Notes on <Kant's Transcendental Idealism> - The Sensible Conditions of Human Knowledge
Three possibilities regard the ontological status of space and time are introduced, first is the absolutistic theory by Newton, which advocated that space and time are real existences. Second is the relational view from Leibniz, according to which they are determinations or relations of things. The third is the critical view, that they belong only to the form of intuition and to the subjective constitution of our mind, apart from which they could not be ascribed to anything whatsoever.
The central concern of Transcendental Aesthetic is to demonstrate the truth of the last claim.
The Representation of Space and Time
In metaphysical exposition of space and time we have proof for space and time are both a priori and intuitions.
The Apriority Thesis
The First Apriority Argument
The first argument involves two claims. One is that the representation of space is presupposed if I refer my sensations to something “outside me”. The second is that space is presupposed if I were to represent objects as outside or external to one another. Here Kant is arguing against the Leibnizian theory of space.
There are two objections to the argument. One is the there is an alternative that representation A may underlie representation B is that A and B correlative and mutually condition one another, instead of A being a priori to B. Paton said this possibility is removed by the second argument(we can think of empty space without object but not the other way around), so the first argument is not sufficient.
However this objection misses the force of Kant’s first argument. What the argument claims is rather that representation of space functions within human experience as a means for the representation of objects as distinct from the self and from each other and we can’t maintain the other way around, that the awareness of ourselves and each other is a condition of representation of space.
While the first argument claims that Kant did not prove enough, the second objection maintains that Kant proves too much. It claims that Kant also proves empirical concepts must be a priori as well in the same sense that space is a priori. For example the concept of red is presupposed when we talk about red things. However, the situations are different since space is not built into the distinctions of things, and red is built into the thought of read things.
The Second Apriority Argument
We can never represent ourselves the absence of space, but we can think it empty of objects.
The objection is that it is grounded on psychological claim. The criterion is not the impossibility of thinking otherwise but our own incapacity to represent this specific element as absent. Another objection is that it is grounded on logical impossibility of conceiving the nonexistence of space. This is obviously unacceptable, since thinking things in themselves means we can represent things to ourselves without space.
There is a third alternative to psychological and logical impossibility, that is, the epistemic conditions. The absence of space is limited to appearances, and space and time are conditions of the possibility of appearances, so this is epistemic.
Kant’s point is not that it is either psychologically or logically impossible to remove(in thought) space and time, it’s rather that it is impossible to do so and still have any sensible content to intuit.
The Intuition Thesis
The First Intuition Argument
The argument assumes the exhaustive nature of the concept-intuition distinction and attempts to show that this representation cannot be a concept and must be an intuition. The proof is in two steps. First step Kant contrasts the relation between space and particular spaces with the relation between a concept and its extension. Second step he contrasts it with the relation between a concept and its intention.
In the first step Kant says the representation of space is singular so it must be an intuition, but actually this is not logically necessary since the concept of “world” is also singular, but it’s not an intuition.
The problem is resolved in the second part of the argument. Main point is that the marks or partial concepts out of which a general concept is composed are all logically priori to the whole, a general concept is thus a collection of marks, this can be applied to “world” as well. However, this is not the case with space and its parts, the parts of space is only given in and through this single space which they presuppose. Space cannot be conceived a a collection or aggregate.
The Second Intuition Argument
This argument is both more complex and more problematic than the preceding one.s It assumes that space is represented as an infinite given magnitude and concludes from this that space is an intuition.
Proof in first edition suffers from the same counterexample of the concept of the world since it is also infinite but we can’t conceive the world as an intuition. The second edition meets these difficulties by showing the different senses in which concepts and intuitions involve infinity. A concept has a complex logical form, involving both extension and an intension. Viewed extensionally, every concept has various other concepts contained under it. Viewed intensionally, every concept contains other concepts within it as its component parts. The smaller the extension, that is, the more limited the sphere of objects to which it applies, the richer the intension, and vice versa.
A concept involves infinity with respect to its extension: it can have an infinite or an indefinite number of concepts falling under it. A concept, however, cannot involve infinity with respect to its intension, because such an infinite concept could not be grasped by human mind. An intuition, by contrast, can have an infinite number of parts within it, this is precisely how space is thought, from this he concludes that the original representation of space is an a priori intuition, not a concept.
However it seems that the doctrine of the infinity of the world in space and time in the thesis of the First Antinomy applies equally to the infinity of space and time if we have the same sense of “infinity”. Although there is evidence saying this is a different conception of “infinity”. In first edition, the infinity of space is defined by limitlessness in the progression of intuition, that is, however large region of space one takes, it is always represented as bounded by more of the same.
The Givenness of Space (Form of Intuition and Formal Intuition)
Here we want to talk about conflict between Transcendental Aesthetic and Transcendental Analytic.
Kant claims that space is represented as an infinite given magnitude. First it is difficult to see how is space given as infinite since it requires conceptual determination. Second the claim that the space and time are given seems to conflict with the end of Analytic that pure space and time are indeed intuited. If they are not given as objects of intuition, in what sense can they be said to be given at all?
The conception of space presupposes a pre-conceptual framework(a “pure manifold”) which both guides and limits this conceptual activity. It is necessary with respect to human cognition without being logically necessary. Every determinate space is represented as part or determination of the one unbounded space, this can be said to be “pre-intuited”, in the sense that it is given together with every determinate intuition as its original ground or condition. Moreover, we can see that “space is represented as an infinite given magnitude” must be taken as a claim about the “form” or essential structure of every determinate representation of space, not as a claim about a unique representation of this infinite space itself. It is a claim about the conceptual conditions (rules) under which it is possible to represent a determinate portion of space.
Perhaps the most illumination text is in the footnote of the second edition of Transcendental Deduction: [B160-161]. This will be revisited in chapter 7. Here we want to talk about the contrast between “form of intuition” and “formal intuition”, both are “Pure intuition”. This reflects the contrast between indeterminate (unconceptualized) and determinate (conceptualized) intuition. There are actually three notion, the first one can be further divided to form of intuiting and form of intuited.
Form of intuiting might seem unnecessary because of the translation of gibt to “contains”, if it is translated to “supplies” then it is clear that Kant is saying space is the ultimate source or ground of the manifold contained in the actual intuition. “The manifold” here is understood as spaces that are given in and through the original representation of space.
The notion of a form of the intuited must be construed as the pre-intuited framework or structure that conditions and is presupposed by the actual representation of regions of space.
“Formal intuition” is meant a determinate intuitive representation of certain “formal” or universal and necessary features of objects qua intuited. A formal intuition is a hybrid, requiring both the form of intuition and a concept by means of which this form is determined in a certain way. Such representation are the products of mathematical construction, which is itself ultimately governed by the given nature of space as the form of the intuited. In other words, this given nature determines what is geometrically possible or constructible. This is why Kant contends that geometry is synthetic.
Geometry and Incongruence
Geometry
The connection between geometry and transcendental ideality of space is indicated in Transcendental Exposition. A transcendental exposition is designed to show that a given body of synthetic a priori knowledge(P) is only possible if there is a representation (Q) with certain specified properties. Q is thus a necessary condition for P, or P -> Q. This the connection Kant tries to establish between geometry and the representation of space as analyzed in the Metaphysical Exposition. Assumption is that geometry is synthetic a priori and the question is then what must be our representation of space in order such knowledge is possible. Note that we are talking about our representation of space not space itself. Kant maintains that this representation must be both intuition and a priori. To prove the ideality of space, the second claim is that this a priori and intuitive character entails that space itself must be a form of outer sense or of sensibility.
Two important conclusions follow from this. First the ideality of space is a necessary condition of geometry as synthetic a priori so the denial of latter does not denial the former. Second the argument from geometry only moves to ideality by way of an appeal to the a priori and intuitive character of the representation of space, so if this can be established independently, the ideality argument can proceed without appeal to geometry.
Incongruent Counterparts
By counterparts Kant means objects that are complete similar to one another with respect to their intrinsic properties but which cannot contained within the same spatial parameters. For example spherical triangles, left and right hands. However, this is even less capable of providing an independent proof of ideality of space than the argument from geometry. The appeal to incongruent counterparts is used to refute the Leibnizian theory of space(relational).
The Ideality Argument
Kant’s Conclusions
The first “conclusion” is that “Space does not represent any property of things in themselves, nor does it represent them in their relation to one another”. The claim is that the representation of space does not contain any properties that can be predicated of things when they are considered apart from their relation to the subjective conditions of intuition.
The second “conclusion” is the “space is nothing but the form of all appearances of outer sense”. Kant endeavors to clarify matters by remarking that it is the subjective condition of sensibility, under which alone outer intuition is possible for us. Kant asserts that “It is, therefore, solely from the human standpoint that we can speak of space, of extended things etc. If we depart from the subjective condition under which alone we can have outer intuitions, …, the representation of space stands nothing whatsoever. This can be ascribed to things only as they appear to us, the objects of sensibility”.
The empirical reality of space can easily be seen to follow from the preceding analysis of function within experience of representation. As a condition of human experience, the representation is applicable to objects qua experience. The problem is o see “how the transcendental ideality of space follows from this same analysis”, it is the difficulty in finding such argument that has led so many interpreters to assume that Kant’s real argument is based on the synthetic a priori character of geometry.
What is needed is an argument that appeals to the intuitive as well as the a priori nature of the representation of space and is capable of generating this ontological result.
In Search of an Argument
After noting that the possibility of mathematics rests upon a priori intuition, Kant raises the question of the possiblity of intuiting something a priori.
Since concepts never relate immediately to objects, they can be formed in dependently of any experience of them. An intuition, however, since it relates immediately to its object, does not so much represent as actually present the object to the mind. It is this immediacy with its presumed apriority that renders the notion of a priori intuition problematic. This seems to require an object somehow be given to the mind before it is actually experienced. So we need to explain how an intuition of the object can precede the object itself.
The problem is this: How is an intuition possible, the content of which is non-empirical, that is, not derived from an affection by an object? Kant notes that it would be impossible if the intuition represented things as they are in themselves. And suggest that even an empirical intuition would be impossible on this assumption.
A priori intuition is possible, if and only if it contains or presents to the mind a form of its own sensibility. The implicit argument consists of two steps. The first shows that an a priori intuition is possible if it contains or presents to the mind a form of sensibility, the second shows that such intuition is possible only if it does this.
The If Portion of the Argument
The first part of the argument maintains that an a priori intuition is possible if it contains or presents to the mind its own form of sensibility. The major issue here are the meaning of “form of sensibility” and whether such a form is the sort of thing that can be intuited.
A form of appearance is a feature of the appearance in virtue of which its elements are viewed as ordered or related to one another in experience. The first apriority argument maintains that the representation of space functions as a form in this sense.
Form of intuition can designate either the formal features or structure of the objects intuitions or the mode or manner of intuiting. In the former sense it is equivalent to form of appearance and is ontologically neutral. In the latter sense it involves explicit reference to mind, not of things in themselves.
Form of sensibility can be taken in two senses, both of which involve a reference to mind.
If portion of the argument maintains that if the content of a given intuition is a form or formal feature of objects of intuition that pertains to these objects only in virtue of the constitution of the mind (its form of intuiting), then that intuition must be a priori. Because first the content of such an intuition would be universal and necessary and second, its source would not lie in the objects themselves, nor in any sensible data produced by the affection of the mind by these objects. So it would also be “pure”, independent of sensation.
The Only If Portion of the Argument
This is an argument by elimination. The two alternative to the Kantian view are the Leibnizian and Newtonian positions.
Paton indicates the limitations of Kant’s argument in the Metaphysical Exposition with a query:
Granting that by means of our pure intuitions of space and time we can know
a priorithe conditions, or forms, of all appearances, why should not space and time be real things which are at the same time conditions, or forms, of things, not only as they appear to us, but as they are in themselves?
It contains two questions: (1) Why can’t space and time be conditions or forms of both appearances and things as they are in themselves (2) Why can’t space and time be “real things” in the transcendental sense and conditions or forms of the experience of “real things” rather than of “mere appearances”?
Both questions are appropriate, but only the second, the Newtonian position, need concern us here, because only it challenges directly the contention that space is a form of human sensibility.
If the accounts in Metaphysical Exposition is compatible with Newtonian view then Kant’s Conclusions do not follow from his premises. It is clear that Kant himself took the account of the representation of space as a pure intuition to rule out the Newtonian as well as the Leibnizian view.
It seems like most of the positions in Metaphysical Exposition are compatible with Newtonian view. As the first step in the resolution of this difficulty, which threatens to underline the overall argument of Transcendental Aesthetic, it’s important to remember that the real issue raised by the Metaphysical Exposition concerns the function of space as a form or condition of human experience. Given this, we can distinguish between two questions (1) Does a particular theory of space hold that space functions in this way? (2) Is this theory capable of accounting for the possibility of space functioning in this way? The author takes the position that Leibnizian theory fails both tests and Newtonian theory fails only the second.
The question is why the Newtonian theory is incapable of accounting for the possibility that space functions as a form or condition of human experience. Or, why is regarding space as an ontological condition incompatible with also regarding it as epistemic condition? We must appeal to an argument by elimination. Space is a form of sensibility is ruled out ex hypothesi, two alternatives remain (1) we have innate idea of space and between this idea and space itself there exists a kind of “pre-established harmony” (2) Our idea of space is derived from the experience of these “real things” and represents a property and condition of them.
Kant does not take the first alternative very seriously (for a good reason).
The second alternative does not fare much better. The problem is that by assuming that representation of space is somehow derived from our experience of things as they are in themselves, it denies the possibility that space can function as a condition of the possibility of the experience of such things. There is a contradiction involved in the assumption that the representation of something that is supposed to function as a condition of the possibility of experience of objects can have its source in the experience of these objects. This is contradictory because it entails that experience be possible apart from something that is stipulated to be a condition of its possibility.
The Newtonians have to admit two eternal and infinite self-subsistent non-entities space and time, which are there (yet without there being anything real) only in order to contain in themselves all that is real (A39/B56). The metaphysical absurdities involved in the conception of absolute space and time are the direct consequences of this “admission”, which the Newtonians cannot avoid because of their transcendentally realistic assumptions.
These argument turns entirely on the epistemic function within human experience of the representation of space, a function that is supposedly established in the Metaphysical Exposition.
Space and Things in themselves (The Problem of the Neglected Alternative)
Might it not be the case both that space is such a form and that things as they are in themselves are spatial? How can Kant deny such a possibility without contradicting his claim that things in themselves are unknowable?
One way to deal with this is to admit that the possibility is left open in Transcendental Aesthetic but is removed in Antinomies. Nevertheless it’s worthwhile to see if Transcendental Aesthetic itself can be saved.
A reference to mind and its capacities is built into the notion of the form of the intuited. It follows from this that if space is such a form then it can’t be meaningfully predicated of objects, when these objects are considered in abstraction from their representation. This demonstrated the meaninglessness of talking about a qualitative identity between the form of representation and form of things in themselves. It shows that the presumed identity would be between a property that only pertains to things in virtue of their being represented in a particular way and one that pertains to things as they are independently of being represented at all. The mind dependence is a defining characteristic of the former and the mind independence of the latter.
We thus conclude that it is possible to construct an argument for the transcendental ideality of space and time on the basis of materials provided in the Transcendental Aesthetic. And the ideality thesis is really a consequence of Kant’s claim that space and time are epistemic conditions.