RENAISSANCE METAPHYSICS AND THE HISTORY OF SCIENCE
III. The main schools of Renaissance
metaphysics - inevitable defects of such sketches as present,
excessive schematisation, over-simplification, too clear cut distinctions
- subsequent chapters correctives to these generalisations - actual
picture especially blurred by extensive permeation of naturalism
- the plausibility and scientific impotence of this.
IV. The services of the Aristotelian
revival of the thirteenth century for later thought - important
as preparatory organisation of scientific knowledge - as a system
rapidly, and by the Renaissance, fully, exploited - the inadequacy
and dangers of its qualitative analysis of nature - its standards
of Reality fatally divorced from intelligibility - doctrine of
essence and accident and assumption of a direct access to facts
through language - ascription of causal efficacy to quiddity -
its wide appeal to experience and qualitative "experiment"
- inadequacies of Aristotelianism as an overall scheme of correlation
- it represented a merely contemplative ordering of knowledge,
providing no assistance to applied science - doctrines of causality
- species and teleology - discontinuities it established in nature
- separation of the realms of faith and reason and consequent
low estimate of powers of mind - the rational and the natural
and the depreciation of mathematics.
V. The evaluation of mathematics
one of principal matters in dispute between Aristotelian and neoplatonist
schools in Renaissance - restricted nature of empirical evidence
producible against Aristotelianism - but general superiority of
mathematical procedures to verbal methods of investigation.
VI. Tradition of scientifically orientated
neoplatonism of Dee - its critical but not hostile attitude to
Aristotelian doctrines - conciliation of Plato and Aristotle a
perennial characteristic of neoplatonism - lack of any differentiation
between Plato and his followers - Pythagoreanism.
VII. The constant characteristics
of neoplatonism in all its varieties - insistence on the mind's
direct access to truth - the status of the universal - ultimate
grounds of knowledge placed at opposite end of scale of being
to sensible - the Idea of the Good, Union with the One and intellectualism
of Christian neoplatonism - the a priori - revelation and the
levels of knowledge - thought always directed towards being -
transformation of Platonic Ideas into modes of considering objects
- and operational conventions - Ideas become essentially functional
for Galileo - reconstitution by scientific neoplatonism of Renaissance
of "objective" as that of which a logical account can
be given.
VIII. The sensible world and neoplatonism
- it awakens individual minds to latent conceptual knowledge -
its derivation from intellectual truth - its consequent rationality
and the new ideal of discoverable natural law - intelligible unity
of the cosmos in neoplatonism of Renaissance - universe no longer
crudely anthropocentric - the "parts" of the universe
- superiority of neo-Platonic mathematical approach over qualitative
atomism - the natural fact considered as a theorem in geometry
pertaining in the same way to a system - Platonic tradition of
the unification of all sciences - and the new stress on detail
and exactitude - the revaluation of nature - the unity of the
natural and intelligible following on the view of the Real as
the logically representable - dialectic and reality in Platonism.
IX. The a priori and mathematics
- sixteenth century stress on mathematical doctrine as fundamental
distinction between Plato and Aristotle - mathematics for Plato
- fusion with Pythagoreanism - the entire certainty of mathematics
- mathematics as the type of objectivity - general sixteenth and
seventeenth century adoptions of these teachings - Roger Bacon's
ideal of "verifying" all the sciences by mathematical
means and John Dee.
X. The connections between neoplatonism
and new science in sixteenth century - structure gradually replaces
tendency as key concept in analysis of nature - the reconciliation
of belief in overall Divine Providence and acceptance of universal
mechanical causality - inspiration given by the Timaeus
- superiority of new mathematical methodology over Aristotelian
induction - beneficial results of spread of Ramus' logic directed
towards psychology rather than "substance" - its connection
with mathematical approach to nature and general advantages of
this - idealism of relation replaces realism of substance - germs
of subsequent science clearly present in Renaissance - Galileo's
neo-Platonic mathematicism - his confidence in reason even when
opposed by experience - the scientific inspiration of Archimedes'
works in sixteenth century - effect of his apparent success in
applying purely a priori methods to establish synthetic results.
XI. The replacement of quality by
quantity as what is taken as fundamental in nature - difficulties
of such an attitude in sixteenth century - lack of pragmatic support
for it - primary and secondary qualities in neo-Platonic tradition
- consequent gradual abandonment of claims of intuition - but
necessity in Renaissance of a Pythagorean metaphysic for defending
alternative doctrine - the new Reality of Renaissance Science
- its standards of value - particular dangers, as evidenced by
Dee, of theory of world as an exemplification of mathematical
truth.
XII. Divinity as the head of the
hierarchy of sciences - consonance of Platonists and Christian
doctrine - views on the nature of God and the soul inseparable
from Renaissance scientific theory - consequent place of qualitative
experience in Dee's mathematics - the Renaissance synthesis and
its multivalent appeal - rational, mathematical, aesthetic, theological
- its intention to be wholly adequate to all the capacities of
man.