rush for discoveries in science, became public; their stakes became the acclaim
of large audiences. The takeoff of rapid discovery in mathematics and science
was the result.
how do scientific networks affect philosophy?
Our main concern for the moment is the effects of the network overlap on the
scientific revolution. Let us briefly consider the effects in the opposite direction,
implied by our world comparisons. What is distinctive about the Western orbit
is that the mathematical-astronomical networks are often very closely inte-
grated with the main philosophical networks: this is so in the key formative
period for philosophy as well as for mathematics in Greece; it is one of the
key lines of development in Islam, and a foil for the important indigenous lines.
Their joint overlap was central for the community of Muslims, Jews, and
Christians which formulated a cosmopolitan “religion of reason” in Spain, and
it continued to shape the interests of Christian philosophers. What does this
mathematized, astronomized, philosophical tradition of the West have that is
distinctive on the philosophical side? The simultaneous creation of abstract
mathematics and self-consciously abstract philosophy in Greece made mathe-
matics into an ideal of transcendent reality. The order of the numbers was
taken as the frame of the universe, on both the lower level of cosmology and
the higher level of theology and ultimately of ontology. One consequence in
the West, lacking in Asia, was an emphasis on a graded hierarchy of being,
from one ontological level down to the next. This hierarchical conception of
the universe made astronomy philosophically much more important in the West
than in the East; the planetary spheres could be identified with gradations of
ontological perfection. Physical science was easy to carry along in a Western
philosopher’s baggage; even if parts of it concerned rather degraded levels of
metaphysical reality, it had a place in the system.
In metaphysics, Western mathematized philosophy was constantly re-
minded of levels of abstraction. Its bias was toward the realism of universals
(just the opposite of the Buddhist bias toward nominalism and world illusion);
this became fruitful for philosophical exploration whenever the energy of
controversy started up, since the concepts of universals and particulars were a
ready-made arena in which one might initiate a dispute. And since the concept
of a hierarchy of abstraction was coordinated with the more concrete cosmol-
ogy of observational science, disputes over nominalism and radical particu-
larism (as in Duns Scotus) could stir up revisions of scientific theory, just as
universals also implied scientific laws. These interconnections explain why so
many of the most innovative medieval Christian philosophers often touched
on scientific topics, if only from the conceptual side. In epistemology, wherever
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