"Our knowledge is conversant about our ideas only. Since the mind, in all its thoughts and reasonings, hath no other immediate object but its own ideas, which it alone does or can contemplate, it is evident that our knowledge is only conversant about them. " (Locke IV: I:1).

"Hume, by his consistency, showed that empiricism carried to its logical conclusion, led to results that few human beings could bring themselves to accept, and abolished, over the whole field of science. the distinction between rational belief and credulity. 
Locke had foreseen this danger. He puts into the mouth of a supposed critic the argument: "If knowledge consists in agreement of ideas, the enthusiast [fanatic] and the sober man are on a level." (Russell, p.703) {2}

Subjectivism: Rationalism-Empiricism 

• Descartes cogito: the starting point of all knowledge -- all we know for certain -- is just the contents of our own minds. 
• Rationalists: subjectivist tendency of this is blunted by their finding, among the contents of minds, innate ideas having objective reality 
• ideas found in all minds: of substance, God, cause & effect, etc. 
• give us factual knowledge of universal truths a priori 
• these truths are about reality -- matters of fact (Hume) or things in themselves (Kant) 
• objective reality is structured in accordance with these ideas & answers to these truths 
• Trouble: competing metaphysical systems & no way to choose between them. {4}{5} 
• Empiricism  
• denies innate ideas 
• universal truths known a priori are trivial  
• not about reality (matters of fact) 
• only reflect the meanings of words or relations of ideas.  

Empiricism: Locke to Hume

• Locke 
• epistemological subjectivism {top left} 
• knowledge (truth) = coherence of ideas: 
• "agreement or disagreement of ideas" {1} 
• as opposed to correspondence truth = thought-reality agreement 
• IMO: conflates truth with justified belief.  
• Worry: consistent fanaticism or insanity <> knowledge {2} 
• residual realism about the external world: simple ideas are externally caused {3}. 
• Berkeley 
• abolishes the things operating on the minds 
• leaving him with finite minds and God:  
• Russell: if he'd been consistent he'd have denied the existence of all minds but his own. 
• Hume 
• abolished mental as well as material substance 
• threw doubt on the cogency of induction and the mind-independent reality of causation 
• still thought of impressions as externally caused!? 
• note: didn't define impressions in this way 
• they're defined by intrinsic (thought internal) marks: faintness & coherence. 
• Kant's Solution: Neither Skepticism nor Dogmatism {7} 
• Kant awakened from his self-confessed  "dogmatic slumbers" 
• to try to save claims of knowledge from skepticism {Russell} 
• without falling into rationalistic dogmatism: i.e., exaggerated claims to knowledge of the ultimate transcendent realities (God, Freedom, Immortality) {6} 

1. Knowledge, as has been shown, consists in the perception of the agreement or disagreement of ideas. (Locke, IV:vii:1) 
2. If it be true, that all knowledge lies only in the perception of the agreement or disagreement of our own ideas, the visions of an enthusiast [fanatic] and the reasonings of a sober man will be equally certain. It is no matter how things are: so a man observes but the agreement of his own imaginations, and talk conformably, it is all truth, all certainty. Such castles in the air will be as strongholds of truth, as the demonstrations of Euclid. That an harpy is not a centaur is by this way as certain knowledge, and as much a truth, as that a square is not a circle. (Locke IV: iv:1) 
3. The . . . simple ideas . . . must necessarily be the product of things operating on the mind, in a natural way, and producing therein those perceptions which by the Wisdom and Will of our Maker they are ordained and adapted to. (Locke IV:iv:4) 
4. Whether the treatment of such knowledge as lies within the province of reason does or does not follow the secure path of a science, is easily to be determined from the outcome. For if after elaborate preparations, frequently renewed, it is to a stop immediately it nears its goal; if often it is compelled to retrace its steps and strike into some new line of approach; or again, if the various participants are unable to agree in any common plan of procedure, then we may rest assured that is very far from having entered upon the secure path of a science, and is merely random groping. In these circumstances, we shall be rendering a service to reason should we succeed in discovering the path upon which it can securely travel, even if, as a result of so doing, much that is comprised in our original aims, adopted without reflection, may have to be abandoned as fruitless. (Bviii) 
5. So far, too, are the students of metaphysics from exhibiting any kind of unanimity in their contentions, that metaphysics has rather to be regarded as a battle-ground quite peculiarly suited for those who desire to exercise themselves in mock combats, and in which no participant has ever yet succeeded in gaining even so much as an inch of territory, not at least in such manner as to secure him in its permanent possession. This shows, beyond all questioning, that the procedure of metaphysics has hitherto been a merely random groping, and, what is worst of all, a groping among mere concepts. (Bxv) 
6. On a cursory view of the present work it may seem that its results are merely negative, warning us that we must never venture with speculative reason beyond the limits of experience. Such is in fact its primary use.  
7. [T]he new point of view enables us to explain how there can be knowledge a priori; and, in addition, to furnish satisfactory proofs of the laws which form the a priori basis of nature, regarded as the sum of the objects of experience -- neither achievement being possible on the procedure hitherto followed. (Bxxiv) 

If you always wore blue spectacles, you could be sure of seeing everything blue (this is not Kant's illustration). Similarly, since you always wear spatial spectacles in your mind, you are sure of always seeing everything in space. (Russell, p.707-8) 

As regards cause however, there is an inconsistency, for the things in themselves are regarded by Kant as the causes of sensations, and free volitions are held by him to be causes of occurrences in space and time. This inconsistency is not an accidental oversight, it is an essential part of his system. (Russell, p. 708) {7}

Ontological Argument

1. God is conceived to be a perfect being, i.e.,  a being having every good quality (or perfection) to the utmost.
2. It's better to be than not to be, i.e., being is a good quality (or perfection).
:. God exists.

To show

• none of our knowledge can transcend experience (pace empiricism) 
• yet knowledge of the experienced world is in part a priori (pace rationalism) 
• not all a priori knowledge is analytic: concerning only meanings of words or relations of ideas 
• some is synthetic: not concerning only relations of ideas but also the structure of empirical reality 

Synthetic a priori knowledge: How is it Possible?

• mathematics shows that it is {1} 
• metaphysics rightly understood{3} 
• the principles of cause & effect, substance, etc. {13} 
• rightly understood as pertaining not to transcendent realities (noumena or things in themselves) 
• but rather to transcendental features of empirical realities (phenomena or things for us) {5} 

Précis of Kant's Solution: His "Copernican Revolution" {4}{6} 

• the outer world occasions only the qualetative "matter" of sensation, but the things in themselves which give rise to our sensations are unknowable; they are not in space and time, not substances, not causes of anything or effects  
• our own minds order these appearances as objects, events, etc., in space and time 
• experiencing them under these "forms of intuition" 
• comprehending them as organized according to categories of the understanding 
• Space and time are in a sense subjective, part of our "apparatus" of perception: forms of intuition 
• you are sure of (sensuously) experiencing everything in space 
• hence the laws of geometry hold universally of the world-we-experience & this is knowable a priori 
• In addition to these forms of intuition, we structure experience in thought in accordance with categories of the understanding deriving from the forms of judgment that are the processes of the understanding 
• of quantity: unity, plurality, totality 
• of quality: reality, negation, limitation 
• of relation: substance-and-accident, cause-and-effect, reciprocity 
• of modality: possibility, existence, necessity 
• An Inconsistency? Russell's criticism {at left}. Kant's reply {8} 

Fallacies & Conundrums arising from misapplication of concepts and forms of intuition to things in themselves

• Antinomies: Insoluble Contradictions 
• the universe is has spatio-temporal limits vs. not 
• every composite is made of simple parts vs. not 
• there is absolute free will vs. not 
• an absolutely necessary being exists vs. not 
• Proofs of the existence of God 
• contra the ontological proof: existence is not a real predicate, so not a perfection {12} 
• contra the cosmological proof: last step is the ontological argument; so it's refuted too 
• physico-theological proof = the argument from design or the teleological argument 
• at best proves a designer 
• not a creator: cosmological proof 
• not a self-caused being: ontological proof. 

Ideas of Pure Reason: Thinkable although unknowable {9}

• certain of these need to be assumed if morality is a genuine possibility not a sham and a delusion {7} 
• God exists. {11} 
• Immortal Souls exist and 

exercise absolute Free Will {10} 

1. If he is to know anything with a priori certainty [the geometer] must not ascribe to the figure anything save what necessarily follows from what he has himself set into it in accordance with his concept. (Bxii) 
2. [Reason] must approach nature in order to be taught by it. It must not, however, do so in the character of a pupil who listens to everything that the teacher chooses to say, but of an appointed judge who compels the witnesses to answer questions which he has himself formulated. (Bxiii) 
3. Hitherto it has been assumed that all our knowledge must conform to objects. . . . We must therefore make trial whether we may not have more success in the tasks of metaphysics, if we suppose that objects must conform to our knowledge. This would agree better with what is desired, namely, that it should be possible to have knowledge of object a priori, determining something in regard to them prior to their being given. (Bxvi)  
4. If intuition must conform to the constitution of objects, I do not see how we could know anything of the latter a priori; but if the object (as object of the senses) must conform to the constitution of our faculty of intuition, I have no difficulty in conceiving such a possibility. (Bxvii) 
5. [A priori] knowledge has only to do with the appearances, and must leave the thing in itself as indeed real per se, but as not known by us. For what necessarily forces us to transcend the limits of experience and of all appearances is the unconditioned, which reason, by necessity and by right, demands in things in themselves, as required to complete the series of conditions. (Bxx) 
6. [N]othing in a priori knowledge can be ascribed to objects save what the thinking subject derives from itself . . . (Bxxiii) 
7. At least this is so, immediately we are convinced that there is an absolutely necessary practical employment of pure reason -- the moral -- in which in inevitably goes beyond the limits of sensibility. (Bxxv) 
8. [T]here is no contradiction [given that "object" has both phenomenal and a noumenal senses] in supposing that one and the same will is, in the appearance, that is, in its visible acts necessarily subject to the law of nature, and so far not free, while yet, as belonging to a thing in itself, is not subject to that law and is therefore free. My soul, viewed from the latter standpoint, cannot indeed be known by means of speculative reason (and still less through empirical observation); and freedom as a property of a being to which I attribute effects in the sensible world, is therefore also not knowable in such a fashion. (Bxxviii) 
9. Thus it does indeed follow that all possible speculative knowledge of reason is limited to mere objects of experience. But our further contention must also be duly borne in mind, namely, that though We cannot know these objects as things in themselves, we must yet be in position at least to think them as things in themselves;} otherwise we should be landed in the absurd conclusion that there can be appearance without anything that appears. (Bxxvii) 
10. [M]orality necessarily presupposes freedom (in the strictest sense) as a property of our will . . . [since] it yields practical principles -- original principles, proper to our reason -- as a priori data of reason, and . . . this would be absolutely impossible save on the assumption of freedom . . . (Bxxviii) 
11. I have therefore found it necessary to deny knowledge, in order to make room for faith. (Bxxx) 
12. 'Being' is obviously not a real predicate; that is, it is not a concept of something which could be added to the concept of a thing. It is merely the positing of a thing, or of certain determinations, as existing in themselves. Logically, it is merely the copula of a judgment. The proposition, 'God is omnipotent', contains two concepts, each of which has its object -- God and omnipotence. The small word 'is' adds no new predicate, but only serves to posit the predicate in relation to the subject. (626-627) 
13. Experience teaches us that a thing is so and so, but not that it cannot be otherwise. (B3) 

• Pure: a priori knowledge not "arising from" experience: which is absolutely independent of all experience {1} {2} 
• Empirical: justified through experience. 

Necessity along with strict universality mark the a priori  {4}

• Induced Universality {3} 
• comparative (tolerating exceptions) or 
• assumed (disconfirmable): "All swans are white": exceptions don't show it never was confirmed. 
• Strict Universality 
• absolute (exceptionless) 
• certain ( nondisconfirmable): "All equilateral triangles are equiangular." 
• Necessary: a priori truths must be true (empirical truths just are). 
• true in all possible worlds 
• i.e., regardless of circumstances 

Examples of a priori knowledge (existence proof)

• Known truths of mathematics. 
• Metaphysical: "Every alteration has a cause." {5} 
• There are also a priori concepts {6} e.g., substance {7} 
• Transcendental Deduction anticipated: "Even without appealing to such examples, it is possible to show that pure a priori principles are indispensable for the possibility of experience, and so to prove their existence a priori." (B5) 

• reason's pursuit of ultimate grounds (or reasons) for things leads in unavoidably beyond experience 
• giving rise thereby to "concepts to which no corresponding object can ever be given in experience" 
• "unavoidable problems set by reason itself" {9}  
• God 
• freedom 
• immortality 

Analytic v. Synthetic Judgments {10} {11}

• Case of affirmative judgments: S is P 
• Analytic 
• predicate concept is covertly contained in the subject concept 
• the connection of the predicate with the subject is thought through identity (contradiction in the negative case) 
• explicative 
• Synthetic 
• predicate concept is not contained in the subject 
• the connection is not thought through identity (or contradiction) 
• ampliative 
• Empirical (a posteriori) judgments all synthetic {12} 
• A priori judgments 
• analytic: definitional & logical truths 
• synthetic  
• mathematics {13} 
• arithmetic: 5+7=12 
• geometry: the shortest distance between two points is a straight line. 
• first principles of physics, e.g.,  
• conservation of matter 
• Newton's 3^rd Law 
• metaphysics: e.g., Every event has a cause. {14} 

General Problem of Pure Reason: "How are a priori synthetic judgments possible?" {15}

• How is pure mathematics possible? 
• How is pure science of nature possible? 
• How is metaphysics, as natural disposition, possible? 
• How is metaphysics, as science, possible? 

Critique as Transcendental Philosophy {16} {17}

• aim: to discover & articulate the necessary conditions of the possibility of synthetic a priori knowledge. 
• in two stems of human knowledge {18} 
• sensibility: by which objects are given 
• understanding: by which they are thought 
"Thoughts without content are empty, intuitions without concepts are blind." (B75)

1. But though all our knowledge begins with experience, it does not follow that it all arises out of experience. For it may well be that even our empirical knowledge is made up of what we receive through impressions and of what our own faculty of knowledge (sensible impressions serving merely as the occasion) supplies from itself. (B1) 
2. [W]e shall understand by a priori knowledge, not knowledge independent of this or that experience, but knowledge absolutely independent of all experience. Opposed to it is empirical knowledge, which is knowledge possible only a posteriori, that is, through experience. (B2-3) 
3. [E]xperience never confers on its judgments true or strict but only assumed and comparative universality, through induction. (B3) 
4. Necessity and strict universality are, thus, sure criteria of a priori knowledge. (B4) 
5. [T]he very concept of a cause so manifestly contains the concept of a necessity of connection with an effect and of the strict universality of the rule, that the concept would be altogether lost if we attempted to derive it, as Hume has done, from a repeated association of that which happens with that which precedes, and from a custom of connecting representations, a custom originating in this repeated association, and constituting therefore a merely subjective necessity. (B5) 
6. Such a priori origin is manifest in certain concepts, no less than in judgments. (B5) 
7. Owing, therefore, to the necessity with which this concept of substance forces itself upon us, we have no option save to admit that it has its seat in our faculty of a priori knowledge. (B6) 
8. But what is still more extraordinary than all the preceding is this, that certain modes of knowledge leave the field of all possible experiences and have the appearance of extending the scope of our judgments beyond all limits of experience, and this by means of concepts to which no corresponding object can ever be given in experience. (B7) 
9. These unavoidable problems set by pure reason itself are God, freedom, and immortality. (B7) 
10. In all judgments in which the relation of a subject to the predicate is thought (I take into consideration affirmative judgments only, the subsequent application to negative judgments being easily made), this relation is possible in two different ways. Either the predicate to the subject A, as something which is (covertly) contained in this concept A; or outside the concept A, although it does indeed stand in connection with it. In the one case I entitle the judgment analytic, in the other synthetic. (B10) 
11. Analytic judgments (affirmative) are therefore those in which the connection of the predicate with the subject is thought through identity; those in which this connection is thought without identity should be entitled synthetic. The former, as adding nothing through the predicate to the concept of the subject, but merely breaking it up into those constituent concepts that have all along been thought in it, although confusedly, can also be entitled explicative. The latter, on the other hand, add to the concept of the subject a predicate which has not been in any wise thought in it, and which no analysis could possibly extract from it; and they may therefore be entitled ampliative. (B10-11) 
12. Judgments of experience, as such, are one and all synthetic. (B11) 
13. All mathematical judgments, without exception, are synthetic. (B14) 
14. Metaphysics . . . ought to contain a priori synthetic knowledge. For its business is not merely to analyze concepts which we make for ourselves a priori of things, and thereby to clarify them analytically, but to extend our a priori knowledge. (B18) 
15. Now the proper problem of pure reason is contained in the question: How are a priori synthetic judgments possible? (B19) 
16. Thus the critique of reason, in the end, necessarily leads to scientific knowledge; while its dogmatic employment, on the other hand, lands us in dogmatic assertions to which other assertions, equally specious, can always be opposed -- that is, in skepticism. (B22-23) 
17. I entitle transcendental all knowledge which is occupied not so much with objects as with the mode of our knowledge of objects in so far as this mode of knowledge is to be possible a priori. (B25) 
18. [T]here are two stems of human knowledge, namely, sensibility and understanding, which perhaps spring from a common, but to us unknown, root. Through the former, objects are given to us; through the latter, they are thought. (B29) 

I understand by a transcendental exposition the explanation of a concept, as a principle from which the possibility of other a priori synthetic knowledge can be
understood. For this purpose it is required (1) that such knowledge does really flow
from the given concept, (2) that this knowledge is possible only on the assumption of
a given mode of explaining the concept. (B40)

Preliminary Distinctions {1}

• Intuitions: presentations: deliverances of sensibility 
• "through which [knowledge] is in immediate relation to its objects. 
• and to which all thought is directed as means. 
• Sensibility: the capacity for receiving intuitions. 
• Sensation: the affect of an object upon sensibility.  {2} 
• Empirical Intuition: intuition related to objects by way of sensation. 
• Appearance: an undetermined object of an empirical intuition: having both matter & form {3} 
• matter: what corresponds to the sensation in the appearance: objectively given 
• form: "determines the manifold of appearances" & "allows of being ordered in certain relations": subjectively imposed. 
• Space & Time the two forms of intuition {4}  
• Space: the form ft outer intuition: perception {5} 
• Time: the form of inner intuition: apperception {6} 

Space the form of outer intuition

• Metaphysical exposition: cannot derive from outer experience because it's presupposed by it: outer experience is only possible under this form. 
• Transcendental exposition: geometry is the a priori science of the laws of space: the conditions under which objects must appear to us. 
• Empirically real & transcendentally ideal 
• ER: phenomena really are in space {7} 
• TI: inapplicability to noumenal objects {8} 

Time: the form of inner intuition

• Metaphysical exposition: cannot derive from inner experiences of duration & change because it is presupposed by experience of duration & change. {9} 
• Transcendental exposition: necessary condition of the possibility of a priori knowledge regarding succession, and ultimately, thereby, of arithmetic.  
• Empirical Reality & Transcendental Ideality 
• ER: mental phenomena really are in time {10} 
• TI: the concept is inapplicable to the self-in-itself : self-in-itself is just as unknowable as the things-in-themselves {11} {12} 
• empirical ego: experienced self 
• transcendental ego: experiencing self 

1. Objects are given to us by means of sensibility, and it alone yields us intuitions; they are thought through the understanding, and from the understanding arise concepts. (B33) 
2. But all thought must, directly or indirectly, by way of certain characters relate ultimately to intuitions, and therefore, with us, to sensibility, because in no other way can an object be given to us. (B33) 
3. That in which alone the sensations can be posited and ordered in a certain form, cannot itself be sensation; and therefore, while the matter of all appearance is given to us a posteriori only, its form must lie ready for the sensations a priori in the mind, and so must allow of being considered apart from all sensation. (B34) 
4. [T]here are two pure forms of sensible intuition, serving as principles of a priori knowledge, namely, space and time. (B36) 
5. By means of outer sense, a property of our mind, we represent to ourselves objects as outside us, and all without exception in space. (B37) 
6. Inner sense, by means of which the mind intuits itself or its inner state, yields indeed no intuition of the soul itself as an object; but there is nevertheless a determinate form [namely, time] in which alone the intuition of inner states is possible, and everything which belongs to inner determinations is therefore represented in relations of time. Time cannot be outwardly intuited, any more than space can be intuited as something in us. (B37) 
7. Space is nothing but the form of all appearances of outer sense. It is the subjective condition of sensibility, under which alone outer intuition is possible for us. (B41) 
8. The true correlate of sensibility, the thing in itself, is not known, and cannot be known, through these representations; and in experience no question is ever asked in regard to it. (B45) 
9. Time is not an empirical concept that has been derived from any experience. For neither coexistence nor succession would ever come within our perception, if the representation of time were not presupposed as underlying them a priori. (B46) 
10. Time is nothing but the form of inner sense, that is, of the intuition of ourselves and of our inner state. (B49) 
11. Everything that is represented through a sense is so far always appearance, and consequently we must either refuse to admit that there is an inner sense, or we must recognize that the subject, which is the object of the sense, can be represented through it only as appearance, not as that subject would judge of itself if its intuition were self-activity only, that is, were intellectual. (B68) 
12. [T]he mind, since it then intuits itself not as it would represent itself if immediately self-active, but as it is affected by itself, and therefore as it appears to itself, not as it is. (B69) 

Now among the manifold concepts which form the highly ] complicated web of human knowledge, there are some which are marked out for pure a priori employment, in complete independence of all experience; and their right to be so employed always demands a deduction. (B117)

The Understanding {1}

• Contrast v. sensibility {2} 
• representative v. presentative {4} 
• active/creative v. passive/receptive {3} 
• Empirical Conception: synthesis of presentations 
• Judgments: synthesis of concepts 
• Anatomy of a Judgment : S is P 
• Schema: [All/Some/The] S is[n't] [possibly/ actually/necessarily] [non]-P 
• If SP1 then SP2 

TABLE OF JUDGMENTS

• Quantity: Universal; Particular; Singular 
• Quality: Affirmative; Negative; Infinite 
• Relation: Categorical; Hypothetical; Disjunctive 
• Modality: Problematic; Assertoric; Apodeictic 

TABLE OF CATEGORIES

• Quantity: Unity; Plurality; Totality 
• Quality: Reality, Negation, Limitation 
• Relation: Inherence/Subsistence; Cause/Effect; Reciprocity 
• Modality: Possibility; Existence; Necessity  

Transcendental Deduction of the Categories {5}

• to show: categorization is a necessary condition of the possibility of experience (possession of a connected manifold of appearances). {7} 
• that it must be organized under [these] categories 
• Contrast to Empirical Deduction: {8} 
•  ED explains how concepts do arise from experience 
• TD shows how impressions must be categorized to be experienced or represented in the first place. {9} 
• Categories are {10} 
• [c]oncepts of objects  general 
• determining intuitions of objects in respect of the logical functions of judgment 
• Understanding synthesizes the manifold of intuition  
• sensibility gives us "manifold" of intuitions 
• all as temporal or "in time" 
• some also space: "outer perception" 
• otherwise a "buzzin' bloomin' confusion" 
• understanding connects them in judgment {11} 
• Discussion (LH) 
• space & time condition the possibility of appearance or presentation of objects -- their perceptual input 
• duration & extension had a priori by objects 
• as sensible or presented 
• Categories condition the synthetic unification of the appearances -- their cognitive uptake in judgments 
• power & substance belong to objects a priori  
• as thinkable or represented 
• The Original Synthetic Unity of Apperception 
• subjective unity: must be possible for the 'I think' to accompany all my representations {12}{13} 
• "Only in so far, therefore, as I can unite a manifold of given representations in one consciousness, is it possible for me to represent to myself the identity of the consciousness in [i.e. throughout] these representations." (B134) 
• simultaneous self-world synthesis 
• objective unification of outer intuitions as an experienced world (under the categories)  
• simultaneously involves the unification of inner intuitions as an empirical self. {15}{17} {18} 
• Knowledge {14}{16} 
• involves conceptual unification of intuitions 
• in -- or as (re)presentations of -- objects. 
• Limited Application of the Categories 
• Cognitive: "as yielding knowledge of things, [the categories] have no kind of application, save only in regard to things which may be objects of possible experience. (B147-8) 
• Speculative: " if no intuition could be given corresponding to the concept, the concept would still indeed be a thought, so far as its form is concerned, but would be without any object, and no knowledge of anything would be possible by means of it." (B146) 
• Outcome:  
• can think objects only through these categories 
• can know objects only through fitting intuitions under these categories; i.e., via application of the categories to the sensory manifold. 
• Conclusion 
• can be a priori knowledge of objects of possible experience as possible objects of experience 

no a priori knowledge otherwise

1. If the receptivity of our mind, its power of receiving representations in so far as it is in any wise affected, is to be entitled sensibility, then the mind's power of producing representations from itself, the spontaneity of knowledge, should be called the understanding. (B75) 
2. 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. (B75) 
3. Concepts are based on the spontaneity of thought, sensible intuitions on the receptivity of impressions. (B93) 
4. Since no representation, save when it is an intuition, is in immediate relation to an object, no concept is ever related to an object immediately, but to some other representation of it, be that other representation an intuition, or itself a concept. Judgment is therefore the mediate knowledge of an object, that is, the representation of a representation of it. (B93) 
5. The objective validity of the categories as a priori concepts rests, therefore, on the fact that, so far as the form of thought is concerned, through them alone does experience become possible. They relate of necessity and a priori to objects of experience, for the reason that only by means of them can any object whatsoever of experience be thought. (B126) 
6. [Categories] are concepts of an object in general, by means of which the intuition of an object is regarded as determined in respect of one of the logical functions of judgment. (B128) 
7. [A]ll combination -- be we conscious of it or not, be it a combination of the manifold of intuition, empirical or non-empirical, or of various concepts -- is an act of the understanding. To this act the general title 'synthesis' may be assigned . . .. (B130) 
8. But a deduction of the pure a priori concepts can never be obtained in this manner; it is not to be looked for in any such direction. For in view of their subsequent employment, which has to be entirely independent of experience, they must be in a position to show a certificate of birth quite other than that of descent from experiences. (B119) 
9. The objective validity of the categories as a priori concepts rests, therefore, on the fact that, so far as the form of thought is concerned, through them alone does experience become possible. (B126) 
10. [Categories] are concepts of an object in general, by means of which the intuition of an object is regarded as determined in respect of one of the logical functions of judgment. (B128) 
11. [A]ll combination -- be we conscious of it or not, be it a combination of the manifold of intuition, empirical or non-empirical, or of various concepts -- is an act of the understanding. To this act the general title 'synthesis' may be assigned . . . (B130) 
12. It must be possible for the 'I think' to accompany all my representations; for otherwise something would be represented in me which could not be thought at all, and that is equivalent to saying that the representation would be impossible, or at least would be nothing to me. (B131) 
13. For the manifold representations, which are given in an intuition, would not be one and all my representations, if they did not all belong to one self-consciousness. As my representations (even if I am not conscious of them as such) they must conform to the condition under which alone they can stand together in one universal self-consciousness, because otherwise they would not all without exception belong to me. (B132) 
14. Understanding is, to use general terms, the faculty of knowledge. This knowledge consists in the determinate relation of given representations to an object; and an object is that in the concept of which the manifold of a given intuition is united. (B137) 
15. Therefore the empirical unity of consciousness, through association of representations, itself concerns an appearance, and is wholly contingent. (B140) 
16. Knowledge involves two factors: first, the concept, through which an object in general is thought (the category); and secondly, the intuition, through which it is given. For if no intuition could be given corresponding to the concept, the concept would still indeed be a thought, so far as its form is concerned, but would be without any object, and no knowledge of anything would be possible by means of it. So far as I could know, there would be nothing, and could be nothing, to which my thought could be applied. (B146) 
17. If . . . we admit that we know objects only in so far as we are externally affected, we must also recognize, as regards inner sense, that by means of it we intuit ourselves only as we are inwardly affected by ourselves; in other words, that, so far as inner intuition is concerned, we know our own subject only as appearance, not as it is in itself. (B156) 
18. I have no knowledge of myself as I am but merely as I appear to myself. (B158) 
19. We cannot think an object save through categories; we cannot know an object so thought save through intuitions corresponding to these concepts. Now all our intuitions are sensible; and this knowledge, in so far as its object is given, is empirical. But empirical knowledge is experience. Consequently, there can be no a priori knowledge, except of objects of possible experience." (B165-6) 

All alterations take place in conformity with the law of the connection of cause and effect. (B232)

• Events = alterations of things (what's at issue) 
• Problem: how to distinguish among impressions {1} 
• objective succession: foundation -> roof 
• subjective succession: roof -> foundation 
• Solution: objective = non-arbitrary = C->E rule governed {2} 
• bodies & physical events: laws of physics 
• minds & mental events: laws of empirical psychology. 

1. Let us suppose that there is nothing antecedent to an event, upon which it must follow according to rule. All succession of perception would then be only in the apprehension, that is, would be merely subjective, and would never enable us to determine objectively which perceptions are those that really precede and which are those that follow. (B239) 
2. The experience of an event [ i.e. of anything as happening ] is itself possible only on this assumption [of an antecedent cause]. (B240)