Is Addition Synthetic? A Revised Look

I've previously considered the question "Is addition synthetic?" in a light sympathetic to Kant, defending his assertion that the arithmetical relation of addends to sum depends on an a priori synthesis. A reread of the Introduction to the Critique of Pure Reason has disturbed the confidence with which I defended Kant and caused me to reconsider my view. I hope to give the issue deeper treatment than before, to give Kant a fair but critical reading, to consider alternative resolutions of the issue, and to find a provisional resolution satisfactory to my own philosophical sense. As always, criticism is welcome.

First, the text itself:

Mathematical judgments are one and all synthetic. Although this proposition is incontestably certain and has very important consequences, it seems thus far to have escaped the notice of those who have analyzed human reason; indeed, it seems to be directly opposed to all their conjectures. For they found that all the inferences made by mathematicians proceed (as the nature of all apodeictic certainty requires) according to the principle of contradiction; and thus they came to be persuaded that the principle of contradiction is also the basis on which we cognize the principles [of mathematics]. In this they were mistaken. For though we can indeed gain insight into a synthetic proposition according to the principle of contradiction, we can never do so [by considering] that proposition by itself, but can do so only by presupposing another synthetic proposition from which it can be deduced.

We must note, first of all, that mathematical propositions, properly so called, are always a priori judgments rather than empirical ones; for they carry with them necessity, which we could never glean from experience. But if anyone refuses to grant that all such propositions are a priori - all right: then I restrict my assertion to pure mathematics, in the very concept of which is implied that it contains not empirical but only pure a priori cognition.

It is true that one might at first think that the proposition 7 + 5 = 12 is a merely analytic one that follows, by the principle of contradiction, from the concept of a sum of seven and five. Yet if we look more closely, we find that the concept of the sum of 7 and 5 contains nothing more than the union of the two numbers into one; but in [thinking] that union we are not thinking in any way at all what that single number is that unites the two. In thinking merely that union of seven and five, I have by no means already thought the concept of twelve; and no matter how long I dissect my concept of such a possible sum, still I shall never find in it that twelve. We must go beyond these concepts and avail ourselves of the intuition corresponding to one of the two: e.g., our five fingers, or (as Segner does in his Arithmetic) five dots. In this way we must gradually add, to the concept of seven, the units of the five given in intuition. For I start by taking the number 7. Then, for the concept of the 5, I avail myself of the fingers of my hand as intuition. Thus, in that image of mine, I gradually add to the number 7 the units that I previously gathered together in order to make up the number 5. In this way I see the number 12 arise. That 5 were to be added to 7, this I had indeed already thought in the concept of a sum = 7+5, but not that this sum is equal to the number 12. Arithmetic propositions are therefore always synthetic. We become aware of this all the more distinctly if we take larger numbers. For then it is very evident that, no matter how much we twist and turn our concepts, we can never find the [number of the] sum by merely dissecting our concepts, i.e., without availing ourselves of intuition.

Just as little are any principles of pure geometry analytic. That the straight line between two points is the shortest is a synthetic proposition. For my concept of straight contains nothing about magnitude, but contains only a quality. Therefore the concept of shortest is entirely added to the concept of a straight line and cannot be extracted from it by any dissection. Hence we must here avail ourselves of intuition; only by means of it is the synthesis possible.

It is true that a few propositions presupposed by geometricians are actually analytic and based on the principle of contradiction. But, like identical propositions, they serve not as principles but only [as links in] the chain of method. Examples are a = a; the whole is equal to itself; or (a+b)>a, i.e., the whole is greater than its part. And yet even these principles, although they hold according to mere concepts, are admitted in mathematics only because they can be exhibited in intuition. [As for mathematics generally,] what commonly leads us to believe that the predicate of its apodeictic judgments is contained in our very concept, and that the judgment is therefore analytic, is merely the ambiguity with which we express ourselves. For we say that we are to add in thought a certain predicate to a given concept, and this necessity adheres indeed to the very concepts. But here the question is not what we are to add in thought to the given concept, but what we actually think in the concept, even if only obscurely; and there we find that, although the predicate does indeed adhere necessarily to such concepts, yet it does so not as something thought in the concept itself, but by means of an intuition that must be added to the concept.

Critique of Pure Reason, B14-B17, Pluhar translation. Brackets indicate translator's insertions, all emphasis original.

That judgments in geometry depend on the immersion of pure concepts in space seems unobjectionable. Indeed, Kant's strongest argument that mathematical judgments are synthetic proceeds by analogy with his claim that "a straight line is the shortest distance between two points" is comprehensible only by assuming the further condition that the concept of a straight line is first to be immersed in Euclidean space. To attempt to elucidate spatial relations without assuming that space exists (even if merely assumed to exist as a necessary condition for making a geometrical judgment in the first place) would be a futile effort, and pure geometrical concepts like that of a straight line would be comprehensible only through the relatively unproductive dissection of concepts analytically, by the principle of noncontradiction. Immersion of pure geometric concepts in space allows an explication of what those concepts entail when considered, not merely as abstract concepts of the mind, but as simultaneously being determinations of a singular intuitive representation (pure space). Because space is an a priori method of representing objects, the pure concepts of geometry lose none of their universal and necessary character for being displayed as determinations of space. For that reason, immersion in space does not destroy the a priori character of geometric concepts; it merely allows them to connect with each other and go beyond mere concepts in geometric judgments. What would be sterile, unproductive definitions of concepts become rich explications of the nature of extension when those concepts are applied to actual space.

This interpretation of Kant's basic claim, that geometric concepts gain their full richness and interrelatedness only when immersed in space, concedes the point far too easily, but for now, I want to postpone criticism and accept it arguendo. Assuming Kant is right, then, the principles of pure geometry are all synthetic a priori. The analogy to principles of pure arithmetic is more difficult. First, it is not clear what singular presentation is necessary to make the principles of arithmetic possible synthetically. There are two, and only two, singular presentations that comprise the full range of pure human intuition - space and time. That geometric principles, considered as possible determinations of the infinite given magnitude that is space, gain full relevance by being considered simultaneously with that space is uncontroversial, even trivial. If the analogy holds for arithmetic, however, then arithmetic principles, such as the simple act of adding seven and five to create twelve as their sum, will have to be determinations either of space or of time.

Addition as a determination of space has some intuitive appeal. Objects, such as the fingers of one's hand (as in Kant's example and in simplistic counting), can be mentally gathered together, first one group, then another, until a new group, the sum of the first two, is formed. Describing this procedure as a determination of space is problematic. For one thing, as Kant says in the Transcendental Aesthetic, all the parts of space are simultaneous. Thus, if "7 + 5 = 12" were regarded as a determination of space, the sum and the addition of the addends would be simultaneous. The mediation that intuition is supposed to provide for this arithmetic procedure would be missing. Contra the case with geometric principles, where properties that are the result of extension become added to pure geometric principles through the medium of space, with addition, space adds nothing.

The alternative, then, is to regard arithmetic principles as requiring immersion in time to become comprehensible. Indeed, the quoted passage, describing the procedure for adding two numbers, is rich in temporal language ("start" "then" "gradually" "previously"). Thus it seems plausible that Kant's describing the procedure as a temporal progression is not accidental, but is meant to reveal the underlying resort to intuition to make even simple arithmetical concepts understandable. To cognize means, indeed, to submit something to a priori synthesis in order to bring it within the range of objects that properly can be considered by the human mind.

The key problem with this interpretation of arithmetic is that it confuses the quasi-temporal procedure of conducting arithmetic operations with a necessary precondition for the very comprehensibility of arithmetic at all. It is natural to regard the binary operation symbolized by "7 + 5" as a command to "regard 7 as given, and add one unit at a time until the number of units added to 7 is equal to 5." That the result of this operation will be the same number as that more succinctly symbolized by "12" is obvious from the laws of mathematics. The question, though, is not whether a successive procedure can produce a single sum identical to a number with an existence independent of that procedure, but whether this identity of the two sides of the equation rests on an a priori, time-based synthesis. Kant's claim could be extended beyond arithmetic to logical operators. Thus, the antecedent in a conditional would be conceived of as given, and the relation between antecedent and consequent would depend on an a priori synthesis (because, presumably, the mind contemplates a unidirectional dependence between them). But a logical tautology, such as "If either p or p then p" is surely analytic. That the conception of a one-way temporal relation (antecedent preceding consequent) can be thought as connected with the concept of implication does not mean that implication is unknowable without being brought under temporal relations. In fact, as those familiar with Kant will know, when time is brought into the pure conceptual relation of a hypothetical syllogism, the relation of causation and dependence, one of the basic concepts of physics, appears. If logic can be implemented in separation from temporal relations, then it is not clear why arithmetic would be different.

The supposed synthetic nature of arithmetic breaks down further when the "7 + 5 = 12" example is examined in all its parts. Leaving aside the relations between numbers (addition and identity), take the numbers in themselves. Take a single number by itself. Because "12" can be broken down into a succession of additions, one unit after another until all twelve are gathered together into the single number, it seems that literally nothing involving numbers is possible without some sort of resort to intuition. Kant himself does not seem to have embraced this expansive view, if his emphasis in the quoted passage on the presence of intuition in the steps of the process of addition can be understood as an implicit limitation. Whatever the case may have been with Kant, it is difficult to see how a single number could be understood as being incomprehensible without resort to the singular presentation of time.

It is possible, however, that space is, after all, if not fundamentally at the basis of arithmetic concepts, at least important to make clear the properties of numbers. Numbers are often visualized as existing on a number line; similarly, time is represented as a one-dimensional progression, the time line. Kant makes the point himself in the Transcendental Aesthetic (granted, the comparison is made to show that, because time can be represented by means of spatial relations, then it has the same character as space, which Kant had just proven was a pure a priori intuition). This does not seem to avail, however. If time is inherently merely an intuition with one dimension in the same way that space is a three-dimensional intuition, then time is merely a kind of space, and only space is the real intuition. Obviously, though, the analogy is merely that, a way of understanding the progression of time by imagining that it occurs along a one-dimensional spatial continuum, not meant to imply that it actually has the same properties as space. And the analogy is not complete. Time proceeds in one direction, inexorably moving through successive inner presentations, whereas space simply exists in its entirety, the whole given at once. One can move, either actually or in imagination, back and forth in space. Time does not work this way. Thus the time line has a further limitation that motion is at a constant rate, in only one direction. Thus, visualizing time as motion along a line is useful when considering relations between events, but it does little to make explicable the nature of time itself. Still less does it serve to make comprehensible the nature of numbers and arithmetic relations. Why the position of the number twelve along the number line should have any of the same features as the position of an event on the time line is unknown. Events occur at different times because otherwise experience would not be comprehensible as a succession of events, and physics as a succession of causes related to effects. Numbers occupy different positions along the number line because numbers describe different quantities.

That last sentence ought to give us pause. It was rather glib. It could express two different views about the reality of mathematical truths. Either different numbers express different quantities by definition, or different numbers correspond to different independently existing objects of nature. Kant, of course, held to the view that objects are what they are because they are for minds and are the product of organizing functions' having been applied to reality to create experience. But there could be a difference between pure mathematics and applied mathematics that would locate at least some of the principles of mathematics in general logic, logic divorced from an intuition. If, however, "mathematical judgments are one and all synthetic," then they must be determinations of intuition (or discursive concepts, but that possibility can be rejected).

What if mathematical judgments are determinations of intuition by analogy? Consider the complex plane, or the mapping of functions on the Cartesian coordinate system. Arithmetic, it turns out, is actually geometry! Now if what Kant had said about geometry, the "easy case" of mathematical judgments' being true only under the assumption of intuition, was correct, then perhaps all mathematical judgments are simply determinations of space. What relation time and number have would be unclear. Despite the appeal of accepting that all mathematical judgments are judgments about spatial relations, this resolution seems merely to promote a mapping relation of mathematical concepts to geometric relations to an expression of ontological significance.

The rot spreads. That geometrical judgments can be made to correspond to determinations of space does not mean that space is a prerequisite for their having content. Twice in the quoted passage, Kant ought to have caught the mistake. First, that counting can be done on the fingers of one's hand does not mean that it necessarily involves intuition. Second, that what Kant admits are purely logical concepts ("a = a; the whole is equal to itself; or (a+b)>a, i.e., the whole is greater than its part") can be analogized with intuition (one can imagine a whole thing occupying a larger space than one of its own parts) means merely that humans rely on intuition to guide thought. But the question "Is addition synthetic?" does not ask whether it is helpful to use intuition to perform additive tasks, but whether addition has meaning only as a determination of one or both forms of human intuition. That all math may be like general logic and merely be easier to deal with in thought when assisted by intuition, rather than depending on intuition to exist in the first place, is not so easily dismissed.

The nagging background question through this discussion is what precisely makes mathematical judgments true. The facility with which I assumed that the Introduction could be understood without dealing with the nature of mathematics was obviously baseless. Without answering that question, the Kantian approach to the issue of how mathematics is synthetic crumbles, as evidenced by the previous paragraph. An examination of that background question is in order.

"7 + 5 = 12" is either analytic or synthetic. If analytic, it is true by definition, because the concept of "7 + 5" includes "12" implicitly. Kant clearly disagrees; but if the truths of mathematics are essentially arbitrary, then they are merely tautologies. Kant's transcendental idealism would deny any necessary correspondence between these tautologies and an experience in the creation of which they did not participate. If this is a scandal, it is a scandal for applied math, not pure math, which can be as analytic as it wants. The possible lack of absolute certainty would not be in the principles of mathematics themselves, but in their universal and necessary application to concrete events in the world. "7 + 5 = 12" can be analytic even if "7 apples added to 5 apples results in a 12-apple collection" depends on a synthesis. Indeed, perhaps this admittedly simplistic distinction between "pure" and "applied" mathematics points the way forward. "7 of object A and 5 of object A makes 12 of object A" is not universal and necessary in the world of sense. The combination of drops of water produces, not many drops of water, but a single new quantity of water. Without knowledge of the cohesive behavior of water, a person would be unable to make any sense of the result. The additional assistance of experience solidifies what would otherwise be merely a contingent connection between "this many drops and that many drops" and "such-and-such quantity of water." Of course, in the water example, reliance on experience and not on an a priori condition for the possibility of experience means that the synthesis involved holds a posteriori. For the synthesis required to apply pure math to experience to hold a priori, it must be a determination of intuition or discursive concepts (the two classes of organizing principles that bring the manifold under a determinate, cognizable structure).

Taking space and time as Kant takes them, and without getting into a discussion either of spatial dimensions in excess of three or of spacetime, it is not immediately clear that mathematics applies to the world of sense through a determination of intuition. To be sure, if space and time were not a priori ways of organizing sense data, then experience would be presented in a haphazard, probably incoherent way (assuming that things in themselves have no inherent qualities that would otherwise make organization possible). Space and time have quasi-subjective qualities (space is outer intuition, time inner) that are not attached to mathematical principles. Of course, if mathematics is merely a determination of space, time, or both, then it is not contradictory to assume that the intuitions contain more relations than mathematics, which consists of determinations of them. The difficulty that causes hesitation in identifying intuition as the act that imbues mathematical significance on experience is the indeterminacy of the "stage" in which data go from being mathematically incoherent to capable of being discussed in mathematical terms. Things in space can be described using geometry; does geometry begin to describe their relations simultaneously with their being considered in space, or does an already-existing necessary relation become additionally interpretable as spatial at that moment? Keep this question in mind, while for now merely recognizing that the supposed a priori synthesis we have been searching for may occur at some other stage in cognition than the intuition-applying stage.

Another stage may be the stage at which discursive concepts make intelligible sense data. It would be wrong to suggest that this stage occurs "after" intuition is applied, but it seems at least plausible to imagine intuition without concepts. No intelligibility, but bare existence in experience, would be possible of such an intuition. Mathematics does not appear comprehensible as a determination of these concepts, in any case. For the objects of mathematics are not things that are otherwise given whose relations must be made clear by external concepts, but things that are created in the act of thinking them. A triangle is a product of imagination, whereas the objects of physics are things actually given. If discursive concepts were necessary to make sense of mathematical objects, then those objects would have to be already-existing, intuited things acquiring conceptual character through thought. This is impossible.

Questions and criticisms abound; it is time for me to say something positive about the issue. I think pure mathematics must be analytic. Mathematics is a branch of logic, or vice versa, and logic is tautological. I do not see what was so apparent to Kant, that something has to be added to the concept of the subject of a mathematical judgment in order to make the predicate inhere in it necessarily. The puzzle remains: why do these tautologies say anything about external reality? For one of two reasons:

First, perhaps Kant was on to something after all. Even if mathematics consists of tautologies, it requires some sort of synthesis to bring those tautologies into experience and make them apply to the manufactured reality of human minds. But it is not insofar as things are thought in space, or in time, or as having certain properties that they can be described by mathematics. Instead, the manifold, even before it is intuited, is susceptible of being described mathematically. The transcendental affinity of the manifold would include, among its very basic features of organization, and agreeableness to mathematics. The transcendental affinity is difficult to understand, and I don't want to get distracted with it. But it is plausible that, whatever original synthesis this affinity accomplishes for the mind's subsequent work, it includes a way of organizing completely random data into mathematically-rich relationships. Thus, intuition finds spatial relationships in the data because of an affinity of the relations the manifold already has to spatial relations. An analogy between pure geometry and geometry applied to space is thus a product of the mind's very first way of organizing experience.

Second, perhaps Kant was simply wrong. Mathematical relations hold among things in themselves, and math is true because it is an inherent feature of things. This is a mathematical realist position. Indeed, if, as Gödel seemed to indicate (I will prudently avoid a tangent on this issue, mostly because I want to treat it in much more depth at a later date!), mathematical judgments are true even if their truth cannot be evaluated by the formal conditions of thought, reality might be mathematical even independent of human minds. One of the very few positive things we could say about noumena (besides that they must exist for experience to exist at all) would be that there are mathematical relations among them. This would establish why mathematics is true - things are just that way - but would fail to respond to Hume's objections about a prioricity.

The danger should be obvious. If Kant is wrong that mathematical judgments are synthetic a priori, then the sharp phenomenal/noumenal distinction collapses. A feature of noumena would be known; moreover, we could not be certain of the universality and necessity of mathematical judgments because they would be products of induction. Additionally, mathematics would really be a kind of metaphysics, a discipline dealing with the nature of things in themselves, so that the sequestration of speculative metaphysics accomplished in the Critique would come to nothing. To say the least, this is a shame.

One remaining interpretation saves transcendental idealism and avoids the murky waters of mathematical realism. Consider Gödel's insight and its apparent significance. It says, essentially, that as we currently understand the mind, it is not possible to determine the truth of mathematics simply by the operation of axioms and rules of inference. Either this is because math is true independently of our minds, or we are fundamentally ignorant about a key aspect of cognition. Under this second interpretation, to say that mathematical judgments are true merely because we pour our own assumptions into them could still be correct. Transcendental idealism can breathe easier, although reconciling this thought with Kant himself is another matter. Kant thought that a proper critique of the power of reason would have to outline all the functions of the mind, broadly indicating what the mind contributes to the formation and understanding of experience. Though specific judgments under the broad sections of the outline would not have to be cataloged in the critique itself, they at least would have to be species of one of the exhaustively-enumerated genera in the critique. This discussion has been attempting to locate mathematical judgments within all the genera, to no avail, and this solution suggests that the enumeration was incomplete. If so, the Critique of Pure Reason was not a total success. In fact, it left inexplicable a rather important type of cognition.

My own view is that mathematics does not depend on human minds for its existence or truth. There are certain things that simply are true, and though this does not seem philosophically satisfactory, a proper skepticism about the reach of the human mind leads to this leap of faith. As with Aristotelian first principles, math is simply true; no further basis on which to rest mathematical truth can be found. Constant reconsideration of this act of faith is what philosophical rigor demands, and if a better-supported position presents itself, I fully expect to change my mind. Given the inherently interesting nature of the discussion, I expect this consideration will not be my last.

Two Dogmas of Transcendental Idealism

There is a tension in the Critique of Pure Reason between the novelty of transcendental idealism, on the one hand, and the terms and ideas of 18th century philosophy, on the other. Kant was, for all his importance in the subsequent development of philosophy, and for all his remarkable originality, still bound by his place and time. He could not shake off the remnants of the old rationalism, though the First Critique certainly laid the groundwork for its complete destruction by the post-Kantians. In a sense, of course, the First Critique was intended not as a radically new vision of philosophy but as an answer to a simple problem - how can knowledge be justified in light of Hume? A patching-up of epistemology, as it turned out, would not do, but it is useful to keep in mind that Kant himself had at least that modest goal in 1781.

There is, as I said, a tension between the new and the old, between a radically different conception of reality and between a modified rationalism/empiricism hybrid as the end result of the critical project. Kant seems as times not quite willing to make the idealist leap and to shut off the noumenal utterly from human knowledge. Thus, in the Refutation of Idealism, real external objects are actually known to exist, not just assumed as placeholders in a vague metaphysics. But if transcendental idealism is to serve fully in purging thought of unnecessary assumptions, it seems positively beneficial to deny real knowledge of independent existences. We can otherwise never be sure that our experience is of properties of the thing itself or properties imputed to things through the mind's modification of objects for experience. By acknowledging that all experience is mind-dependent, transcendental idealism gives up the impossible goal of real knowledge and settles for knowing the mind's forms of thought themselves, confident that an inventory of concepts will serve as the only possible substitute for a mystical metaphysics of noumena. This assumption of a complete break between reality and experience is disquieting to some because it seems to imply throwing out the touchstone of truth (objectivity) for radical subjectivism. In fact, the whole purpose of the First Critique was to show how this so-called "subjectivism" is in the fact the only way of vindicating objectivity - we can be certain of those aspects of experience that we ourselves contribute, because those forms of thought are universal and necessary, and what is universal and necessary cannot be false. Against Hume's objections, nothing better seems to have been raised.

Transcendental idealism could serve two purposes. It could provide a critique of the grounds of knowledge, allowing us to see what we contribute to experience and what an independent reality contributes, but allowing room for direct knowledge of things through some faculty other than cognition. On the other hand (and this path seems to have been taken by Hegel, among others), transcendental idealism can serve as executioner of the rationalism/empiricism dichotomy and as propaedeutic to a new way of thinking that locates the reality of experience in thought itself. Even this radical idealism can leave room for the existence of mind-independent things, but it utterly rejects possible knowledge of them. In other words, mind-independent things could exist, although we could never know how or if they do, and, in any case, they are completely irrelevant to theory and practice in all fields.

The radical second path is more consistent with the critical project. Once Kant has made the ideality of space and time (and thus of all reality that can be presented to the senses, or that can be considered as a possible object of the senses [i.e., geometry and arithmetic]) seem self-evident, and once he has gone on to locate the basic elements of physics in the mind, not in the (independent) world, the question "How can knowledge be objective if we contribute to its creation?" is turned on its head; instead, it becomes difficult to fathom how knowledge of independent things is possible or could be known with certainty. If the mind must change things in order to understand them, mind-independent knowledge is incoherent. Coming at transcendental idealism in the 21st century, we can criticize Kant more freely for not making the leap. Once Kant himself introduced mind-dependence in such stark fashion to the intellectual world, it quickly (although not immediately) became impossible to discuss knowledge without assuming something like transcendental idealism going on in every branch of it (though such a revision of metalogic was rather late in coming; still, it appears to be here now, at least). Thus the nonsense view now is that real knowledge is possible; before Kant, the nonsense view was that knowledge was still knowledge after being filtered by subjective demands.

Of course, the discussion above hardly gets into what Kant seems not to have considered - whether mind and experience exist in a reciprocal relation of modification (Hegel would dare to say "clarification"). It took a further development in idealism to propose that the instrument of knowledge could change itself, or be changed by reality. Although experience, for Kant, may be a constant product of cognitive organization, the forms of thought were fixed - thus objectivity. Saving objectivity in light of Hegel is, perhaps, an impossible task; it is left as an exercise to the reader (!).

The Cure for Idealism

Kant's Refutation of Idealism (B 274-279) has the curious, and I am sure unintended, effects of begging the question and of making the existence of the self depend on the existence of (actual) external objects. The goal in this section is quite clear, and quite reasonable; perhaps it is even necessary to explain how transcendental idealism differs from other forms of idealism, those of Descartes and Berkeley specifically. Descartes and the rationalist philosophy that developed after him were confronted with experience of innate ideas with dubious, perhaps merely coincidental (in the case of Leibniz) correspondence with external reality. Erecting barriers around the mind in order to preserve the objectivity of its judgments, the rationalists had found themselves embarrassingly unable to prove how the mental could coincide with the physical. Whatever correspondence did exist, human thought was essentially ideal, dealing with modifications of itself and knowing only its own states, with interaction being difficult to prove and unnecessary anyway. That external objects could exist was accepted, but their relevance was questionable. Kant called this "problematic idealism;" external objects are possible (thus the modality of judgments about their existence is problematic: "It is possible that..."). Contra what Kant terms Berkeley's "dogmatic idealism," where external objects are not real at all, being merely fictitious nodes around which ideas (the only realities) coalesce.

Transcendental idealism is otherwise. Reality as perceived by the mind is ideal in the sense that things appear in experience to be other than they are in themselves, but this ideality is the effect of application of intuition and the categories to realities that must exist prior to thought in order to become (when modified by the cognitive faculty) objects of experience. Far from proving that external objects do not exist or that their existence is only possible, not actual or necessary, transcendental idealism requires external objects to give experience content at all. Keep that in mind while pondering the Theorem in the Refutation:

The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me.

Consciousness of my existence proves that external objects exist because my consciousness of my existence would not come about without the existence of external objects:

Hence determination of my existence in time is possible only through the existence of actual things that I perceive outside me.

Several problems: idealism is not refuted by showing that I present objects as being outside myself (in space instead of as part of my inner experience), but by showing that the realities to which these presentations correspond are actually something outside myself. Because "outside" and "external" are spatial terms, applying only to objects in experience, it is unclear how anything can be ontologically distinct from myself, and certainly is seems impossible, in transcendental idealism, for an external object to be ontologically external. Also, if inner experience cannot be determined without juxtaposition to outer experience, inner experience itself is contingent on outer experience, and, further, it is determinable only negatively. Inner experience can be described only as "whatever is not outer experience," with no inherent features of its own. This view seems dangerously close to denying that a self exists at all, for its experience of itself (inner experience) is nothing more than a negation. If inner experience cannot be determined at all beyond such a negation, it is experience of a non-entity. It would be awfully depressing not to be anything.

The Proof of the Theorem starts off on a bad foot:

I am conscious of my existence as determined in time. All time determination presupposes something permanent in perception. But this permanent something cannot be something within me, precisely because my existence can be determined in time only by this permanent something. Therefore perception of this permanent something is possible only through a thing outside me and not through mere presentation of a thing outside me.

Nothing objectionable is present in that passage until the last sentence, which actually contradicts the Critique's limitation of knowledge to the world of phenomena. Going through the argument: Inner intuition is organized temporally. So far, so good; and if anyone objects at this point, he must either leave Kant to the Kantians or read the Transcendental Aesthetic again. Temporal organization is possible only on the presupposition that a permanent "time" exists against which all temporal relations are compared. Again, as long as the Kantian conception of time is assumed at the outset (and, again, anyone who disagrees probably just disagrees with Kant and sees no efficacy of this Refutation of Idealism anyway, for it is, for him, nothing but a bolstering of a diseased structure of mistaken philosophy), this seems true. Moving on, the permanent thing giving substance (forgive the word!) to sequentiality and simultaneity cannot be in inner experience itself, for the coherence of that experience is itself contingent on the existence of the permanent thing. Thus the permanent thing cannot be the self. Now Kant trips over a confusion of levels: the permanent thing through which inner intuition gains its coherence must be an actually existing thing outside the self, not a mere presentation of permanence. Permanence is, however, a part of the concept of substance; up until this Refutation, I would have thought Kant perfectly committed to the idea that the presentation of permanence is that which makes inner experience possible. The operation would be something like this: the self, whatever it is, includes as part of its reality-interpreting function a presentation of permanence. This permanence is the result of the mind's operation on raw experience, not an ontologically independent permanence that the mind perceives. Having manufactured this permanence in its conception of reality, the mind now has the material to begin presenting the self to itself, as inner experience. Instead of taking that reasonable course, Kant declares that inner experience must be juxtaposed against an actually existing permanence that the mind is somehow able to perceive without having made it an aspect of presentation. What is that actual permanence but a noumenal reality, though? If presentation, then phenomenon; if not presentation, then noumenon.

The slip from phenomenal to noumenal conceals the question-begging inherent in a statement like "There are things actually outside me because I am conscious of things outside me." That statement makes sense if the consciousness of external objects includes consciousness of their actual externality, not merely consciousness that they are presented as being outside me. But consciousness in transcendental idealism is always about presentations, so that the statement collapses into the obvious fallacious "There are things actually outside me because I think them as outside me." Be careful, Immanuel; such thought makes the ontological argument work.

A footnote to Comment I to the Proof is also fraught with impermissible assumptions:

In the preceding theorem, the direct consciousness of the existence of external things is not presupposed but proved, whether or not we have insight into the possibility of this consciousness. The question concerning that possibility would be whether we have only an inner sense, and no outer sense but merely outer imagination. Clearly, however, in order for us even to imagine something - i.e., exhibit it to sense in intuition - as external, we must already have an outer sense, and must thereby distinguish directly the mere receptivity of an outer intuition from the spontaneity that characterizes all imagining. For if even outer sense were merely imagined, this would annul our very power of intuition which is to be determined by the imagination.

Levels-confusion abounds in this footnote. The idealist argument against which Kant launches this footnote is that what is called "outer sense" may merely be an aspect of inner sense. Inner sense would be divided between "Things I present as part of inner sense belonging to me" and "Things I present as part of inner sense belonging to things other than me." That things are presented in two different ways (I and other-than-I) does not imply ontological distinctness between them. "Outer imagination" would be the faculty of presenting at least a part of inner sense as other-than-I, although, as inner sense, it would properly belong to the self and to nothing outside the self. Kant's response to that idea is shrouded in an obscure locution, but he seems to claim that even outer imagination assumes the existence of outer sense, which must be distinguishable from inner sense and apply to a different set of objects entirely. For the mind to imagine something as outer, it must at least be able to think externality; the idea of externality could not arise except if there were an independent faculty (outer sense) capable of receiving data about actually external objects and functioning as the receiver and interpreter of that kind of data. Against the idealist theory that inner sense is bifurcated between inner-sense-of-me and inner-sense-of-not-me, Kant argues that outer sense is a sense in its own right, not merely an artificial modification of inner sense, and that the objects of outer sense are always different from the single object ("I") of inner sense.

Far from clearing things up, that explanation assumes away the problem. Granted there is something properly called the "outer sense," how exactly does that sense operate any differently from "outer imagination," and why does the existence of outer imagination as an activity of the self assume that outer sense must exist and be about independent realities? I can only imagine something if I could have intuition of it; in other words, imagination is only possible on the assumption of possible intuition. It does not follow that I must have an actual outer sense capable of perceiving things actually outside me in order to imagine things as being outside myself. That "outer sense," whatever it is, is presented as being a receptivity (and thus presented phenomenally as being a faculty for taking in data from external objects and organizing those data into a coherent outer experience) does not mean it is actually a receptivity instead of a spontaneity. Certainly something must give experience content, unless intuition is capable of creating content from itself (which would make it intellectual intuition), so that something must exist besides the self which intuits, in order to provide the raw material for the intuition the self has of other things. Pinning down just what intuition arises from external things and what intuition arises from the self is a tricky business, though, and that is precisely what Cartesian idealism was all about. If intellectual intuition is to be avoided (and that massive issue requires more discussion that I can presently give it), some aspects of experience must be caused by something other than the mind's spontaneity. That the objects of outer sense would correspond precisely with those external causes would be convenient, a helpful confirmation of the correctness of transcendental idealism and empirical realism, but, alas, nothing about the nature of outer sense seems to bear indicia of actual externality. Kant recognizes that not all experience actually arises from external causes:

It does not follow, from the fact that the existence of external objects is required for the possibility of a determinate consciousness of ourselves, that every intuitive presentation of external things implies also these things' existence; for the presentation may very well be (as it is in dreams as well as in madness) the mere effect of the imagination.

but fails to understand how difficult it is to tell whether a specific experience has an internal or external cause:

Whether this or that supposed experience is not perhaps a mere imagining must be ascertained by reference to its particular determination and by holding it up to the criteria of all actual experience.

All actual experience may be imagined. What then?

An an aside: is the self presented as an external object when it is intuited? "Inner sense" is not really pure awareness of the self, but awareness of the self as intuited in time. Thus the self is altered even when it is conscious of its own existence. Therefore, even inner sense is a presentation of something other than the noumenal self, something not self-identical. That ought to be disturbing for Kant. If the self is presented as something not identical to itself, it is presented as if it were an external object, with the attached proviso "but this is really the self's inner experience." If presentation corresponds to reality, the self as intuited in time is an external object to the real self. This is an awfully unfortunate conclusion.

Kant avoids the intuition problem by denying it:

The consciousness that I have of myself in the presentation I is not an intuition at all, but is a merely intellectual presentation of a thinking subject's self-activity.

I don't see how this is anything other than a reliance on intellectual intuition, for the very phrase "intellectual presentation" indicates the mind's non-empirical presentation of its own activity. Despite Kant's saying that this consciousness is not an intuition, it is a presentation and must, therefore, be presented to the mind somehow, i.e., through some intuition. How else is the mind to receive a presentation but through intuition? If the presentation "I" does not involve intuition, not even inner intuition, I would contend, following Kant's own argument throughout the First Critique, that it is entirely empty of content. Being empty of content, it is a mere thought-entity, and "I" is an empty word to the extent it refers to a thing divorced from intuition. Thus my previous point stands: "inner sense" is an intuition of something not precisely identical with "I".

Working from that aside, does not the Refutation of Idealism lead to skepticism about the existence of the self? Inner sense and its temporally-determined states are impossible without the existence of an actual external permanence against which the self and its successive states can be measured. By understanding the self in opposition to the external, the "I" as understood in itself becomes nothing more than what can be understood without such an opposition, but it ends up becoming nothing. Inner sense as the perception of the self as a quasi-external object allows consciousness to jibe with transcendental idealism's principle that only what is subject to cognition's forms can be experience for us. "I" as self-awareness without intuition becomes a single letter signifying no real object. The "I" is known only through a distinction between external and internal objects that holds only for experience. If this distinction were ontological, the "I" might survive, but as it is, the "I" is a mere artifact of empirical intuition! In different words: if the "I" depends for its existence on external realities, but those realities are external in only an ideal sense, the "I" has merely ideal existence, and no metaphysical existence. The Refutation has taken many victims in its broad sweep.

What is the title of this post all about, exactly? It's about my suggestion that Kant's cure for idealism was worse than the disease, and that a better solution to the problem is to deny that it is a problem for transcendental idealism. The whole Critique is an exercise in showing how incoherent metaphysics is. Idealism is a question about the metaphysical relations between subjects and objects; to that extent, idealism is nonsense. Objects do not exist except for minds, and what those things are in themselves is unknowable, because the mind can know only what it has made an object of knowledge. Reality only matters insofar as it is for minds; therefore, the very question about what things are like in themselves is meaningless. To those who believe the chasm between reality and perception is major philosophical problem, this solution is not satisfactory. But, following Kant, if that chasm cannot be bridged, and need not be bridged in order to give order, coherence, and objectivity to experience, then the problem diminishes in relevance to nothing. Where knowledge is impossible, ignorance is no evil. That acceptance is the true cure for idealism.

A Critique of Language?

A problem, and the source of disagreement, from F. Max Müller's preface to his 1881 translation of the Critique of Pure Reason:

Kant has shown us what can and what cannot be known by man. What remains to be done, even after Kant, is to show how man came to believe that he could know so much more than he can know, and this will have to be shown by a Critique of Language

"Language," Hamann writes, "is not only the foundation for the whole faculty of thinking, but the central point also from which proceeds the understanding of reason by herself." And again: "The question with me is not, What is Reason? but, What is Language? And here I suspect is the ground of all paralogisms and antinomies with which Reason has been charged." And again: "Hence I feel almost inclined to believe that [our] whole philosophy consists more of language than of reason, and the misunderstanding of numberless words, the prosopopoeias of the most arbitrary abstraction, the antitheses; nay, the commonest figures of speech of the sensus communis have produced a whole world of problems, which can no more be raised than solved. What we want is a Grammar of Reason."

A blogger asks:

Is that a fair summation for that time and could we argue that Wittgenstein has now completed the task?

If Wittgenstein completed that task, and Müller does not state precisely what he means (he attaches a footnote to the first quote, citing some lectures of his which seem to be extremely difficult to find, especially without the benefit of a subscription to obscure journal databases), Kant himself does not appear to have agreed with Hamann about the source of reason's confusion. In fact, seeking the confusion and error engendered by the inappropriate use of reason in language merely shifts the level of critique; it adds no particularly valuable insight beyond that offered by a critique of reason. The remaining question is this: Why is reason compelled to answer questions that apply to objects outside the proper domain of reason itself?

What Müller probably envisioned was a critique examining not just reason's capacity for making judgments (Kant had already provided that), but a deeper critique going a level below that of reason, examining the ability of human language to connect words in certain ways. The possible ways in which the human mind can coherently connect words to form ideas explains the possible ways that judgments can be formed, so that the power of reason itself depends, as a prior condition for its existence, on the power of language. The rules of language would make up Hamann's "Grammar of Reason" in the same way that the rules of judgment comprise logic. Shifting levels only relocates the proper area to explore and (hopefully) to discover the source of metaphysical error. Further, hoping for a perfect avoidance of all error, and a concomitant rejection of all metaphysical speculation, was neither desirable nor possible for Kant. Metaphysics, while not possible as a science, functions as a storehouse of useful concepts of ideal (though never quite real) perfections.

Language, like reason, is led so easily into error not because of its deficiency, but because of its power. Language must be powerful enough to allow its users to make an essentially infinite number of sentences in order to allow meaningful communication among sophisticated organisms. Increasing levels of abstraction in thought are reflected in increasingly abstract and universal words. The advantage of such abstraction is comprehensiveness of explanation and concision; the disadvantage is vagueness and distance from the concreteness of experience. Language consists in an array of shortcuts and abbreviations (as universal quantification, for instance, stands for an innumerable amount of individual predications), but it often confuses its user into thinking that the shortcuts are not shortcuts at all, not abstractions or artificial limitations on (or extensions of) reality but instead independently significant concepts. This kind of thinking led Plato to reify universals - the abstraction "man" grew from a convenient shorthand for a collection of traits and a name of a class of individuals into a thing in its own right. The Form of Man then, by giving reality to the individual instantiations of the form, became regarded as ontologically prior to individual men, and thus more real than any man ever could be.

As with language, so with reason. Reason, in order to make sense of physical change, assumes an underlying unchangeable material persisting through the changes. Something must be assumed to endure because "Nothing comes from nothing, and nothing perishes into nothing," but change is real; therefore, change must consist in alterations of the characteristics of a permanent something, and not in real creation or destruction. Berkeley rightly criticized this concept as artificial, unnecessary, and dubious, for the simple reason that this material substance could quite literally be shown to have no inherent characteristics. Characteristics are always things the substance acquires, and the unlimited capacity for this featureless substance to be affected and altered was its entire existence. Never hot, never cold, because hot and cold are merely modifications of the permanent substrate, it was the exact center of the onion. Qualities were merely the layers of that onion, and when peeled away, they exposed an utter emptiness at the center. Properly, then, substance was nothing, a convenient fiction but a dangerous dogma.

While Berkeley had his own reasons for denying the reality of material substance, it is not hard to find other mischief perpetrated by the dogmatic acceptance of substance as a real metaphysical object. Substance is permanent; substance is a thing that is never a predicate of anything else, but always the subject. The Cartesians seized upon this property of substance, permanence, the one thing it never lost in the unending flux of physics, to establish the immortality of the soul. Soul is mind; mind is always the subject of thought, never the modifications, never the specific things thought; therefore, the mind (and the soul, since they are identical) is a substance; further, substance is permanent; therefore the mind is immortal. Here is a grand metaphysical claim, and a great comfort to humanity, derived purely from concepts of reason!

A critique of the concept of substance refutes the conclusion that the immortality of the soul can be inferred from a simple law of reason, and it unmasks the subtle leap from thought to reality. Substance is a property of reality insofar as reason understands that reality. The mind must posit a permanent substrate to provide the enduring subject on which we hang the countless predicates experienced in the world. If substance did not exist, then objects could literally wink in and out of existence, without any sort of law governing their creation and destruction; further, any hope of doing such mundane tasks as balancing a chemical equation would be futile. That the mass of smoke and ash produced from the combustion of wood should equal the mass of that wood assumes that the smoke and ash are products of a certain operation upon the wood; if, instead, smoke and ash pop into existence ex nihilo, it is not apparent a priori that they bear any relation to the wood at all. Now attempt to search for that thing that is responsible for the conservation of mass and energy, and you will find it in no experience. It does not come from experience; it is not an inductive generalization from a number of experiences, but it is a concept that gives coherence to experience that otherwise would be rather random. That thing which makes the matter and energy endure in their proper proportion is the idea of substance.

Substance is merely an idea (more properly, following Kant's careful selection of terminology, a concept), not a thing conceived of as being a real object. Substance exists because it is a shortcut for the omnipresent permanent thing that exists in all instances of change. Substance itself is nothing. Things-in-themselves are neither permanent nor transitory, not relating to one another in time at all. Berkeley is right - substance is not a metaphysical object - but he is also wrong - substance is as real a concept as any other we have. It simply is not a concept applicable to things-in-themselves.

If substance is not an object of metaphysics, why was anyone ever led to believe it was? Two possible explanations come to mind. First, reason was used carelessly by those rationalists who elevated substance to such a status. If those people had only thought more clearly and been more precise in their inferences, they would have avoided error. A Critique of Language would cure the corresponding linguistic misuse by dissecting words and by showing the proper and improper ways of combining those words into meaningful sentences. Just as "The soul is substance" is a nonsense sentence that confuses a concept of experience with a property of things-in-themselves, it is a linguistically deficient sentence that uses an ambiguous connector to relate two ill-defined terms. If only "soul," "is," and "substance" were properly understood, and their relations clarified, we could avoid misusing them like that.

Kant himself had a different explanation in mind for erroneous metaphysical speculation, and in fact viewed metaphysics as absolutely indispensable for reason:

Whatever has its basis in the nature of our powers must be purposive and be accordant with their correct use - if only we can prevent a certain misunderstanding and thus can discover these powers' proper direction. Hence presumably the transcendental ideas will have their good and consequently immanent use, although when their signification is misunderstood and they are taken to be concepts of actual things, they can be transcendent in their application and can on that very account be deceptive.

What is the good use to which these ideas can be put? The ideas set up models of reality (of the totality of reality) that allow the whole world to be understood, even if not in concrete detail (because our lives are far too short and our physical limitations too great to comprehend every feature of every event through the entire history of the universe), at least as a coherent, rational whole. The mind itself can be understood, not as a metaphysical object actually known through pure concepts, but as a condition of all possible experience that must be assumed to be permanent, numerically one, &c. for the myriad aspects of experience to be unified in one perceiving and cognizing subject. Finally, the idea of a supremely perfect, necessary Being allows us to assume a world created intelligently and imbued with purpose.

The transcendental ideas allow us to approach reality as if the "I" were a Cartesian ego, as if the world were a whole whose parts and thoroughgoing relations were at least capable of being utterly known by us, as if an all-powerful, perfect God created the world and everything in it. That is how man came to believe he could know more than he could know; not because he can know everything (such is the flawed ideal of the old metaphysics) but because he can and must believe more things than he can affirmatively know. Error creeps in when the things naturally believed are taken to be things known in perfect detail, in themselves.

Someone ought at this point to object that Kant's reason for recognizing value in the transcendental ideas may not be valid. That Kant said this or that is a good answer for addressing a matter of textual interpretation, but it resolves the philosophical problem only if we agree with Kant (and, incidentally, all this implies that Müller either did not regard Kant's reason as satisfactory [probable] or did not even understand what Kant's reason was [unlikely for someone who had to have translated and, consequently, read the entire Critique of Pure Reason]). An alternative view, entirely consistent with the Critique's skepticism about metaphysical speculation, is to reside comfortably in Humean doubt. Comfortably not in the sense that such skepticism is easy to handle, because, after all, following Hume would require us to reduce our importance as selves virtually to nothing by admitting that the self is nothing more than a locus of ideas. The soul, far from being the most important thing in the world, would be an empty place where some things happened to occur, but which itself could serve equally well as the vacuum it is. Lacking souls entirely, we should not be surprised to learn that immortality is impossible, for if all that exists is material, then all that exists is perishable; the empty "I" persists in exactly the way space exists; having no reality and thus no existence in the first place, it will keep on being nothing indefinitely. God being a concept not derived from matters of fact and not posited as a mere idea must be a nonsense concept with no real object, and besides that, the idea that one perfect Being exists as the cause for a thoroughly imperfect world is an untenable strain on logic at best. What is comforting in all this agnosticism is the awareness that these confusing, metaphysical things cannot be known by us, so that even if they did exist, we could never know. We can stop short a painful, fruitless journey by answering reason's questions with categorical denial. This denial leaves more time for living, less time for worrying about fairy tales.

Certainly skepticism, whether dogmatic (denying that metaphysical objects exist at all) or Pyrrhonean (neither affirming nor denying metaphysical claims), is a solution to the Transcendental Dialectic. It is unsatisfactory insofar as it denies the value of faith in the transcendental ideas when concrete knowledge is not possible. There are really three issues here relating to the use of transcendental ideas which critical philosophy itself recognizes can never be known scientifically. First, the ideas may encourage good behavior and thus have value for a healthy moral life. Second, the ideas may provide rough outlines of at least some of the properties of the metaphysical existences (the noumena) the illusions of which they are (even a mirage discloses something). Third, the ideas may not give knowledge themselves but may suggest connections among phenomena that disclose deeper truths about those phenomena that reason, unaided by the ideas, would not be capable of discovering. The first and third potential beneficial effects of the ideas have textual support in Kant; the second does not seem to have such support. Whatever support these interpretations have, they must stand up to our critique and the critique of all philosophy if they are to have anything other than historical value.

On to the first purported benefit. Objects in experience cannot act freely. Every event in nature is the effect of a prior cause in nature. Ethics seems to have no application to these occurrences. Because human actions are phenomenal, they must be the result of the operation of physical laws. Telling physical law to stop so that we can do the right thing is impossible. However, if the self is an immortal soul created by God, and which has spontaneous causal efficacy, then ethics is possible in the first place. The noumenal self must be capable of acting freely, and must be the metaphysical "cause" of the actions of the empirical self, if moral responsibility can be reconciled with natural causality. The soul must be a person, identical through time, in order for it to be morally responsible. If the soul now differs from the soul a second ago, then the soul now cannot be responsible for what the previous soul did. So far, so good.

Whether the assumption of the soul's immortality is really necessary for the moral life is trickier. Kant certainly thought so. He saw it as unbearably unjust that sinners in this life are often happy and saints often miserable. Because this result is incompatible with justice, the soul must be capable of receiving punishment or reward after the death of the body. Because that punishment or reward can only come from an infinitely wise and just lawgiver, God must fill that role. If the "right" thing is whatever produces happiness, though, then no injustice exists. Only if correct moral conduct is based on something other than pleasure or happiness is a happy sinner a troubling possibility. Further, because the transcendental idea of immortality cannot be known, perhaps the person who rejects it as if it were false is much better off than the one who accepts it as if it were true, because he can do as he wishes without fear of future punishment. The transcendental idea is a comfort only if we hold to a system of morality that does not equate virtuous conduct with conduct that will produce happiness. If we were utterly convinced that such a morality must be true on other grounds (as Kant did, though a discussion of that will take us too far afield in this post), then the idea of immortality is a comfort and seems to restore justice.

Another benefit of an assumption of immortality of the soul is it allows us to obey a command otherwise impossible: to be perfect. At any instant, a human cannot be perfect. If, however, he improves himself daily, by gaining knowledge and by purifying his will, he will constantly grow closer to perfection. Asymptotically approaching perfection, he will be perfect at infinity; that is, if the line of his life continues forever, he will eventually attain perfection.

These benefits for the moral life are contingent as benefits on our adopting a certain ethical outlook. Kant found this outlook to be the only correct one and correspondingly needed to assume the transcendental ideas in order to construct a reality where that outlook was consistent with the facts. Even those who disagree with Kantian morality should understand the very real benefit transcendental can bestow in ethics: if an ethical theory is held to be true, but for some reason assumes the existence of things which are not possible objects of experience, transcendental ideas can fill in those gaps. Obviously, the theory must rest on firm ground prior to having unprovable ideals posited as bases for the reality of the theory, and transcendental ideas cannot be used to assume away other difficulties. To take just one example of the positive use of such ideas, what would utilitarianism be without a moral calculus? Yet that such a calculus is possible only upon certain nonempirical assumptions about pleasure. Possibly ethics cannot exist without some use of the ideas.

Second potential benefit: If phenomena are the result of the application of forms of thought to noumena, then surely noumena cannot be completely beyond our grasp. On the one hand, we can restrict the possible properties of noumena by noting what the mind adds to experience, then negating all those things of noumena. If our minds impose space upon objects, then noumena must not exist in space; and if time is a form of inner intuition, not applicable to things as they are in themselves, then time must not apply to noumena. This negative definition of a noumenal reality is not knowledge of noumena itself, but it can guide metaphysics by closing off certain avenues of inquiry and trimming the maze of possible paths in order to simplify the search.

On the other hand, that noumena are capable of being understood in some way indicates that they in themselves have some property that is expressible in terms we understand. That noumena can be organized temporally, even though such organization transforms them into something other than they are in themselves, does indicate at least that they are susceptible of existing in time. Further, it is not quite clear what application of intuition and concepts to reality does to change them. Perhaps space, time, and the categories are like silhouettes obstructing a light source. The light emanating from the source is the noumenon; the light that isn't obstructed by the silhouettes is the phenomenon. Thus the phenomenon is exactly like the noumenon in the parts that we are capable of detecting, and the only change to it is that some parts are beyond our possible comprehension. Similarly, some frequencies of electromagnetic radiation are not visible, though a part of the spectrum is. Another alternative way of explaining the change noumena undergo is analogous to, say, a device that converts the light emitted by the source in the previous analogy into sound. Each frequency of light is replicated by a certain frequency of sound, and the intensity of the light is reproduced as loudness of the sound. Here, unlike in the previous analogy, nothing of the noumenon remains; no light at all reaches us, rather than some. But all the light has been converted into sound, and all of that reaches us. So all of the light reaches us in some form, although, as before, the exact nature of the noumenon itself is not revealed.

This line of reasoning unfortunately will not bear fruit. It seems that noumena must at least be capable of producing phenomena such as we actually experience. There must be something to the noumenon that allows it to appear as this phenomenon and not as another. However, that something in the noumenon must not be identical to the something in the phenomenon. The noumenon must have some property that allows it to appear as spatially extended in experience, but without actually being spatially extended itself, because extension is an aspect of things provided by reason. The noumenon must have something like space that isn't space. What that something is is entirely beyond our ability to know. It seems the transcendental ideas do not actually allow knowledge of noumena, except in a negative sense, by listing all the things they are not.

The third, final possible benefit of transcendental ideas: The idea that the self is actually identical throughout cognition, not merely observed as something that has not yet become something different in all experience we have so far had, is probably indispensible even if it cannot ever be known to be true. The expectation that "I" will not suddenly become another person, or split into several persons, or stop existing while still having thoughts, strengthens the connection of ideas in the mind without allowing strict cognition of any connection. Thus Hume is correct: an identical self is never an object of experience, and can never be an object of experience. This hole in experience is filled by the idea of personhood, the Cartesian ego, which, although it cannot be an object of experience nor derived from experience (such derivation being merely inductive, if possible at all, and thus not capable of giving any idea of absolute permanence), we rely on more than anything we actually perceive, no matter with what vividness and clarity. Although "I think" is an empirically known truth, something more than merely "There is a thing that is thinking" is stated by it. In the Analytic, regarding the transcendental unity of apperception, Kant says:

The I think must be capable of accompanying all my presentations.

while in the Paralogisms, he claims "I think" is empirical. Whether or not he recognized a tension between these views (views in the same book, no less), the difference between "There is a thing thinking" and "I think" should provide a clue to the value of idea of personhood. "I" must be a unity for experience to be united spatially (seen as a continuum of objects and not merely as completely discrete things incapable of interacting with each other) and temporally (so that what the ego perceives now and what it perceives a second later are known to be succeeding intuitive "snapshots" of the same ego). This unity is implicit in all judgment, in all experience generally, and is not identical to space, time, or the categories. It exists prior to them, allowing them to form a coherent experience by unifying all the parts of space, all the parts of time, and all the conceptually-known objects and events into one thing, experience generally. What that experience is of is known only as "I".

The idea of the world as a whole allows us speculatively to go beyond any concrete thing experienced and beyond all possible experience in order to consider the whole universe, the whole history of time (from its beginning, if any exists, to its end, if that exists), and the smallest increments of space and time. This has had documented benefits throughout the history of science. Observing the relatively gross effects of, say, radiation on an object, one can speculate that the minute parts of it must be constituted just so in order to have such large effects. Without microscopic observation, it cannot be known what the extremely small particles making up the thing are like. When such observation is impossible (because technology has not advanced to allow such fine observation, or because some sort of unavoidable limit to direct observation has been reached), something can be known that is not experienced. In the case of the unavoidable limit (a limit imposed by the universe itself and not by our own deficiency), the thing known is not a possible object of experience.

To be sure, in the case of indirect observation of minute phenomena, what is known is not precisely the unknowable thing but its effect on things that are knowable. Ultimately, it seems, what we know are our own states, and not any truly existing independent things at all. The Refutation of Idealism has a unique solution to that difficulty:

I am conscious of my existence as determined in time. All time determination presupposes something permanent in perception. But this permanent something cannot be something within me, precisely because my existence can be determined in time only by this permanent something. Therefore perception of this permanent something is possible only through a thing outside me and not through mere presentation of a thing outside me.

Though found in the Transcendental Analytic, this argument is right on target about the transcendental ideas. Real, metaphysically distinct things outside myself must exist because the sheer fact of having experience at all presupposes their existence, not merely as objects in experience but as real, independent things. This kind of inference from what is known (inner experience) to what must exist for that known thing to exist itself (a metaphysically distinct world) goes on literally every second of human existence. That it should occur in speculation about the origins of the universe, about time, about the smallest particles possible, &c. is not surprising at all.

The skeptic will ask, "Doesn't this kind of thinking lead to credulity? You say that we can know things we can never directly observe, even though it is that observation which is supposed to bring knowledge. Why not assume magical forces, psychic powers, or any such nonsense?" The use of the transcendental ideas must be subject to limiting conditions, of course. Precisely because they go beyond all possible experience, they must be used carefully and subject always to what can determinately be known. If ideas contradict experience, experience must always win out. If ideas are consistent with actual experience, they have found their proper role, because they can expand knowledge that already exists by suggesting possible connections that experience alone could not find. If, however, ideas are consistent merely with possible experience, then their operation is likely to lead merely to confusion and error. The ideas are not to be invoked in the place of rigorous observation and analysis. They simply urge us to consider everything in the world as related to everything else in a way that reason could discover, if it had infinite time and resources to consider all of universal history as a single object.

If the Supreme Being is the cause of the world, then the world can be expected to be imbued with purpose. This purposiveness is not weak, a mere application of teleological terms to descriptions of events known to occur solely due to mechanical laws of nature (the stone's purpose was to fall to the ground) but strong (the heart's purpose is to pump blood throughout the body). However, it can't be strong enough to contradict reason's laws, which interpret phenomena as interacting according to mechanical laws. Instead, purposiveness's place is in judgments about groups of phenomena, about their relations over time, and about reciprocal interaction. A biological organism exhibits best the utility of regarding the world, and parts of that world, as driven by purpose. The answer "Because its purpose is to carry oxygen to and carbon dioxide away from cells" to the question "Why does blood flow?" is correct in a way that transcends phenomena. The phenomena themselves, and the laws of physics governing them, contain no data whatsoever about purpose. From the fluidity of blood, its chemical composition, its pressure, its temperature, and the motion induced in it by the heart, one never finds attached the idea that it is providing support to a living thing. The mechanical account cannot explain why blood flows instead of doing nothing at all. Explaining the function of the blood as a process in an organism, whereby it tends to sustain the continued arrangement of that organism instead of its dissolution into dead tissue (essentially mere matter), and whereby it receives sustenance itself from the body's other organs, allows biology and anatomy to reach greater insight and thus accumulate more knowledge about reality. Where the purpose of an organ is not yet known, theories about its function operate on the premise that it must have such a function. No one would consider it plausible that an organ is "just there" in the same way that someone observing a particular grain of sand dismisses any teleological explanation of its current position.

Even so, the idea of purpose is not real purpose. When breaking down the components of the human body, or of any creature, we do not expect to find a purpose organ, purpose fluid, or the purpose system. Purpose is not a real thing that will be experienced, but merely a convenient organization method for the mind. As in all cases of ideas that are not universal laws of nature, the principle of purpose can give rise to illusion. The illusion in the case of biology is what Aristotle called the soul and what we might call "living force." Living force, as a metaphysically distinct object of experience, is beyond our capacity to understand. But considering reality as if certain things were imbued with such a force, and understanding the behaviors of those things as effects of the interplay of physical laws and living force, allows biology to break free from being a mere branch of physics and allows it to produce meaningful results.

A fine line exists between believing we know more than we can know and between assuming things we could not know in order to better understand what we do know. If Müller wished to eliminate the Transcendental Dialectic, then he wished to destroy a useful tool. The power to imagine things that do not exist can sharpen our knowledge of the things that do exist. If a Critique of Language would shrink the expressive power of language in order to tiptoe around metaphysical bogeymen, then I hope it never will be done.

Introduction

Welcome to Critical Philosophy.

A short introduction is in order. I am a law student and possessor of an undergraduate degree in philosophy. Though my time is monopolized by study of the law, I have not yet been cured of the philosophy bug. One might say that I have had the fate to be in love with metaphysics. Though I cannot favor her with my undivided attention, still I cannot avoid a temptation to transcend the mundanity of American jurisprudence and engage in speculation about the principles of knowledge and reality. This blog will provide a way to relieve that urge by indulging it.

This blog will concentrate on Kant's critical project and its impact on subsequent philosophy. Kant's position in the history of Western thought cannot possibly be elevated more by anything I could write here, though I hope to emphasize that position, both by reminding those who forget what an impact Kant has had these past two centuries and by informing those who are ignorant of his immense importance and continuing relevance. The Critique of Pure Reason overthrew the accepted wisdom of its day in a way every bit as revolutionary as Newton's laws of motion rocked the foundations of physical science. Philosophy before Kant is obsolete in light of his critique of the origin and justification of cognition; though many attempt to return to the naive views of (for instance) Descartes or Locke, they always come to grief. Corresponding to Kant's effect on philosophical positions prior to him is a deeply-felt effect on all subsequent philosophical investigation. The movement known as German idealism, though growing in its own haphazard way in directions different from and sometimes contrary to those indicated by Kant himself, owes its existence to Kant's transcendental idealism. 20th-century philosophy of language owes a debt to Kant's recognition of the capacity of the tool of cognition to affect the perception of the objects of that cognition. In even subtler ways, even bitter enemies of Kant (like Friedrich Nietzsche and Ayn Rand) have absorbed Kant's epistemological and ethical theories and take them into account, often unconsciously, in the explication of their own thought.

Therefore, although philosophy has moved on since 1781, when Kant published the first edition of his Critique, it has grown out of the soil of critical philosophy. Investigating the history of philosophy before and after Kant, this project will be able to show how old problems in philosophy had new light shed on them by transcendental idealism, and how philosophers since Kant have dealt with the problems he himself introduced to the world. Even if a specific Kantian solution to an issue strikes us as insufficient, it provides a philosophically mature way of considering the issue, and will enable us to reach a more satisfactory resolution in the end.

Of course, in some fields - metamathematics, for instance - I will argue precisely against Kant. But even in those areas, Kant states the opposition thesis and develops the argument for it intelligently, and having such worthy opposition will enable us to understand all the nuances without fighting straw men.

Ultimately, despite the concentration on Kant, this blog will be a philosophical blog with general scope. Kant may be the focus of the orbit, but that orbit will be eccentric indeed. I freely invite the reader to offer criticism, to provide correction wherever needed, and to join me in the effort to understand the world better through an uninhibited critique of reason, sense, and reality.