaterial thing” (because we can doubt the existence of external things but not of our own thought). These statements are part of a pseudo-science called rational psychology which has as its main topic the demonstration of the existence and character of the soul. Kant is going to contest it by arguing that we cannot cognize the soul.

- the basic paralogism that bolster the illusion is this:

(M) “What cannot be thought otherwise than as subject does not exist otherwise than as subject, and is therefore substance”;

(m) “Now a thinking being, considered merely as such, cannot be thought otherwise than as subject.”

(C) “Therefore it also exists only as such a thing, i.e., as substance.

It clearly is a fallacy of equivocation. In (M) “thought” means something which might be given to intuition (as an objective ego object of inner experience), whereas in (m) “thought” refers solely to the form of the subject, its transcendental function of unifying cognitions in the unity of consciousness. We are confronted with a categorical error, a “sophisma figurae dictionis”, which breaks down in four related mistaken inferences.

Kant says that this inference is unavoidable because in a certain sense is natural, or reasonable, to think that a subject is a substance, but according to the lesson of the Analytic, this is not the case with respect to I-think. The only things that can be said of it are: (i) it is always a subject and never a predicate; (ii) it is a logically simple subject; (iii) it remains identical with itself with respect to any manifold; (iv) it is distinct from external things. Until we learn the lesson of the Analytic, that no objective self is possible without sensible intuition, we are inclined to fall victims of the fallacious inference.

Kant’s way to refute the paralogism in question is to underline the fact that one of the condition of application of the category of substance to a manifold is “persistence”. Now, we have no persisting intuition of our inner state, so of ourselves as inner object. So, the category of substance cannot properly apply to the “I”, which retains only the consciousness of our thinking. (B 412-413). This is of course a criticism we may raise only against the grain of the Analytic.

- Kant’s discussion of the paralogisms deals also with two related topics: (1) the purported demonstration of the immortality of the soul, and (2) with the alleged claim that it is possible to doubt only the existence of the external world.

The first target is represented by Mendelssohn’s Phaedo. Mendelssohn maintains that the soul has intensive, not extensive, magnitude (it cannot be divided into parts), so cannot disappear through a process of division or separation. Kant’s reply is that, even granted the former point concerning the intensive character of mind, the latter cannot follow. It is possible that the soul expires due to a process of “gradual remission of all its powers” or “elanguescence” (B 414). The simplicity of the soul cannot be identified with its timeless essence or continuity.

The second point concerns the relation with Descartes’ picture of self-awareness and self-knowledge. The analytic proposition according to which “the I of apperception,…., is a single thing that cannot be resolved into a plurality of subjects” cannot imply the synthetic conclusion that that same I is a substance. The same is true if we consider the analytic proposition that “I distinguish my own existence from other things outside me” (B 409); it does not follow from that the synthetic proposition that I’m a thinking being of which only I can have certain knowledge.

Kant recognizes the unique character of self-consciousness without reifying it or hypostasising it; he recognizes the privileged access of first person experience, but this is entirely an empirical question.

- Kant didn’t mean to derive disastrous consequences from his critics of rational psychology. Actually, Kant intends to provide a better alternative to traditional metaphysics of the soul, one that would be capable of better support a morality of freedom. Rational psychology, he says, cannot be a “doctrine” but a “discipline, setting impassable boundaries for speculative reason in this field” (B421). Both materialism and spiritualism fall within the illusion generated by the paralogism. Only in the practical domain the question of the immortality could find a solution.

Lecture 9, Dialectic II: Antinomies (book 2, chapter 2) B 432-488.

The chapter, which is structured in nine sections, can be divided in three main parts with regard to its content: a) Kant expounds the complete list of cosmological ideas (deriving them again from the table of categories) which are intended to represent a complete knowledge of the world; b) Kant proceeds to show that such alleged attempts entangle reason in unavoidable contradictions, i.e. the antinomies; c) Kant undertakes to solve the antinomies (relying upon transcendental idealism).

- The first part, that covers the first two sections, is devoted to the elucidation of the overall meaning of the “cosmological contradictions”. Kant begins by relating the problem at the base of the antinomies to a specific type of syllogism, the hypothetical one (remember that the categorical type of syllogism is related to Paralogisms), which makes “the unconditioned unity of objective conditions in appearances its content” (B 433). From the false pretension to reach the unconditioned unity of the objective synthesis of all appearances, arises out a “wholly natural antithetic”, which “leads reason into the temptation either to surrender itself to a skeptical hopelessness or else to assume an attitude of dogmatic stubbornness..” (B 434). In this context, Kant speaks significantly of the “euthanasia of pure reason” as if pure reason has to confront again with skepticism. A second warning concerns the method of investigation (B 434). Let’s consider both in turn, starting from the latter.

“Transcendental ideas” concern “absolute totality in the synthesis of appearances”, hence, they might be called “world-concepts” (B 434) as distinct from the “ideal” which will be the object of the following chapter and concerns “the absolute totality of the synthesis of the condition of all possible things in general”. The first term, world-concepts, qualifies the relation of reason to the world, while the second “ideal”, specifies the relation of reason to the idea of God. So, the main theme of this chapter is cosmology, while theology is the main theme of the next.

The “transcendental antithetic” (B 448) is “an investigation into the antinomy of pure reason, its causes and its result.” Kant points out that this kind of antithetic is not the result of an arbitrary question, but a necessary result of the application of reason to the possible totality of the unity of the conditions of the synthesis of the appearances (B 449-50).

But how these unavoidable illusions come about? The inference, or principle, that guides reason beyond the possible employment of the understanding is this: “If the conditioned is given, then the whole sum of conditions, and hence the absolutely unconditioned, is also given..” (B 436). Kant stresses further that “This happens when for a given conditioned reason demands an absolute totality on the side of the conditions (under which the understanding subjects all appearances to synthetic unity), thereby making the category into a transcendental idea, in order to give absolute completeness to the empirical synthesis through its progress toward the unconditioned 8which is never met with in experience, but only in the idea.)” (B 436). This passage clarifies what is that drives reason beyond the understanding to the point of transforming the category in an idea: the reason’s impulse toward completeness.

The problem is that this impulse to a complete knowledge cannot be satisfied because it expands beyond possible experience (so here reason is leaving aside the world of sensibility, and starts hypothesizing using ideas, or more carefully, producing ideas by transforming the categories of the understanding).

Reason thinks the completeness at issue in two radically different and contradictory ways: either as the absolutely first term of the series of appearances (thesis), or as the infinite series in which each term is conditioned and only the series as a whole is unconditioned (antithesis). Kant applies this distinction to the four classes of categories he expounded in the table of the categories: quantity, quality, relation and modality. Then, as in the chapter on the Principles, Kant divides the four classes in two part, the first two are named “mathematical”, the second two “dynamical”. We have therefore four antinomies or for pairs of

contradictory inferences. The four theses are typically endorsed by rationalism, while the antitheses by empiricism.

- The conflict between rationalists and empiricists, and so the conflict of reason within itself, cannot be resolved by recurring to experience. This may lead reason to skepticism, which according to Kant, “undermines the foundations of all cognition, in order, if possible, to leave no reliability or certainty anywhere.” (B 451). Kant’s preferred method is the skeptical method, which is to be kept separate from skepticism. Kant assumes the role of the “impartial referee” (B 451), and accept the initial outcome of the conflict: neither side decisively defeats the other. Kant therefore recognize that there are good grounds for both of the conflicting positions. The skeptical method consists in an investigation on “whether the object of the dispute is not perhaps a mere mirage at which each would snatch in vain without being able to gain anything even if he met with no resistance..” (B 451). The method allows Kant to raise an objection against both the alternatives: their approaches say more then they know. Transcendental idealism can show that they are both wrong, or, more carefully, that they both reach only a part of the truth.

In the second part of the chapter, which covers roughly sections from three to six, Kant expounds the antinomies along with their contradictory consequences.

THESIS ANTITHESISQUANTITY

The world has a beginning in time, and in space it is also enclosed in boundaries.

The world has no beginning and no bounds in space, but is infinite with regard to both time and space.

QUALITYEvery composite substance in the world consists of simple parts, and nothing exists anywhere except the simple or what is composed of simples.

No composite thing in the world consists of simple parts, and nowhere in it does there exist anything simple.

RELATIONCausality in accordance with laws of nature is not the only one from which all the appearances of the world can be derived. It is also necessary to assume another causality through freedom in order to explain them.

There is no freedom, but everything in the world happens solely in accordance with laws of nature.

MODALITYTo the world there belongs something that, either as a part of it or as its cause, is an absolute necessary being.

There is no absolutely necessary being existing anywhere, either in the world or outside the world as its cause.

In the mathematical antinomies, each thesis wrongly assume one of two possible alternative (one based on the concept of finitude, the other on the concept of infinitude). Actually, they starts from false presupposition because there could be a third alternative: that the infinite is not actually given but only potentially given.

The first antinomy is concerned not only with the history of the universe but also with the history of mankind. The series runs indeterminately far back and is thus indefinite rather than infinite. Kant’s reply to the antinomy is that the “infinite” should be taught as “potentially given” rather than actually given.

The second antinomy is concerned with whether the world is composed of ultimately simple parts or not. Kant suggests a third alternative: material substances do have parts, but they are divisible into other material substances.

The third antinomy is the most frequently discussed.

In the last part, Kant offers his solution to the problem: transcendental idealism. Kant follows methodologically ancient skepticism, but instead of resigning himself to a suspension of judgment, he proposes a constructive solution. Kant is not an observer of controversies but a critical epistemic judge who offers a new certainty by recognizing the ultimate ground of the dispute.

The method of the “antitheses” was well known in the protestant world due to Schultz, Baier and Anton. The latter, gave a theological explanation of the raising of the antinomies (contradictions spring from the fallen nature of men or original sin). Kant dismantles the inner dialectic of faith and offers a critic of ideology.

To recognize that both thesis and antithesis are wrong, we need to draw upon transcendental idealism: all knowledge requires intuition and cosmological ideas lack such a reference to sensibility. This lack explains the contradiction and also the lack of objectivity of the concept involved in the dispute: the word “world” claims an absolute completeness, but in fact it cannot have any reference to experience because is never given as an absolute complete whole within space and time. It can only be thought and is therefore a noumenon. As Paralogisms, also Antinomies are affected by a category mistake: they confuse a thing in itself with the sum of all appearances. We need to bear in mind that nevertheless the word “world” is not meaningless: is the idea that guides our empirical research toward the totality of appearances. Cosmological ideas do not have “constitutive” status but only “regulative” status: they do not describe the way the world is objectively, but the way in which the investigation of nature advances (subjectively) toward a comprehensive body of knowledge.

Transcendental idealism accomplishes a threefold task: (i) it diagnosis the antinomies; (ii) overcomes the antinomy itself; (iii) reveals an original regulative function for the cosmological ideas.

As a conclusion, we might say that Kant is offering here a severe critique of ideology. Traditional metaphysics has reified ideas, while the first Critique interprets them dynamically. Kant acknowledges the open-ended character of scientific investigation.