The Critique of Pure Reason
My preferred way of engaging with books is reconstruction. These notes were created during my reading process to aid my own understanding and not written for the purpose of instruction. With that said, I’ve decided to share these unedited notes on the off chance they are helpful to other readers.
Objective
Kant wrote CPR in the age of the enlightenment which was an age of sharp criticism founded on a mechanistic metaphysics influenced by Newtonian physics. This mechanistic view coupled with the universal urge to put ideals under the microscopic of rational criticism threatened traditional moral and religious beliefs. CPR shows that a critique of reason through the means of reason alone is able to bound the domain of reason to its appropriate use, namely science and math but not metaphysics and religion. He is attempting to maintain both the authority of reason with the authority of religion.
“For the main question is always this: what, and how much, can understanding and reason cognize independently of all experience?”
“Once metaphysics has been brought by this critique onto the secure path of a science, it is able to encompass completely the entire realm of the cognitions pertain ing to it. Hence it can complete its work and put it aside for the use of posterity, as capital that can never be increased.”
“A cursory survey of this work will leave one with the impression that such a metaphysics benefits us only negatively, viz., by instructing us that in [using] speculative rea son we must never venture beyond the boundary of experience; and this instruction is indeed its primary benefit. But this benefit becomes positive as soon as we become aware that the principles with which speculative rea son ventures beyond its boundary do not in fact expand our use of reason; they unfailingly narrow it, as we find when we examine them more closely.”
“I have therefore found it necessary to deny knowledge, in order to make room for faith.”
Overview
“How are synthetic a priori propositions possible? This question is often times understood to frame the investigations at issue in Kant’s Critique of Pure Reason. In answer to it, Kant saw fit to divide the question into three: 1) How are the synthetic a priori propositions of mathematics possible? 2) How are the synthetic a priori propositions of natural science possible? Finally, 3) How are the synthetic a priori propositions of metaphysics possible? In systematic fashion, Kant responds to each of these questions. The answer to question one is broadly found in the Transcendental Aesthetic, and the doctrine of the transcendental ideality of space and time. The answer to question two is found in the Transcendental Analytic, where Kant seeks to demonstrate the essential role played by the categories in grounding the possibility of knowledge and experience. The answer to question three is found in the Transcendental Dialectic, and it is a resoundingly blunt conclusion: the synthetic a priori propositions that characterize metaphysics are not really possible at all. Metaphysics, that is, is inherently dialectical. Kant’s Critique of Pure Reason is thus as well known for what it rejects as for what it defends. Thus, in the Dialectic, Kant turns his attention to the central disciplines of traditional, rationalist, metaphysics — rational psychology, rational cosmology, and rational theology. Kant aims to reveal the errors that plague each of these fields.” — SEP
Kant grounds necessity in the faculties of the observer and achieves a Copernican revolution in philosophy: we are the law-givers rather than simply law-followers.
The Question of Synthetic A Priori
An elucidation of Kant’s emphasis on the importance of synthetic a priori concepts over its analytic counterpart will lead me to explain the existence, importance, and ubiquity of synthetic a priori from a Kantian position.
The existence of synthetic a priori is not an uncontended one. Kant needs to first argue against the Empiricist position that we have no access to strictly universal truths and all a priori truth are merely a posteriori concepts with the illusion of universality. “From a repeated association of what happens with what precedes, and from our resulting habit of connecting presentations” He then needs to show that the distinction between analytic and synthetic is a valid one.
Kant describes the necessary and sufficient conditions of a priori truth as strict universality and necessity. A necessary and universal judgement cannot be the result of observation and must be true on its own or preceding from judgement that are themselves necessary. While its truth value must not be dependent upon any empirical observations yet one might need experience to gain the requisite concepts to postulate these a priori truths. “First, then, if we find a proposition such that in thinking it we think at the same time its necessity, then it is an a priori judgment; and if, in addition, it is not derived from any proposition except one that itself has the validity of a necessary proposition, then it is absolutely a priori. Second, experience never provides its judgments with true or strict universality, but only (through induction) with assumed and comparative universality; hence [there] we should, properly speaking, say [merely] that as far as we have observed until now, no exception is to be found to this or that rule. If, therefore, a judgment is thought with strict universality, i.e., thought in such a way that no exception whatever is allowed as possible, then the judgment is not derived from experience, but is valid absolutely a priori.” To realize their existence and necessity, one ought only look at judgements such as “All Bachelors are Single” and certain math propositions to understand that their truth value is not dependent on anything empirical. Furthermore, we have forms of cognition such as space and time that seems necessary and therefore must be a priori concepts that resides in our cognitive powers. Q: I’m still not convinced on the necessity of space? Can’t I reason in symbolic logic and cognize that way without space? If space and time are inescapable why can’t they be properties of reality instead of what my consciousness imbues upon them? We have no input for space but we have no input for color either (is that true we do get wavelengths but we don’t get a third dimension, we necessarily must construct it).
Kant goes on to illuminate the difference between synthetic and analytic judgements. Analytic judgements access the definition of the concept, and therefore is necessarily a priori: “I can formulate my judgment without going outside my concept, and hence do not need for it any testimony of experience.” Synthetic judgements, on the other hand, go beyond the definitions of the concept and thus necessarily rely on something more for its truth value; all empirical judgements are synthetic. A litmus test to differentiate is that only the negations of analytic statements are contradictions. Yet there appears to be a class of synthetic a priori judgements, most notably in arithmetic, such as “5+7=12” that is a priori in its universality but the predicate is nowhere to be found through a dissection of the subject. Hence Kant makes a distinction between synthetic and analytic a priori. The key question of Kant’s text is to answer how are these synthetic a priori judgements possible since they cannot use experiences which have no universal authority to relate concepts.
Kant argues that to reject the possibility of synthetic a priori would be to commit the Humean error of announcing that “everything that we call metaphysics would amount to no more than the delusion of a supposed rational insight into what in fact is merely borrowed from experience and has, through habit, acquired a seeming necessity.” Such a stance would destroy any pure philosophy, but one ought only look at arithmetic to see the possibility of synthetic a priori.
The first critique that can be leveled at this juncture is that the subjectivity of definitions and categories makes it impossible to objectively differentiate between synthetic and analytic a priori and even a priori and a posteriori. If we were to define event as “impermanent action with a starting cause” then the judgement “all events are caused” wouldn’t be, as Kant proposed, a synthetic judgement. Furthermore, consider an alternate but plausible universe before the discovery of the first black swan where biologists defined swan as “white bird with elongated neck”. In this world the judgement “all swans are white” is a priori rather than a posteriori and the discovery of the first black swan might inspire the creation of a distinct category rather than the alteration of the original. Due to the subjectivity of definitions and whole taxonomies, the distinction between synthetic/analytic and a priori/a posteriori seem equally subjective.
Another critique that can be leveled is simply that I can define “5+7” to be 12. However if we conceive of human knowledge as pryphorian trees we can only define things by putting restrictors on the parent subset. Cat is a purring mammal is ok.. But george is son of Jeb is not ok… (the latter implies a relation)…this is quite convincing.
After Kant explains the existence of synthetic a priori, he goes on to elaborate on its importance which can be broken down to its authority and expansiveness.
Synthetic a priori, being an a priori, implies necessity and universality. For us to build knowledge we must ensure that our foundations are sound, for if we build off of a posteriori judgements we have no certainty of our conclusions. As a anti-model he proposes Plato who left world of sense and into the realm of ideas but “failed to make headway because he had no resting point against which-as a foothold”. Only by seeking “assurance through careful inquiries that the foundation had been laid” on a priori principles can our conclusions have universal authority.
But unlike analytic a priori judgements whose insights must remain within the confines of the subject’s definition, synthetic a priori are expansive. “For they do add to the concept of the subject a predicate that had not been thought in that concept at all and could not have been extracted from it by any dissection.”
Synthetic a priori’s importance is rooted in the fact that it is the only mode of judgement which both has universal authority as well as expansiveness to further our knowledge beyond the elucidation of concepts. This feature, Kant promises, will prove to be extremely foundational when we go beyond the world of sense “where experience cannot provide us with any guide or correction.” It is in this sphere we make “treasured inquiries into the unavoidable problems of reason: [God, Freedom, and Immortality].”
Lastly, Kant shows the ubiquity of synthetic a priori propositions behind our most fundamental sciences. In mathematics, other than a few propositions such as “a=a”, all propositions are synthetic. One ought only look at the absence of the predicate in the subject in even as simple a statement as “5+7=12” to confirm its status as synthetic. In the natural sciences, synthetic propositions such as “quantity matter remains unchanged” are the cornerstone upon which scientists build their edifices of knowledge. Likewise, metaphysics “Metaphysics is not at all concerned merely to dissect concepts of things that we frame a priori, and thereby to elucidate them analytically. Rather, in metaphysics we want to expand our a priori cognition. In order to do this, we must use principles which go beyond the given concept and which add to it something that was not contained in it”.
The ambition of Kant’s claim of ubiquity is to distill down the problems of these three vast fields into one question: How are synthetic judgements possible a priori? In answering this, Kant explains, we will have explained how mathematics, metaphysics, and the natural sciences are all possible. “Much is gained already when we can bring a multitude of inquiries under the formula of a single problem.”
To conclude, Kant maintains that philosophy should focus on synthetic a priori judgements by proving their existence, demonstrating their importance through their authority and expansiveness, and lastly their ubiquity in our most important fields of inquiry.
Transcendental Aesthetic: Space and Time
Kant’s solution to the problem of synthetic a priori in math for statements such as “The angles of all triangles sum up to be 180” is that space and time are the forms of our sensibility. That is to say space and time are empirically real (since we interact with the entire world through sense, empirical evidence must take upon these forms as well) but transcendentally ideal (it is an idealist position in so far as that we are spatio-temporal cognizers and these laws root from us).
Kant points to the fact that our eyes only get inputs in two dimension and that we don’t sense time as some of the evidence that space and time is contributed by us.
A transcendental faculty is a faculty that is necessary for cognition, thus Kant grounds necessity in the faculties of the observer and arrives at a Copernican revolution in philosophy: we are the law-givers rather than simply law-followers.
Kant would answer the original question like this: triangles all sum up to be 180 because the form of our intuition is a Euclidean space. That is how we are able to achieve this synthetic a priori truth.
Transcendental Analytic: The Categories
“Therefore all possible perceptions, and hence also everything whatever that can reach our empirical consciousness, i.e. all appearances of nature, must in regard to their combination be subject to the categories. Nature … depends on ... the categories as the original basis of its necessary law-governedness.” (B165) Again, what is the thesis and has Kant made it at all plausible?
Kant thesis is that there a priori categories we can apply to objects in perception even if we did not generalized these concepts from empirical perception, as a result all of our empirical sciences can be said to be governed by a priori rules which are universalized. Categories are labels one can assign to an object such that all truths about that category apply to the object.
Kant does not have any problem with empirical categories such as “white” or “hard” because we can simply refer to them in experience. But there is a certain set of a priori categories -- substance, cause, etc. -- that are not derived from sensibility. In opposition to Hume, who believes we thus cannot use these a priori categories, Kant’s project is to argue for the necessity of them.
I will argue that in the transcendental and metaphysical deductions alone, Kant only convinces on the necessity of categories, but does not plausibly defend the necessity for the a priori categories he posits in the metaphysical deduction.
My essay will begin by examining the metaphysical deduction: describing its purpose and showcasing it’s irrelevance to Kant’s thesis. I will then trace Kant’s argument in the transcendental deduction: object cognition requires synthesis, synthesis requires transcendental unity of apperception (TUA), and finally TUA requires the application of categories to objects. Finally, I will defend my position on the shortcomings of Kant’s argument before discussing the ramifications of Kant’s conclusions on the universality of our natural laws.
I will necessarily need to sacrifice the detail of reproduction of Kant’s argument due to the wide scope of his argument.
1. The Metaphysical Deduction
In the metaphysical deduction, Kant argues that understanding is a function of judgement, proceeds to create an exhaustive table of the types of human judgement, and deduces the necessary a priori categories that the judgements refer to.
Yet, his project in this section is merely one of laying the groundwork, our thesis of interest is not contingent upon it. Thus, I will begin my discussions from the transcendental deduction.
2. Object Cognition necessitates Synthesis
We begin the transcendental deduction with object cognition: our ability to form representations of objects. Kant argues that we are presented with a manifold of sensory data, and thus, this capacity must be dependent on our ability to synthesize. Specifically we need to be able to synthesize wholes from particulars (Apprehension), synthesize sensory data with mere reproductions (Imagination), and synthesize according to rules (Apperception). I will now show the necessity of each of these synthesis for object cognition.
2.1 Synthesis of Apprehension
In order to have object cognition we need to produce from disjoint parts a comprehensible whole. The unintuitive quality of this statement speaks to how intuitively our ability of synthesis works -- we do not even consider it a step of processing to create wholes out of parts.
Kant gives the example of the church. Visually, you might take in it’s dome first and then the flying buttresses and glass windows, all while you are in motion. There is no inherent order and unity within the sensory data itself. It is our capacity, specifically the synthesis of apprehension, which creates the entire cognition of the church from these parts. “For the imagination is to bring the manifold of intuition to an image” (A120).
Without this ability we would be dealing with essentially dots of sensory data, as the windows, dome, and buttresses themselves are combined.
2.2 Synthesis of Imagination
Now, suppose the dome of the church is obscured. Clearly our faculties of object cognition would not conceive of the church as being domeless. We compensate mentally for our visual impairment by reproducing the missing element from our memory.
The synthesis of imagination reproduces elements that are not directly available to our sensory faculties.
2.3 Synthesis of Apperception
To conceive of an object, we also need to be able to subject these objects to certain rules.
Take writing the sequence “1,2,3” on the board. When we say or write the next symbol “4” it is not merely the production of a meaningless sound or arrangement of pen strokes. It has a meaning provided by the sequence it is in which is governed by a rule, namely, the counting rule.
If we lost this ability to subject our objects of cognition to rules, we could not even produce the next character in the sequence, let alone consider it meaningful. “Without the consciousness that what we are thinking is the same as what we thought an instant before, all reproduction in the series of representations would be futile. For what we are thinking would in the current state be a new representation, which would not belong at all to the act by which it was to be produced little by little” (A103).
After establishing the necessity of synthesis for object cognition. Kant goes on to show the necessity of TUA for synthesis.
To practice the synthesis of apperception mentioned in 2.3, one must realize the unity of the consciousness producing the rule. Only with the confidence that the consciousness that says “3” is the same that is about to say “4”, can we meaningfully apply the counting rule to our previous example.
Kant turns the metaphysical question of the “I” into an epistemic necessity: in some manner we need to conceive of our stream of consciousness as identical to even carry out the rules which we synthesis (although Kant is hesitant to assign any metaphysical corollary to this “I”). And this identity condition, this unity between consciousness temporally is what the TUA claims. “The concept of combination carries with it, besides the concept of the manifold and of its synthesis, also the concept of the manifold's unity” (B 131).
Without TUA we would have no basis to believe that the rules we apply to our objects are valid. At this point we have established the necessity of TUA for synthesis, and thus, object cognition.
3. TUA Requires the Application of Categories
Kant’s final move to show that object cognition requires the application of categories is by reversing the arrow of causality in our previous section. Object cognition is necessary for TUA just as TUA is necessary for object cognition.
The only way that TUA is possible is if we repeat this act of synthesis across a temporal manner. Consider a subject in a vacuum observing nothing but an orange. The only way he is assured of his continued stream of consciousness, TUA, is by observing that he is continually synthesizing the same orange and that the same orange belongs to the same consciousness. “For the manifold presentations given in a certain intuition would not one and all be my presentations, if they did not one and all belong to one self-consciousness … They surely must conform necessarily to the condition under which alone they can stand together in one universal self-consciousness, since otherwise they would not thoroughly belong to me” (B132).
Kant completes his argument by stating that these necessary conditions to recognize representations as “mine”, that they belong to the same consciousness, is precisely that they conform to the categories: “Therefore everything manifold, in so far as it is given in one empirical intuition, is determined in regard to one of the logical functions of judging, in as much as through this function it is brought to one consciousness as such. The categories, however, are indeed nothing but precisely these functions of judging insofar as the manifold of a given intuition is determined in regard to them. Hence, by the same token, the manifold in a given intuition is subject necessarily to the categories” (B143).
4. Plausibility
Kant, starting from object cognition, successfully argues for the necessity of our application of categories in general. But he does not explain, at least in the transcendental and metaphysical deductions alone, why we need a priori categories.
If our TUA is dependent upon “one of the logical functions of judging, in as much as through this function it is brought to one consciousness as such,” then surely we can sustain our TUA through empirical judgements based on empirical categories. Instead of using the orange’s substance, which is an a priori category, to ground our TUA, it seems just as plausible we can use our continued perception of whiteness to unite our conscious states through time.
There is a missing link in Kant’s argument that only these a priori categories can ground an agent across time, allowing him to establish TUA.
6. Nature
Kant’s thesis is meaningful to his contemporaries discussion of natural laws because it would enable them to claim universality from mere empirical observations.
Kant’s Copernican revolution in epistemology would enable scientists, especially newton and his three laws, to explain the universality of their empirical laws by claiming that they are necessitated by the a priori categories. This will not be fully satisfying to some scientists, because these laws would only be able to be applied to our representations of things rather than things in and of themselves:
“Concepts that prescribe laws a priori to appearances and hence to nature regarded as the sum of all appearances … exist not in themselves but only relatively to the subject in whom the appearances inhere insofar as the subject has senses … Things in themselves would have their law-governedness necessarily, even apart from an understanding that cognizes them. But appearances are only presentations of things that exist uncognized as regards what they may be in themselves … Therefore all possible perceptions, and hence also everything whatever that can reach empirical consciousness, i.e., all appearances of nature, must in regard to their combination be subject to the categories.” (B163-B165)
Metaphysics into Epistemology
In the transcendental analytic, Kant turns metaphysics into epistemology. Instead of arguing for substances, causes, or selves he argues that these categories are necessities for our cognition to function, and that no matter if they exist metaphysically we must conceive of them epistemically to even cognize!
Refutation of Idealism
Kant does not consider himself an idealist philosopher. Mostly because he argues that self-consciousness (TUA) can only be achieved by object perception through time. It is only through the permanence of other’s things through time that the self can be cognized. This argument inverts the primacy of inner over outer experience of the idealist philosophers.
Transcendental Dialectic: the impossibility of Metaphysics
The first two sections has been positive: laying solid groundworks for what other philosophers thought to be impossible. This section, the answer to the third question “how is synthetic a priori knowledge of metaphysics possible?”, shows the impossibility for what other philosophers thought to be the most solid groundworks of all.
Transcendental idealism is the belief that all of our discussion so far has been localized in the phenomenal realm: the realm of sensibility and objects of our cognition. But there also exists a noumenal realm that is the realm of things-in-themselves. Because, by definition, these objects are not objects of our cognition they do not conform to our categories and thus our reason cannot generate any synthetic a priori knowledge about metaphysics. That is not to say we cannot have practical “proofs” for these three categories which is exactly the project he undertakes in his second critique.
Kant formed three antinomies of reason by assuming that there is no noumenal realm and everything could be accessed by reason (transcendental realism). Antinomies are directly opposing statements: p and not p which are both shown to be true. It is meant to show that one of the assumptions that lead to the antinomy is wrong, namely transcendental realism.
Free Will
The free will problem can be defined as such: 1. All events are caused. 2. Human actions are free. 3. If an action is caused then it cannot be free. Yet these three premises cannot be all true at once. Different philosophers have rejected different parts of this system. Seen under this historical light, Kant’s project of defending free will in the first critique is both ambitious and modest: ambitious, because he wants to preserve full determinism in our natural world coexisting with an uncompromised capacity of human agency; modest, because he is merely showcasing the possibility and not proving it’s actuality.
In the third antinomy, Kant aims to show how both the thesis — there is both causality from nature and freedom — and the antithesis — there is only causality from nature — are true, which would force us to reexamine our assumptions that led to this clear contradiction. He proves the truth of the thesis through a reductio of the antithesis. He shows how the latter reduces to an incomplete series of events that happens “without a cause sufficiently determined a priori” — an impossibility as shown in the second analogy (A446). He proves the truth of the antithesis through a reductio of the thesis. The latter is reduced to the claim that there must exist a “state that has no connection of causality with the preceding state of the same cause” (A447). This is rejected by the groundwork laid out prior to the third antinomy, arguing how everything in the empirical world must abide by natural laws.
Kant aims to resolve this seeming paradox through transcendental idealism, the claim that there is a phenomenal realm of appearances which abide by empirical laws and a noumenal realm of things-in-themselves which we have no access to. The common premise that led to this “P and not P” situation which therefore must be rejected is that “every effect in the world must arise either from nature or from freedom” (A538). That is to say an effect can be both caused by freedom and the laws of nature if we don’t make the mistake of taking appearances in the phenomenal realm as noumenal: “for if appearances are things in themselves, then freedom cannot be saved.” (A537). Instead, once we realize that we have an intelligible character in the noumenal realm, which does not abide by the properties of time, it at least gives us the possibility of freedom because it can escape the grasp of natural causality which only has domain in the phenomenal realm. “For insofar as this subject is noumenon, nothing occurs in it and there is found in it no change requiring dynamical time determination and hence no connection with appearances as causes. Therefore, this active being would to this extent be independent and free in its actions from all natural necessity, which is found only in the world of sense” (A540).
What might be the mechanism of this human agency? Kant does not intend to give a full proof but instead gives us a sketch of what could be a possibility. Human agency, Kant suggests, relies on our ability to reason. Reason is different from our “empirically conditioned abilities, because it examines its objects merely according to ideas and according to these ideas determines the understanding” (A547). Because reason “is not subjected to the form of time” the causality of reason in it’s intelligible character is freed from this natural law which only appearances in time are governed by (A552).
Kant anticipates an opponent’s critique: in what capacity can reason be called free, if all of the empirical appearances of the decisions that it makes are already determined and made necessary by natural laws (A551). What the opponent fails to grasp is that Kant is suggesting something more radical. He is suggesting that reason operates in an atemporal manner and makes all of its decisions in a timelessly instant manner that is then injected into our temporal world. This is Kant’s own form of Leibnizian correspondence that he has yet to prove but merely argues the possibility for.
By operating under the framework of transcendental idealism, Kant removed the false premise behind the third antinomy showing how “both of the mutually conflicting propositions may be true simultaneously in a different reference” (A561). In this project, he has argued for the possibility of transcendental freedom — the ability to create new causal chains — which gives room for practical freedom — the ability to refrain ourselves from the coercion of sensibility through our intelligible character in the noumenal realm.