Contrary to later (modern, especially positivist) accounts of the Middle Ages, Medieval science understood the role of observation, measurement, and experiment.
But the focus on the empirical raises a
central problem - one we've seen since
the Pythagoreans and Thales: given our use of abstract theoritical
principles - most centrally, mathematics - in our accounts and
explanations of the physical/material world - how are we to understand
the relationship between the things known by mind (theory)
and the things known through senses (the objects of our observation,
measurement, and experiment)?
This question is dealt with most directly in the Middle Ages in
the debate concerning the univerals. Robert Grosseteste provides
an apparent philosophical solution - one that lays part
of the metaphysical and epistemological foundations
of the emerging philosophy/natural science.
Alioto
notes that while
Aristotelian science was studied largely "out of the textbook,"
so as to focus on an exegesis [interpretation] of the text, with
a view towards discovering "...why things happened,
their causes, and to find out what deductions could be made from
accepted or inducted principles," -- there was also a second
dimension to medieval science,
...vaguely similar to the
lab part of our modern course. There was an emphasis upon observation,
measurement, and even experiment. To be sure, it took a secondary
seat to the study of the text, and its practitioners hardly got
their hands dirty. It did, however, stress the procedures we would
equate with the lab. (135)
"This method was called
by Albert the Great the "Pythagorean" approach. It certainly
had many ancestors besides Pythagoras, and we may simply call
it the practical quantitative tradition of measurement."
(136)
Examples:
Astronomical/astrological
observatories, "in which it was more important to insure
the accuracy of tables than to speculate upon the reality of the
spheres."
"The Hermetic tradition,
although fragmentary in the Middle Ages, gave rise to the alchemist's
laboratory where experiments were conducted based upon the texts."
"the Archimedean geometrical
tradition in statics"
"the importance of weights
and measures" -- increasing with developing commercial interests
of the later Middle Ages
"In optics the mathematical
treatment of light rays and theories of vision were combined with
Aristotle and the medical tradition of Galen."
Most importantly -- "In
a basically agricultural society such as Medieval Europe,"
the application of Euclidian geometry in surveying. (136)
Euclid also applicable to
the geometrical analyses of optics and astronomy.
A middle ground emerges here.
Both Euclid and Aristotle were taken as "the best illustrations
of true scientific methodology. The actual application of geometry
to natural phenomena represented a kind of intermediate science,
falling between the rigorous demonstrations of pure mathematics
[Euclid, Elements] and the logical deductive causality
of natural philosophy [Aristotle, Posterior Analytics]."
([emphasis added, C.E.]: 136)
Leonardo Fibonacci of Pisa as taking up this "intermediate science." [1220: The Application of Geometry]
A merchant concerned with
commerce: encountered Arabic numeration and algebra. His "Liber
abbaci popularized algorism (arithmetic founded upon Arabic
notation) which had attracted little attention inside the schools.
We hear Roger Bacon admonishing theologians to study the system
in order to better acquaint themselves with the art of numbering."
(136f.)
STATICS
(in medieval terms, the science of weights)
Again, its practical applications
would seem to lie in areas of commerce. There was, however, a
theoretical tradition, derived from a pseudo-Aristotelian work
(possibly done by Strato) called Mechanical Problems, as
well as from the methods of Archimedes received through the Arabs.
The most significant contribution of the medievalists was to
combine these two traditions. ([emphasis added, C.E.]: 137]
See description of Jordanus,
p. 137 -- all of which serves as an example of "some application
of mathematics to natural phenomena."
The Problematic:
the relationship between mathematics and natural phenomena
Alioto points out that a "methodological
problem" exists regarding any effort to apply mathematics
to natural phenomena [a problem illustrated most forcefully by
Plato and his arguments for the primary reality of the Forms].
Alioto gets to this with an example from Euclid:
Recall the Euclidian method
of deduction from axioms and common notions. One of the latter
states that things which coincide are equal. Thus Euclid proved
that two triangles were congruent by placing one upon the other
and showing that the given angles must coincide. This may seem
perfectly self-evident on paper using perfect triangles.
But may we say that in the physical world the universal triangle
remains uncorrupted through the act of movement? In fact, we might
easily contend that mathematical definitions tell us nothing about
their actual existence in the physical world. Where, then, do
the principles of mathematics come from?
[Recall here, however, that
Plato develops the doctrine of the Forms precisely in order to
justify and ground mathematical knowledge. Again,
look at the notes, on "Plato and
the Development of Science," I.E.2.]
We might attempt to escape
the question of the relationship between mathematical definitions
and relations, on the one hand, and particular phenomena observed
through the senses, on the other, -- formulated here in an especially
Platonic framework -- by taking an Aristotelian
approach: on such an approach, remember, we would say that the
forms or the universals are somehow in particular things
in some sort of form/matter combination. This approach, however,
also runs into a roadblock:
And if universals are immanent
in things, as Aristotle said, how can we actually maintain that
universals are in any way different from their singulars. The
unity of a universal, a triangle, is in all triangles; yet, even
if we can show this universal for every triangle, we still have
the problem of unity in diversity. There still exists a logical
hiatus between the universal or formal definition and the thing
which is actually observed or measured -- between the lecture
and the lab. (138)
That is, if Plato emphasizes the difference between perfect, unitary, universal Forms knowable by the mind and sense phenomena as imperfect manifestations or reflections of these Forms --
Aristotle so far collapses the difference between the two, so that it becomes difficult to "see" how the universal or form (as the underlying unity knowable by the mind) is sufficiently distinct from diverse, particular objects of sense-knowledge.
Somewhat in the way we saw
with Anaxagoras and
his "seeds" -- to say that things are what they are
because they are what they are (i.e., hair is hair because hair
"seeds" predominate in it [Anaxagoras]; or, a "chair"
is a chair because it contains the form chair [Aristotle]) seems
unsatisfactory as an explanation. In logical terms, it
is simply circular. In terms of the structure of explanation
we seem to be interested in since at least the PreSocratics, if
not in mythopoetry itself -- there is no simplifying structure
of explanation which accounts for the diversity of many
different changing things in the world of sense by tracing it
to a unitary, underlying set of causes or forces (e.g.,
water, aer, the unlimited, the Good, etc.)
This methodological problem receives an apparent resolution in the work of Robert Grosseteste (1168-1253) [FRANCISCAN]
Defines scientific knowledge
as the definition or discovery of the universal -- which could
be grasped apart from divine illumination [contra
Augustine!]
Only before the fall was the
human mind able to grasp in one act both the essence and singular.
In the corrupted material world, knowledge had to begin with the
senses, and scientific knowledge could be achieved only through
demonstration, whose instrument was the syllogism. (138)
[Note: as his name suggests,
this is an English thinker: this orientation towards sense-knowledge
as the basis of knowledge not only points backwards towards Aristotle,
but also forward to Anglo-American empiricism as a traditional/cultural
assumption about what constitutes knowledge.]
Roughly, what Grosseteste comes to in the problem of the universals is to attempt a middle ground between Plato and Aristotle.
In the Aristotelian direction, he argues that we somehow move from an inspection of various geometrical figures (called "resolution") to a process of reconstituting "...these qualities theoretically in our minds," so as to arrive [how?] at the definition -- for example, of a right-angled triangle. And, as with Aristotle, Grosseteste insists that this universal definition or premise in fact exists in real things as their form and cause. "But [in the Platonic direction] the universal is neither one triangle nor many; rather it seems to be a logical entity outside the corporeal world!" (138f.)
Even so, because such universal
definitions, propositions, claims, etc. are only "suggested"
in this reconstitution process -- they fall short of attaining
the status of ultimate reality ascribed to the Forms by Plato.
And it is just this ontological status of the universals [neither "purely" Aristotelian nor "purely" Platonic] that not only serves as a justification of the relevance of mathematics to sense-world phenomena: it further serves as a metaphysical justification of the need to experiment in the development of scientific knowledge.
So Alioto notes:
...the premises gained through induction...are only hypotheses when they are generalized into a universal statement about all right triangles. As hypotheses, they can be doubted. A hypothesis is for Grosseteste simply a formal assumption of our expectation. In order to convert our hypothesis into a scientific demonstration which reveals the actual state of its existence we must go out and experiment....
Experiment seemed to mean
for Grosseteste what it means for us: a controlled procedure designed
to verify or falsify a hypothesis. In effect, it is a test of
our definition, coming after induction. In fact we may deduce
actual consequences not included in the original generalization.
Through experiment and observation we may distinguish the true
causes from the possible, grounding our demonstration in the factual
world. (139)
And, just as mathematics is
justified as a mode of knowing the material world by a change
in the metaphysical or ontological status of the universals --
so it is further justified through a metaphysical conception of
the universe: "...the actual structure of the universe was
generated by a self-diffusion of light (lux)....the primordial
cause of all natural effects. And Grosseteste explicitly held
that such causes must be expressed by lines, angles, and figures."
(139)