In his 1772 letter to Herz, Kant claimed to have found the “key to the whole secret of metaphysics” to be the answer to the question of how presentations make reference to objects. More specifically, the presentations relevant to metaphysics are “the pure concepts of the understanding” which are not abstracted from experience but “have their sources in the nature of the soul.” Kant denied that these concepts produce their objects, so the puzzle was how it is possible for pure concepts to have reference to objects at all.
It might be thought this this puzzle belongs to the domain of semantics, or perhaps to epistemology. (That is, it belongs to a general theory of the meaning of concepts, or to a theory of knowledge through concepts, respectively.) But Kant claimed that it is a metaphysical problem, and we must see why he thought that it is.
At this point, we must introduce a piece of Kantian terminology which will be used throughout what follows. The German word ‘Erkenntnis’ is translated in our text as ‘cognition’ as a cognate of the Latin ‘cognitio’ which Kant associates with it at A320/B376. (But note that it can be, and has been, translated as ‘knowledge.’) Cognition is a species or kind of presentation. Specifically, it is a ‘perception,’ or presentation with consciousness, which refers to an object.
So we can re-state the question of the reference of pure concepts in terms of cognition: how is it possible for pure concepts of the understanding to be cognitions? Here we must make a distinction that is fundamental to Kant’s philosophy. Besides pure concepts of the understanding, Kant recognizes other pure cognitions. Since there are two kinds of cognitions, concepts and intuitions (that is, presentations which purport to present objects generally or individually), there are (at least potentially) two kinds of pure cognitions. We will refer to the pure concepts as “rational” or “philosophical” cognitions. Pure intuitions will turn out to be “mathematical” in character. (See A713/B741 for more on the distinction between rational and mathematical cognition.)
Kant held that metaphysics is the science of the principles of pure philosophical cognitions. Part of that science, he contended, is the demonstration of how pure rational cognition is possible at all. (That is, one of the tasks of metaphysics is to show how pure rational concepts whose origin is solely in the understanding can have reference to objects.)
In the chapter entitled “The Architectonic of Pure Reason” (A832/B860), Kant gave a systematic account of the organization of metaphysics. He called the part of metaphysics dealing with the possibility of pure rational cognitions “transcendental philosophy.” (Alternatively, he called it “propaedeutic,” “critique,” and “ontology.”) Transcendental philosophy is the primary subject-matter of the Critique of Pure Reason. Kant’s primary task there was to show how there can be pure rational cognitions. Transcendental philosophy must also explain the possibility of pure intuitions. The part of the Critique that deals with pure concepts is called “Transcendental Logic,” while the part which deals with pure intuitions is called “Transcendental Aesthetic.” Given that transcendental philosophy succeeds in showing how pure cognitions are possible, the remaining task for metaphysics is to provide a system of pure rational cognitions—what Kant calls “physiology.”
According to Kant, there are two distinct objects to which pure concepts may apply. One is nature, and the other is the freely acting human being. Accordingly, there is a metaphysics of nature and a metaphysics of morals. The “theoretical” metaphysics of nature deals with what is, while the “practical” metaphysics of morals deals with what ought to be. In this course, we will be examining almost exclusively the metaphysics of nature or theoretical metaphysics.
A further distinction is between the kinds of objects which are taken to be the referents of pure concepts. There are two possible kinds of objects: those that can be met with in experience, and those which cannot be met with in experience. The former are called “immanent” and the latter “transcendent.” (Note that to be “transcendent” is to be beyond the limits of experience, and this notion must not be confused with “transcendental” philosophy, which is concerned with the possibility of pure cognition.)
Kant regarded immanent metaphysics as the only legitimate kind—a claim which he tried to justify in the Critique. It consists of two branches, which are distinguished by two kinds of nature. The system of corporeal nature is rational physics, and that of thinking nature is rational psychology.
Transcendent metaphysics has two branches. Transcendental cosmology has as its intended object the whole of nature (which is beyond the scope of experience), while transcendental theology takes us even further from experience, by linking the whole of nature with a being that is “higher” than nature itself and is responsible for its existence and form. The part of the Critique called “Transcendental Dialectic” attempts to show that transcendent metaphysics is based on fallacious reasoning. Kant tells us that one of the roles of metaphysics is to act as a “censor” by showing the illegitimacy of transcendent metaphysics.
In the final chapter of the Critique, “The History of Pure Reason” (A852/B880), Kant looks back on the prior attempts at metaphysics and finds “edifices” that are “only in ruins.” He describes three different ways to approach metaphysics: in terms of the objects of rational cognition, the origin of rational cognition, and the method of metaphysical investigation.
The Object of Pure Rational Concepts
Two kinds of object of metaphysics have been investigated: objects of the senses (elsewhere called “phenomena”) and objects of the intellect (elsewhere called “noumena”: see the chapter “On the Basis of the Distinction of All Objects As Such into Phenomena and Noumena,” A235/B294).
The sensualist claims that all concepts have reference only to objects of the senses because there are no other objects beyond objects of the senses. Any purported noumenon is merely the product of the imagination. Kant takes Epicurus as his exemplar of a sensualist metaphysician. The sensualists allow that there are “concepts of the understanding” (presumably pure concepts), but their use is only “logical.” Kant appears to mean by this that they are used only to organize our understanding of the phenomena, but they have no reference to any intelligible object that corresponds to them.
The intellectualist claims that pure concepts refer to intelligible objects, and that these objects alone are real. Plato is taken to be the foremost philosopher of the intellectualist school. According to the intellectualist, the product of the senses is nothing but illusion. Although he is not mentioned in “The History of Pure Reason,” Berkeley was held by Kant to have been an intellectualist and to have drawn the conclusion that bodies are illusory. (See especially the Appendix to the Prolegomena.)
The Origin of Pure Rational Concepts
As for the origin of pure rational cognitions, again there are two possibilities: experience or something independent of experience. Kant holds that if the origin of pure rational concepts is independent of experience, it is to be found in reason itself.
The empiricist holds that pure rational concepts are derived from experience. Aristotle, Epicurus, and Locke are taken to be representatives of the empiricist school. Kant implies that empiricism is consistent only if coupled with sensualism. If all our concepts have their origin in the senses, they should be applied only to sensible objects. He takes Aristotle to task for applying empirical concepts beyond experience, presumably because Aristotle inferred the existence of a non-sensible object, the prime mover. Locke is an even greater offender, since he infers the existence of a transcendent God and infers as well that the human soul is immortal. Moreover, he claims that these two non-empirical propositions “can be proved with the same evidence as can any mathematics theorem (even though both objects lie entirely outside the bounds of possible experience)” (A854/B882).
The noologist takes the origin of pure rational concepts to be in reason, independently of experience. Plato and Leibniz are said to be representatives of noology. Kant discusses Plato in the context of intellectualism, but his discussion in fact concerns Plato’s noologism. Concepts refer to objects only indirectly, through common characteristics. If the intellect is to be able to refer to objects directly, it might intuit these objects. Hence, the noologist Plato requires that there be an “an intuition through pure understanding unaccompanied by the senses” (A854/B882). Kant dismisses any application of the understanding to intelligible objects (via intellectual intuition) as “mystical.” Leibniz, on the other hand, did not claim that reason is able to intuit objects. His noology requires nothing more than the presence of pure concepts in the intellect, and his approach keeps “sufficient distance from Plato’s mystical system” (A854/B882). We will look in detail at how Kant took Leibniz’s noology to work in the next section.
The third and final historical divisions of practitioners of metaphysics regard method, specificially with regard to the metaphysics of nature. Kant first distinguishes between naturalistic and scientific method. Then within scientific method he distinguishes between dogmatic and skeptical method. He concludes by noting that his “critical” method is an alternative to the dogmatic and skeptical.
Naturalism in metaphysics is described as giving priority to common reason over speculation in metaphysical investigation. Some do this blamelessly simply because they lack insight. Others absurdly claim that by “the neglect of all artificial means,” one is able to expand one’s cognition (A855/B883). Kant does not mention any names here, but in the Preface to the Prolegomena, he criticizes “common sense” philosophers such as the Scottish philosophers Thomas Reid, James Oswald, James Beattie, and Joseph Priestly.
The dogmatic version of the scientific method in metaphysics is represented by Christian Wolff. Kant does not describe the dogmatic method here. In a section entitled “Pure Reason in its Dogmatic Use,” he describes a dogma as an informative proposition, based solely on concepts, intended to apply to objects necessarily (A736/B764). In terms of our discussion, a dogmatic method is one in which concepts are held to refer directly to objects without the involvement of intuitions. Kant’s treatment of Leibniz’s metaphysics, in the next section, illustrates the use of the dogmatic method.
The skeptical method, represented by David Hume, makes no dogmatic pronoucements; quite the contrary. Kant describes Hume’s method in the Preface to the Prolegomena. Like Kant’s own method, Hume’s sought to understand how pure rational concepts might refer to objects. But as an empiricist, he held that the origin of these concepts must be found in sensible objects. Hume showed “irrefutably” that the pure rational concept of cause has no reference to sensible objects, given that its origin is sought in those same objects. The only real difference between the “skeptical” and the “critical” method adopted by Kant is that the former merely discovers the source of the problem, while latter seeks the origin of pure concepts in the human intellect itself and (allegedly) shows how pure concepts with this source can have reference to objects.
Kant’s Critique of Pure Reason was written in German for a German audience. That audience was most familiar with the philosophical tradition begun by Leibniz, then modified and systematized by Leibniz’s younger contemporary Christian Wolff. Kant’s textbook for his metaphysics lectures was the Metaphysics by the Wolffian philosopher Alexander Gottlieb Baumgarten. Much of Leibniz’s philosophical work, on the other hand, was unpublished and unknown. The rudiments of Leibniz’s metaphysics, as it was understood by Kant, can be found in his 1714 paper “Monadology,” which was published in German translation in 1720. Kant in the Critique made reference to Leibniz’s commentary on Locke, New Essays Concerning Human Understanding, which was translated into German in 1768.
The period before the publication of the Critique of Pure Reason is called by scholars Kant’s “pre-critical” period. In this period, he wrote a number of papers in the Wolffian mode. Then, as he testified in the Prolegomena, “my remembering David Hume was the very thing which many years ago first interrupted my dogmatic slumber and gave my investigations in the field of speculative philosophy a quite new direction” (Preface, Ak 4:260).
The Critique itself says little about Wolff explicitly, but the organization of the Transcendental Dialectic, in which traditional metaphysics is rejected, is based on Baumgarten’s classification of metaphysical theories. Leibniz, on the other hand, is subject to detailed criticism in “The Amphiboly of the Concepts of Reflection.” After the publication of the Critique, a defender of Wolff named Johann August Eberhard charged that Kant’s metaphysics was really based on Wolffian principles, a charge Kant vigorously contested in On A Discovery According to which Any New Critique of Pure Reason Has Been Made Superfluous by an Earlier One (1790).
As was seen in the last lecture, Kant thought that they key to metaphysics was to investigate the way in which pure concepts of the understanding get their reference to objects. In its most general application, this is what Kant called the “critical” method. It begins by investigating the origins of our presentations and then asks how it is that these presentations and the principles governing them apply to objects. The critical method is contrasted with an uncritical “dogmatic” method (A856/B884) that has been described above. Wolff is cited as a practitioner of the dogmatic method.
The dogmatic method in metaphysics aims at certainty, “by establishing principles in a law-governed way, determining concepts distinctly, trying for strictness in proofs, and avoiding bold leaps in inferences” (Bxxxvi). To attain its end, it borrows from the method of mathematics, which Kant as well as Wolff regarded as being absolutely secure. Thus, the dogmatic method in metaphysics proceeds through the use of definitions, axioms and demonstrations, upon which “the solidity of mathematics rests” (A726/B753).
Some famous instances of the use of the dogmatic method can be found in Descartes (Replies to Objections II) and Spinoza (Ethics), though Kant does not mention either of these in the Critique. Wolff’s metaphysical works and Baumgarten’s Metaphysics somewhat more loosely follow this format. (Here we follow Baumgarten’s presentation.)
The Principle of Contradiction
Baumgarten begins in §7 by defining “negative nothing” (nihil negativum) as a subject with contradictory predicates A and non-A. Kant’s example is “a two-sided rectilinear figure” (A291/B348). Such a thing is impossible, and from this we get the fundamental principle of metaphysics (which functions as its sole axiom): the “principle of contradiction.” Specifically, it states that nothing has contradictory predicates. Baumgarten represented the negative nothing as the null quantity zero, and so the equation for the principle of contradiction is “0 = A + non-A.”
In Kant’s treatment, the negative nothing is an “empty object without concept,” which is an impossible object. It “is opposed to possibility inasmuch as the concept annuls even itself” (A292/B348). Now we can define “something” as that which is not negative nothing (§8). Its concept would not contradict itself, it is not both A and non-A, and so it is possible. So for Wolff and Baumgarten, the principle of contradiction is the principle of possible. We shall see later in the course that Kant had a different principle of possibility.
Leibniz held that the principle of contradiction is a fundamental principle of reasoning: “Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false” and another principle to be discussed shortly (“Monadology” § 31). Leibniz treated his principle more widely than did Baumgarten in his application of it to metaphysics: it is the basis of all “truths of reasoning” (§§33-35). Truths of reasoning, such as the truths of mathematics, are necessary truths whose negations are impossible, in that they would violate the principle of contradiction. This is not to say that we prove them to be true by application of the principle, however. They cannot be proved to be true because, upon analysis, they simply say that a thing is identical to itself.
The Principle of Sufficient Reason
Baumgarten went on to give an argument, based on the principle of contradiction, for the principle of the excluded middle, that “every subject includes one or the other of all non-contradictory predicates”: for any A, everything is either A or non-A (§ 7). A further principle is that “every subject is a predicate of itself”: A is A, the “principle of identity” (§11).
At this point, Baumgarten introduced as new definition, that of a reason: “that from which it can be cognized why something is” (§14). That of which a reason is a reason is called the “consequent” of it. The “principle of reason” is that “nothing is without a reason” (§20). Baumgarten reproduced Wolff’s bad argument for this principle. In effect, it states that if a thing had no reason, then nothing would be a reason. But a reason is something, and therefore possible, while nothing is impossible. So if a thing had no reason, the principle of contradiction would be violated. This argument contains a basic error, for to say that “nothing is a reason” is not to say that a something called “nothing” is a reason, but just to deny that there is a something which is a reason. Kant noted in the Critique that it “is universally confessed by the experts” that “all attempts to prove the principle of sufficient basis have been futile” (A783/B811).
Leibniz attempted no such thing. He stated that the second fundamental principle of reasoning is “that of sufficient reason, in virtue of which we hold that there can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise, although these reasons usually cannot be known by us” (“Monadology,” §32). This principle applies to “truths of fact.” Unlike the truths of reason governed by the principle of contradiction, truths of fact are contingent, their negations being possibly true (§33).
The principle of sufficient reason can be used to prove that God exists, according to Leibniz. For if the existence of all beings were contingent, i.e., if each one depended on another as the reason for its existence, an unacceptable infinite regress would be generated (§§36-39). Kant recounted this argument in the Critique (A605/B633, footnote 195) and rejected it outright (A610/B638).
The fundamental error in the dogmatic method, according to Kant, is that it fails to distinguish between the kinds of objects to which its definitions and principles are supposed to apply. Wolff and Leibniz thought that these principles apply in the same way to all objects, to things in general. They do not take into account the way in which objects are presented to the mind. Specifically, Wolff and Leibniz held that their principles apply to objects as they are presented to the pure understanding. That is to say, things are presented through the use of pure concepts—concepts not abstracted from sensuous presentations.
As stated in the last lecture, Leibniz held that the same objects are presented both to the pure understanding and to sensibility. The purely conceptual presentations to the understanding are clear, while the concrete presentations to the senses are obscure. In fact, Baumgarten simply defined sensibility as the faculty of obscure presentations (§§520-1). On Kant’s view, the distinction between clear and obscure presentations belongs to logic, not to psychology.
In the “Amphiboly of the Concepts of Reflection,” Kant allowed that given Leibniz’s assumption that metaphysics treats of the objects of the pure understanding, some of its principles would necessarily apply to these objects. These principles involve the most general relation of concepts to one another. Kant held that there are exactly four ways in which any concepts A and B can be compared, with respect to:
The Identity of Indiscernibles
Concepts may be compared with respect to identity and difference. If concepts refer to objects just as they are thought by the pure understanding, then the result of the comparison would apply to the objects. Now suppose that A and B are the same, in the sense that all the characteristics that make them up are the same. In that case, the objects falling under those concepts would be the same as well. So we have the principle of the identity of indiscernibles: if all the characteristics of object A and object B are the same, then object A is the same as object B.
Interestingly enough, Leibniz seems to have rejected the thesis Kant ascribed to him. In his fifth paper in the correspondence with Clarke, Leibniz stated:
When I deny that there are two drops of water perfectly alike, or any two other bodies indiscernible from each other; I don’t say, ’tis absolutely impossible to suppose them; but that ’tis a thing contrary to the divine wisdom, and which consequently does not exist. (§25)There is no conceptual problem with the distinctness of A and B which have the same characteristics. The problem rather lies with Leibniz’s application of the principle of sufficient reason. Leibniz would say that there would be no reason sufficient for A’s having been created in the place and time it was, rather than where B is.
On Leibniz’s view, as reflected by Wolff and Baumgarten, concepts are made up of characteristics which may be more or less complex. But ultimately, there are simple characteristics of which all concepts are composed. They held further that there is no conflict between the simple characteristics. The only way concepts can disagree is when one concept has a characteristic that another lacks. So if we have A composed of M and N, while B is composed of M and non-N, there is a conflict between them.
This allowed Leibniz to point to a solution to a tricky problem in the metaphysics of God. He noted that any alleged proof of God’s existence must first establish that God is possible. Now recall that a thing is impossible, a negative nothing, if it is contradictory, if its concept contains A and non-A. So God would be impossible only if God’s concept contains a negation. If, however, the concept of God were composed entirely of positive simple characteristics, it could not contain any negation, in which case God would be possible. As Kant put it,
The adherents of Leibniz find it not only possible but also natural to unite, without any worrisome conflict, all reality in one being. For they are acquainted with no conflict other than that of contradiction (whereby the concept of a thing is itself annulled) . . . . (A273-4/B329-30)
Some characteristics of things are intrinsic to that thing and some are relational. Some of the relational characteristics of things are “location, shape, contiguity or motion” (A274/B330). In fact, any spatial characteristic of a thing is relational. The only purely non-relational characteristics of which we are aware are states of mind.
One of the concepts of the pure understanding is that of substance, which can be defined as something which is not the characteristic of any other thing. If we are not to take substance as an unknown substratum (as did Locke), we must assign it some characteristic. By the definition, these characteristics are not characteristics of anything else. As Kant understood Leibniz, this meant that the defining characteristics of substance are intrinsic. “As objects of pure understanding, . . . , every substance must have intrinsic determinations and forces that concern its intrinsic reality” (A265/B321). Since the only available characteristics are states of mind, substances are one and all states of mind.
A further feature of Leibnizian substances is that they are simple. Leibniz invented a word for his simple substances: ‘monads.’ Kant claimed that the simplicity of Leibnizian substances is also the result of the comparison of concepts. It is supposed to follow from the fact that monads have only intrinsic characteristics (though it is not clear in the first place why substances cannot have accidents that are relational characteristics). He states that even the components of matter are simple for Leibniz, “having in his thought taken from them everything that may signify extrinsic relation, and hence taken from them also composition” (A266/B322).
But this is not how Leibniz argued for the existence of monads. In Section 2 of the “Monadology,” Leibniz’s premise was the existence of compounds: “And there must be simple substances, since there are compounds; for a compound is nothing but a collection or aggregatum of simple things.” Further, Leibniz argued that the characteristics of monads are intrinsic on the grounds that no monad can be affected by any other monad because such affection would requires parts, while monads are simple (§7). “It follows from what has just been said, that the natural changes of the Monads come from an internal principle, since an external cause can have no influence upon their inner being” (§11). Indeed, Kant got the argument backwards, claiming that, “since everything is engaged only inwardly, i.e., with its presentations, one substance’s state of presentations could not stand in any efficacious linkage whatsoever with that of another substance” (A275/B331).
The final way in which concepts may be compared is with respect to whether they determine (are predicated of) another concept or whether they are determined by another concept. Suppose our concept of body has the three characteristics attraction, impenetrability and extension (as is suggested at A265/B321). Then extension is a determination and body is a determinable. We might say equivalently that extension is a form and body is the matter which takes on that form.
Now let us apply this distinction to concepts of objects. According to Kant, in an object of the pure understanding, matter is prior to form. Something must be determinable in order for there to be any determination: this is a conceptual priority. Transferred directly to objects, this priority means that objects as determinable are more basic than the characteristics that determine them. The determinables for Leibniz are monads with their intrinsic characteristics of perception.
Space and time are determinations of monads, on the Leibnizian view. So the monads do not depend on space and time; rather, space and time depend on them. “Hence space and time were possible as bases and consequences—space only through the relation of substances, and time through the connection of their determinations among one another” (A267/B322). Once again, it seems that Kant has not got the argument straight. Leibniz was concerned about a number of aspects of postulating space and time as something real. Moreover, in the fifth paper in the Clarke correspondence, he seems to have argued that the kind of relation space would have to be could only be ideal (§47). In this regard, he compared space to a genealogical line, which is a merely ideal thing.
Kant maintained that if the concepts on which we reflect refer to objects of the pure understanding, the principles derived from their comparison would apply to those objects. He stated explicitly regarding the Leibnizian doctrine of space and time that, “thus it would have to be, if pure understanding could be referred directly to objects, and if space and time were determinations of things as they are in themselves” (A267/B323). This doctrine of space and time would also hold of the objects of sensuous presentation, if their characteristics were the same as those of the intelligible objects (though perceived confusedly).
But this is all moot, because Kant held that the characteristics of the objects of sensuous presentation cannot be derived from the mere comparison of concepts in the pure understanding. What Leibniz did not recognize is that the objects of sensuous presentation are given to the human mind only through sensibility. Because there are two distinct sources of presentations—the pure understanding and sensibility—there are two distinct ways in which our concepts might refer to objects. So when we compare concepts, we must first reflect on which of the two cognitive faculties are supposed to generate their objects.
Therefore transcendental reflection, i.e., [consciousness of] the relation of given presentations to one or the other kind of cognition, will alone be able to determine their relation to one another; and whether these things are the same or different, agreeing or conflicting, etc., cannot be established immediately from concepts themselves by mere comparison; but this can be established solely by distinguishing, by means of a transcendental deliberation, the kind of cognition to which they belong. (A262/B318)(Reflection is “transcendental” rather than empirical because it concerns the most basic structure of the mind, which is not available to our internal experience of ourselves.)
Once the concepts under consideration are confined to their proper spheres, Leibniz’s principles lose their application to sensible objects. Most importantly, the characteristics of these objects are not intrinsic but are one and all relational. Once intrinsicness is lost, the principles of the identity of indiscernibles, of positive realities, and simplicity of substance all fall to the ground. We are not in a position as of yet to say why, as this depends on Kant’s positive views about sensible objects.
We can make a start toward this end by turning to the Preface to the second edition of the Critique. Here, Kant gives us the basis for his solution to the problem of presentation. Recall that this problem is how pure concepts of the understanding (now called “a priori” concepts) apply to the objects of sensuous presentation, now called objects of experience. This is a problem because these concepts are generated spontaneously in the mind, while the objects are given from an external source. We would like to say that our pure concepts match the objects, but such a connection would be pure coincidence if our concepts must conform to the characteristics of the given object.
Kant’s solution is to turn everything on its head, just as Copernicus had done. What all the metaphysicians before him had assumed was that our concepts get their reference by conforming to objects. Kant proposed (as an “experiment”) that instead, objects must conform to our concepts.
For experience is itself a way of cognizing for which I need understanding. But understanding has its rule, a rule that I must presuppose within me even before objects are given to me, and hence must presuppose a priori; and that rule is expressed in a priori concepts. Hence all objects of experience must necessarily conform to these concepts and agree with them. (Bxvii-xviii)Most of what will concern us in the rest of this course involves figuring out how this is supposed to work.
Like most revolutions, this one has its price, a “disturbing result that seems highly detrimental to the whole purpose of metaphysics as dealt with in the second part [of the Critique, the Transcendental Dialectic]” (Bxix). In securing the application of pure concepts to objects of experience, we at the same time give up any pretensions to knowledge of “objects insofar as they can merely be thought” (Bxviii). Thus the part of the Critique that deals with pure concepts, Transcendental Logic, is divided into two parts. The first part shows how they apply to the objects of experience. The second, Transcendental Dialectic, shows the consequences, mostly negative, of the attempt to extend the reach of these concepts beyond the limits of experience.