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§8 [30–31]

mathematics became, as it was for Spinoza and Descartes before
him, the *prototype of all scientificity* and thus also of the *cognitive character*
of philosophy.

To be sure, it is a great *error,* and one that is still definitive everywhere today, to believe that this *predominance* of mathematics and mathematical thinking in the seventeenth and eighteenth centuries was restricted only to the external construction of philosophical systems, the articulation of their concepts, and the ordering and sequence of their propositions. The only thing correct in this opinion is this: the mathematical must be understood here in a broader, more fundamental sense, not as the particular methodology of some particular mathematical domain.

b) The Greek concept of the teachable and learnable

(τὰ μαθήματα) and the inner connection between the

“mathematical” and the “methodological”

When Spinoza titles his main work *Ethica more geometrico demonstrata,* the geometrical method here does not mean, say, the procedure of analytic geometry; Spinoza is thinking of Euclid’s procedure in his *Elements,* and of this procedure in its general formal sense, not as restricted to definite spatial elements and forms. The mathematical as μάθημα, the teachable as such, that which can be learned in a preeminent sense; μάθησις, learning, μανθάνειν.

And what is that? Here we can see more clearly if we investigate how the Greeks, to whom we owe the word μαθήματα and thus the discovery of the matter itself, distinguished the μαθήματα from other things. Within the whole domain of beings and of that which can become an object in this or that way, the Greeks are familiar, among other things, with (1) τὰ φυσικά (cf. above), that which arises, grows, and passes away on its own; (2) τὰ ποιούμενα, what is produced by manufacture; (3) τὰ χρήματα, things insofar as they are in use in a particular sense; (4) τὰ πράγματα, the things we have something to do with (πρᾶξις). All four domains are distinguished by the fact that the *objects that belong* to them in each case become *accessible in a particular way of experiencing and dealing with them,* and only in this way. Threatening and favorable natural phenomena, tools, weapons, means of nourishment and exchange, raw materials, and the like—all this is always encountered only in particular experiential contexts, according to particular directions of human concerns, in a particular historical situation in each case.

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