Kant´s Notion of a Transcendental Schema. Lara Scaglia

metaphysical causes (Newton 1730, p. 377): while the former are either immediately evident or proved by induction, the latter are often obscure or impenetrable, their relation to the events they are supposed to produce is unknown and lies beyond our possibility of knowledge. However, Newton seems to abandon the rigid separation between science and metaphysics when he refers to the existence of space and time as absolute in his Philosophiae naturalis principia matematica from 1687. This work led at first to the atheistic interpretation of Newton’s doctrine. Due to being accused of atheism, Newton was obliged to add a Scholium Generale to later publications of the work in order to defend himself.

      The Scholium to the Definition of the Principles opens with the distinction between absolute and relative quantities, namely, of time and space. Time can be regarded as absolute, independent from the existence of things of experience but also as relative, as a measurement or limitation (hours, days, years) of the infinite duration of absolute time. In his attempt to provide an explanation of the existence of absolute space, Newton relies on the first law of motion: since the possibility of a rectilinear, uniform motion lies in the absence of acceleration, a reference to absolute time, which has no limitations and so can explain the possibility of such infinite movement, is needed. Together with absolute time, absolute space is presupposed, intended as the field in which bodies are situated: it is not a relation between objects, but rather a primary location, unique and with no relation to anything, but containing all relations within itself.

As presented, Newton alternates between the need to free science from metaphysical assumptions and the reference to principles whose nature cannot be scientifically justified. How can this ambiguity be explained? As Ernst Cassirer remarks, Kant will avoid the risk of mixing the sensible and intelligible realms (for instance, by referring predicates such as ‘where’ and ‘when’ to objects of the pure world, like God, and by grounding relative space and time on metaphysical principles): “The ‘infection’ the contagium, of the intelligible by the sensible, which emerges so clearly in Newton’s theory concerning God, is avoided;” ←52 | 53→(Cassirer 1922, p. 121, transl. L.S.)⁶⁰. Maybe the clearest passage in which this problem can be seen is the following:

“He is not eternity or 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. Since every particle of space is always, and every indivisible moment of duration is everywhere, certainly the Maker and Lord of all things cannot be never and nowhere.” (Newton 1687, transl. A. Motte, p. 441)⁶¹

      In Newton’s work, on the one hand it seems that one of his main attempts consists in providing objective grounds to science through the reference to demonstrated claims, on the other hand these claims seem not to be sufficient, and need the reference to principles which belong to other fields of knowledge. Another and maybe easier solution is to stress the influence exerted on Newton by metaphysicians and theologians of the time, such as Henry More, and, in general, by his attempt to find a conciliation between science and religion so as to defend himself against the accusation of atheism.

      Confronting the same question concerning the nature of space and time, Leibniz situated himself in direct opposition to Newton. His Epistolary with Samuel Clarke (between 1715 and 1716) can be regarded as emblematic of the contemporary focus on the relation between metaphysics and sciences and the nature of the principles of knowledge. The epistolary originates from a letter sent by Leibniz to Caroline of Wales, in which he distanced himself from the Newtonian theory of absolute space and time. Then she put the philosopher in contact with Clarke, a theologian of Westminster and defender of Newton’s perspective. Influenced by the recent publication of the paradoxes of Zenon in Pierre Bayle’s Dictionnaire historique et critique (Bayle 1702) Leibniz affirms that space cannot be absolute, otherwise there would be something that cannot be explained by a cause, as required by the principle of sufficient reason: if space were uniform, absolute, there would be no difference between one point and another and consequently insufficient reason to explain why God situated bodies in these points and not in others. Similarly, if time were independent from things, there ←53 | 54→would be no reason why things happen in one moment rather than in another. But, then, what are time and space? Leibniz proposes not considering them as absolute positions, but as relations: space is an order of coexistences, while time is one of successions. As he affirms they are no-things nor attributes, but rather idealitas, in the sense that they consist of relations, orders, abstracted from material objects and then provided with universality and necessity in opposition to the overflowing matter of senses. In this sense, they are defined as idealitas and not objects, res. The problem is: if space and time derive from sensibility, then the sciences based on them (physics and mathematics) depend on sensible objects, which are contingent, and cannot be universal or necessary. Is the claim of mathematics and physics to be considered as universal and necessary only an illusion, or can it be justified?

      Kant’s 1770 conception of space and time as forms might be interpreted as a first, successful attempt to provide an original solution to this question. If some sciences (such as geometry and arithmetic) are based on space and time and if Kant’s forms of sensibility do not derive from senses, then it is possible to justify their universal and objective value. However, Kant’s doctrine still has some limitations.

2.2.3 The limitations of Kant’s Dissertation and the need of a further solution to the question of objectivity

Although Kant’s conception of space and time distinguishes him from previous traditions, he is still very influenced by the Wolffian division between inferior and superior faculties, receptivity and spontaneity, thus generating incoherences, or at least ambiguities in his doctrine - for instance, regarding his account of sensibility and the distinction between phaenomena and noumena -. More specifically, Kant defines sensibility as receptivitas, the faculty through which the subject can be affected by the object, while the understanding is conceived as the faculty of representing what is not present in the senses. Whilst the former deals with things as they appear (uti apparent), the latter focuses on things as they are (sicuti sunt). This division reechoes the traditional separation between primary qualities, which belong to the things in themselves and are grasped through the understanding⁶², and secondary qualities that depend on the subject and its sensibility. But, as already stressed, sensibility cannot be defined as passive, since it is ←54 | 55→characterised by the pure forms of intuitions, through which impressions do not affect the subject, as it were, automatically, but according to an order.

      Then, if on the one hand the doctrine of space and time exposed in the Dissertation opens the way to a new approach to the problem of knowledge, on the other hand it contains limitations and incoherences, as underlined by Kant himself. As he states in the famous letter to Herz from 21st February 1772, the most important philosophical question focuses on the link between representations and objects. What causes this link? While it might be easy to explain it in reference to sensibility (as it could be possible to affirm that representations reflect objects as they are produced by their affection) on the other hand the relation between the intellectual action and objects is harder to justify. In the letter to Herz, Kant provides only a negative definition of the understanding’s activity: it is the faculty of representing things we are not affected by, it is not an abstraction from the senses, and neither is it a production such as the efficient causality of an intuitive understanding. Unfortunately, Kant does not delve into detail with this kind of action, nor does he explain whether, and if so how, such activity possesses an objective significance: how can it not simply be a product of the imagination? How is its reference to actual things (sicuti sunt) justified? Are there forms and schemata similar to the ones of sensibility also for the understanding? If the reference to space and time as schemata allows Kant to explain the possibility of the objective value of sciences and of our sensible experience as well, why should not a similar solution be valid also for the activity of the understanding? As Kant himself puts it in the letter to Marcus Herz from 21st February 1772: