*Discourses Concerning Two New Sciences*

From:
Configurations

Volume 9, Number 1, Winter 2001

pp. 37-64 | 10.1353/con.2001.0007

*Configurations* 9.1 (2001) 37-64

*Purdue University*

*Duke University*

Galileo's *Discourses Concerning Two New Sciences* is,
indisputably, one of the founding documents of the modern,
mathematical sciences of nature. As such, it is not surprising that
it is more discussed (or, more accurately, referred to) than read.
Galileo is accepted as the founder of a mathematized physics -- one
in which time, space, and motion are treated as physically
measurable and, theoretically, mathematical quantities, and in
which laws of motion, depending only on these quantities, are
abstracted from the other properties that material bodies possess.
He is also known as the founder of an experimental physics in which
such physical objects, suitably idealized (or, more specifically,
measurable quantities associated with them, or with their idealized
and mathematically formulated laws), are subject to verification
and detailed examination. The *Two New Sciences* is the work
in which all of this is set forth as the culmination of Galileo's
lifelong study of the problems of motion and force, or weight
("force" is not exactly Galileo's term, but it is used by Stillman
Drake in his translation).

However, even a cursory reading produces a number of seemingly
perplexing and unexpected features, which significantly complicate
this view. There is, for example, enough mathematics in the text to
persuade both mathematically inclined and nonmathematically
inclined readers of the central role of mathematics in Galileo's
science; indeed, the quantity and level of mathematical argument is
sufficient to dissuade many nonmathematically inclined readers from
penetrating very deeply into the text. On the other hand, the text
is by no means purely mathematical in nature, and the
nonmathematical aspects may, in a perverse manner, dissuade the
mathematically inclined from taking the text as a whole seriously
enough to give it more than a selective reading. This combination,
although found elsewhere in Galileo's works, presents particular
complexities here, and this may help to account for the relatively
low level of readership of the *Two New Sciences* and the
prevailing, somewhat stereotyped views of the book.

To address these and other issues that arise in confronting this
text, we present here a reading of *The Two New Sciences* that
attempts to account for both its content and form, for both its
mathematical/ scientific aspects and some of the more literary
aspects of its structure. Our aim is to point out and explore some
key aspects of Galileo's conception of the mathematical sciences of
nature, and the ways in which this conception differs from certain
accepted views of his project as well as from certain views of the
nature of mathematical physics (as we would call it now) that arose
in the wake of his work. Accordingly, the emphasis of our analysis
is more "critical" or "philosophical" than "historical," arising
from a textual reading of the *Two New Sciences* and the
exploration of the architecture of its key concepts, accompanied by
a somewhat closer-than-customary analysis of Galileo's mathematics.
We will discuss the consequences of our readingat the end of this
article. We would like, however, to state at the outset four key
points that arise from our analysis, since, on these points in
particular, Galileo's approach to science and his views differ
notably from those of many practitioners, philosophers, and
apologists of modern science, who often try to identify Galileo as
a principal precursor. Our four points are as follows:

(1) While mathematics is a crucial and defining dimension of Galilean sciences, mathematical arguments enter these sciences in more complex and diverse ways than is commonly thought.

(2) Similarly, the plural term sciencesmust be taken quite seriously, for Galileo's concept of science entails, and his scientific practice enacts, a plurality of sciences.

(3) Galileo's concept and practice of science instantiate radically distinct views of certain notions traditionally associated with the project of modern science, such as mathematical and scientific "objectivity," "reality," and "truth," which have been the subject of long-standing debate as well as much recent controversy.

(4) Galileo's discourse, at least in theTwo New Sciences, explicitly positions scientific discourse and concepts in relation to culture and history.

### Placing the New Sciences

We recall the...

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