Saturday, July 4, 2015

Kant’s space contrasted with Aristotle’s ‘space’

I put Aristotle’s ‘space’ in brackets, for it stands for topos, which means ‘place’. The Greek-English Lexicon of Liddell and Scott registers a wide range of meanings for topos, such as ‘place’, ‘region’, ‘district’; ‘place or part of the body’, esp. ho topos (i.e. topos qualified by a definite article) pudendum muliebre; ‘place, passage in an author’ –  ‘space’ does not figure among these. And yet, what we mean by ‘space’ is discussed by Aristotle as topos; he opens the 4th book of his Physics as follows: “The physicist (ton phusicon) must have a knowledge (anankê gnȏrizein) of Place (peri topou), whether there is such a thing or not (ei estin ê mê), and the manner of its existence (kai pȏs esti) and what it is (kai ti esti), both because all suppose that things which exist are somewhere (ta te gar onta pantes hupolambanousin einai pou) and because ‘motion’ (kai tês kinêseȏs) in its most general and primary sense (hê koinê malista kai kuriȏtatê) is change of place (kata topon esti), which we call ‘locomotion’ (hên kaloumen phoran).” (Ar. Physics, 208a27-32; tr. by R.P. Hardie and R. K. Gaye; I shall use their translation in this entry; by using the capital P when introducing the topic of ‘place’, the translators appear to be expressing their unease concerning ‘place’ standing for Aristotle’s topos.)

Aristotle says that the question ‘what is place?’ presents many difficulties (echei pollas aporias), for it does not appear to be the same thing (ou gar t’auton phainetai) to those who examine (theȏrousin) the relevant facts concerning it (ex hapantȏn tȏn huparchontȏn). Aristotle notes that he is the first to investigate this concept: ‘We have inherited nothing from previous thinkers (oud’ echomen ouden para tȏn allȏn), whether in the way of a statement of difficulties or of a solution (oute proêporêmenon oute proêuporêmenon peri autou).’ (208a32-b1)

Aristotle begins by giving voice to those views that ascertain the existence of topos as an entity in its own right: ‘The existence of place (hoti men oun estin ho topos) is held to be obvious (dokei dêlon einai) from the fact of mutual replacement (ek tês antimetastaseȏs). Where water now is (hopou gar esti nun hudȏr), there in turn, when the water has gone out as from a vessel, air is present (entautha exelthontos hȏsper ex angeiou palin aêr enestin,). When therefore another body occupies this same place (hote de ton auton topon touton allo ti tȏn sȏmatȏn katecheiˑ), the place is thought to be different from all the bodies which come to be in it and replace one another (touto dê tȏn engignomenȏn kai metaballontȏn heteron pantȏn einai dokeiˑ). What now contains air (en hȏi gar aêr esti nun,) formerly contained water (hudȏr en toutȏi proteron ên), so that clearly the place or space into which and out of which they passed was something different from both (hȏste dêlon hȏs ên ho topos ti kai hê chȏra heteron amphoin, eis hên kai ex hês metebalon).’ (208b1-8) Identifying topos with chȏra, and chȏra with chaos (Liddell and Scott list ‘space’ as one of the meanings both of chȏra and of chaos), Aristotle refers to Hesiod’s ‘First of all things came chaos to being’ as ‘implying that things need to have space first (hȏs deon prȏton huparxai chȏran tois ousi), because he thought (dia to nomizein), with most people (hȏsper hoi polloi), that everything is somewhere and in place (panta einai pou kai en topȏi). If this is its nature (ei d’ esti toiouto), the potency of place must be a marvellous thing (thaumastê tis an eiê hê tou topou dunamis), and take precedence of all other things (kai protera pantȏn). For that without which nothing else can exist (hou gar aneu tȏn allȏn ouden estin), while it can exist without the others (ekeino d’ aneu tȏn allȏn), must needs be first (anankê prȏton einai); for place does not pass out of existence (ou gar apollutai ho topos) when the things in it are annihilated (tȏn en autȏi phtheiromenȏn).’ (208b27-209a2)

To a certain degree, Kant’s view of space chimes with this “Hesiod’s and most people’s” view of space: ‘We never can imagine or make a representation to ourselves (Man kann sich niemals eine Vorstellung davon machen,) of the non-existence of space (dass kein Raum sei), though we may easily enough think (ob man sich gleich ganz wohl denken kann,) that no objects are found in it (dass keine Gegenstände darin angetroffen werden.). It must, therefore, be considered as the condition of the possibility of phenomena (Er wird also als die Bedingung der Möglichkeit der Erscheinungen,), and by no means as a determination dependent on them (und nicht als eine von ihnen abhängende Bestimmung angesehen,), and is a representation a priori (und ist eine Vorstellung a priori,), which necessarily supplies the basis for external phenomena (die notwendigerweise äusseren Erscheinungen zum Grunde liegt.).’ (B38-39, tr. J. M. D. Meiklejohn)

Both in Kant’s and in “Hesiod’s and most people’s” view, objects, things, animals and human beings, are located, move or rest in space in front of us and around us. But for Hesiod and most people this space is real and the objects in it are real things, whereas for Kant the objects in space are nothing but sensory presentations (Vorstellungen) and space itself is nothing but a sensory presentation, an a priori presentation to boot.

Aristotle does not view topos as an entity without which nothing else can exist, while it can exist without the others, and so he asks, ‘if it is (ei esti), what is it (ti esti), is it some sort of bulk of body (poteron onkos tis sȏmatos), or is its nature different (ê tis hetera phusis)? … Now it has three dimensions (diastêmata oun echei tria), length, breadth, depth (mêkos kai platos kai bathos), the dimensions by which all body is bounded (hois horizetai sȏma pan). But the place cannot be body (adunaton de sȏma einai ton topon); for if it were there would be two bodies in the same place (en t’autȏi gar an eiê duo sȏmata) … What in the world then are we to suppose place to be (ti gar an pote kai theiêmen einai ton topon)? If it has the sort of nature described (toiautên echonta phusin), it cannot be an element or composed of elements (oute gar stoicheion out’ ek stoicheiȏn hoion te einai), whether these be corporeal or incorporeal (oute tȏn sȏmatikȏn oute tȏn asȏmatȏn): for while it has size (megethos men gar echei), it has not body (sȏma d’ ouden). But the elements of sensible bodies are bodies (esti de ta men tȏn aisthêtȏn stoicheia sȏmata), while nothing that has size results from a combination of intelligible elements (ek de tȏn noêtȏn ouden gignetai megethos) … By asking these questions, then (dia men oun toutȏn), we must raise the whole problem about place – not only as to what it is, but even whether there is such a thing (ou monon ti estin, alla kai ei estin, aporein anankaion).’ (209a2-30)

The difficulties Aristotle raises concerning ‘space’ chime with the absurdities that Kant ascribes to those, who ascribe to space and time absolute reality: ‘Those who maintain the absolute reality of time and space (die, so die die absolute Realität des Raumes und der Zeit behaupten,) … as essentially subsisting (als subsistierend,) … must find themselves at utter variance with the principles of experience itself (mit den Prinzipien der Erfahrung selbst uneinig sein müssen.). For (Denn,) … they must admit two self-subsisting nonentities, infinite and eternal (so müssen sie zwei ewige und unendlich für sich bestehende Undinge {Raum und Zeit} annehemn,), which exist (welche da sind) (yet without there being anything real {ohne dass doch etwas Wirkliches ist},) for the purpose of containing in themselves everything that is real (nur um alles Wirkliche in sich zu befassen.). (B56-57)

Aristotle rejects the view of space as an entity in its own right as vehemently as Kant does; in the end he defines topos as ‘the boundary (to peras) of the containing body (tou periechontos sȏmatos) at which it is in contact with the contained body (kath’ ho sunaptei tȏi periechomenȏi’ (212a6). Aristotle explains: ‘We say that a thing is in the world, in the sense of in place (epei de legomen einai hȏs en topȏi en tȏi ouranȏi), because it is in the air (dioti en tȏi aeri), and the air is in the world (houtos de en tȏi ouranȏiˑ); and when we say it is in the air, we do not mean it is in every part of the air, but that it is in the air because of the outer surface of the air which surrounds it (kai en tȏi ouranȏi ouk en panti, alla dia to eschaton autou kai periechon en tȏi aeri phamen einai); for if all the air were its place (ei gar pas ho aêr topos), the place of a thing would not be equal to the thing (ouk an isos eiê hekastou ho topos kai hekaston) – which it is supposed to be (dokei de ge isos einai,), and which the primary place in which a thing is actually is (toioutos ho prȏtos en hȏi estin).’ (211a23-29)

Kant does not refer to Aristotle by name in Section I of his ‘Transcendental Aesthetic’, which is devoted to space, but he undoubtedly views him as one of those ‘metaphysical natural philosophers’ (metaphysische Naturlehrer), who ‘regard space and time as relations (contiguity in space or succession in time), abstracted from experience, though represented confusedly in this state of separation (und Raum und Zeit gelten ihnen als von der Erfahrung abstrahierte, obzwar in der Absonderung verworren vorgestellte, Verhältnisse der Erscheinungen {neben oder nacheinander},)’. (B57)

How does Kant view space? In the ‘Transcendental Exposition of the Conception of Space’ (Transzendentale Erörterung des Begriffs vom Raume) he writes: ‘Geometry is a science (Geometrie ist eine Wissenschaft,) which determines the properties of space synthetically, and yet a priori (welche die Eigenschaften des Raumes synthetisch und doch a priori bestimmt.). What, then, must be our representation of space (Wass muss die Vorstellung des Raumes denn sein,), in order that such a cognition of it may be possible (damit eine solche Erkenntnis von ihm möglich sei?)? It must be originally intuition (Er muss ursprünglich Anschauung sein;), for from a mere conception (denn aus einem blossen Begriffe), no propositions can be deduced which go out beyond the conception (lassen sich keine Sätze, die über den Begriff hinausgehen, ziehen,), and yet this happens in geometry (welches doch in der Geometrie geschieht.).’ (B 40-41)

What does Kant mean when he says that geometry ‘determines the properties of space synthetically, and yet a priori? To make sense of this point, we must grasp Kant’s conception of synthetical judgments and of his concept of a priori.

In Sextion IV of his ‘Introduction’ entitled ‘Of the difference between analytical and synthetical judgments’ (Von dem Unterschiede analytischer und synthetisher Urteile) he says: ‘In all judgments (In allen Urteilen,) wherein the relation of a subject to the predicate is cogitated (worinnen das Verhältnis eines Subjekts zum Prädikat gedacht wird), this relation is possible in two different ways (ist dieses Verhältnis auf zweirlei Art möglich.). Either the predicate B belongs to the subject A (Entweder das Prädikat B gehört zum Subjekt A), as something (als etwas,) which is contained (though covertly) in the conception A (was in diesem Begriffe A {verstecktweise} enthalten ist;); or the predicate B lies completely out of the conception A (oder B liegt ganz ausser dem Begriff A,), although it stands in connection with it (ob es zwar mit demselben in Verknüpfung steht.). In the first instance (Im ersten Fall), I term the judgment analytical (nenne ich das Urteil analytisch), in the second, synthetical (in dem andern synthetisch).’ (B 10)

Kant elucidates the analytical judgments by the following example: ‘When I say (wenn ich sage) “All bodies are extended (alle Körper sind ausgedehnt),” this is an analytical judgment (so ist es ein analytisches Urteil). For I need not go beyond the conception of body (Denn ich darf nicht über den Begriff, den ich mit dem Körper verbinde, hinausgehen) in order to find extension connected with it (um die Ausdehnung, als mit demselben verknüpft, zu finden,), but merely analyse the conception (sondern jenen Begriff nur zergliedern), that is become conscious of the manifold properties which I think in that conception (d. i. des Mannigfaltigen, welches ich jederzeit in ihm denke, mir nur bewusst werden), in order to discover this predicate in it (um dieses Prädikat darin anzutreffen.).’ (B11)

The synthetical judgments he elucidates as follows: ‘When I say (wenn ich sage), “All bodies are heavy (alle Körper sind schwer,),” the predicate is something totally different (so ist das Prädikat etwas ganz anderes,) from that (als das,) which I think in the mere conception of a body (was ich in dem blossen Begriff eines Körpers überhaupt denke.). By the addition of such a predicate (Die Hinzufügung eines solchen Prädikats), therefore, it becomes a synthetical judgment (gibt also ein synthetisches Urteil.). (B 11) Kant maintains that all judgments of experience (Erfahrungsurteile) are synthetical: ‘Though at first I do not at all include the predicate of weight in my conception of body in general (ob ich schon in dem Begriff eines Körpers überhaupt das Prädikat der Schwere gar nicht einschliesse,), that conception still indicates an object of experience (so bezeichnet jener doch einen Gegenstand der Erfahrung), a part of the totality of experience (durch einen Teil derselben,), to which I can still add other parts (zu welchem ich also noch andere Teile eben derselben Erfahrung, als zu dem ersteren gehörig, hinzufügen kann) … Thus it is experience (Es ist also die Erfahrung,) upon which rests the possibility of the synthesis of the predicate of weight with the conception of body (worauf sich die Möglichkeit der Synthesis des Prädikats der Schwere mit dem Begriffe des Körpers gründet,), because both conceptions (weil beide Begriffe,), although the one is not contained in the other (ob zwar einer nicht in dem anderen erhalten ist,), still belong to one another (only contingently, however, as parts of a whole, namely, of experience, which is itself a synthesis of intuitions (dennoch als Teile eines Ganzen, nämlich der Erfahrung, die selbst eine synthetische Verbindung der Anschauungen ist, zueinander, wiewohl nur zufälligerweise, gehören.).’ (B 11-12)

Kant calls such knowledge a priori, ‘which is independent of experience’ (von der Erfahrung unabhängiges Erkenntnis), in contradistinction to empirical knowledge, which has its sources a posteriori, that is, in experience. A priori propositions are characterized by necessity (Notwendigkeit), and absolute universality (strenge Allgemeinheit); they can be either pure or impure: ‘Pure knowledge a priori is that with which no empirical element is mixed up (Von den Erkenntnissen a priori heissen aber diejenigen rein, denen gar nichts Empirisches beigemischt ist.). For example, the proposition (So ist z. B. der Satz) “Every change has a cause” (eine jede Veränderung hat eine Ursache,), is a proposition a priori (ein Satz a priori,), but impure (allein nicht rein), because change is a conception (weil Veränderung ein Begriff ist,) which can only be derived from experience (der nur aus der Erfahrung gezogen werden kann.).’ (B 3) An example of a synthetic proposition, which is a priori and pure, Kant derives from geometry: ‘”A straight line between two points is the shortest,” (Dass die gerade Linie zwischen zwei Punkten die kürzeste sei,) is a synthetical proposition (ist ein synthetischer Satz.). For my conception of straight (Denn mein Begriff von Geradem) contains no notion of quantity (enthält nichts von Grösse,), but is merely qualitative (sondern nur eine Qualität.). The conception of the shortest (Der Begriff des Kürzesten) is therefore wholly an addition (kommt also gänzlich hinzu,), and by no analysis can be extracted from our conception of a straight line (und kann durch keine Zergliederung aus dem Begriffe der geraden Linie gezogen werden.). Intuition must therefore here lend its aid (Anschauung muss also hier zu Hilfe genommen werden,), by means of which and thus only (vermittels deren allein), our synthesis is possible (die Synthesis möglich ist).’ (B 16)

The Anschauung [the expression ‘intuition’ is misleading] that must here ‘lend its aid’ is a pure, non-empirical Anschauung, which Kant explains as follows: ‘If I take away from our representation of a body, all that the understanding thinks as belonging to it, as substance, force, divisibility, etc., and also whatever belongs to sensation, as impenetrability, hardness, colour, etc (wenn ich von der Vorstellung eines Körpers das, was der Verstand davon denkt, als Substanz, Kraft, Teilbarkeit usw., imglewichen was davon zur Empfindung gehȏrt, als Undurchdringlichkeit, Härte, Farbe usw. Absondere,); yet there is still something left from this empirical intuition (so bleibt mir aus dieser empirischen Anschauung noch etwas übrig,), namely, extension and shape (nämlich Ausdehnung und Gestalt.). These belong to pure intuition (Diese gehören zur reinen Anschauung,), which exists a priori in the mind, as a mere form of sensibility, and without any real object of the senses or any sensation (die a priori, auch ohne einen wirklichen Gegenstand der Sinne oder Empfindung, als eine blosse Form der Sinnlichkeit im Gemüte stattfindet.).’ (B 35)

After all these preliminaries, Kant’s ‘Transcendental Exposition of the Conception of Space’ can be properly understood in all its significance: ‘Geometry is a science (Geometrie ist eine Wissenschaft,) which determines the properties of space synthetically, and yet a priori (welche die Eigenschaften des Raumes synthetisch und doch a priori bestimmt.). What, then, must be our representation of space (Wass muss die Vorstellung des Raumes denn sein,), in order that such a cognition of it may be possible (damit eine solche Erkenntnis von ihm möglich sei?)? It must be originally intuition (Er muss ursprünglich Anschauung sein;), for from a mere conception (denn aus einem blossen Begriffe), no propositions can be deduced which go out beyond the conception (lassen sich keine Sätze, die über den Begriff hinausgehen, ziehen,), and yet this happens in geometry (welches doch in der Geometrie geschieht.). But this intuition must be found in the mind a priori, that is, before any conception of objects (Aber diese Anschauung muss a priori, d. i. vor aller Wahrnemung eines Gegenstandes, in uns angetroffen werden.), consequently must be pure, not empirical intutition (mithin reine, nicht empirische Anschauung sein.). For geometrical principles are always apodictic (Denn die geometrischen Sätze sind insgesamt apodiktisch,), that is, united with the consciousness of their necessity (d. i. mit dem Bewusstsein ihrer Notwendigkeit verbunden.) … Now, how can an external intuition anterior to objects themselves, and in which our conception of objects can be determined a priori, exist in human mind (Wie kann nun eine äussere Anschauung dem Gemüte beiwohnen, die vor den Objekten selbst vorhergeht, und in welcher der Begriff der letzteren a priori bestimmt werden kann?)? Obviously not otherwise (Offenbar nicht anders,) than in so far as it has its seat in the subject only, as the formal capacity of the subject’s being affected by objects, and thereby obtaining immediate representation, that is, intuition (als so fern sie bloss im Subjekte, als die formale Beschaffenheit desselben, von Objekten affiziert zu werden, und dadurch unmittelbare Vorstellung derselben d. e. Anschauung zu bekommen, ihren Sitz hat,); consequently, only as the form of the external sense in general (also nur als Form des äusseren Sinnes überhaupt.).’ (B 40-41)


Concerning my remark that the expression ‘intuition’ for Kant’s Anschauung is misleading. If we are to grasp Kant’s concept of Anschauung, we must properly take in Kant’s view that experience in its totality is itself a synthesis of ‘intuitions’ (eine synthetische Verbindung der Anschauungen). All sensory perceptions – read colour of a rose, sharp blade of a knife, a pleasant smell of the dinner on the table – all these are parts of our empirical ‘intuition’, Anshauung; Kepler’s laws of planetary motion, Newton’s law of gravity are all a priori ‘intuitions’, though impure, for motion and gravity are notions derived from experience; Pythagorean theorem – ‘the square of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the other two sides’ – is a pure a priori ‘intuition’, for none of the notions involved in it is derived from experience.

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