Abstraction metaphysics

Stage 2 The age of metaphysics. The supernatural beings (gods) are replaced by abstract terms, powers or entities. 

In theoretical terms, the non-Marxist tag can be largely attributed to a lack of engagement with the labour theory of value. For Sebastiani (1994 108), Kalecki s silence on this issue could be interpreted either as a tacit acceptance or as a tacit rejection of Marx s premises . Kerr (1997 23), in her textual analysis of Marx and Kalecki, takes the first position, aiming to make explicit what Kalecki often left as understood in the more abstract presentations of his analysis . In contrast, Brus (1977 59) reported that Kalecki felt a strong distaste for the Marxian theory of value, which he considered metaphysical and (if I am not mistaken) never wanted to discuss . 

Aristotle characterizes mathematics in slighdy different ways in different places. Nonetheless, in each characterization, he emphasizes the idea that mathematicians somehow ignore or abstract away from the physical aspect of material substances. In Metaphysics XI, Aristo-de says that a mathematician studies his object after leaving out what is sensible, such as heaviness and lightness, and instead studies, qua quantities and qua continuous, quantities that are continuous in one, two or three dimensions. 

In Metaphysics XIII 3, Aristode says that mathematicians study sensible material substances but in their study ignore or abstract away their physical aspect. 

The principles in (1) - (5) thus show that the underlying picture about the relationship between substance, form and body can be made precise. But it is really the underlying picture that is of interest. The picture is of a metaphysical principle, namely form, which is connected to two fundamental aspects of the world substance and motion. The presence of form confers both substantiality and the capacity for motion on a physical body. And its abstraction from body leaves something of a metaphysical shadow, a genus in die category of quantity, which can only have only accidental being. 

With such a characterization of mathematics, one would expect there to be something in material composites that corresponds to the various objects that mathematicians study, though one would expect the existence of such entities to be dependent on mobile substances. In the case of extension, one could take such a stuff to be the intelligible matter Aristotle mentions at Metaphysics 1036a3. Extension is intellectual matter because, in its pure form, i.e. in the form in which mathematicians study it, it is abstracted away from any conditions of mobility and sensibility that characterize its actual existence. Mathematicians study the features of extension qua quantity, not qua matter of a mobile, sensible substance. Indeed, in chapter 6 I shall argue that quantity as such just is extension. So, the study of quantity turns out to be for Aristode primarily the study of extension. In this way, extension is not only a highest kind that mathematicians study but also the most basic matter that admits of some essential structure. Extension, of course, does not actually exist in the form in which mathematicians study it. Rather, it exists in material composites as the matter for sub-... 

Consciousness of what For consciousness to BE consciousness must be conscious of some THING--not necessarily a physical thing—it may be metaphysical, as Love, the consciousness of feeling, or Life, the consciousness of being. But whether concrete or abstract, it really amounts to the same thing. 

We believe we have very clearly shown in previous lessons how that the abstract and the concrete are but different phases of one and the same thing. Nor can the mind be said to be master of a thing, until it understands how to convert it into one state or the other at will—that is, to make the metaphysical physical, or the reverse. And this essentially is alchemy, or transmutation. 

Now, if this were altogether a spiritual matter, as many try to imagine, how is it that it can be described as a "saffron-colored powder, very subtle, and almost impalpable, of a very pleasant odor," etc. This only shows, as we have taught in earlier lessons, that the abstract becomes concrete, the metaphysical physical, the invisible visible, and so on. The two appearances are but conscious phases of the one eternal fact of being. Through the mastery of the Stone, man learns that he IS MASTER OF ALL ELEMENTS, and that he may manipulate them at will to his own advantage. 

In the abstract, it might be tempting to imagine that irreducible complexity simply requires multiple simultaneous mutations—that evolution might be far chancier than we thought, but still possible. Such an appeal to brute luck can never be refuted. Yet it is an empty argument. One may as well say that the world luckily popped into existence yesterday with all the features it now has. Luck is metaphysical speculation scientific explanations invoke causes. It is almost universally conceded that such sudden events would be irreconcilable with the gradualism Darwin envisioned. Richard Dawkins explains the problem well ... 

Natural science proper is physics. It has a pure and applied part. The pure part is strictly apodeictic (proper in the strong sense). The applied part needs the assistance of principles of experience (4 469) and is proper in the weak sense. An example of strong/pure and weak/applied proper science would be pure and applied geometry. Physics is based on a priori principles, both from mathematics and philosophy (a metaphysics of nature) 3 natural science proper presupposes metaphysics of nature (4 469).4 The use of mathematics introduces the pme part of science, and at the highest level of abstraction there is the metaphysical a priori. 

When John Gorham assumed the Erving Chair of Chemistry at Harvard in 1817, he received a wonderful congratulatory letter from John Adams. The retired President expressed the view that matter is a mere metaphysical abstraction and that he could not comprehend atoms and he could not help laughing at molecules. Near the end of his delightful letter he exhorts ... 

Admittedly metaphysical analysis led to the same results but it gave only abstract principles, while now these same abstract principles, put into practice, are illuminated by example and fortified by success. 

But perhaps Lavoisier s greatest contribution,particularly for our story, was one already mentioned briefly in chapter 1 Lavoisier was highly critical of the classical abstract element scheme of the Greeks and subsequent chemists. By adopting an empiricist approach, he attempted to eradicate any talk of abstract elements or principles in favor of elements as simple substances, which could be isolated and which could not be further decomposed. This anti-metaphysical departure may have been just what was needed in chemistry at the time, although Lavoisier did not succeed in completely dispensing with the need for elements as principles, as many authors have pointed out. ... 

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