History of Science - Study Guide - Outline - Origins to Newton - Dr Robert A. Hatch
H  I  S  T  O  R  Y     O  F     S  C  I  E  N  C  E
Dr Robert A. Hatch  -  University of Florida


I. 'Pre-Scientific' Thought:
A. Frankfort's view of myth:
1. A subjective mode of explanation/description of Nature, based on an 'I-Thou' intimacy with Nature; hence, a highly individual approach to phenomena concentrating on specific aspects rather than general patterns.
a. This approach was decisively overturned by the Pre-Socratics who developed a supposedly objective 'I-It' relation with Nature.
B. Giorgio de Santillana's view of myth:
1. Many myths seem global in character, indicating that, in spite of vast geographical separation, various cultures were attempting to explain a 'shared experience'.
a. This shared experience was a comprehension of large cosmic events such as the precession of the equinoxes.

b. The capability of 'primitive' cultures to comprehend such events is indicated, if Gerald Hawkins is right, by Stonehenge.

II. Egyptians and Babylonians:
A. Mathematics
1. The Egyptians seem to have been quite primitive in arithmetic, depending on the method of duplication both for multiplication and division. Moreover, by insisting on expressing complex fractions in unit-fraction series, they had no capability of dealing effectively with fractional computation. Geometry was perhaps more sophisticated in Egypt but was still at a crude level according to our evidence.
a. The Egyptians were individual-problem oriented. They made no apparent attempt to derive general cases, theorems, or proofs.
2. The Babylonians, because of their sexagesimal computational system (with its Place-Value Notation) as well as their simple, two-symbol numbering system, were so adept at arithmetical procedures as to be able to solve types of quadratic, quartic, etc., equations. Consequently geometry was not well developed.
a. The Babylonians do appear to have initiated a case-study approach to arithmetic by discussing general problems, but they did not develop a systematic approach like that of the Greeks.
B. Astronomy:
1. Egyptian astronomy was generally primitive except for a reasonably sophisticated emphasis on calendrics and subsequent attempts to reconcile solar and lunar cycles. The Egyptians developed the 365 day year as well as the 24 hour day.

2. Babylonian astronomy was more moon-oriented than Egyptian astronomy and was consequently more involved with eclipse cycles, etc. Through totally arithmetic means the Babylonians were able to construct tables which demonstrated a recognition of recurring, patterned variations (for example, the zig-zag function).

a. The Babylonians did not, however, develop any known cosmological model to systematize their observations or derived tables.
C. Medicine:
1. Both the Egyptians and Babylonians, at least in the early stages, seem to have been empirical in their approach to surgery and pharmacological lore. However, the later Babylonians (that is, Assyrians) tended to combine medicine more and more with the abstract "science" of astrology.
III. The Greeks:
A. Metaphysics--the search for ultimate Being or Reality:
1. From Thales onward the Greeks tended increasingly toward metaphysical and physical speculation. Metaphysically the search was for a general, eternal principle (for example, the 'stuff' --physis-- or the 'order'-- logos) underlying the universe. Physically the search was for logical, causal explanations of natural phenomena within the given metaphysical framework.

2. Plato and Aristotle--the two most influential Greek philosophers:

a. Plato, in his quest for a coherent metaphysics, relied on the eternal Forms as the ultimate basis of reality. Thus, geometry was a perfect example of a real science involved with real entities (perfect, changeless circles, triangles, etc. ). In terms of our comprehension of things, the Forms are irrevocably implanted in our minds, so that we are able to recognize things by their similarity, however imperfect, to those perfect Forms. Hence, we recognize various "species" by their similarity to the universal Forms.

b. Aristotle, on the other hand, accepted the reality of the world as it appears here and now. For him it was only the combination of Form and Matter that gave reality (actuality) to things. Furthermore, as evidenced by his view of causality, Aristotle, unlike Plato, accepted the notion of process or change as a genuine feature of Nature. Our knowledge of forms is not prior (implanted) but comes from inductive abstraction of similarities from similar classes of things.

B. Astronomy--tendency toward conceptual models:
1. Problems encountered and described/explained:
a. Daily (diurnal) motion.

b. Periodic planetary, lunar, and solar motions in opposite direction to daily motion.

c. Retrograde motion.

d. Apparent changes in velocity.

e. Other, more subtle irregularities and long-term periodicities in various orbital motions.

2. Basic assumptions behind Greek astronomy:
a. Geocentricity (geocentric and geostatic):
1. Assumed basically because Greek physics, with no notion of inertia, could hardly deal effectively within the framework of a moving-earth system.
b. The notion of perfect circular motion, or compound circular motion, around a central point.

c. The Cosmos is finite.

3. Eudoxean system--further refined and modified by Aristotle:
a. System of nested, concentric spheres rotating in such a way as to account, through compounded motions, for gross orbital appearances.
1. One fatal flaw in this concentric sphere system was its inability to account for obvious variations in distance between Earth and various planets (indicated by increasing and decreasing apparent size and brightness).
4. Ptolemaic system--based on Hipparchus:
a. System of Deferents, Epicycles, and Equants, all in varying sizes and velocities depending on the complexity and irregularity of various planetary orbits (for example, the sun's orbit was simple whereas Mercury's was quite complex, calling for added circular motions to account for the high irregularity).

b. The Ptolemaic system was mathematically more accurate and was thus ultimately more acceptable to astronomers than the Eudoxean/Aristotelian model. Nonetheless, Aristotle's system prevailed up to the 17th century for the common understanding of the cosmos.

C. Aristotelian Physics:
1. Basic Notions:
a. Natural Place, Natural Motion, and Violent Motion.

b. Four Elements: Earth, Water, Air, Fire (and the Fifth Essence: Aether).

c. Change, Motion, and Growth are all aspects of the same thing--that is, the actualization of the potential or, in terms of the four causes, the attaining of something to its Final Cause by the proper meshing of the Formal and Material Causes (Form + Matter) through the agency of the necessary Efficient Cause.

1. In terms of actual motion Aristotle believed the velocity of any object in motion was contingent on the force of propulsion as well as the resistance of the medium traversed.  Thus:   V = F/R
a. From this it is obvious that velocity in a void (where R = 0) would be infinite. Hence, the existence of void is impossible.

b. The 'equation' is not universal because it does not hold in cases where R exceeds F.

c. Moreover, in violent (projectile) motion it is necessary that there be a continually active propulsive force (Efficient Cause) to counteract the constant tendency of the body to seek its natural place.

D. Mathematics:
1. The Pythagoreans, steeped in number mysticism, were metaphysically rooted in number atomism.

2. However, the discovery of the irrationality of 2 (what G. de Santillana calls "the crisis of the irrational") forced the Greeks to abandon the Pythagoreans' arithmetical analysis of nature in favor of geometry.

a. This was aided by the development of a critical attitude toward logic fostered by the Eleatics and carried forward by Aristotle.
3. Thus, mathematics became a matter of developing a logical, axiomatic system of universal geometrical proofs or theorems. This was carried even into what we would consider purely arithmetical realms such as the study of ratios (fractions).
a. Development of methodologies:
1. Analysis and Synthesis
2. Method of Exhaustion
b. Hence, Euclid's Elements, as a textbook treatment of geometry, was merely a logical compilation of theorems, many of which were developed and proven by earlier mathematicians such as Eudoxus.
4. In short, geometry became paramount in Greek thinking, governing not only mathematical thought but astronomical model building that emerged with Eudoxus, Aristotle, and Ptolemy in particular.
E. Medicine:
1. Hippocratic Corpus (ca. 400 B.C.): tendency toward:
a. Theory of the four Humors; disease was considered an imbalance in distribution--notion of disharmony as root of illness.

b. Clinical diagnosis and prognosis.

2. Dogmatists--Alexandria (Hellenistic period):
a. 'A reasoned theory of medicine'--overriding theoretical principles to explain diseases and facilitate cures.
3. Empiricists--Alexandria (Hellenistic period):
a. More 'clinically' oriented than the Dogmatists.
4. Galen--tended toward Dogmatism in medical explanation.
a. Comparative anatomy through animal dissections.

b. Physiology of three Spirits (pneuma) carried by the ebb and flow of venoarterial system.

F. Biology:
1. Aristotle--founded Lyceum in Athens ca. 335 B.C.
a. The Lyceum, for 2 generations after Aristotle, became an important center of biological (as well as physical) investigations until its transfer to the Museum of Alexandria.

b. Emphasis on observation--actual dissection and controlled 'experimental' investigations.

c. Taxonomy--attempts at classifications according to 'species' and 'genus' determined by certain 'class' characteristics (like 'red-blooded' and 'non-red-blooded').

1. Notion of Life as a 'great chain of being' graduating from less to the more 'vital' (for example, Plants--Animals).

2. Theophrastus (student of Aristotle)--Continuation of Lyceum and its investigatory goals, especially in Botany.


I.  Alexandrian-Hellenistic Science
A.  The Museum of Alexandria and the institutionalization of knowledge.
1.  Center of Classical research which provided the beginnings of institutional science.

2.  Emphasis placed on scholarship and textual criticism.

3.  Strong neo-platonic bent (that is, more mystical interpretation of Plato)

4.  Important scientific thinkers.

a.  Ptolemy:  synthesis of mathematical-observational astronomy.

b.  Diophantus:  development of algebra.

c.  Galen:  medical thought, anatomy, physiology.

II.  Roman Science
A.  A rather superficial record-keeping encyclopedic tradition (Pliny, Seneca, Boethius, Varro, etc.).

B.  A dilettantish approach to Greek science among the elite, typified by handbooks dealing only with the product of Greek inquiry; emphasis on rhetoric.

C.  Lack of original scientific-philosophic though.

D.  Some translations to Latin of Greek mathematics and Aristotelian metaphysics (Boethius).

E.  Emphasis was on technology:  aqueducts, water wheel (Vitruvius), military applications, agriculture.

F.  Apparently no conscious decision to apply scientific thought and knowledge to social problems accompanied this technology.

III.  Science in the Arabic World
A.  Arabic Science:  intelligent continuation of the Greek model.
1.  Unlike Alexandrian science, tendency was toward Aristotle.

2.  Major efforts:  medicine, mathematics, and astronomy, refinement of uses of algebra.

3.  Major contribution of Arabs was transmission of Aristotelian corpus to Christian West.

B.Translation of Greek Science.
1. Before 900 A.D., basically a period of translating activity rather than original thought.

2. School at Jundishapur, founded 428 by Christians; originally a medical school; in the sixth century became a center for translation of Greek works.

3. Hunayn ibn Ishaq (c. 850): translations of Galen, Ptolemy's astronomy, Euclid's geometry, other technical treatises.

C.  Mathematics.
1. Major Islamic interest was algebra, with some trigonometry and geometry.

2. Used Babylonian and Greek sources, especially Diophantus and Euclid.

3. 6th c. Hindu mathematical sources: Suddhanta, Aryabbata; "Arabic" numerals were introduced from India.

4. al-Khwarizmi (early 9th c.): began process of algebraization (al-jabr), introduced Indian mathematics to Arabic world.

D.   Astronomy.
1. Observatory at Baghdad established 9th c. (Thabit ibn Quarra).

2. Astronomical observations carried out at Samarkand; astronomical tables compiled.

3. Moorish Spain was also a center of astronomical studies.

4. Islam elaborated and revised Ptolemaic astronomy and compiled new astronomical tables. Astrology was closely tied to astronomy, alchemy to astrological-astronomical interests.

E.   Medicine.
1. Al-Razi (Rhazes), ca. 900: comprehensive medical treatises.

2. Avicenna: Canon on medicine. Commentaries on Aristotle and Plato.

3. Al-Jabir (Geber), late 8th-early 9th c.: medical works and alchemy.

4. Ibn Nafis (13th c.): Could not find Galen's septa in the heart and proposed another scheme for circulation of the blood.

5. Alchemy was also connected to medicine.

F.   Alchemy.
1. Islam took over the alchemical tradition from the laboratories at Alexandria.

2. Hermes Trismegistes: supposed author of a body of mystical-alchemical writings, identified with the Egyptian god Mercury (Hermes; Thoth; Moses); gave rise to the Hermetic tradition in alchemy.

3. The mystical philosophy of "all is one" led to attempts to transmute one substance to another, especially to gold; also the four-element theory of the Greeks allowed for the transformation of one element to another, or differing combinations of the elements.

4. Alchemy also represents a philosophic search for interrelatedness, unity, coherence .

5. Idea of an elixir, a magical medicine that would cure anything and everything.

6. The period from 900-1100 was one of writing commentaries with little original thought, as compared to the earlier period which emphasized translation alone; Averroes (12th c.) the Commentator on Aristotle, added neo-Platonic elements to Aristotelian thought; but in general Arabic sciences tended to concentrate on aspects of Greek learning that were of practical value, especially mathematics, astronomy, medicine.

IV. Ancient, Medieval, and Renaissance Technology
A.   Technological development remained largely independent of science until the l9th century.

B.   Early Technology.

1. Developed at a much earlier date than the philosophical speculation of the classical world.

2. Broad scope of technological development involving increasingly sophisticated processes; for example, metallurgical art for tools, weapons, and objects of art.

3. Generated an artisian-craftsman class which would not come to any semblance of power until the late middle ages.

C.   Greco-Roman Technology: The Question of Power.
1. Greek approach: mechanistic inventions were not connected as a power source; technological speculation was not directed to practical applications, for example, Hero of Alexandria's "toy" steam engine.

2. Roman approach: practicality becomes the dominate factor in attempts to devise new power sources. This new approach would continue into the Christian West with certain social, religious, and technical developments which, it is argued, brought about the Renaissance search for power through technology.

D.   Medieval Technology: The Feudal-Manorial System.
1. Period of innovation extending from 6th-9th centuries with general application 1 1 th- 1 2th centuries.
a. Agricultural innovations: iron plough, 3-field rotational system, harnessed horsepower, etc.

b. Military innovations: use of the horse, hardened iron, stirrups, etc.

2. Attitude change occasioned by technological innovation and Christian theology.
a. Development of a manipulative and dominating attitude toward nature with respect given to the ethic of hard work.

b. Monastic combination of the ideal of meditation and labor, for example, the Benedictine rule.

E.   Renaissance Technology: The Search for Power.
1. Renewed appreciation of and search for mechanical power.

2. Greater diversification of approaches to and control of the natural world, for example, clock mechanisms, printing, and resulting psychological changes.

V.   Scholasticism & Medieval Universities
A.   Philosophy.
1. Until the 12th century, medieval philosophy was basically neo-Platonic, loosely reconciled with Christian theology.
a. Patristic doctrines of late Roman period: Tertullian, St. Augustine; philosophy regarded as subservient to theology.

b. Boethius (late 5th to early 6th c.): translations and commentaries on Aristotle's logical works; Consolation of Philosophy.

2. During the 12th century Aristotle's natural philosophy was transmitted from the Islamic World.
a. Spain became a center of translation from Arabic to Latin, especially at Toledo by Gerard of Cremona.

b. Aristotle was incorporated into the medieval philosophical-theological tradition, especially in the writings of Thomas Aquinas.

3. The problem of Universals: Do abstract qualities or essences associated with groups of individuals have existence outside of material things? Rosellinus (Roscelin), early 12th c.; William of Champeaux, early 12th c.; Peter Abelard, 12th c.

4. William of Occam (early 14th c.): Nominalism: only individual, material objects can be known; the mind cannot abstract essences from a material thing. There is no such thing as a Universal: the essential tenet of Nominalism.

5. The Scholastic tradition.

a. Characterized by logical debates and presentations, using a method of contrast, similar to that established by Abelard's Sic et Non.

b. Based largely on Aristotle.

c. A very structured, logical, textual approach to questions of natural philosophy, rather than an approach to Nature itself.

B.   Medieval Universities.
1. The Universities grew out of the late 11th century.

2. Church organization of the medieval universities (Aristotle; Christian theology; Latin discourse; uniform curriculum) provided a high degree of standardization and allowed mobility from one university to another for teachers and students.

3. 'Undergraduate' curriculum centered on the Seven Liberal Arts.

a. Trivium (verbal): grammar, rhetoric, logic.

b. Quadrivium (mathematical): arithmetic, geometry, astronomy, music.

c. Logic and natural philosophy were Aristotelian, geometry was Euclidean, astronomy was Ptolemaic (or simplified by Sacrobosco)

4. The Universities originated as professional training centers.
a. Salerno (the first university): Medicine.

b. Bologna: Law.

c. Paris (arose from the cathedral school): Theology.

d. Oxford (especially Merton College): Mathematics.

e. Oxford and Paris became the leading European universities.

VI. Medieval Physics: General
A.   The science of motion is the core of medieval physical thought.
1. Worked within the classical framework of a logical qualitative approach to mechanical problems, especially the approach suggested by Aristotle.

2. Sought to clarify the formulation of problems surrounding motion such that questions could be posed and answered.

3. Primarily a logical exercise in mechanics with little empirical investigation.

4. Argument by analogy from theology and philosophy.

B.   Medieval dynamics and Impetus theory.
1. Weak point of Aristotelian science was its discussion of motion, for example, the necessity of a constant, external agent to account for motion.

2. Medieval discussion of dynamics centered on this problem of the cause of motion and its expression in terms of impetus.

C.  11th to 13th Centuries.
1. Confined to translation of, and commentaries on, Aristotelian works.

2. Most of Aristotle's physical concepts accepted without serious criticism.

3. Thomas Aquinas baptized Aristotelian cosmology into Christian framework.

D.   14th Century Scholastics.
1. Critical approach to Aristotle.

2. Preoccupied with logic of terms and propositions, that is:

a. What does Aristotle mean when he says that the velocity of a moving object is directly proportional to the force and inversely proportional to the resistance?

b. Is this law or proposition logically valid?

3. Debated idea of matter and form. Questions include:
a. Does Aristotle's forms (or essences) have existence independent of the imagination?
1. Nominalists, against Aristotelians and Platonists, argued in the negative. Forms are only a product of the imagination.

2. Above position has been interpreted as the shift from the idea that science should look for the 'nature' of things (that is, essence) to the idea that science is a discipline whereby one talks or writes about natural phenomena more accurately (that is, the linguistic study of scientific propositions to determine their logical validity).

b. Is the intention and remission of forms (the change in intensity of such qualities as heat, motion, faith, goodness, etc. ) a fluent form of a flux of forms?
1. Notice that motion is thought of as a quality.

2. Flux of forms = idea of change as a series of states.

3.   Fluent form = idea of change as a state in its own right.

E.   Scholasticism and Medieval Physics.
1. Scholastic preoccupation with terms led to classification of physics into kinematics and dynamics.
a. Kinematics: descriptive (quantitative) account of motion apart from its causes.

b. Dynamics: causal (qualitative) account of motion.

2. Dynamics and the concept of Impetus: Jean Buridan.
a. Aristotle's Physics stated that a continuous external agent was required. (All motion requires a mover.)

b. Buridan argued that motion could be better explained by the idea of an original impetus imparted on a projectile.

1. Idea similar to that of John Philoponus (600 A.D.).

2. Impetus, once imparted on a projectile, keeps it in motion.

3. Decrease in acceleration explained by decrease of strength of impetus owing to resistance of the medium.

4. Is concept of impetus similar to modern concept of inertia?

c. Buridan further speculated that God may have impressed an original impetus on the celestial spheres which, once imparted, kept the spheres in continuous motion since there is no resistance in the heavens to sap the strength of the originally imparted impetus.

d. Possible implications of Buridan's speculations:

1. Would make unnecessary the supposition that the celestial bodies were made of a special element (that is, Aristotle's quintessence or fifth element) which could move only with circular motion.

2. Could rid heavens of the spirits and intelligences which Aristotle introduced to account for the sphere's movements. (More mechanical view of the universe?)

3. Made less distinct the Aristotelian dichotomy between terrestrial and celestial physics. Motion on earth and heavens could be accounted for by the same idea.

a. Celestial: impetus + no resistance = uniform continuous motion. (However, does not explain circular motion.)

b. Terrestrial: impetus + resistance accounts for acceleration and deceleration of motion on earth.

3. Medieval Kinematics.
a. Attempted clarification of concepts of velocity, resistance, etc.

b. Classification of different kinds of motion.

1. Uniform motion.

2. Diform motion (accelerated motion).

3. Uniform diform motion (uniformly accelerated motion).

4.  Diform diform motion (nonuniform accelerated motion).

c. Debate concerning motion as a flux of forms or as a fluent form.
1. Occam (Ockham): motion is a flux of forms (series of states).

2. Others argued that motion was a fluent form (that is, a state).

d. Consideration of motion as a state in itself rather than a series of integral states made possible speculation on the relations between various factors involved in motion. Whereas Aristotle had preferred to compare speeds to speeds, forces to forces, and resistances to resistances, scholastics like Buridan, Thomas Bradwardine, and Nicole Oresme attempted to make explicit statements on the relationship between all of these factors.
1.  Thomas Bradwardine: Attempted what seems to be one of the earliest efforts to use algebraic functions to describe motion; to show how the dependent variable, v (velocity) was related to the two independent variables: f (force) and r (resistance). Although the function he came up with was incorrect, Bradwardine had formulated the Aristotelian 'law of motion' metrically as a function so that it could be quantitatively refuted.

2.  Nicole Oresme: Attacked the problem of accelerated motion (and variation of other 'qualities') by graphic constructions. Treatment of kinematic problems (as with Bradwardine) were posed as imaginary possibilities for theoretical analysis and without empirical application.

e.  Discussion of motion by scholastics was part of much more general debate (the intension and remission of forms).
1. Essentially logical exercises.

2. No application of theories to practical situations.

3. Could not break out of Aristotelian framework.

VII.   Medieval Astronomy
A.  Amalgamation of Classical Conceptions of the Heavens.
1. Aristotelian system: provided a spherical, physical model compatible with medieval physics.
a. Earth conceived as a material point at center of concentric, quintessential spheres.

b. Idea of quintessential spheres was later replaced by common concept of solid, transparent crystalline spheres.

c. Superimposed spheres account for perfect, circular motion.

2. Ptolemaic view: provided a nonobservational, mathematical model which would 'save the phenomena' or 'save the appearances'.
a. The mathematical treatment of Ptolemy gave a better description than the Aristotelian model.

b. Ptolemaic system was used by professional, mathematical astronomers rather than the Aristotelian, cosmological model.

B.  Medieval Approach to Astronomy.
1. Popularization and extension of the Ptolemaic, computational tables coupled with an attempt to refine Ptolemy.

2. Aristotelian metaphysical approach was combined with Christian theology which gave the medieval world a comprehensive cosmological picture, for example, Aquinas and Dante.

3. Revival of a mystical, Platonic approach in the 15th century.

a. Platonic-Pythagorean doctrines of order, harmony, simplicity, balance, proportion, etc. were more in conformity with Ptolemaic geometrical model than Aristotelian cosmology.

b. Revival of Platonism in the late middle ages and Renaissance provided alternate cosmological system for those thinkers dissatisfied with the inconsistencies and predictive limitations of the Aristotelian cosmos.

Dr Robert A. Hatch  -  University of Florida

I. Astronomy/Physics:

A. Copernicus: Bequeathed the problem of explaining away Aristotelian physics in moving earth system.  The problem, as Galileo later stated it, was to 'move the earth without a thousand inconveniences.'

B. Kepler:

1. Creative but ineffectual stab at explaining planetary system via 'magnetic' physics --notion of local gravity; 'magnetic' force of sun pulling planets around in coaxial orbits.

2. Three Laws: a. Ellipses: The planets move on elliptical paths.

b. Areas: A radius vector from the sun to a planet sweeps out equal areas in equal times.

c. Periods: For any two planets, the times squared are proportion to the cube of the mean distance from the sun.

C. Galileo: Fundamental solution of Copernican problem.
1. Circular Inertia.

2. Free-Fall; uniformly accelerated motion.

3. Nature is fundamentally mathematical. II. Metaphysics/Epistemology:

II.  Metaphysics/Epistemology:
A. Skepticism:
1. Reformation/Counter-Reformation debate - theological skepticism.

2. General anti-scholastic/anti-Aristotelian sentiment stemming partly from Humanism and partly from introduction of Neo-Platonic/Hermetic corpus.

3. Revival of ancient 'Empirical' skepticism through new translations of works of Pyrrho--'Pyrrhonist' skepticism (for example, Montaigne).

B. Two essential outcomes of skeptical movement:
1. 'Constructive Skepticism' -  Descartes: 
a. Deny everything until you can no longer deny: 
1. Therefore, I am;

2. Therefore, God is, and is perfect, not a deceiver;

3. Therefore, the world is real, and reality is characterized and known by its clearness and distinctness.  (What is clear and distinct about reality?  Its geometricity.)

4. Therefore, the world is really only matter (EXTENSION) and motion.

b. Mathematics, as a perfect science, becomes the guideline for Descartes' thinking, causing his search for explanations in terms equaling the clarity and distinctness of mathematical proof.
1. Thus his physics, physiology, etc., were necessarily highly deductive; induction serves only a minor function in giving initial grounds for deduction.

2. Mechanism:

a. Vortices:
1. Three 'elements' -- a modified form of corpuscular atomism.

2. Animals are machines.

3. Mind/Body dualism in man.

c. Thus Descartes leaves a vast legacy of mechanistic physics to his disciples--Cartesians--who flourish throughout the 17th century and into the first half of the 18th.
2. 'Phenomenalist/Positivist' Reaction:
a. Search for some hypothetical model that is not necessarily metaphysically true but that is totally functional/fruitful for science or general knowledge.

b. Atomism: Space-Matter dichotomy:

1. Conducive to the kinematic analysis of Nature.

2. Mathematically oriented in terms of physical explanation.

3. 'Mechanical Philosophy.'

III. Methodology:
A. Hermetism:
1. Alchemy--kitchen recipe approach to chemistry with heavy mystical overtones.
a. In practical terms, however, it was highly empirical with constant 'laboratory' testing of chemical combinations and distillations.
1. Consequent development of various assaying techniques, invention of nitric acid in 16th century, etc.

2. Natural Magic: Manipulation of Nature, not so much by mystical as by practical means. Man becomes master of Nature and approaches divinity.

B. Anti-Aristotelian Sentiment:
1. Invective by men like Peter Ramus who felt that Aristotelian methodology was totally sterile--attempts to devise new and better methodologies.
a. This sort of attitude was reflected in alchemists like Agrippa and Paracelsus who extolled practical experience over book-learning.
C. Francis Bacon:
1. Spokesman and symbol for Experimentation (inductive)--probable roots in the Natural Magic tradition.

2. Utilitarianism: Science must be beneficial to society--ideal of progress.

3. Thus Bacon's methodology, though simple, was conceived to be totally new and anti-Aristotelian.

D. Scientific Societies:
1. 'Institutionalization' of science within various scientific societies, especially the Royal Society, which claimed Baconian roots.

2. Establishment of learned journals (for example, Philosophical Transactions of the Royal Society (London 1665) and Journal des Scavans (Paris 1665) served to disseminate knowledge and determine scientific priority.

Dr Robert A. Hatch  -  University of Florida

I.  Nicolas Copernicus (1473-1543)

A. Astronomical Background.
1. Ptolemaic astronomy, within the general framework of Aristotelian physics, dominated contemporary astronomical thought--a mathematical, nonobservational approach concerned with 'saving the phenomena'.

2. Basic premises of ancient astronomy:

a. Geostatic and geocentric cosmos.
b. Celestial bodies possess uniform, circular motion around a central point.
c. Celestial bodies are composed of a fifth element, the quintessence.
d. The cosmos is finite.
3. Difficulty developed concerning the Ptolemaic use of the equant, which violated the aesthetic concept of uniform motion, and the use of epicycles, which put the center of motion on a geometric point other than a center of a deferent.

4. Primary weakness of the existing Ptolemaic schema: it did not entirely "save the phenomena," that is, observational-theoretical discrepancies had become apparent.

B. The Copernican System.
1. Introduced three celestial motions.
a. Diurnal rotation of the earth on its axis.
b. The earth, and the planets, revolve around the sun.
c. A conical axial motion of earth to explain the fixed orientation of earth in space.
2. Copernicus was a mathematical, not an observational, astronomer, and the mathematical apparatus of his system was as complex as Ptolemy's, employing the same geometrical devices (except the equant).

3. Copernicus sought to purify ancient astronomy, not to overthrow Ptolemy; not a 'revolution' in the technical sense, in that either system would 'save the phenomena' to some degree; the Copernican system only altered the geostatic and geocentric premise of ancient astronomy.

4. Copernican advantages were limited to a somewhat simpler computational technique and the introduction of a more intelligible order in the heavens, for example, removal of the ad hoc constructions needed to describe retrograde motion and the ordering of planets.

5. The main disadvantage of the Copernican system was its violation of Aristotelian physics--the physical problems involved with the heliocentric system called for a new, as yet nonexistent, physics.

C. Motivation for the Copernican System.
1. Copernicus was educated at Cracow and Bologna in a critical atmosphere that called for the reform of Ptolemaic astronomy and cosmology.
2. Renaissance Platonic-Pythagorean influences stressed unity, coherence, and harmony in the cosmos in addition to accounting for observed phenomena.
D. The Copernican 'Revolution'
1. A 'revolution' inadvertently, in that Copernicus was a conservative who sought to purify, not destroy, ancient astronomy.

2. Its revolutionary aspect lay in its violation of Aristotelian physics and the implicit requirement of a 'new' physics which caused natural philosophers to think, and look, in a new astronomical frame of reference.

II. Johannes Kepler (1571-1630)
A. Background of Keplerian Astronomy.
1. Platonic and Pythagorean elements, especially a mystical sense of mathematical harmony in the cosmos, for example, the use of the five regular polyhedra to account for the planetary orbits, The Cosmographic Mystery (1596).

2. The heliocentric Copernican cosmos with uniform circular motion.

3. The mechanical ideas of the Renaissance, particularly "clockwork" as a suggestive conceptual model for celestial physics.

4. Existence of 'powers' such as magnetism and light which could be used to account for the physical force necessary to drive the celestial machine.

5. Kepler was a highly competent mathematician.

B. Kepler and the Tychonic System.
1. Brahe provided Kepler with the best collection of observational (empirical) data in existence.

2. He set Kepler to work on the problem of the orbit of Mars, that is, the planet's nonuniform motion with respect to the center of its orbit:

a. Disregarded the use of equants and epicycles as a solution.
b. Formulated the Area Law: in equal time intervals a planet will sweep out equal areas (Second Law).
c. Kepler settled on the ellipse as an orbital path, that is, planetary orbits are elliptical (First Law).
C. Synopsis of Keplerian Astronomy.
1. A nonempirical, mathematical commitment to the area law and the geometrical cosmos of elliptical orbits--the data were observational but the commitment was philosophical.

2. Introduced a type of 'physical' unity, that is, a solar 'power' or 'virtue' moves the planets in their orbits.

3. The account of elliptical orbits was based on the assumption that the sun and the planets were magnets, an action between "animate souls" which served to attract, or be attracted by, the sun thus drawing the planets into elliptical paths.

4. No quantitative elements have been introduced--a qualitative analysis expressed in terms of mathematical harmonies, for example, the square of a planetary period is proportional to the planet's mean distance from the sun, T [squared] is proportional R [cubed] (Kepler's Third Law ).

5. Kepler thought he had penetrated the structural reality of the cosmos and in so doing, was forced to seek a 'new' celestial physics.

III.  Galileo Galilei (1564-1642)

A. Intellectual Roots of Galileo's Science.
1. Copernican astronomy and the implicit necessity of a 'new' physics to replace Aristotelian mechanics.

2. A long tradition in mechanics extending from the ancient world and middle ages through the Renaissance (for example, Aristotle, Philoponus, Avempace, the Merton and Parisian schools, Padua), and especially the works of Archimedes.

B. Galileo and Astronomy.
1. Galileo was a confirmed Copernican and given to the concept of circular motion.

2. Galileo wrote for a literate but nontechnical reader in his defense of Copernicus, and not as a professional astronomer--his arguments and evidence were polemical and perhaps propagandistic.

3. Galileo's 'facts' differed from the traditional data of astronomy in that they were derived from qualitative telescopic observations.

4. Observational data obtained with the telescope:

a. Stellar 'population explosion' implying an expanded cosmos.
b. The topography of the moon was similar to, or more pronounced than, that of the earth; the earth-like moon moves around the earth--why can't the earth move around the sun?
c. The phases of Venus were inexplicable in terms of Ptolemaic cosmology; Ptolemaic scheme no longer viable.
d. The satellites of Jupiter, moving with, and approximately in the same plane as the planet, suggested more than one center of rotation in the solar system and, by analogy, the earth's rotation around the sun.
e. Sun spots implied that the heavens are not perfect (to reinforce the argument of the moon's topography); these data were obviously unknown to Aristotle or Ptolemy.
C. The Problem of Falling Bodies.
1. His early work in the 1 590s dealt with falling bodies as a problem in dynamics approached in terms of the self-expending impetus theory of Oresme and Avempace, V is proportional to W-R.

2. Inspired by Archimedes and Benedetti, Galileo used hydrostatics as a model for his science.

3. In his later work, Galileo abandoned the dynamical approach in favor of kinematics.

4. He proceeded to clarify, restate, and systematize medieval problems in kinematics while giving them a more complete mathematical expression, for example, problems suggested by the Odd Numbers Law relating distance to time (S proportional to t squared) and velocity to distance (V proportional to S), out of which he came to relate velocity to time (V proportional to T), and eventually, S = 1/2at [squared].

5. After 1609, Galileo's kinematic treatment of an idealized model identified falling bodies as a case of uniformly accelerated motion and thereafter demonstrated it with his inclined plane experiment.

D. Projectile Motion.
1. Galileo's work developed out of the impetus theories of contemporary physics, especially those of Tartaglia and Benedetti.

2. In his later theory (1632), no force is necessary to keep a body moving on a level (frictionless) plane; a body, as such, has no inclination to move or remain at rest, it is indifferent.

3. Thus, if a body is indifferent to motion, no mover is required to sustain movement once a body is in motion.

4. Motion is now a state rather than a process, and rest is motion of zero speed in a continuum.

5. Galileo's conception of inertia as circular motion was an attempt to save Copernican circularity, particularly in the absence of any known force which could 'bend' rectilinear motion into an orbit.

E. Galileo's Method.
1. Galileo argued that theoretical conclusions required experimental verification even if the experimentation was mental rather than empirical.

2. He was a thinker about nature and thought in terms of ideal situations rather than the complexities of the sensate world.

3. Expressed confidence in deductive, reasoned conclusions: Archimedean mathematics applied to physical problems rather than extensive experimental programs.

IV. René Descartes (1596-1650) and the Mechanical Philosophy
A. Background of the Mechanical Philosophy.
1. Derived from ancient atomism but reworked by 17th century thinkers such as Descartes, Gassendi, Huygens, Hooke, and Boyle.

2. Reaction against the animistic philosophies of the Renaissance, notably Hermetism.

3. Conceived as an alternative to existing Aristotelian metaphysics.

B. Basic Tenets of the Mechanical Philosophy.
1. Viewed nature as composed of inert (without quality) matter in motion.

2. All causality involved matter in contact with matter--no action at-a-distance.

C. Cartesian Mechanical Philosophy.
1. Descartes, reacting against Renaissance skepticism, sought to affirm the existence of certain knowledge.

2. The conclusions of mathematics, especially those of geometry, are demonstrable, that is, start with true premises (clear and distinct ideas) and proceed deductively to certain conclusions.

3. Mathematics accepted as a model, though not the essence, of knowledge.

4. Descartes' methodical doubt reduces existing substances to two types:

a. Res cogitans (thinking stuff): immaterial thought or mind.

b. Res extensa (extended stuff): geometrical extension or matter.

5. All that exists outside the mind is matter: only primary qualities exist, that is, motion, size, shape, number, location, place; secondary qualities are illusory (soft, hard, hot, cold, wet, dry, etc.).

6. The universe is a plenum, that is, it is 'full' with no void possible.

7. Matter is of three types, classified as to size: First matter, fine (chips); second matter, medium (spheres); and third matter, gross (chunks), that is, respectively, material light, aether, and ordinary, visible matter.

8. The interaction between the various forms of matter occur as the result of vortex action; the universe is composed of vortices or whirlpools of matter. Vortices explain the varying periods and uniform orbital directions and inclinations of the planets.

9. Formulated the concepts of rectilinear inertia and the conservation of motion.

V. Francis Bacon (1561-1626) and the Baconian Method

A. Opposition to Scholastic and Renaissance Philosophy: The Idols.
1. The Tribe: weaknesses of human nature, that is, prejudice, passions, limited mental and sensory faculties.

2. The Cave: weaknesses of environment, that is, education, habit, prejudice, predisposition of approach to philosophical-scientific questions.

3. The Market Place: semantic difficulties arising from confusing words with things.

4. The Theatre: philosophical systems or theories which direct the mind beyond the data of experience to unsupported generalities.

B. Basic Assumption: The Simplicity of Nature.
1. Scientific progress is a matter of finding the correct method, that is, the correct method is equivalent to truth:
a. If nature is approached in the appropriate manner, the truth can be found.

b. Error is the result of defective methods.

2. The ultimate goal of science is practical utility for the benefit of mankind.

3. The method is the 'tool' of the intellect: it enables the mind to overcome its weaknesses, and can compensate for disparity of mental ability.

4. The function of method is to collect data from the natural world and refashion it (the bee)--it is not just empirical cataloguing (the ant) and it is not a matter of pure speculation (the spider).

C. The Baconian Method.
1. The basic premise: observe nature with the senses--proceed inductively from observations (data) to generalities (axioms), and form deductive conclusions which can be tested by experimental evidence.

2. The method of exclusion:

a. Tabulate all possible causes of an observed effect.

b. Observe nature to see what causes actually exist in the given physical circumstances.

c. Exclude all but one, that is, the result of the crucial experiment.

VI. Isaac Newton (1642-1727) and the Newtonian Synthesis
A. Elements of the Synthetic, "New" Physics.
1. Galileo's idealized formulation of the law of freely falling bodies, d = 1 /2at [squared].

2. Galileo's analysis of terrestrial inertia: a body is indifferent to uniform rectilinear motion and is as 'natural' as rest.

3. Descartes' conception of rectilinear inertia existing in Euclidean space and the implied rejection of privileged spatial position.

4. Kepler's 'discovery' of his three laws of celestial motion, especially the The Third Law, T squared is proportional to the mean Radius cubed.

5. Huygens' and Borelli's work on centrifugal forces, terrestrial and celestial respectively, suggested an inverse square relationship, as well as the analogy from light made explicit by Boulliau.

B. The Problem and the Test Case: Lunar Motion.
1. Lunar motion was essential to both Aristotle and Newton:
a. The lunar orbit was the demarcation line for the Aristotelian two-world system (sublunar/superlunar regions).

b. The connection of lunar-terrestrial motion under the same principle was the crux of the Newtonian argument.

2. Newtonian assumptions:
a. The Copernican hypothesis: the earth is a planet.

b. The hypothesis that inter-planetary space is empty, that is, free space.

3. The problem was to explain the configuration of planetary orbits, that is, what mechanism or force can account for the orbital alteration of a planet's rectilinear path.
C. The Moon's Orbit and the Unification of Terrestrial-Celestial Physics.
1. Problem of translating the moon's rectilinear acceleration into the centripetal acceleration necessary to account for the lunar orbit--assume circular Copernican orbits.
2. Problem of demonstrating that lunar acceleration represents a ratio equivalent to that of free fall on the earth, implying the same gravitational force: the inverse square law.
3. Problem of justifying the mathematical treatment of the earth's total mass as concentrated in a single mass point at the earth's center; Newton's solution rested upon his invention of the calculus, his "fluxions", which could be used to consider the intricacies of the problem.

4. The final stage was to transfer the concept of force for a planetary orbit in relation to the sun, based on the moon-earth test case to a universal, reciprocal gravitational relationship which applied to all matter

D. Components of Newtonian Physics.
1. Matter: an infinite number of separate, hard, and unchangeable particles which are not identical.

2. Motion: the relational state which moves particles from place to place in an infinite void of free space without affecting them.

3. Space: the infinite homogeneous void in which the particles, and the bodies they form, move.

4. Attraction: the undefined unifying force which is not a constructive element but rather a "hyperphysical" power or mathematical statement describing how the universal components are connected.

E. The Destruction of the Aristotelian Cosmos.
1. Considerations of such concepts as perfection, harmony, teleology, formal and final causality, and value are removed from scientific discussion.

2. The world was no longer viewed as finite and hierarchically ordered: quantitative considerations replace qualitative ones.

3. The celestial and terrestrial worlds are no longer philosophically and scientifically distinct; astronomy and physics have been geometrically unified.

F. The Mathematical Generation of Homogeneous, Abstract Euclidean Space.
1. The common sense world of the pre-Galilean cosmos is replaced by an idealized mathematical universe.

2. Newtonian science attempted to synthesize mathematics and experiment: the integration of theory and experience under the 'direction' of the inverse square law.

3. The Newtonian pattern of empirical-deductive knowledge provided both physical and intellectual unity for the 18th-century universe.  Alexander Pope suggested:  

Nature and nature's laws 
Lay hid in night, 
And God said 
'Let Newton be' 
And all was light.  

The Enlightenment is sometimes called 'Newton's Century.'