Transcript CVSP 203 Common Lecture: Descartes and the Foundations of

1
4
2
5
3
The Players in Our Drama
The Need for Context
• Modernity first and most generally constitutes itself as a rejection of or
battle against the pre-modern. It largely views itself as “new,” “original,”
and “revolutionary.” So one cannot understand the modern without
understanding the pre-modern (or the modern view of the pre-modern,
even if this is not accurate). So context is necessary.
• In particular, early modern science in Descartes and Bacon did not begin
simply as a rejection of an older, supposedly incorrect, set of views or
“facts,” but in a new way of doing science altogether, a new way of
deciding what is true and what is false (or so it claims!).
• For fear of the Catholic Church, Descartes intentionally hid his true
intentions in the Discourse and the Meditations. To Mersenne, 1641: “…
and I may tell you, between ourselves, that these six Meditations contain
all the foundations of my physics. But please do not tell people, for that
might make it harder for supporters of Aristotle to approve them. I hope
that readers will gradually get used to my principles, and recognize their
truth, before they notice that they destroy the principles of Aristotle.” His
plan was to show his method is better for religion itself, and oh, by the
way, also supports Copernicus and his view of science.
1. Brief Historical Background and Menu
• Some Dates: (322 BC) Death of Aristotle – (90 - 168 AD) Life of Ptolemy – (1543)
Copernicus’ On The Revolutions published – (1596) Descartes Born – (1619) Descartes
discovers the universal method of science in a stove heated room – (1632) Publication
of Galileo’s Dialogue Concerning the Two Chief World Systems – (1633) Galileo
condemned by the Inquisition for heresy and formally denies Copernicanism;
Descartes decides not to publish his physics, since it teaches the motion of the Earth –
(1637) Descartes publishes the Discourse on the Method, but still suppresses his
physics – (1641) Descartes publishes Meditations on First Philosophy [i.e. on
metaphysics] – (1644) Descartes publishes Principles of Philosophy, which contains his
metaphysics and his physics of the entirety of nature in several volumes – (1650)
Descartes dies in Sweden – (1687) Sir Isaac Newton publishes his Principles, which
contain his famous three laws of motion and the inverse square law for universal
gravitation.
Menu for This Lecture
• Review Aristotle’s understanding of science (physics or “natural
philosophy”), and particular his views on the use of mathematics.
• Look briefly at Ptolemy’s Aristotelian model of the solar system (at
that time viewed as the whole universe).
• See the view of the relationship between physics and mathematics
is present in Ossiander’s Introduction to Copernicus’ On the
Revolutions of the Heavenly Spheres. Also that expressed by Pope
Urban VIII, who was Pope when Galileo was condemned for
Copernicanism in 1633.
• Review Copernicus’ and Galileo’s actual views on the nature of
physics and the role of mathematics in it, and in particular Galileo’s
disagreements with the Aristotelians of his day.
• Introduce Descartes and the Origin of the Discourses in an attempt
to justify the Copernicus’/Galileo’s mathematical view of nature.
• Examine the main parts of Descartes’ strategy for justifying this.
• Draw some conclusions for science and philosophy.
A. Traditional “Aristotelian” Position
• Mathematical models are useful hypotheses,
i.e. “useful fictions.” Yet no matter how useful or
beautiful or simple a model may be, it cannot be
true if it conflicts with the results of “natural
philosophy”. Since the job of the Astronomer is
to invent the most useful hypothesis, they are
not concerned with truth at all.
The Aristotelian Order of Science
Physics or “Natural Philosophy”: Concerns the
Motions and Changes of Physical Bodies – Draws
its first principles from Metaphysics.
Guided by experience (the senses) and
metaphysics. (Gives the real reason. Answers the
Question: Why?)
Astronomy and Mechanics:
Concerns Forms Separate from
Bodies. Branches of Mathematics
Aimed at Calculation and Incapable
of Demonstrating Principles of
Physics. (Only describes what we
see. Not concerned with why. Does
not give reasons.)
First Philosophy or Metaphysics: The
Fundamental Science, which Demonstrates
the Principles used in all Other Sciences.
Cycle
Epicycle
Ptolemaic Eccentric Model
Copernican or Heliocentric Model
From Ossiander’s Preface to Copernicus’ On the
Revolutions of the Heavenly Spheres (1543)
• “For it is the job of the astronomer to use painstaking and skilled observation in
gathering together the history of the celestial movements, and then – since he cannot
by any line of reasoning reach the true causes of these movements – to think up or
construct whatever causes or hypotheses he pleases such that, by the assumption of
these causes, those same movements can be calculated from the principles of
geometry for the past and for the future too.”
• “For it is sufficiently clear that this art [i.e. astronomy] is absolutely and profoundly
ignorant of the causes of the apparent irregular movements. And if it constructs and
thinks up causes – and it has certainly thought up a good many – nevertheless it does
not think them up in order to persuade anyone of their truth but only in order that
they may provide a correct basis for calculation.”
B. Position of Pope Urban VIII (Friend of
Galileo, but also Pope when Galileo is
condemned.)
• God is infinite beyond our comprehension in terms of both
knowledge and power, thus no supposed explanation we give
can be certain in the least. That is, since God is so great, we
must admit that he could do anything in any way, and surely
in ways that surpass our comprehension. “It would be
excessively bold if someone should want to limit and compel
divine power and wisdom to a particular fancy of his [i.e., if
the physicist should insist that he/she can demonstrate
anything true of nature]” (Galileo, Dialogue Concerning the
Two Chief World Systems, 270).
C. Copernicus, Galileo, Descartes, et al.
• Despite Ossiander’s Preface, Copernicus did intend to demonstrate the true nature physical
motions of the planets. But he did not have any solid empirical evidence. Rather, he believed his
system to be true, because he thought it the most systematic and beautiful, and thus most fitting
to be a work of God. Since this system was mathematical, however, he asserted that one can see
this truth only with “the vision of the mathematician.”
• While we cannot know all things, as God does, we can know individual things with as much
certainty as God. These are the things we conceive and prove using mathematical arguments.
This is possible because God created the world in accordance with mathematics.
• Galileo: “[Natural] Philosophy is written in this all-encompassing book that is constantly open
before our eyes, that is the universe; but it cannot be understood unless one first learns to
understand the language and knows the characters in which it is written. It is written in
mathematical language, and its characters are triangles, circles and other geometrical figures;
without these it is humanly impossible to understand a word of it, and one wanders around
pointlessly in a dark labyrinth” (The Assayer, 1623).
Summary of Galileo’s Position Against
the Aristotelians
• 1. The Aristotelians rely too much on AUTHORITY,
TRADITION and BOOKS instead of THEIR OWN JUDGMENT.
• 2. The Aristotelians are too “EMPIRICAL,” i.e. they rely too
much on the bare evidence of the senses (e.g., the Earth
does not move, bodies naturally slow down, etc.)
• 3. The Aristotelians do not employ MATHEMATICAL
DEMONSTRATIONS, and indeed falsely believe that
mathematical truths are not EXACTLY true in the physical
world (e.g. they believe no argument using perfect spheres
or perfectly smooth surfaces has any validity in the physical
world where there are no perfectly smooth spheres)
What must be done to prove Galileo
right?
• Prove, somehow, that mathematics is the key to the method of they
physical sciences. How? Answer: Find a new metaphysics that
replaces the Aristotelian Metaphysics and shows that physical
reality is ESSENTIALLLY MATHEMATICAL. (Descartes: Prove God
exists and created the world using mathematics! But how??)
• Prove that one can only reach the truth by trusting one’s own
judgment (quiets the Aristotelians once and for all).
• Prove that the human mind is capable of absolute certainty, i.e.
God-like Knowledge, in those instances where it 1) relies on its own
judgment fully and 2) employs mathematics properly. (Partial
Answer to Pope Urban VIII)
• Show that this metaphysics agrees better with the Christian Religion
than does Aristotle’s (Full answer To Urban VIII) – That is, show the
same metaphysics that supports a mechanical view of the universe
also proves God’s existence, immortality of the soul, etc. Crazy!?
2. Descartes and the Origins of the Discourse on
the Method (published anonymously, 1637)
0) Descartes Life in Brief: Birth (1596) – Schooling – Research, Travels: Beeckman and the
Corpuscular Philosophy – Stove heated Room: Universal Method of Science – Suppression of his
Physics – Publication of the Discourse – Meditations on First Philosophy – Principles of Philosophy
- Death
1) He first discovered no certainty in knowledge gained from books, custom or even his own
experience, and thus resolved to accept nothing as truth that was not certainly true.
“Thus I gradually freed myself from many errors which may obscure our natural light
and make us less capable of heeding reason.” (10)
“But regarding the opinions to which I had hitherto given credence, I thought that I
could not do better than undertake to get rid of them, all at one go, in order to replace them
afterwards with better ones, or with the same ones once I had squared them with the standards
of reason.” (14-15)
2) He then reflected on how science could best be constructed, and found common knowledge to
be defective mainly in its lack of a single secure method. It was an accumulation of materials from
different sources, when it should be one well-structured whole.
3) He looked to logic and mathematics for help in discovering a universal method,
because they were most reliable, but found even these too defective.
4) Finally he resolved on four rules: i) Accept nothing that is not certain, ii) break all
problems down into their simple parts, iii) understand all complex matters on the basis
of their parts, and iv) practice running through his reasoning several times so he could
see all the parts of his argument combined into a whole.
5) Finally, at the end of the Part Two, Descartes reveals that this method requires a
new foundation, and so an investigation into Metaphysics or First Philosophy:
“But observing that the principles of these sciences must all be derived from
philosophy, in which I had not yet discovered any certain ones, I thought that first of
all I had to try to establish some certain principles in philosophy. And since this is the
most important task of all, and the one in which precipitate conclusions and
preconceptions are most to be feared, I thought that I ought not to try accomplish it
until I had reached a more mature age than twenty-three…” (21-22)
3. Descartes’ Metaphysical Strategy for Founding
Modern Science (Discourse, Part Four – Meditations)
• Step 1. Deny every supposed truth that can be doubted at all. (Methodological Doubt):
Result – Customs or traditions, books (Aristotle) and the senses (experience!) are not sources of
certain truth.
retreat into the mind or soul, which alone I know immediately
• Step 2. Discovery of the fundamental truth, “I think, therefore I exist” [Aside: Discovery at
the same time of the true nature or essence of the self: thinking.]
• Step 3. Examine this fundamental undeniable truth to discover what makes it impossible to
deny. This is found in its being absolutely “clear and distinct.” Adopt these as the Ultimate Criteria
of Truth.  If the idea can be made clear and distinct in my mind, accept it as certain; if not,
reject it as false.
• Step 4. Prove from within my own mind (thinking self) that God exists. Proof One: I am aware
of myself as imperfect or as limited. But to think myself as limited, I must have the idea of
something unlimited. I cannot be the source of this idea, and indeed no being less than God could
be the source of it. Therefore, God exists. Proof Two: The idea of God is the idea of a being with
all perfections. Existence is a perfection. Therefore, God exists.
• Step 5. Prove God is not a deceiver. Proof: Deception is only suitable to a being
with limited power. God is of unlimited power. Thus God cannot deceive. God is
therefore truthful.
• Step 6. If God is truthful, then since he is the creator of my being, everything that I
clearly and distinctly represent to my mind will necessarily be true. Put differently: If
God is good and truthful, then he certainly will not make it that I am deceived when I
use the best and indeed the only guide to truth that I find within myself.
4-5-6: “However much the best minds study this question, I do not believe they
will be able to give any reason sufficient to remove this doubt unless they presuppose
the existence of God. For in the first place, what I took now as a rule, namely that
everything we conceive clearly and distinctly is true, is assured only for the reasons
that God is or exists, that he is a perfect being, and that everything in us comes from
him. It follows that our ideas or notions, being real things coming from God, cannot be
anything but true, in every respect in which they are clear and distinct.” (38)
• Step 7. The Clincher for Mathematical Physics: The most clear and distinct
representations, and indeed the only clear and distinct representations, that I have of
external physical things, are those treated in geometry. Therefore, external physical
things in reality have nothing other than geometrical characteristics: “The essence of
bodies is extension.” Thus colors, heat, cohesion and even weight, must be reducible
to geometrical properties. (e.g., heat is only motion of small bodies)
Descartes’ Strategy
God: creator of me and
the world, most perfect,
so also all powerful, all
knowing, all good, so all
truthful and not a
deceiver.
I think,
so I am
World Clearly
and Distinctly
in My Mind
Because of God
The World
as it Really
is
Major Conclusions for Science:
1) Genuine knowledge is only possible through
mathematics, and indeed, through the construction of
mathematical models, the entire truth of the physical
world can be known.
2) The Aristotelian natural philosophy, which does not
employ a mathematical method, is necessarily false.
3) Every physical body, including therefore also the
human body, is entirely nothing but a machine, i.e. the
operations of the whole depend upon and are a
necessary consequence of the character of the parts
from which it is constructed in exactly the same way as
a geometrical description of a body is composed of the
geometrical descriptions of the parts.
General Major Conclusions for Philosophy
1) To the extent that the body is determined by its
mechanism, it acts independently of the soul.
2) Since clarity and distinctness can only be “seen” in one’s
own mind, the only path to truth is by reliance on one’s
own judgment. No need to listen to the Aristotelians or give
Authority to Aristotle!
3) Since we know and can prove using clear and distinct ideas
(mathematics!) that things can happen in no other way
than this, Pope Urban VIII is wrong. We can demonstrate
natural truths with certainty. To Mersenne, 1640: “I would
think I knew nothing in physics if I could say only how
things could be, without demonstrating that they could not
be otherwise. This is perfectly possible once one has
reduced physics to the laws of mathematics.”