notes on kant’s c.p.r.
January 29, 2015 § Leave a comment
Immanuel Kant’s (1724-1804) Critique of Pure Reason (1781 & 1787; hereafter CPR) had several aims, one aim had to do with getting at an understanding of how we come to know things by the use of reason. A rigorous critique of reason for Kant includes detailed ways in which our knowledge of the empirical world combines with reason, and how universal and necessary knowledge is justified apart, and combined with, empirical knowledge claims. In order to accomplish these goals, Kant picked up where his predecessors left off. Although there were others, Gottfried Wilhelm Leibniz (1646-1716) and David Hume (1711-1776) represent two predominate philosophical trends from which Kant was influenced, and from where he wished to start his legendary critique.
Leibniz was a rationalist, and Hume was an empiricist. Kant, in the CPR would refer to each, respectively, as a dogmatist and a skeptic. These two modes of philosophical thinking are also referred to by Kant as “transcendental realism.” He writes of them, “hence the transcendental realist conceives outer appearances […] as things in themselves that exist independently of us and our sensibility […]” (A369). In short, this is the typical, and ordinary, way of thinking about objects as distinctly separate from our thinking of them. But how does this apply to Leibniz and Hume?
Leibniz is a transcendental realist, because in his rationalist way of thinking about the world, he separates knowledge into a system that favors the rational over the contingent (empirical). Leibniz divides knowledge of truth in two ways, the rational part of the way man knows things is known as a “truth of reason.” These truths of reason are necessarily and universally true and cannot be contradicted. Such truths are classified as the laws of nature, pure mathematics, and so on. As for contingent truths, Leibniz refers to these as “truths of fact.” Truths of fact are contingently true and are known to us via the senses, i.e. in an empirical way. In Leibniz’s rationalist understanding of the world, God and our God-given rationality are sovereign over and beyond what can be known as a truth of fact. Since the world we know by the senses—a truth of fact—is essentially contingent, then the only way to be sure of things is to appeal to an all prevailing reason. Again, this is a form of transcendental realism because the contingent world of the senses is completely reliant on the rational way in which we come to understand it (i.e. the subject and object are separate).
Hume, on the other hand, is a transcendental realist due to his skeptical empiricism. Hume’s division of knowledge is commonly referred to as “Hume’s fork.” There are, for Hume, “relations of ideas” which are otherwise known as truths of reason, necessary truths such as natural laws, pure mathematics &c. are included in this category. And there are “matters of fact,” the substantive world which is empirically known via the senses. Matters of fact also bear the marks of contingency. Since Hume’s philosophy draws all of its conclusions from an empirical way of understanding, even the associations of ideas can be traced back to an experiential origin. For Hume’s radical skepticism, reason and contingency are not necessarily compatible, therefore a quest for reason in the midst of the sensible becomes pointless (vacuous, arbitrary, &c.). Habit and association are what we have to rely on to put the world together as knowledge (re: inductively).
Both of these views present problems when it comes to justifying an objective (empirical) knowledge that relies on necessary and universal claims to truth (re: scientific knowledge). In Leibniz’s world, rational thinking only affirms itself without proper recourse to the contingent world. And as for Hume’s empiricism, all we have is the sensible world. Therefore for Hume, any recourse to universal necessity becomes unnecessary, and any thought of a fundamental structure that underlies experience becomes only a series of associative habits.
Enter Kant’s “Copernican revolution.” It should now be remarked that this turning from transcendental realism represents what Kant will name transcendental idealism, whereby cognition plays an active role in the way objects are understood, and subjective cognition is no longer separate from the objects of cognition (objectivity). Describing and elucidating transcendental idealism is another primary and critical goal of the CPR. Kant’s emphasis had to do with how transcendental idealism subjectively constitutes the objective world for man. In the 1787 “Preface” to the CPR Kant writes, “Thus far it has been assumed that all our cognition must conform to objects. […] Let us, therefore, try to find out by experiment [i.e. a central project of the CPR] if we assume that objects must conform to our cognition” (Bxvi). It is here that we find Kant demonstrating that objects must conform to our cognitive reasoning, instead of a turn to the objects themselves, or to our reasoning alone. Kant’s transcendental idealism seeks to reconcile rational and empirical philosophy by means of a counter-intuitive change of cognitive perspective. Copernicus shifted astronomical perspective away from a supposed position on an unmoving and centered earth. He took on the perspective of what the universe (and rotating solar-system) would look like if we were on the sun. Heliocentrism ended up making more (calendric) sense than a Ptolemaic system. It was this Copernican thought experiment that changed the way we thought about our calendar and our place in the solar-system, and the universe.
Kant’s new transcendental idealism also changed the way we understand that the very structure of our cognition determines the way objects appear to us. The CPR will be a heroic, systematic and scrupulous attempt to show how cognition does this.
Quite often when we are introduced to the first two (of the four above knowledge terms) a priori and a posteriori, a priori knowledge is typically defined as coming before experience. If we start with this common way of designating a priori knowledge we find ourselves confused, since Kant, in the CPR, explicitly states in the first sentence of the “Introduction,” “There can be no doubt that all our cognition begins with experience” (B1). A way to fully explain how a priori knowledge (reason) is combined with experience (empiricism) would be by way of Kant’s transcendental philosophy, “I call transcendental all cognition that deals not so much with objects as rather with our way of cognizing objects in general insofar as that way of cognizing is to be possible a priori” (A12-B26). A priori knowledge does not happen because of experience, instead, it’s the governing cognitive structure of experience, and it shows itself via necessity and universality discerned apart from the contingency of experience. That is to say, the necessary and universal aspects of cognition are a means by which a priori knowledge is made evident.
To begin with we’ll explicate what these terms mean, with Kant’s special emphasis on synthetic/a priori judgments, and transcendental idealism. Then we’ll continue, by looking at how the four types of knowledge/judgments (a priori, a posteriori, analytic, and synthetic) are comparable to the (above mentioned) “transcendental realist” positions of Leibniz and Hume. We will close with a brief explanation of Kant’s synthetic/ a priori judgment and its connection to transcendental idealism.
The first order of business will be to look at a priori and a posteriori knowledge (alternately referred to by Kant as cognitions). Avoiding the typical way of defining a priori knowledge as ‘prior to experience,’ we will instead define it as having to do with the rational ways in which we know things necessarily, universally, and as irrefutable. A classic example of an a priori cognition is: ‘all bachelors are unmarried.’ With this knowledge claim we immediately think of it as experientially irrefutable. Without being ridiculous, we cannot think of any case whereby a bachelor is married. Once a bachelor becomes married he is no longer a regarded as a bachelor. A bachelor, by definition, is necessarily unmarried, and this necessity holds universally. Unmarried bachelorhood cannot be refuted by the man becoming married. Once we see that a knowledge claim withstands a test of irrefutability, it can then be said to be necessary and universal—hence it is a priori knowledge.
Similarly, a posteriori knowledge is often thought of as happening after experience, but this too adds confusion (for the above mentioned reasons, i.e. all knowledge starts with experience). It makes more sense to regard a posteriori as contingent knowledge that is experientially refutable. The raw material of experiential life is a posteriori, and the rational structuring principle of life is a priori. A posteriori knowledge also accounts for contingency.
Kant was not satisfied to simply retain a priori and a posteriori as the sole means by which we understand things, so he introduced what he called analytic and synthetic judgments. Analytic judgments are usually statements or propositions about the world, having to do with predication. When I say something about an object, I predicate an object. With an analytic judgment, predication is contained within the subject. With a synthetic judgment, predication is not contained in the subject. Analytic and synthetic judgments rely on identity to tell them apart. With analytic judgment the subject predicate link is explicative. Kant’s also calls this “elucidatory” (A7-B11). In other words, the predicate explains, and explicates the subject. As with Kant’s example “all bodies are extended” (A8-B11). The predicate term ‘extended,’ explicates bodies in space, i.e. all bodies have extension, and no body is without extension. With synthetic judgments the subject predicate link is expansive. In other words, the predicate expands the meaning of the subject. Kant’s example is “all bodies are heavy” (A7-B11). The predicate requires us to go elsewhere (re: into experience) to explain the subject. In his example the respective weight of things has to be investigated to know what is heavy, and what is not heavy.
Also, for an analytic judgment to be true, the contrary of the predicate has to be self-contradictory, that is to say, contradiction of the predicate would be inconceivable. With the judgment “all bodies have extension,” no refutation (contradiction) can be conceived of, we cannot think of a physical body as un-extended. Then, with a synthetic judgment to be true, the predicate’s denial is not self-contradictory, that is to say, a contradiction of the predicate is conceivable. As with the judgment “all bodies are heavy,” a refutation can be conceived of, that is, we can immediately think of a physical body that is lightweight, e.g. ultra fine dust particles, &c.
But how are these four terms connected? (a) An analytic/a posteriori judgment is an impossible connection since we cannot appeal to experience to predicate an analytical judgment. (b) Synthetic/ a posteriori judgments rely on experience to expand predication of a judgment. (c) And analytic/a priori judgments are really about logical truth and pure reason, these judgments rely on necessity and universality for their truth claims. (d) Then there is Kant’s special (transcendental idealist) case of synthetic/ a priori judgments, whereby we know something with a priori knowledge, yet, in order to make a judgment about it we must expand the knowledge claim synthetically (more on the transcendental idealist position below).
And what about the empiricism and the rationalism of the transcendental realists, a.k.a. Hume, the skeptic, and Leibniz, the dogmatist?—how do these positions line up with priori/a posteriori knowledge and analytic/synthetic judgments? Both thinkers acknowledged the basic a posteriori/ a priori distinction, yet neither acknowledged these forms of knowledge as intrinsically combined. For Hume, necessity is thought of as vacuous, which is to suggest that an analytic/a priori judgment is something that cannot be founded in experience, therefore, the only valuable combination for him is the synthetic/a posteriori judgment. Hume’s skeptical empiricism allows for a priori and analytic reasoning for mathematics, yet he famously favored inductive reasoning. Contrariwise, Leibniz’s metaphysical rationalism ultimately favored the analytic/a priori, since the substantive contingency (a synthetic/a posteriori judgment) of experience is only a mirror of the rational mind of the subject (and God). Therefore, his dogmatism only allowed for the precedence of reason. The world of the rational subject and the world of substantive contingency only mirror each other and never-the-twain-shall-meet in Leibniz’s system.
Kant’s transcendental idealist innovation was with the synthetic/a priori judgment. An example of this, offered in the CPR, is mathematical: “7 + 5 = 12” (B15). Here, we know that the sum is necessary and universal, we can’t think of another way to add these two numbers without being ridiculous—knowledge of this sum is a priori. Likewise, when we work on the problem out we can possibly get it wrong (this point is made more evident with larger more cumbersome numbers. With “7 +5” the sum is too obvious). A judgment of this sum is conceivably refutable, i.e. it is synthetic, and we might make a mistake in our calculations. Essentially a primary focus of Kant’s CPR is directed at explicating synthetic/a priori claims. His philosophy deals explicitly with synthetic/a priori knowledge, otherwise known as transcendental idealism. Kant wanted to lay down a foundation for science and mathematics while attempting to solve a few of the inherent problems of dogmatic rationalism and skeptical empiricism.
After the “Prefaces” and “Introductions” of the CPR, Kant then takes us through the arguments of the “Transcendental Aesthetic” (A19-B33—A49-B73). It is in the “Transcendental Aesthetic” where Kant proposes the idea that objects are given to us by way of sensual intuition. Basic intuition can be thought of as another word for experience (in an everyday sense of the word). Intuition describes how we are affected by objects, as much as it describes our primary and fundamental receptivity of the empirical world. Kant distinguishes between outer and inner intuitions, whereby space refers to all our outer intuitions, and time refers to all our inner intuitions. “Pure” intuition refers to “all presentations in which nothing is found that belongs to sensation” (A21-B35). This means that for Kant, ‘pure’ is another way of describing what is transcendentally ideal. Essentially, when we (theoretically) extract from all sensible intuition such things as the understanding of concepts, and when we (theoretically) extract the sensual components from experience, we find what Kant refers to as the transcendental, i.e. that specific and unique part of our intuition of space (and time) that is necessary—the a priori. Simply questing for the a priori is not the sole objective of Kant’s expositions on space and time, he also wants to show how if space is an intuition, then it is a synthetic judgment. Likewise, if space and time are synthetic/a priori judgments, then for Kant, space and time are transcendentally ideal.
In the CPR the “Transcendental Aesthetic” is divided into to two sections, “Section I” covers Kant’s arguments for the a priority of our knowledge of space, how space is known via intuition, and how his conclusions about space provide a justification for the synthetic/a priori basis for geometry and the sciences. The first subsection of “Section I” (§2) is titled the “Metaphysical Exposition of This Concept,” (hereafter MetEx), the second subsection (§3) is titled the “Transcendental Exposition of the Concept of Space” (hereafter TransEx). In a footnote Kant explains the difference between the MetEx, and the TransEx: the MetEx of space “investigates the nature of the presentation of space and shows that this presentation is a priori…” This is where Kant demonstrates that space is known to us a priori. And the TransEx of space “shows that and how from the a priori presentation of space something else that is a priori follows—viz., synthetic a priori cognitions.” That is to say, the TransEx of space shows that the science of space, geometry, relies on synthetic/a priori cognitions of space.
The MetEx of space subsection is further divided into four main arguments, grouped into two areas of emphasis, whereby 1 and 2 are arguments for the a priori cognition of space, and arguments 3 and 4 are arguments for space as an intuition, rather than as a concept. Let’s elaborate more on these arguments. In argument 1, Kant basically makes the claim that space is not an abstraction from empirical data. We don’t know about space by experiential reduction, nor do we know about space by the relationships of things. Space is, rather, the underlying part of all outer experiences (re: it is a priori). In argument 2, space is easily thought of without objects, but we cannot think of objects without space. Therefore, space is necessary (it is a priori) and it underlies the “presentation” all of our outer intuitions (A24-B39). Instead of moving consecutively to argument 3, we will jump to argument 4, since this argument allows for a better preliminary understanding of Kant’s argument that space is not a concept, as it is discussed in argument 3.
Kant has already provided two arguments (1 and 2) that the cognition of space is known to us a priori. Now he has to demonstrate that judgments about it are known synthetically as an intuition, instead of analytically, and he has to clarify that space is not a universal concept. With argument 4 it is important to know the difference between the instances of a concept, versus the particulars of an intuition of space. With the instances of a concept, each particular instance of a concept falls under the concept and each instance is not part of the concept as a whole. Each instance of a concept is merely an instance of the concept, rather then an intrinsic part of the concept. An accumulation of like concepts does not constitute a whole concept—i.e. every instance of a table does not make for the entire concept of a table. We don’t know about space by comparing a multitude of space-like concepts. We do, according to Kant, have an intuition of space whereby its particulars are thought of (cognized) as parts of the whole of space. Another way of thinking about this distinction would be to compare the relationship of parts and wholes of an intuition of space. Parts of space do not operate in the same way as concepts do, since space is thought of as an individual “infinite magnitude” (A25-B40). This is to suggest that the particulars of space cannot also contain individual “infinite magnitudes.” The particulars of space are not under space conceptually, they are space intuitively. Particular spaces cannot be taken apart in the same in the way that the concept of an object can be taken apart. When space is divided up into particular parts it does not lose any its spatial qualities, it just is another magnitude of space. Since space is an individual “infinite magnitude” it is not a universal concept (that is to say, it is not analytic)—it is a synthetic/a priori intuition.
Now to argument 3, where Kant repeats that we do not know about space by a reduction of empirical relations, that space is a priori, and that space is not a universal concept. In this argument we also find that the parts of space cannot precede the whole, and since we do not experience space via empirical abstraction, we do, however, experience space via one experience of it, “space is essentially one” (A25-B40). Again, as mentioned in argument 4, the particulars of space are not to be thought of as the particulars of concepts, if space is singular and individual, then a particular of space cannot be taken away that will alter our intuition of space. So our intuition of space does not have to do with comparing conceptual relations, we have to go out into the experience of space to answer questions about it, that is to say, we have to experience space with our intuition—synthetically. We must go beyond conceptual relationships to properly cognize judgments about space. Space is not contained in an analytic concept of space.
Lastly, the argument for the TransEx of space is meant to show that due to the synthetic/a priori intuition of space, the science of space (geometry) is made possible. The MetEx of space already argued that space is a synthetic intuition and that it is an a priori cognition. A transcendental judgment of space makes geometry possible, because, as we’ve shown, mathematics, geometry, &c., require a priori necessity, as much as they require synthetic predication (whereby a contrary is possible). Arguing for transcendental idealism is a primary aim of Kant’s CPR, and the “Transcendental Aesthetic” is no exception to this claim. It too shows that our intuitions (and our knowledge) of space and time are transcendentally ideal.
Kant’s expositions for time, more-or-less, line up with his expositions on space in the “Transcendental Aesthetic” sections from the CPR, with a few modifications. As noted above, when we (theoretically) extract conceptuality, and the basic sensual qualities from experience, we are left with the “pure” intuitions of space and time. Time, like space, is an a priori intuition. Under Kant’s terms, the designation “pure” usually means a priori, and whenever we are dealing with a priority for Kant, we are dealing with the transcendentally ideal. And as mentioned above, if space is intuited as an outer experience, then time is intuited as having to do with inner and outer experience.
For the subject of time, we will not repeat some of the forgoing issues mentioned with the space arguments. Although most of the issues apply to the intuitions of time in much the same way as did the intuitions of space. However, given time’s specific layout in the CPR, we will organize arguments 1 and 2 (the MetEx of time) as the arguments for the a priority of time. And arguments 4 and 5 (of the MetEx of time) are offered as the arguments for the time as an intuition rather than a concept. The TransEx of time consists of argument 3 (from the MetEx) whereby time is positioned as a synthetic judgment that justifies science (or the science of time, whatever that may be, temporal axioms, motion, &c.).
In the first argument in the MetEx of time, time cannot be known through empirical abstraction, just as we cannot know space by way of empirical abstraction. We do not necessarily know about time by comparing empirical events. Time underlies all empirical ways of knowing about it (A31-B47). We already presuppose infinite time in all cognition of things and events. Therefore, cognition of time is a necessary condition of the experience of temporal things and events. Time is intuited in an a priori way (i.e. it is transcendental). In argument 2, Kant presents time as a necessary presentation of experience underneath all intuitions of objects. In other words, time is easily thought of without the presentation of objects, yet we cannot think of objects without the presentation of time itself. Basically, how time gets filled with objects, happens contingently—we have the notion that time can be filled differently—events could have been otherwise. “Appearances, one and all, may go away; but time itself (as the universal condition of their possibility) cannot be annulled” (A32-B47). Therefore, time is a priori.
The two remaining arguments for time from the MetEx (aside from argument 3) are arguments 4 and 5, which offer justification for time as an intuition rather than by conceptualization. In argument 4, time is not a universal concept for Kant. Basically, the instances of concepts are to be differentiated from the parts of time. A concept’s relation to its instances is not the same as parts of time are intuited. For example, if we take the concept of a desk, each instance of a desk does not constitute part of the concept of a desk—an agglomeration of desks does not make for a total concept of a desk. Each desk is a particular instance of the concept desk. An intuition of time does not work the same way. Time’s particulars are not instances of the concept of time. Time’s wholeness is individual, when time’s particulars are brought together, they constitute the wholeness of time, and “different times are only parts of one and the same time…” (A32-B47).
Related to argument 4 is argument 5, to repeat, Kant is trying to establish that time is not conceptual, in other words, time is not analytic, and we are not comparing ideas in order to intuit time. We have to intuit time experientially, i.e. synthetically in order to make an intuitive cognition of it (transcendentally). So in argument 5, Kant’s temporal concerns are similar to his spatial concerns. Due to the infinity of time, time’s individual parts can only be known with respect to the whole. Time’s parts are limitations of the whole. Still we do not need a whole experience of time to know about time intuitively—we only need a single presentation of it to know it as time.
As for the TransEx of time, argument 3 belongs to it instead in the MetEx. It is here, in the TransEx of time, where Kant restates a point made in argument 4 (in the MetEx of space), “Time has only one dimension; different times are not simultaneous but sequential (just as different spaces are not sequential but simultaneous)” (A32-B47). Time has to be experienced to be known, this experience is known intuitively in a sequential way. If time’s intuitive sequence is not known to us analytically, it is known to us synthetically. The a priori and necessary intuitions of time are not analytic. We do not know about time conceptually. We do not know about time by comparing ideas. Another way of putting this would be to say that time is a transcendentally ideal cognition. Transcendentally ideal cognitions explain Kant’s synthetic/a priori judgments about the world, namely these judgments are necessary and about the contingent world of experience (re: judgments having to do with science). This is also where Kant writes about change and motion, made possible via the intuition of time. “Let me add here that the concept of change, and with it the concept of motion (as change of place), is possible only through and in the presentation of time [as an intuition, not a concept]” (A33-B49).
We will see that the spatiotemporal concerns of the “Transcendental Aesthetic” will be for Kant a cognitively fundamental way to get to the rest of the work of the CPR—conceptual understanding relies on spatiotemporal intuitions.
There is a wonderful metaphor Kant offered in the “Preface” to the first edition of the CPR, where metaphysical dogmatism is characterized as the reign of despotic reason, because of this it still retained traces of barbarism and civil wars ensued. Eventually these civil wars culminated into a state of anarchy, whereby the skeptics (of empiricism) who were nomads, would manage to continue the reap chaos (Aix-x). We already know that Kant intended the CPR to contend with a few philosophical issues of his day, namely the rationalism of Leibniz (Wolff, &c.) and the empiricism of Hume. Kant anoints each, the dogmatist and the skeptic respectively. The contention basically had to do with the manner in which each position, according to Kant, was unable to get at knowledge that was both about the world and necessarily true.
In order to see how Leibniz’s dogmatist position applies to analytic statements as substantive, and how Hume’s skeptical position considered a priori knowledge to be vacuous, we will consider each as a way that precludes problems raised in Kant’s CPR. In epistemology we have two distinctions concerning the ways in which things are known to be true (rationally): a priori (necessary) and a posteriori (contingent), these two epistemological classifications were used prior to Kant’s usage. It is also known that Kant introduced two finer distinctions related to the way we make rational judgments about things: analytic (where the predicate is found in the subject, and a contrary is inconceivable) and synthetic (where the predicate is not in the subject, and a contrary is conceivable). We will not demonstrate how these are combined for Kant, Leibniz, and Hume [This subject was explicated previously. See question/answer 2 above.]. We will show that for Leibniz, a substantive position must be strongly related to Kant’s analyticity, whereas Hume’s denies the sovereignty of the a priori.
For Leibniz’s rationalist metaphysics it is commonly known that when reason and contingency conflict, reason always prevails, because ultimately, reason is the only way in which we understand the world. This means that Leibnizian “truths of reason,” which rely on necessity are more important that “truths of fact” which rely only on contingency. But what about a Leibnizian claim that any substantive statements we make about the world are necessarily true? Recall that Leibniz was (for Kant) a “transcendental realist” which meant that objects in the world are mind-independent. For anything to be a truth of reason it had to conform to logical analysis. Essentially under Kant’s rules, if an analytic judgment means that predication is contained in the subject (i.e. to be a judgment of truth, we have to turn to a priori and analytic reasoning), and that a synthetic judgment means that the predicate is not contained in the subject (for it to be a judgment of truth, we have to turn to experience). This must mean that in Leibniz’s terms, if “matters of fact” only reveal contingent truth, then “truths of reason” have to be analytic. The only way to understand the truth of something has to do with the analysis of reason. In other words, in order to say anything substantive about the world, we, if we are followers of Leibniz, have to turn to reason only, since contingency is not useful in Leibniz’s rationalist circumstances. All finite reality mirrors the infinite rationality of God, therefore all meaningful reality must be analytic.
Hume’s empiricism, on the other hand, presents another set of difficulties that are tied to his speculative claim that a priori knowledge is vacuous, arbitrary, &c. Hume presents a straight-forward account of the vacuity of a priori reasoning when he discusses causality. Also, recall “Hume’s Fork” whereby, “relations of ideas” more-or-less represent necessary and mathematical truth, and “matters of fact” represent empirical contingency. If a priori and deductive reasoning relates to what is necessary, then Hume tries to downplay necessary connections by way of inductive reasoning. Put simply, the logical (a priori) connections that are made between causal events are more-or-less habitual for Hume. Usually when we see one event follow another, we connect the cause to the event by way of a priori necessity. Hume’s emphasis is that the a priori connection cannot—no matter how hard we try to find it—be found in experience. Any a priori connection, for Hume, is brought into empirical situations without any tangible determinations of it.
Each philosopher, Leibniz and Hume, attack what the other cherishes. Hume attacks a priori reasoning as vacuous and arbitrary, and Leibniz supports an idea that all reality is essentially rational. As we see for each position, the means by which we justify scientific objectivity become tenuous and strained, since both philosophers admit to clear delineations between subject and object relations in the world. The idea that all substantive truths are analytic for Leibniz becomes something that is difficult to justify, but it seems that he had to appeal to God’s infinite wisdom, and his principles (i.e. the principle of sufficient reason and the predicate in notion principle) to establish his radical claims. Hume had different problems, since it becomes difficult to account for the ways in which necessity is justified simply by means of habit, association, and inductive reasoning. Each philosophical phase, rationalism (dogmatism) and empiricism (skepticism) becomes a study unto itself, but most importantly for our uses, under Kant’s transcendental idealism, exemplified in the CPR, the warring factions began to work together toward something that looked like peaceful reconciliation.
 Kant, Immanuel, The Critique of Pure Reason, translated by Werner S. Pluhar, Indianapolis, IN: Hackett Publishing Co. 1996, 76.
 Kant, Immanuel, The Critique of Pure Reason, 76.
 Since the MetEx appeals to the experience of space, and the TransEx appeals to the way a synthetic/a priori intuition of space leads to geometrical and scientific discoveries, a skeptic (like Hume) could deny the relevance of science, but he cannot, in kind, deny the relevance of existence.
 Alternately referred to as expositions; here I will opt to refer to them as arguments.
 This description looks a lot like innatism, because it suggests that our cognition of space is nothing but an in-born trait. But in argument (3) Kant seems to refute this by making the case that we know about space in one single experience of it. The a priority of space is known in conjunction with experience, thus explaining the synthetic/a priori way that space is cognized—i.e. we can’t have one (a priori) without the other (experience).
 Also see footnote 3.
 Kant writes in first line of the TransEx for time: “I may refer for this exposition to No. 3, where, for the sake of brevity, I put among the items of the metaphysical exposition what in fact is transcendental” (B49).
 See footnote #5, from essay 3 on space.
 As noted with space, the TransEx of time shows that the scientific grounding for the intuition of time are synthetic/a priori judgments. This argument may not convince a skeptic like Hume. But the MetEx expositions for time show that the synthetic /a priori judgments of time are primary for experience itself and Hume cannot deny the primacy of experience.
 In Leibniz’s Discourse on Metaphysics we find (this is often termed the “predicate in notion principle,” PIN,) from §VIII: “This being so, we are able to say that this is the nature of an individual substance or of a complete being, namely, to afford a conception so complete that the concept shall be sufficient for the understanding of it and for the deduction of all the predicates of which the substance is or may become the subject.” Leibniz, Gottfried, Leibniz: Discourse on Metaphysics, Correspondence with Arnauld, and Monadology, translated by George R. Montgomery, LaSalle, IL: The Open Court Publishing Co., 1950, 14-15.
 Hume writes in An Enquiry Concerning Human Understanding (after presenting his celebrated billiard-ball example that aims to dispel an a priori connection between cause and effect): “In a word, then, every effect is a distinct event from its cause. It could not, therefore, be discovered in the cause, and the first invention or conception of it, a priori, must be entirely arbitrary.” Hume, David, An Enquiry Concerning Human Understanding, LaSalle, IL: Open Court Publishing Co., 1958, 29-30.
 Noted above in §VIII of Leibniz’s Discourse on Metaphysics.
Altman, Matthew C. A Companion to Kant’s Critique of Pure Reason. Boulder, CO: Westview Press, 2008.
Buroker, Jill Vance. Kant’s Critique of Pure Reason: An Introduction. New York, NY: Cambridge University Press, 2006.
Hume, David. An Enquiry Concerning Human Understanding, and Selections from A Treatise on Human Nature. LaSalle, IL: The Open Court Publishing Co., 1958.
Kant, Immanuel. Critique of Pure Reason. Translated by Werner S. Pluhar. Indianapolis, IN: Hackett Publishing Company, Inc. 1996.
Leibniz, Gottfried. Leibniz: Discourse on Metaphysics, Correspondence with Arnauld, and Monadology. Translated by George R. Montgomery. LaSalle, IL: The Open Court Publishing Co., 1950.