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, p. 7).
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 necessarily
so.
- 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 insight.
- 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.
Footnotes:
1. Rene Descartes, Discourse on Method, Trans. L. J. Lafleur.
(Bobbs-Merrill, 1950).
2. Rene Decartes, Meditations, Trans. L. J. Lafleur. (Bobbs-Merrill,
1960).
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
Publishing, 1960)
5. Descartes did, however, contribute greatly to mathematics which is
the proper place of application for his deductive method.
Tim
Nordgren, 5-17-98
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