Rene Descartes (1596-1650)
It has been said that both modern philosophy and modern mathematics began
with the work of Rene Descartes. His analytic method of thinking focused attention on the
problem of how we know (epistemology), which has occupied philosophers ever since.
Descartes was educated at the renowned Jesuit school of La Fleche where he was taught
philosophy, science, and mathematics. He earned a law degree and then volunteered for the
military in order to broaden his experience. When his duties allowed he continued his
studies in mathematics and science. Eventually he became dissatisfied with the
unsystematic methods utilized by the previous authorities in science, since he concluded
they had not "produced anything which was not in dispute and consequently
doubtful" (1, p. 6). The only exception to this was in the field of mathematics which
he believed was built on a "solid foundation" (1, p.5). Medieval science, on the
other hand, was largely based on authorities from the past rather than observations in the
present, therefore Descartes decided to conduct a personal plan of investigation. But, for
Descartes, even his personal observation of the "book of nature" (1, p. 7) was
not sufficiently beyond doubt because of his concern about the "deception of the
senses." After consideration of all the previous methods of inquiry Descartes decided
that there must be a better way; and in his Discourse on Method he wrote, "I
eventually reached the decision to study my own self, and choose the right path" (1,
Descartes aspired to rebuild a new system of truth based upon an unquestionable first
principle which, like the fulcrum of Archimedes, would allow him to "move the earth
from its orbit and place it in a new orbit" (2, p. 23). The first principle that he
finally felt was self evident was summarized in the statement, "I think, therefore I
am" (1). Descartes believed that he could then use his new method of reasoning to
build on such a first principle, ultimately leading to the unification of all knowledge.
The method developed by Descartes was based on the following rules (1, p. 12):
- The first rule was never to accept anything as true unless I recognized
it to be evidently such: that is, carefully to avoid precipitation and prejudgment, and to
include nothing in my conclusions unless it presented itself so clearly and distinctly to
my mind that there was no occasion to doubt it.
- The second was to divide each of the difficulties which I encountered
into as many parts as possible, and as might be required for an easier solution.
- The third was to think in an orderly fashion, beginning with the things
which were simplest and easiest to understand, and gradually and by degrees reaching
toward more complex knowledge, even treating as though ordered materials which were not
- The last was always to make enumerations so complete, and reviews so
general, that I would be certain that nothing was omitted.
In short, his method required (1) accepting as "truth" only
clear, distinct ideas that could not be doubted, (2) breaking a problem down into parts,
(3) deducing one conclusion from another, and (4) conducting a systematic synthesis of all
things. Descartes based his entire philosophical approach to science on this deductive
method of reasoning.
Descartes was highly optimistic about his plan to reconstruct a new and fully reliable
body of knowledge. He even wondered if among "all things knowable to men" there
might not be a proper application of his method so that "there cannot be any
propositions so abstruse that we cannot prove them, or so recondite that we can not
discover them" (1, p. 13). The apparently global scope of Descartes' speculations
might lead some to conclude that his epistemology demanded the rejection of all authority,
including the Bible. In point of fact, he considered himself a good Catholic and with
respect to the "truths of revelation" he clearly stated, "I would not have
dared to ... submit them to the weakness of my reasonings" (1, p.5). Ultimately it
was his religion that kept him from living in a cocoon of personal introspection. However,
Descartes did plant the seeds for later dissent from the theistic view of the world
allowing for the humanistic dependence on human reason alone. It was left to the humanists
who followed to assert an all encompassing rationalism that would take human reason as the
sole measure of what constitutes "truth."
Francis Bacon (1561-1626)
Francis Bacon has been called the major prophet of the Scientific
Revolution. At the age of twelve Bacon went to study at Trinity College, Cambridge, later
acquired an education in law, and was eventually admitted to the bar. He next embarked on
a political career in the hope that it would allow him to advance his emerging ideas for
the advancement of science. In due time he acquired a seat in the House of Commons, was
knighted, held the position of Lord Chancellor and Baron Verulam, and Viscount St. Albans.
He gained fame as a speaker in Parliament and as a lawyer in some famous trials in which
he was considered an expert on English constitutional law. An outstanding thinker, Bacon
was motivated to write in areas as far-reaching as science and civil government in a
battle against the old order of scholasticism with its slavish dependence on accepted
authorities. He advocated the view that whatever the "mind seizes and dwells upon
with particular satisfaction is to be held in suspicion" (3, p 477). His passion for
the advancement of natural philosophy was rooted in his belief that science was dependent
on and the key to technological progress. Much of his greatest philosophical effort was
applied to the Novum Organum in which he described the inductive method of
reasoning for the interpretation of nature.
Bacon was very critical of those in the scholastic tradition who jumped from a few
particular observations to remote axioms, and then deduced intermediate axioms through
syllogistic demonstration. He also took a dim view of those empiricists who had been
side-tracked with experiments done in depth without reference to related phenomena, since
they were unjustified in the breadth of their generalizations. According to Bacon there
were four categories of false knowledge, or "idols," that had captured the minds
of the men of his day. They are paraphrased as follows (3, pp. 470, 471):
- Idols of the tribe: False notions due to the human nature and
common to all men. An example would be geocentricity which was due to the limits of human
- Idols of the cave: Personal interpretations due to individual
makeup or disposition. An example would be Gilbert's "magnetic world view."
- Idols of the market-place: The problem of language and the
confusion of words and terms. An example of this relates to the problem with definitions
of words which likewise depend upon words.
- Idols of the theatre: The dogmas of philosophies that are
received from wrong "laws of demonstration." This involves the results of the
Aristotelian method of syllogistic argumentation.
In contrast to these, Bacon said that a true science progressed "in a
just scale of ascent, and by successive steps not interrupted or broken, we rise from
particulars to lesser axioms; and then to middle axioms, one above the other; and last of
all to the most general" (3, p. 519). In short, his method required (1) accumulating
a store of particular empirical observations, (2) from these inductively inferring lesser
axioms, (3) from these inductively inferring middle axioms, (3) and then proposing the
most general of notions, each in progressive steps. If we read modern meaning into the
language used by Bacon, we might see a foreshadowing of the idea of a hypothesis in a
"lesser axiom" and a theory in the "middle axiom." This would make his
method agree with the mature conception of science in use today; however, the context
indicates that his ideas were not yet so fully developed. Bacon also argued that this
inductive method "must be used not only to discover axioms, but also notions,"
which may be taken to correspond to the concept of a paradigm, but again this may be
reading into the text. In any case, it is clear that Bacon's view of the scientific method
is progressive and cumulative.
The radical commitment to empiricism advocated by Bacon may imply for some that he did not
accept any knowledge that was not received by personal observation. This is a mistakenly
narrow interpretation of Bacon's view of natural philosophy which he believed was given as
the "most faithful handmaid" of religion (3, p. 509). Bacon actually saw his new
way of acquiring knowledge as a fulfillment of Biblical prophecy concerning the last days:
"Many shall go to and fro, and knowledge shall be increased" (Dan 12:4).
Further, he saw the technological advancement of science as a restoration of the
"dominion mandate" (Gen 1:28), and thus he wrote, "man by the fall fell at
the same time from his state of innocency and from his dominion over creation. Both of
these losses however can even in this life be in some parts repaired; the former by
religion and faith, the latter by the arts and sciences" (4, p. 267). There was,
however, reason to believe that Bacon's views would play into the hands of humanistic
concerns, since he also believed that his inductive method would "extend more widely
the limits, of the power and greatness of man," and one day "embrace
everything" (3, pp. 527, 536). For those who later advocated a "scientific world
view," this prediction was claimed to be fulfilled.
Comparison and Contrast of the Methods of Descartes and Bacon
The differences between the methods of Descartes and Bacon are many and
deep, but there are also many things they have in common. Each of these pioneers advocated
the complete overthrow of all the methods and most of the results of the authorities that
came before them. Both of these men demanded a new standard of precision, since there were
so many examples of sloppy reasoning and observation that littered the path of the science
of the past. There was also a common commitment to doubt in general and a concern about
the "deceptions of the senses" (3, p. 474). In addition, they believed in the
reduction of problems to their smallest constituent parts as a general principle.
Descartes and Bacon each saw himself primarily in the role of an advocate for science and
therefore they contributed very little to any particular field of empirical science (5).
Finally, both of these men were uniquely gifted to promote the particular aspects of
science that were eventually crucial to its advance.
The most obvious difference in methodology between Descartes and Bacon was related to
their procedures for reasoning. Descartes began with intuitively derived principles that
were taken as the premises in the standard deductive method of reasoning, but Bacon began
with empirical observations that were used to inductively educe higher axioms. Descartes'
method was a "top down" approach, whereas Bacon's was "bottom up." So
strong is this particular contrast that it seems at times that Bacon was writing
specifically about Descartes' method as an example of what was wrong in science. A crucial
difference in the background of the two men is seen in the mathematical mastery of
Descartes as compared to the mathematical neglect of Bacon. Descartes is noted for his
great accomplishments in the areas of algebra and geometry, whereas Bacon's spoke little
of mathematics since his area of expertise was law. Background may explain the
similarities in the method of Descartes which parallels that of mathematical proofs. For
Bacon the empirical observations he emphasized for science may parallel the kind of
"eye witness" evidence he required when building a case in a court of law. In
view of Descartes background it appears obvious that his exemplar would be found among the
mathematicians who he said "alone have been able to find some demonstrations, some
certain and evident reasons." Therefore, he decided to "begin where they
did" (1, p. 13). In spite of Bacon's distinguished background he was actually very
pragmatic in his pursuit of an exemplar which he found among the "mechanics." It
was the "mechanical arts which were founded on nature and the light of
experience" (3, p. 493). Because of this observation he was greatly impressed with
the discovery of printing, gunpowder, and the magnet. In his view "no empire, no
sect, no star seems to have exerted greater power and influence in human affairs than
these mechanical discoveries" (3, pp. 538, 539). It is important to note that as
different as the methods of Descartes and Bacon were, when the their exemplars are
synthesized into one, we have an anticipation of the modern mathematical-experimentalist.
We can now see that when taken together, Rene Descartes and Francis Bacon were germinal
for the modern scientific method.
1. Rene Descartes, Discourse on Method, Trans.
L. J. Lafleur. (Bobbs-Merrill, 1950).
2. Rene Decartes, Meditations, Trans. L. J. Lafleur.
3. Hugh G. Dick (ed.), Selected Writings of Francis Bacon. (New
York: Modern Library, 1955)
4. Fulton H. Anderson (ed.), The New Organon. (New York: Macmillan
5. Descartes did, however, contribute greatly to mathematics which is the
proper place of application for his deductive method.
Tim Nordgren, 5-17-98