Absolute or substance?

I Tempus absolutum verum et Mathematicum, in se et natura sua

absque relatione ad externum quodvis, æquabiliter fluit, alio-

9_{In the ontology of the German philosopher, rather, the material bodies were the phe-}

nomenal appearance of the real substances, the monads, which definitely had a spiritual nature.

que nomine dicitur Duratio; relativum apparens et vulgare est sensibilis et externa quævis Durationis per motum mensura, (seu accurata seu inæquabilis) qua vulgus vice veri temporis utitur; ut Hora, Dies, Mensis, Annus.

II Spatium absolutum natura sua absque relatione ad externum quod- vis semper manet similare et immobile; relativum est spatii hu- jus mensura seu dimensio quælibet mobilis, quæ a sensibus no- stris per situm suum ad corpora definitur, et a vulgo pro spatio immobili usurpatur: uti dimensio spatii subterranei, aerei vel cælestis definita per situm suum ad Terram. Idem sunt spatium absolutum et relativum, specie et magnitudine, sed non perma- nent idem semper numero.

[New09], Def., Schol., §§ I-II

In a sense, as M. Dorato explains (in [ADLZ05], p. 23), in this locus the absoluteness seems to have nothing to do with any meaning of substance. The relative time, in fact, would be the measure of the absolute time, or, better, of a lapse of time (a duration), through the motion of something sensible, which in itself is not time (e.g., astronomic motions). The same applies to relative space. Thus, the distinction between absolute and rel- ative seems to be gnoseological, i.e., between the transcendent object of knowledge and its phenomenal and epistemic apprehension. But what is this transcendent object? Since it is clear in the text that the relative time (or space) is a measure of a magnitude, the absolute time (or space) should be this magnitude, which is meant as a mathematical, and then ideal, but also real (verum) ordered structure.

There is something tacit and somehow problematic in this position. We shall talk thereabout soon, but, first, we need to highlight an apparently clearer point. About the kind of mathematical structure he is talking about, Newton seems to affirm the same one can find in Leibniz: the quantities refers to the order of succession (for time) and the order of position (for space).

In Tempore quoad ordinem successionis; in Spatio quoad ordinem situs locantur universa.

[New09], Def., Schol., § IV

Thus, the essential content of space and time as ordered structures seems to be the same for the alleged fathers of substantivalism and rela- tionalism. Indeed, when Newton talks of space, he writes that the absolute

and the relative one are identical "in species and magnitude". So, one can conclude that space and time, regardless of whether absolute or relative, are mathematical, but nevertheless real structures consisting in an ordered set having a metrics.

According to Newton (see [Ear89], p. 8) the absolute character of time requires that the metrics is "intrinsic to temporal intervals", and so inde- pendent of the one used (in theory and in practice) by the observers, who are often compelled to operate with approximations and necessarily with reference to sensible instruments and units of measurement. In this sense, one (Dorato) can say with good reasons that the absolute space and the absolute time are quantities in the sense of "limits" of the succession of in- creasingly more accurate measurements of temporal intervals and spatial distances ([ADLZ05], pp. 26-27, 31). Thus, the distinction between "ab- solute" and "relative", with regard to time and space, would be epistemo- logical rather than gnoseological: it is the difference between an abstract notion, which works as a regulative definition (according to Dorato, with axiomatic value also for the laws of motion), and its actual instances in the scientific practice.

But, at this point, the tacit difficult that I have mentioned above arises. The absolute spatiotemporal magnitudes, and then absolute space and ab- solute time, are supposed to be mathematic idealizations, but also some- thing real. But, then, what kind of reality can an idealization have? Since Newton seems to agree on that point with Leibniz, space and time cannot be substances in the sense of set of individual points with intrinsic iden- tity like the material objects. On the other hand, they are not thought of as mere relations among bodies either. So, Newton writes in the unpublished De Gravitatione et equipondio fluidorum:

De extensione jam forte expectatio est ut definiam esse vel substan- tiam vel accidens aut omnino nihil. At neutiquam sane, nam habet quendam sibi proprium existendi modum qui neque substantijs ne- que accidentibus competit. Non est substantia tum quia non absolute per se, sed tanquam Dei effectus emanativus, et omnis entis affectio quædam subsistit; tum quia non substat ejusmodi proprijs affectio- nibus quæ subtantiam denominant, hoc est actionibus, quales sunt cogitationes in mente et motus in corpore. Nam etsi Philosophi non definiunt substantiam esse ens quod potest aliquid agere, tamen om- nes hoc tacite de substantijs intelligunt, quemadmodum ex eo pateat quod facile concederent extensionem esse substantiam ad instar cor- poris si modo moveri posset et corporis actionibus frui. Et contra haud concederent corpus esse substantiam si nec moveri posset nec sensationem aut perceptionem aliquam in mente qualibet excitare.

Præterea cum extensionem tanquam sine aliquo subjecto existentem possumus clare concipere, ut cum imaginamur extramundana spatia aut loca quælibet corporibus vacua; et credimus existere ubicunque imaginamur nulla esse corpora, nec possumus credere periturum es- se cum corpore si modo Deus aliquod annihilaret, sequitur eam non per modum accidentis inhærendo alicui subjecto existere. Et proinde non est accidens. Et multo minus dicetur nihil, quippe quæ magis est aliquid quam accidens et ad naturam substantiæ magis accedit. Nihili nulla datur Idea neque ullæ sunt proprietates sed extensionis Ideam habemus omnium clarissimam abstrahendo scilicet affectio- nes et proprietates corporis ut sola maneat spatij in longum latum et profundum uniformis et non limitata distensio. Et præterea sunt ejus plures proprietates concomitantes hanc ldeam, quas jam enumerabo non tantum ut aliquid esse sed simul ut quid sit ostendam.

[New06], § 11-13

There is really a plenty of themes in that text, but we shall consider only the points relevant for our discussion. Regarding the sense of space and time (extension) as abstractions, the last sentences are particularly clear: space (and time) is an idea that one can derive "from abstracting the affec- tions and properties of bodies", and "idea" here has an axiomatic (Platonic) sense. Indeed, the properties connected to that idea are to be displayed not only as "something that is", but also as "what should be". Thus, the ab- stracted properties of space, like "the uniform and unlimited distention", are element of a definition. And this fact, that there is an abstracted idea and there are defining properties of space and time, excludes the possi- bility that the latter are nothing, also when one admits that they are not substances or accidents (relations). But, again, the problem remains: what kind of real thing is such an idea?

From a Leibnizian perspective the answer would be simple, the very reality being considered as spiritual. Newton, on the contrary, seems not to follow an idealistic point of view. Indeed, after having denied that ex- tension can be a substance as an a se being, he introduces another concep- tion of substance, which is strictly connected to an empirical point of view: a substance is something that is active and passive, in the double sense that it is capable of motion (moving and being moved) and/or capable of thinking, and therefore it can be a material body or a mind; moreover, a substance produces affections in sensitive subjects, i.e., it is (at least indi- rectly) perceivable. But space and time, though subsisting in a world of perceivable substances, are not perceivable in themselves. Therefore, they cannot be substances. But they cannot be mere relations either, because

they are thinkable also in a universe totally void of bodies. The latter fact, moreover, strengthens the insight that space and time are not perceivable, but only deducible by abstraction from what is perceivable. So, since the abstraction here mentioned seems to indicate that space and time accord- ing to Newton are not only "ideas in mind", the possibility that at the end of the fair they can be considered as something similar to Hartmann’s cat- egories becomes more concrete.

Of course, it is not important for our discourse to evaluate whether this can be an authentic interpretation of Newton’s view, and, on the other hand, one can sustain that the concept of category or principle is not so clear, and thereby it is not an answer to the question of what kind of real- ity ideal abstractions, like absolute space and time, are. Moreover, Newton affirms that space and time are more similar to a substance than an acci- dence. Thus, we should understand if this similitude is applicable also to Hartmann’s categories.

I shall give other specifications about these concepts in the next chap- ters, while in the following paragraph we can consider a little longer how the point of view of the Latvian philosopher can be connected to Dorato’s lecture of the Newtonian position.

4.2.2.1.2 What is time relative to? In [ADLZ05] (p. 30) Dorato proposes