KANT AND SPACE

KANT AND SPACEKANT AND SPACEI. Overall Claim:

'And so metaphysics according to its aim at least, consists simply of synthetic a priori propositions' (B18).1. We need two cognitive faculties to arrive at knowledge claims: Thoughts without content are empty, intuitions without concepts are blind (A51/B75).

2. Leibniz intellectualised appearances, just as Locke [] sensualised all concepts of the understanding, i.e., interpreted them as nothing more than empirical or abstract concepts of reflection. Instead of seeking in understanding and sensibility two sources of representations which, while quite different, can supply objectively valid judgments of things only in connection with each other, each of these great men holds to one only of the two, viewing it as an immediate relation to things in themselves. The other faculty is then regarded as serving only to confuse or to order the representation which this selected faculty yields (CPR, A271/B327)

3. The problem is that neither recognised that sensibility is a separate and distinct cognitive faculty from understanding (concepts) and reason (ideas). Locke and Leibniz only recognise a difference of degree between concepts and perceptions (eg CPR A 44).

CLAIM:

If Metaphysics is possible we need to be able to make synthetic a priori judgments; this implies that we need to have a priori concepts and intuitionsE.g.: All geometrical propositions are necessary and universal however they cannot be known by mere reflection on concepts. Eg. The proposition the straight line between two points is the shortest is a priori (i.e. it is necessary and universal) and synthetic since its truth cannot be established by analysing the concept a straight line; i.e. the truth does not follow from the meaning of its constitutive term. The concept of the shortest is wholly an addition, and cannot be derived through any process of analysis from the concept of the straight line (B16).

If it is a priori the truth depends neither on empirical facts if it is synthetic it is not conceptually true.

Intuition therefore must be called in: only by its aid is the synthesis possible (B16)

Claim:

Geometry is a science which determines the properties of space synthetically, and yet a a priori. What then, must be our representation of space, in order that such knowledge may be possible? It must in its origin be an intuition . Further, this intuition must be a priori, that is, it must be found in us priori to any perception of an object How, then can there exist an intuition which precedes the objects themselves? Manifestly, not other than in so far as the intuition has its seat in the subject only [this] is the only explanation that makes intelligible the possibility of geometry, as a body of a priori synthetic knowledge (B41).

Regressive argument:

1. The propositions of geometry are synthetic and a priori PREMISE (this is taken as a given)

2. This is possible only if space is a human form of intuition

3. Hence 2. Must be the case.

II. Newton & Leibniz/ClarkeA.

"1. Absolute, true, and mathematical time, of itself and from its own nature, flows equably without relation to anything external. [Relative, apparent and common time is some sensible and external measure of duration ...]2. Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces which our senses determine by its position to bodies".

(Scholium)

B.

"... [God] is eternal and infinite, omnipotent and omniscient; that is, his duration reaches from eternity to eternity; his presence form infinity to infinity; [...] He e is not eternity and infinity, but eternal and infinite; he is not duration or space, but he endures and is present. He endures forever and is everywhere present; and by existing always and everywhere he constitutes duration and space. [...] He is omnipotent not virtually only but also substantially [...] In him are all things contained and moved. [...] As a blind man has no idea of colours, so have we no idea of the manner by which the all-wise God perceives and understands all things".

(General Scholium)

Newton: Vulgarily space and time are regarded as relative, i.e. as distances between sensible objects or events. In reality there is in addition to such relative spaces and times absolute, the mathematical space and time. There are infinite homogenous, continuous entities entirely independent of any sensible object or motion by which we try to measure them.

1. Time flows equally from eternity to eternity.

2. Space exists at once in infinite immovability.

3. Time and space do not change but are immovable by their own essence. If they could be changed they would be moved out of themselves; thus to regard the primary places of things, or parts of absolute space as movable is absurd.

B. Leibnizs Third Paper

Some modern Englishmen maintain that space is a real absolute being. But this involves them in great difficulties, for such a being must needs be eternal and infinite. Hence some have believed it to be God himself, or one of his attributes, his immensity. But since space consists of parts, it is not a thing which can belong to God.

As for my opinion I have said more than once that I hold space to be something merely relative, as time is: that I hold it to be an order of co-existences as time is an order of successions. . But if space is nothing else but that order or relation, and is nothing at all without bodies but the possibility of placing them, then those two states, the one such as it now is, the other supposed to be in the quite contrary way, would not at all differ from one another. The difference therefore is only to be found our our chimerical supposition of the reality of space itself. III. KANT

1) Agreed with Leibniz There are dangerous theological consequences of Newton's position: "as condition of all existence in general, they must also be the conditions of the existence of God" (B71). [Leibniz-Wolffian Monadology: Reality consists of non-spatial, non-temporal, un-extended simple substances; space, time, and motion are phenomena derivative from this underlying monadic realm. I.e. no contingent thing is capable of causing another. Prior to the existence of things God has established a harmony of their individual future causal developments. This pre-established harmony is so thoroughgoing and precise that things give the semblance of interaction].

2) Agreed with Newton: Space (and time) cannot be relational as Leibniz claimed. Eg. Incongruent counterparts.IV INCONGRUENT COUNTERPARTS: Kants argument: Concerning the ultimate ground of the differentiation of directions in space (1768)

I. There is real difference between left and right hands

II. There is no adequate explanation of the difference that does not posit absolute space

For

a) It cannot be explained by the differing relations between the parts of hands since these are the same for left and right hands (internalist position)

b) It cannot be explained by the relations left and right hands bear to other material objects since a hand would be either left or right if it was the only material object that existed. (externalist position)

c) There is no other adequate explanation that does not posit absolute space (absolute position)

III. The supposition that absolute space exists does adequately explain the difference

IV. Hence, granted that left and right hands exists, absolute space exists and has a reality of its own.

Agreed with Leibniz: Space must be an appearance. Space is our way of seeing the world but does not mirror reality. Those who maintain the absolute reality of space and time, whether as subsistent or only as inherent, must come into conflict with the principles of experience itself. For they 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. (A9/B56). I.e.., if the parts of absolute space are not visible or sensibly distinguishable, they remain ultimately inaccessible to us.Berkeley's idealism (degrading bodies to mere illusions) makes a certain amount of sense when it is viewed as a response to Newton.

V. KANTS SOLUTION:

Space is neither transcendentally real (Newton) nor empirically ideal (Leibniz) but transcendentally ideal: Instead of viewing space and time as conditions of the possibility of things in themselves, we should view them as conditions of the possibility of our knowledge or experience of things. Instead of being "two eternal and infinite, self-subsistent non-entities" they now becomes "two sources of knowledge" (Erkenntnisquellen) (A38/B55). VI SPACE is our OUTER SENSE

Kant's notion of outer sense alludes to Newton's divine sensorium. Rather than referring to a sensroium deity we should be thinking of a sensorium huminasA sense through which one can become perceptually aware of objects as distinct form the self and its states. It does not already involve a reference to space. Although the representations of space must be regarded as the condition of possibility of representations of objects, the reverse should be also true, namely that representations of objects are the conditions of the possibility for the representation of space.

We can think space and time as empty of objects however we cannot experience or perceive empty space or time.

The A version asserts that every single region or extent of space, no matter how large is encompassed by a surrounding homogenous space, no matter how large.

The B version emphasises the fact that any given number of distinct regions no matter how many are encompassed by a single homogenous space.

A& B Space is limitless and all encompassing.

Melnick refers to the preintuition or pre-conception of space and time. The unbounded space can be pre-intuited VII SPACE IS A PRIORI AND A FORM OF INTUITIONA. Why Space is A PrioriSpace is not derived from experience. The representation of space cannot, therefore, be empirically obtained from the relations of outer appearances. On the contrary, outer appearance is only possible at all through that representation.

Space is a necessary a priori representation which underlines all outer intuitions. We can think space and time as empty of objects however we cannot experience or perceive objects empty space or time.

It is a sense through which one can become perceptually aware of objects as distinct form the self and its states. It does not already involve a reference to space.

Melnick refers to the pre-intuition or pre-conception of space and time.

B. Why Space is a Form of Intuition and NOT a Concept

1. Concepts are general representations (discursive)They can be divided hierarchically into part whole relations. E.g. Species genus.

Physical object

Animal

Cow

The content of the concept physical object is the content of the concept cow = extension. The content animal has a smaller extension but a greater intension than the content of the concept physical object. Hence the part is greater than the whole.

2. Space is an infinite given magnitude

There is no hierarchical relation between parts and wholes but the part is contained in the whole. The content of the whole is greater than the content of the part.

Space cannot be a concept (indeed, concepts cannot be infinite!).

Hence, Space cannot be a concept:

1) We can represent to ourselves only one space within which diverse spatial relations and positions can be determined.

2) Space is an infinite given magnitude CPR A25/B39-40). It is unbounded (we cannot represent its boundary and it is infinitely divisible).

3) The infinite parts of spaces are contained within space, whereas the infinite possible instances of a concept fall under the concept.

C: Formal versus form of intuitionForm of Intuition

the aspect of spatiality

transcendental ideal indeterminate space

It gives us a manifold, i.e. it enables us to speak of points in spaceFormal Intuition

Determinate pure intuition

a priori combination or synthesis - its unity is specified via the categorical concepts and only yields a space

Space and Time are the manner in which intuitions occur. Space and Time outside the intuitional situation are transcendentally ideal. Space and time however are empirically real as regards to possible experience.

CONCLUSION:

Our exposition therefore establishes the reality, that is, the objective validity, of space in respect of whatever can be presented to us outwardly as object, but also at the same time the ideality of space in respect of things when they are considered in themselves through reason, that is, without regard to the constitution of sensibility. We assert then, the empirical reality of space, as regards all possible outer experience; and yet at the same time we assert its transcendental ideality in other words, that it is nothing at all, immediately we withdraw the above condition, namely, its limitation to possible experience. and so look upon it as something that underlies things themselves (A28/B44).

SOME DEFINITIONS

By transcendental idealism I mean the doctrine that appearances are to be guarded as being, one and all, representations only, to things in themselves, and that time and space are therefore only sensible forms of our intuition, not determinations given as existing by themselves. To this realism there is opposed a

Transcendental realism which regards time and space as something given in themselves, independently of our sensibility. The transcendental realist thus interprets outer appearances (their reality as granted) as things-in-themselves, which exist independently of us and our sensibility, and which are therefore outside us the phrase outside us being interpreted in conformity with pure concepts of understanding. It is, in fact, this transcendental realist who afterwards places the part of the empirical idealist. After wrongly supposing that objects of senses, if they are to be external , must have an existence by themselves, and independently of the senses, he finds that, judged from this point of view, all our sensuous representations are inadequate to establish their reality (A369).

KANT: Space and Time are the manner in which intuitions occur. Space and Time outside the intuitional situation are transcendentally ideal. Space and time however are empirically real as regards to possible experience. QUESTIONS:

1. Strawson: Kant assumes that Euclidean geometry is a synthetic a priori science Kant: It makes intelligible the possibility of geometry, as a body of priori synthetic knowledge (B41).

It is strictly possible and logical to conceive (to think without contradiction) the concept of a figure which is enclosed within two straight lines . However it is not possible to construct a figure in space which would correspond to such a concept (Cf. CPR B268/A220/1).

2. Why can space not pertain only to appearances and the thing in itself?

Kants response:

By noumenon we mean a thing so far as it is not an object of our sensible intuition, and so abstract from our mode of intuiting it, this is a noumenon in the negative sense of the term (CPR B307).

Newton:

GENERAL CLAIM

In order to become an object of experience everything must be

1.given as an extensive and intensive magnitude (Intuition)2.it must be thought as suspending in a framework of concepts which yield connection, e.g. substance, cause interaction (Construction)

3.It must be synthesized by the transcendental unity of apperception

In D Walford & R Meerbote eds: The Cambridge Edition of the Works of Immanuel Kant. Theoretical Philosophy, 1755-1770. Cambridge: Cambridge University Press 1992: 377-416.

Query 28 Opticks (app A): there is a being incorporal, living, intelligent, omnipresent, who in infinite space, as it were in his sensory sees the thins themselves intimately and thoroughly perceives them, and comprehends them wholly by the immediate presence for himself Leibniz objected that clearly God would not need a sense organ in order to perceive his own creation.