The Scientific Revolution saw major changes in how science was approached and natural philosophy was studied. Key figures like Copernicus, Kepler, Galileo and Descartes established a more mathematical and empirically-based approach focused on experimentation and observation over philosophical speculation. Newton built on this work in his Philosophiae Naturalis Principia Mathematica, formulating the laws of motion and universal gravitation that came to dominate scientists' views of the physical universe for centuries.

1. The Scientific
Revolution
Kepler, Galileo,
Descartes, and Newton

2. • -Individuals, such as Nicholas
Copernicus, began to use mathematical
calculations to reveal how the world,
and other planets ought to move.
• Copernicus, paving the way for all
future astronomers, argued that his
calculations must be physically true.
• He offered abstract mathematical
arguments to support his claims
regarding natural philosophy

3. Kepler
• Johannes Kepler was a German mathematician, astronomer, and astrologer.
• - A key figure in the 17th century scientific revolution, he is best known for
his laws of planetary motion, These works also provided one of the
foundations for Isaac Newton's theory of universal gravitation.
• - As a convinced Copernican, Kepler was able to defend the new system on
different fronts:
1. against the old astronomers who still sustained the system of Ptolemy,
2. against the Aristotelian natural philosophers,
3. against the followers of the new “mixed system” of Tycho Brahe—
whom Kepler succeeded as Imperial Mathematician in Prague—
4. and even against the standard Copernican position according to
which the new system was to be considered merely as a computational
device and not necessarily a physical reality.

4. • - Kepler mastered, like the best scientists,
the most complicated technical issues,
especially in astronomy, but he always
emphasized his philosophical, even
theological, approach to the questions he
dealt with:
• - God manifests himself not only in the
words of the Scriptures but also in the
wonderful arrangement of the universe
and in its conformity with the human
intellect.
• - Thus, astronomy represents for Kepler,
if done philosophically, the best path to
God.

5. Scientific Realism
• Realism is a constant and integral
part of Kepler's thought, and one
which appears in sophisticated
form from the outset.
• The reason for this is that his
realism always runs parallel to his
defense of the Copernican
worldview, which appeared from
his first public pronouncements
and publications.
• Traditionally, realism more
generally is associated with any
position that endorses belief in the
reality of something.

6. • Scientific Realism is an
epistemically positive attitude
towards the outputs of scientific
investigation, regarding both
observable and unobservable
aspects of the world.
• Scientific realism also means that
to accept scientific theory is to
think that it is at least
approximately true, and that later
and more successful theories are
closer approximations of truth.

7. Instrumentalism
-Instrumentalism, on the other hand, treats science
as an instrument to explain and predict phenomena
rather than an approximation of the objective reality.
-Instrumentalism sees the focus of realism as
irrelevant and instead suggests that science is an
instrument and it should be evaluated based on how
good it can produce predictions and usable results.
-Hypotheses and scientific laws are nothing more than
“instruments” for describing and predicting
phenomena (seldom for explaining them).

8. Kepler and Realism:
• -Building off the writings of Copernicus,
Johannes Kepler argues in a similar way for
the viability of mathematical descriptions of
reality.
• - Kepler suggests that the purpose of a
hypotheses is to actually describe a physical
phenomenon.
• Kepler gives a detailed explanation of what
constitutes an astronomical hypotheses: “…
(the astronomer) promises to demonstrate
with syllogistic necessity both those
observed positions of the stars…and also, so
he hopes, those which are about to appear
in the future”

9. - With this definition Kepler presents a clear distinction
between a true astronomical hypothesis and a false one,
namely, accurate calculations and the prediction of future
phenomena.
- This allows Kepler to demarcate between astronomy and
non-astronomy, and to claim that any hypothesis that does not
meet this definition is clearly false.
- A hypothesis must “…be true in every respect” . Hypotheses
are not simply devices used to organize data, but rather they
tell us something real about the world.

10. Galileo
-Galileo Galilei 15 February 1564 – 8 January 1642), was an Italian astronomer,
physicist, engineer, philosopher, and mathematician who played a major role in the
scientific revolution during the Renaissance.
-- His contributions to observational astronomy include the telescopic confirmation
of the phases of Venus, the discovery of the four largest satellites of Jupiter (named
the Galilean moons in his honour), and the observation and analysis of sunspots.
-- Galileo's championing of heliocentrism and Copernicanism was controversial
within his lifetime, when most subscribed to either geocentrism or the Tychonic
system.
- Galileo later defended his views in Dialogue Concerning the Two Chief World
Systems, which appeared to attack Pope Urban VIII and thus alienated him and the
Jesuits, who had both supported Galileo up until this point.

11. • -The philosophical thread that runs through
Galileo's intellectual life is a strong and
increasing desire to find a new conception of
what constitutes natural philosophy and how
natural philosophy ought to be pursued.
• What Galileo accomplished by the end of his
life in 1642 was a reasonably articulated
replacement for the traditional set of
analytical concepts connected with the
Aristotelian tradition of natural philosophy.
• He offered, in place of the Aristotelian
categories, a set of mechanical concepts that
were accepted by most everyone who
afterwards developed the ‘new sciences’, and
which, in some form or another, became the
hallmark of the new philosophy.

12. • In the place of Aristotle Galileo left only
one element, corporeal matter, and a
different way of describing the
properties and motions of matter in
terms of mathematics.
• In doing so Galileo changed the
acceptable way of talking about matter
and its motion, and so ushered in the
mechanical tradition that characterizes
so much of modern science, even today.
• -. Galileo introduces an approach to the
study of nature that is centered on
mathematics.

13. •In his book The Assayer, Galileo states the following:
•“Philosophy is written in this grand book, the universe, which
stands continually open to our gaze. But the book cannot be
understood unless one first learns to comprehend the
language and read the letters in which it is composed. It is
written in the language of mathematics, and its characteristics
are triangles, circles, and other geometric figures without
which it is humanly impossible to understand a single word
of it; without these, one wanders about in a dark labyrinth.”

14. • - Rather, true knowledge is gained by
reading the book of nature. Nature,
according to Galileo, is something
which presents itself to us and is
something which can be understood
through the use of mathematics.
• - mathematics is something that is
found in nature and is the means by
which nature operates.
• - The naturalization of mathematics
allowed Galileo to legitimate sciences
which had previously been considered
of secondary importance, most notably
Galileo established mechanics as a
science.

15. Galileo and the Church
• - In late 1632, after publishing Dialogues on the Two Chief World
Systems, Galileo was ordered to go to Rome to be examined by the
Holy Office of the Inquisition.
• - Finally, in April 1633 Galileo was called before the Holy Office.
This was tantamount to a charge of heresy, and he was urged to
repent.
• -Specifically, he had been charged with teaching and defending the
Copernican doctrine that holds that the Sun is at the center of the
universe and that the earth moves.
• - Galileo was called four times for a hearing; the last was on June 21,
1633. The next day, 22 June, Galileo was taken to the church of Santa
Maria sopra Minerva, and ordered to kneel while his sentence was
read.

16. •I have been judged vehemently suspect of heresy,
that is, of having held and believed that the sun in
the centre of the universe and immoveable, and that
the earth is not at the center of same, and that it does
move. Wishing however, to remove from the minds
of your Eminences and all faithful Christians this
vehement suspicion reasonably conceived against
me, I abjure with a sincere heart and unfeigned faith,
I curse and detest the said errors and heresies, and
generally all and every error, heresy, and sect
contrary to the Holy Catholic Church. (Quoted in
Shea and Artigas 194)

17. • - Legitimacy of the content, that is, of the
condemnation of Copernicus, is much more
problematic.
• - Galileo had addressed this problem in 1615, when
he wrote his Letter to Castelli (which becomes known
as the Letter to the Grand Duchess Christina).
• - In this letter he had argued that, of course, the Bible
was an inspired text, yet two truths could not
contradict one another.
• - So in cases where it was known that science had
achieved a true result, the Bible ought to be
interpreted in such a way that makes it compatible
with this truth.
• - The Bible, he argued, was an historical document
written for common people at an historical time, and
it had to be written in language that would make
sense to them and lead them towards the true
religion.

18. Rene Descartes
• René Descartes was a French philosopher,
mathematician, and scientist.
• He has been dubbed the father of modern
philosophy, and much subsequent Western
philosophy is a response to his writings,
which are studied closely to this day.
• Descartes's influence in mathematics is
equally apparent; the Cartesian coordinate
system
• -Rene Descartes, building off of Galileo,
sought to establish what he called the
“mathesis universalis,” or the universal
mathematics.

19. • The reason for basing all sciences on
mathematics is simple, Descartes states that
“Of all the sciences so far discovered,
arithmetic and geometry alone are, as we have
said above, free from the taint of falsity or
uncertainty” .
• - Descartes claims that mathematics alone
arises from pure and simple “intuition,” that
is, mathematical propositions are not derived
from sense experience, which is subject to
interpretation.
• The combining of arithmetic and algebra with
geometry, by demonstrating a direct
correlation with the numbers used in the
former with the figures in the later, resulted in
what Descartes called “analytical geometry”.

20. • - By linking arithmetic and algebra with geometry Descartes was able to formulate
a mathematical way of describing space.
• - To use the words of E.A. Burtt, “He perceived that the very nature of space or
extension was such that its relations, however complicated, must always be
expressible in algebraic formulae…”
• - Descartes speculations concerning the nature of matter and extension lead him to
posit his famous vortex theory.
• - The implication of Descartes statement is that motion and rest are inherent
qualities of matter itself. An object moves because God has created that object to
move. This statement also excludes the existence of a vacuum.
• - Space consists of a fine matter that Descartes refers to as “ether”. The universe is
essentially “full” of matter and an object moving through space is communicating
this property of motion through the impact of the object against other matter.

21. Isaac Newton
• -Sir Isaac Newton 25 December
1642 – 20 March 1726 was an
English physicist and
mathematician who is widely
recognized as one of the most
influential scientists of all time and
as a key figure in the scientific
revolution.
• -His book ("Mathematical
Principles of Natural Philosophy"),
first published in 1687, laid the
foundations for classical mechanics.
Newton made seminal
contributions to optics, and he
shares credit with Gottfried Leibniz
for the development of calculus.

22. • -Newton's Principia formulated the laws
of motion and universal gravitation,
which dominated scientists' view of the
physical universe for the next three
centuries.
• -By deriving Kepler's laws of planetary
motion from his mathematical
description of gravity, and then using
the same principles to account for the
trajectories of comets, the tides, the
precession of the equinoxes, and other
phenomena, Newton removed the last
doubts about the validity of the
heliocentric model of the Solar System.
• - This work also demonstrated that the
motion of objects on Earth and of
celestial bodies could be described by
the same principles.

23. Principia
• -In Book I of Principia, Newton opened with definitions and the
three laws of motion now known as Newton's laws.
• 1. (Law of inertia): A body at rest remains at rest and a body in
motion continues to move at a constant velocity unless acted upon
by an external force.
• 2. A force F acting on a body gives it an acceleration a which is in
the direction of the force and has magnitude inversely proportional
to the mass m of the body: .
• 3. Whenever a body exerts a force on another body, the latter exerts
a force of equal magnitude and opposite direction on the former.
This is known as the weak law of action and reaction.

24. • -Book II presented Newton's new scientific philosophy which came to replace
Cartesianism.
• -When Newton wrote the Principia between 1684 and 1686, he was not contributing to a
preexisting field of study called mathematical physics; he was attempting to show how
philosophers could employ various mathematical and experimental methods in order to
reach conclusions about nature, especially about the motions of material bodies.
• -These rules were stated in the Principia and proposed that
• (1) we are to admit no more causes of natural things such as are both true and sufficient to
explain their appearances,
• (2) the same natural effects must be assigned to the same causes,
• (3) qualities of bodies are to be esteemed as universal,
• and (4) propositions deduced from observation of phenomena should be viewed as
accurate until other phenomena contradict them.

25. • "As in mathematics, so in natural philosophy the investigation of
difficult things by the method of analysis ought ever to precede the
method of composition. This analysis consists of making
experiments and observations, and in drawing general conclusions
from them by induction...by this way of analysis we may proceed
from compounds to ingredients, and from motions to the forces
producing them; and in general from effects to their causes, and
from particular causes to more general ones till the argument end in
the most general. This is the method of analysis: and the synthesis
consists in assuming the causes discovered and established as
principles, and by them explaining the phenomena preceding from
them, and proving the explanations."