A Guide to Dimensions
ARISTOTLE
METAPHYSICA
Key Points and Concepts:
1. The first paragraph of Metaphysica contains a view perhaps not shared by our students: That we naturally desire to know, to understand, just for the sake of knowing and for no other reason. If we come to know only for the purpose of some other end (money, power, status) then we would not “take such delight in the use of our senses.” It might be pointed out that modern textbook authors in economics more closely hold Jeremy Bentham’s view that humans are essentially inert unless motivated by great reward or starvation, i.e., there must be a practical end before we’ll do anything.
2. A. is concerning himself with why we wonder. By focusing on the motivation and capability of the observer he places humans squarely within that which they observe. He wants to get at that relationship between the mind and that which the mind contemplates.
3. A. also seems to be saying that only with the development of a leisure class was this readily apparent (the desire to know for knowledge’s sake); and only then could it reach its fullest expression. Of course, one could also argue that only with the development of a leisure class was there a group of people who just sat around thinking and therefore found it necessary to justify the grapes, persimmons and the slaves fanning them on those humid afternoons in Athens.
4. A.’s categorization of this relationship between the observing human mind (he dismisses the sensory apparatus of lower animals) and that which it observes exactly parallels the class divisions in society. Manual laborers who experience nature or indeed anyone who actually engages in a practical act (the physician who cures Socrates of a fever) is less likely to know why what they do succeeds or fails. True knowledge (art and science) comes when someone can step back and perceive the universal as opposed to the particular and thereby discover the why of things - their true cause.
5. But the universal is embedded in the particular and the particular is experienced through the senses (those lowly faculties used by mere laborers) so A. finds that the world seems to be structured in a way that allows our curiosities to be satisfied. ["..we do not regard any of the senses as wisdom; yet surely these give the most authoritative knowledge of particulars."] So, it's the combination of the structure of the world and our senses that creates a natural path to wisdom (the world is perfectly knowable), but it's this natural puzzlement that kicks our butts onto the path. (Why is a toddler into everything?; Why does an infant grab the glasses off your face?).
6. Lastly, A. distinguishes his inquiry from the early Greeks when he states that "..wisdom is knowledge about certain causes and principles." So, the world is not just to see and to accept, but to investigate, to move from the general to the particular by categorizing and systematizing sensory experience.
PHYSICS
Key Points and Concepts:
Particular --------- Genus Complex
(economist) (expert) (Paul Hancock, the economist) (a bald man)
Incidental --------- Genus By Itself
(man) (living creature) (Particular: an economist ) (Incidental: a man)
* It appears that the object of the action is also actualized, i.e., the person in need of a forecast of GDP has a potentiality of being satisfied, which will be actualized when he receives the forecast. This would also be true in the case of art – a painting is there waiting to be painted, a statue crying out to be sculpted.
(The six modes of causation are underlined in the schemata above. The genus is just the generic version of the particular or the incidental mode of causation.)
“…that our teeth should come up of necessity … being organized in a fitting way...”
This flirts with natural selection which would deny A. the notion that things in nature occur “for the sake of something”, i.e., have an embedded purposiveness. For example, the spider doesn’t build its web to secure food but because of its genetic inheritance. A. responds that since teeth occur regularly and spontaneous events occur rarely then teeth occur for an end (i.e., there are only two reasons why natural events occur – spontaneously or for an end). A. escapes by the …
On The Heavens
1. The Stuff: Earth, Air, Fire and Water (plus a fifth element called the quintessence). How they move: straight, circular or a combination. The natural place: The place to which the stuff naturally moves. The natural motion: upward, downward and around (earth and water down; air and fire up).
2. A. seems to accept the numerology of the Pythagoreans when he comments on the significance of threeness, but he likely is positing this peculiarity of the physical world (beyond a 3-D world there is nothing) as an imagined Pythagorean, i.e., it is something that remains to be explained perhaps but it does not imply a separate mathematical realm.
3. A. places the circle and circular motion above that, hence primary to, the straight line and rectilinear motion. This is so because the circle is complete which cannot be said of either an infinite line (the infinite line can never be complete) or a finite line (you can always extend a finite line). What's the point of this? A. leads his discussion to the conclusion that those bodies which lie in the heavens (which are spherical and eternally circle earth) are of "superior glory" proportionate to their distance from earth - the farther a planet or star from earth the more smooth and perfect it appears. One must recognize the syllogistic method of carefully crafting premises which lead inevitably to a conclusion. the sphere is primary and since the heavens are of superior glory they must be spherical.
4. In Book I, Chapter 3, A. describes the properties of things as being heavy or light and naturally moving upward or downward relative to their "essential nature." There is a natural order here and a sense of balanced totality. The earth can possess no heaviness or lightness "as a whole," i.e., its essential nature is to be immobile since it is what everything is either moving away from or toward. Again, things actualize their potentiality- they are what they are because of some inner principle. In Book II, Chapter 14, A. comes back to this question of earth being the center of the whole using the argument of angles - since all things that are heavy move toward the center and we observe that they move at right angles to the earth then the earth must be the center (note: A. referred to comets as exhalations from the earth).
5. The earth and the heavens are indestructible because they are spherical and (in the case of the heavens) describe a circular motion and "there can be no contrary notion to the circular," i.e. it is eternal. In a sense A. is describing a kind of Conservation Principle which comports well with the notion of the circle. If you flip the circle over 180 degrees it will still look the same. If you rotate it, it will still look the same and if you come back tomorrow, it will presumably look the same. Its inner principle is to be complete, unchanging and eternal.
EUCLID
"There is geometry in the humming of the strings. There is music in the spacings of the spheres." Pythagoras 5th century. B.C.E.
Key Points and Concepts:
1. This reading introduces the student to the rigor of an axiomatic system. Although most have had exposure to geometry in some form, none will have read the Elements in the original.
2. Euclid’s careful definitions of a point, a line, a surface and on to circles, squares and triangles was an attempt to understand nature’s forms with complete certainty. It should be noticed that although a point and a line can be imagined they cannot be drawn given Euclid’s definitions. They only exist in a derivative sense.
3. These basic axioms were intended to be so simple that they could be accepted as true just by understanding them.
4. Euclidian geometry dominated through to the late 19th century. It was believed to have unlocked the secrets of the structure of reality- a structure that was independent of the human mind. By establishing his geometry, Euclid hoped to discover a divine architect, a thinking entity behind the creation of the world.
5. This system of deductive reasoning- starting with simple, obvious truths (unproved) and deducing from them less obvious truths- would be replaced by the scientific method in which observation, measurement, experimentation and the inductive approach is featured.
6. Still Euclid’s proofs allowed Aristotle’s invention of the syllogistic system which can be read in Prior Analytics of Book I in Aristotle in which A. states that the subject of inquiry is proof and in Pythagoras (even farther back in 582 B.C.) who believed that a basic harmony existed in nature as seen by the discovery of the octave in a plucked string. Nature’s harmony was there to be discovered.
7. Euclid lived during Aristotle’s grandson’s time. He clearly was in the tradition of Pythagoras and in particular A.’s syllogistic logic. Jonathan Lear argues that Euclid never did state all of his implicit assumptions, therefore never produced a fully axiomatized geometry.
8. The postulates in E. are the axioms. The simple truths that are assumed without the need of proof. The first four are self-evident and the fifth is actually a demonstration of the definition of parallel lines. Later in the semester it will be shown that two parallel lines do meet if drawn on a sphere.
9. While the Postulates have to do with lines and points-things one can do and things one can know from diagramatic representation- Common Notions have to do with more abstract properties of things in general which can be represented by symbols (letters or numbers). Euclid’s first proof will make use of some of these assumptions (which ones?).
10. Although the construction of an equilateral triangle seems simple to us today, this proof (and the others in the Elements) was a sharp departure in reasoning even from Aristotle. Here, from a few simple propositions one could follow a path of ironclad reasoning to a more elegant construction. This reasoning would have the highest degree of rigor only if it followed directly from the explicitly stated axioms (i.e., no truths necessary for the proposition have been left out).
11. The first two constructions below do follow from the axioms. The last construction seems to follow also but Euclid has failed to provide an axiom that assumes the existence of a point C. Only with the aid of the diagram (supposedly only a heuristic device) is it obvious there is a point C.
Postulates used:
1. to draw a straight line from any point to any point.
3. to describe a circle with any center and any distance (and def. 15 and 16)
Postulate used:
3. to describe a circle with any center and any distance (and def.s 15 & 16
Postulate used:
1. To draw a straight line from any point to any point. (def.s 15, 16 and com. notion 1)
PTOLEMY
1. Ptolemy was the first to devise a geometrical representation of the solar system that predicted the motions of the planets with considerable accuracy.
2. At the same time, he set out to confirm the Greek's view of geocentrism and the spherical and well-ordered heavens. The heavens are not to be understood by science, they're the province of theology, but the abstract tool of mathematics is the perfect tool for demonstrating the harmony of planetary motion and the spherical heavens.
3. The practical, physical world (white, hot, sweet and soft) is sub-lunar, imperfect, and in constant change. The celestial sphere is perfect and eternal.
4. He sets out to prove the "...evident and certain from the observations of the ancients and our own..." by means of geometrical demonstrations (the earth is the center, is spherical, is as a point to the fixed stars, and is immobile). Ptolemy made no claim that his model described reality some say, only that it would predict the positions of the planet at any time (the Rosetta Stone, it might be noted, was a priestly decree praising Ptolemy's work).
5. P. argued that the heavens described a sphere because a) the stars always described the same angular distance with the earth (no knowledge of how far the stars were from the earth, and no instrumentation capable of measuring angles finer than 5 minutes existed) and b) since the heavenly bodies ought to describe arcs that are "least impeded and most facile"- that's the circular (or the spherical for bodies).
6. The earth is spherical because a) during lunar eclipses, for example, someone situated in the western hemisphere sees the eclipse before someone situated in the eastern hemisphere,
b) the stars appear and disappear as we move toward either pole, and mountains seemingly rise from the ocean as we sail towards them. c) If any other shape:
If concave, someone on earth at B would see the stars only after someone at A would.
If flat, the rising stars would be visible to both at the same time.
Only if the earth were a sphere would a person in the east see the rising stars first.
7. Earth is the center of the universe, for if it were not:
a) The shadows of the gnomon (the fin-shaped, upright part of a sundial) at sunrise would not be on a straight line with those at sunset in planes parallel to the horizon.
b) If placed off-center, some parts of the earth would have no autumnal and other parts no vernal equinox or they would occur at irregular intervals between the solstices.
8. The earth is a point relative to the heavens:
a. We can always see exactly half the stars.
b. Whereas, a person at A would see far less than half the stars if the earth were relatively larger.
9. The earth is immobile:
a. It cannot shift from the center for reasons that demonstrate why it is in the center.
b. Aristotle's reasoning: If it were not the center it would be moving, since all things move toward the center, etc.
c. Since there is no above or below relative to the earth, there can be no movement upward or downward, i.e., the center is its natural place.
d. If it rotated on its axis (and therefore that explained the apparent celestial revolution), it would have to rotate at a speed that would produce absurd phenomena:
Since the earth was known to be about 25,000 miles in circumference since Eratosthenes made his calculations in Alexandria in the 3rd century B.C., and a day lasts 24 hours, the earth's speed would have to exceed 1000 mph around its axis at the equator.
1. animals would be left hanging in the air.
2. You would never see a bird or a cloud move east.
10. Again, Ptolemy's greatest contribution was explaining planetary motion while preserving the Greek geocentric hypothesis. He did it using epicycles- local orbits of the planets as they moved about the earth. This was necessary to explain the retrogradation of the planets.
Since earth is closer to the sun and hence traveling faster than Mars (and all the outer planets) it appears that Mars at some point is traveling backwards (retrogradation) when actually earth has caught and passed Mars. Ptolemy never knew this, so he had to construct very precise revolutions of Mars (and the other outer planets) as it simultaneously described the larger orbit you see on the diagram. That would preserve the appearance that was vital to both church doctrine and Aristotelian thought.
To preserve the illusion of the appearance, Ptolemy proposed the following:
Here is a link to a Smithsonian Institute website that has an animated illustration of retrogradation and the Ptolemaic explanation shown above. Professor Jim Wright found this and I snatched it from his website.
Copernicus
Key Points and Concepts
1. As stated in footnote 1, the introduction was authored by a cohort (or apologist) with the apparent purpose of smoothing the way with the clerics. Osiander based his defense of the Copernican model on the fact of its relative simplicity and proffers that it was objectively arrived at through observation; and no less divinely inspired than that of Ptolemy. Note: Osiander never signed the introduction.
2. "...there is no medicine for the bite of a sycophant..." C. knew he was espousing ideas that would be viewed as heresy by the church. To deflect this certain assault he chose to alternately be servile (his preface is laced with fawning language), defiant (those who don't see the correctness of his thesis are as stupid as "drones...among bees"- an interesting parallel with T. Kuhn's 'normal science'), and boastful ("...this book contains...the general set-up of the universe;" "mathematics is written for mathematicians"- [who will see I am right]). Much rich language here. Note: The work was published just after his death in 1543.
3. C.'s greatest contribution was his development of the heliocentric model in which he demonstrated that all the phenomena observed from earth could be more easily explained by the earth revolving about the sun while simultaneously rotating on its own axis. The earth, he said, was only one of six (known) planets that revolved about the sun. Some points about his contribution:
a. He accepted some of Ptolemy's and Aristotle's views and logic:
-Tthe circular motion of the planets (whereas we know they describe ellipses)
-.All objects seek their natural place.
-.Reasons why they believed the earth to be spherical.
-.The earth is as if a point relative to the celestial sphere.
b. He did not prove the heliocentric model but only demonstrated that it was a more simple and elegant way of explaining the observed phenomena. He admitted to finding only fourteen observations to support his argument.
4. Copernicus' ideas were inspired not by the advance of instrumentation (the telescope was invented in Naples in the 1590's and perfected by Galileo in 1609) but by the insight from the travels of Columbus, Balboa, and Magellan and the clumsiness of the Ptolemaic system.
5. To the argument that the earth would be torn apart by the violence of its rotation on its axis, C. argued that the same objection, many times magnified, would apply to the ancient's belief in a daily revolution of the whole celestial sphere about the earth (more weakly he argues that the reason clouds, birds, and we don't fly off the spinning earth is due to the fact that all things in earth's atmosphere have "an acquired movement" given to them by earth).
6. To the argument that retrogradation was explained by epicycles (separate planetary orbits about points in space in addition to the orbit around the earth), C. explained that the successively faster revolution of planets placed closer to the sun accounted for this "appearance."
..."those which describe a smaller circle turn more quickly than those which describe a greater circle." (so,a slower speed is attributed to each planet successively from Mercury out to Saturn- see the Ptolemaic section on retrogradation).
..."therefore if some movement should belong to the earth it will appear, in the parts of the universe which are outside...[such as Mars, etc], as the same movement but in the opposite direction, as though the things outside were passing over."
"...the stoppings, retrogressions, and progressions of the wandering stars are not their own...[but]...borrow the appearances of this movement...[from the earth's movement].
7. Further evidence C. cites to support his belief that earth was just one of six known planets to revolve about the sun was that, for example, when Venus was in apogee it was farther from earth and in perigee closer to earth:
"...for us watching from earth, it happens that the transits of the planets, on account of being at unequal distances from the earth, appear greater when they are nearer than when they are farther away...thus in the case of equal arcs of an orbital circle which are seen at different distances there will appear to be unequal movements in equal times." (i.e., when Venus is closer it appears to be moving faster). For example, if you see a train crossing your line of sight from a few miles away it will appear to be moving between two points at a slower rate of speed than if it is only, say, 500 yards away (and moving at the same speed).
Which C. argues can be explained by the fact that:
"...the earth is not at the centre of the circles in which they revolve."
8. But C. further admits doubt when he writes:
"It is not yet clear whether the earth draws near to them and moves away or they draw near to the earth and move away." (If all six revolve about the sun in different concentric orbits how could it be otherwise than that both movements occur?)
9. In reply to Ptolemy's reasoning that earth could be nowhere but at the center since we always see half the stars at night, C. states:
"...the horizon always bisects the ecliptic, which is a great circle of the sphere. But on a sphere, if a circle bisects one of the great circles, then the circle bisecting is a great circle. Therefore, the horizon is a great circle...nevertheless the line passing through the centre of the earth and the line touching to the surface are necessarily different; but on account of their immensity in comparison with earth...[they]... appear to be one line."
It appears the Earth is the center only because of the immensity of the universe.
So (more simply) the Earth could be way off-center and we'd still see half the stars from horizon to horizon.
Note: The geocentric model proposed that the whole celestial sphere rotated daily on its axis (the celestial poles) while the Sun took its own orbital path (the ecliptic) through the celestial sphere, taking one year to complete its journey. The celestial sphere spun the sun around each day but it was in a slightly different (one degree further east) position among the stars (fixed relative to one another). At its greatest, the tilt of the celestial equator away from the ecliptic was thought to be 23 1/2 degrees. This was in explanation of the seasons. During the summer solstice the sun would be shining onto the northern hemisphere of earth and during the winter solstice onto the southern hemisphere.
Further note: The Heliocentric model explains the change in seasons this way:
10. The Copernican Revolution did not extend to an understanding of gravity. He simply applied the Aristotelian notion of things being assigned an inner principle of heaviness, lightness, and natural place.
"I myself think that gravity or heaviness is nothing except a natural appetency implanted in the parts by the divine providence.."
Galileo
Chronology:
1609 Henry Hudson sails up the Hudson River and Samuel Dé Champlain paddles up Lake Champlain
1610 Sidereus Nuncius (The Starry Messenger) published in the same year Galileo trains his telescope on the moons of Jupiter
1615 Letter to the Grand Duchess Christina of Tuscany written (first published in 1636)
1616 Decree of Catholic Church prohibiting the advocacy of the Copernican system
1632 Dialogue Concerning the Two Chief World Systems published
1634 Galileo convicted, recants, house arrest
1642 Galileo dies
1834 Green Mountain College founded
1835 Works of Copernicus and Galileo removed from the Index of Prohibited Books
1992 Pope John Paul II acknowledges that the Catholic Church erred in condemning Galileo for advocating heliocentrism.
1995 Green Mountain College offers first course in Dimensions of Nature
Points and Concepts:
1. G., the first great experimenter, cared not a bit for answering why questions. Answering how was tough enough. At seventeen he measured the swinging of a lamp in the cathedral of Pisa, comparing it to his own pulse to confirm the regularity of its cycles. Three-quarters of a century later, on the basis of those findings, the first pendulum clock was built.
2.. Excerpt 1 of the Two Chief World Systems (Two Sciences) Dialogue presents G.'s preference for proof by demonstration or experimentation rather than relying solely upon the elegance and logical grounding of an argument. One can see that his approach is essential since he is trying to convince us of something that is counterintuitive:
"[that]...uniform motion in a straight line has no discernable effects."
First, what is he trying to demonstrate here, why it is important, and what implications does his method have for human inquiry?
a.. G. wishes to show that we cannot distinguish motion from rest when we are inside a vehicle using as a frame of reference all the things contained with us. A ball thrown up in a closed, moving vehicle will come down in our hand just as it would if the vehicle were at rest, etc.
"The cause of all these correspondences of effects is the fact that the ship's motion is common to all the things contained in it, and to the air itself."
b. By demonstrating this phenomenon G. undermined the argument that the earth couldn't move (or rotate) or we would be able to detect it (by feeling the motion) or demonstrate it by observation of physical properties (dropping a ball from a tall tower).
p.s. On the N.P.R. program "Car Talk," Tom asks Ray how he can tell whether he is walking to Boston or bringing Boston to him. Ray answers that not only does he believe the latter, but that he's sure the earth spins faster during the Boston Marathon.
c. The implications of G.'s discoveries were, and remain, profound:.
First, we begin to recognize that "..what we perceive is a representation of reality and could differ from it in essential ways.." (Barrow, p. 149). [Send in Marwine and Throop].
Second, this recognition causes us to separate the observer from the observed (contrary to Aristotle), the subjective (the imagined, and untrustworthy senses) from the objective (the real, the mathematically rendered). In other words, Dualism comes onto the stage, accompanying the scientific revolution. This is most evident in the work of Descartes (hence the term "Cartesian Duality).
"...there being a great temporal disparity between the pace at which the mountains behave and the way people think." (McPhee: L.A. Against the Mountains)
"Viewers are as much a part of the landscape as the boulders they stand on." (Silko: Landscape, History, and the Pueblo Imagination)
3. In the Letter to the Grand Duke of Tuscany, to whom he was subsequently employed as a mathematician, we apparently witness one of the first obsequious dedications written as a cover letter. G. was forty-five and the Grand Duke was at the tender age of twenty. Henceforth, the style of writing would be the standard for grant requests and dissertation proposals.
"Your virtue alone, Great Hero, can, by Your name impart immortality to these stars."*
*Neither this dedication in 1610, nor the letter to the Grand Duchess in 1615 dissuaded the Roman clerics from issuing a decree in 1616 forbidding him from holding or defending the Copernican system. This letter, however, accompanied the publication of the Sidereus Nuncius and may have influenced the Council of Ten to allow its publication, writing that:
"..there is nothing [in the book] contrary to the Holy Catholic Faith, principles, or good customs.." (Anthology, p. 50).
The Dialogue Concerning the Two Chief World Systems, published in 1632, violated the decree in a flagrant manner - although the preface stated the Dialogue was merely a mathematical fantasy (see Hofstadter, Godel, Escher, Bach: An Eternal Golden Braid, pp. 478-479, in which they muse about why G. chose three characters for his Dialogue) and that divine knowledge assured us of the immobility of the earth, G. published it in Italian, instead of Latin, to reach a wider audience. At seventy he was placed under house arrest for the remaining ten years of his life.
Sidereus Nuncius
1. Although the beginning of the scientific revolution is marked by Copernicus in 1543, great significance can be assigned to the perfection of the telescope (and instrumentation generally) from 1609. A line can be traced from the telescope, through Newtonian mechanics, to Turing and the start of the computer age. It marked the movement away from the unquestioned authority of the church, the Greek philosophers and ancient mythology. Cause became less important than simple description, qualitativeness less important than quantitativeness. (The Greek philosophers' science was lamentably lame because they eschewed measurement- something an artisan or a slave would do). Kepler wrote:
"To measure is to know."
2. When G. trained the telescope on the moon he found it to be "..uneven, rough, and crowded with depressions and bulges...like the face of the earth itself." The earth could no longer be thought of as necessarily separated from any of the other celestial bodies. It rendered the heavens more material and less divine.
3. Some comments on the discovery of the moons of Jupiter:
a. G. simply carefully watched and measured the changes in relative positions of Jupiter and the four "stars." The writing is a model of the "lab report": dispassionate, revealing the process of thought as it is led by the process of observation , highly detailed and repetitive. The difference perhaps is that he does not begin with a question to which he seeks an answer. He is more in the tradition of an explorer.
b. G. first assumes the three objects around Jupiter are fixed stars. He continues to watch because they're unusually bright, and arrayed in a straight line parallel to the ecliptic.
c. His frame of reference is shattered when on the third night only two stars appear, now placed to the east and in front of Jupiter's path. This he believed could only be explained by the movement of the "stars" themselves. [Note: In footnotes 82 and 83 we learn that G.'s telescope is too crude to allow him to separate two satellites placed close together, nor to see those in the planets glare] After only four nights of observations, he writes:
"I therefore arrived at the conclusion, entirely beyond doubt, that in the heavens there are three stars wandering around Jupiter like Venus and Mercury around the Sun." (subsequently he would find a fourth)
d. Finally, by using a fixed star as a referent (reminiscent of using his pulse to measure the lamp's cycles), G. is able to confirm that these "stars" are planets that: "..sometimes follow and at other times precede Jupiter by similar intervals, and are removed from him toward the east as well as the west by only very narrow limits, and accompany him equally in retrograde and direct motion...[and]...complete their revolutions about him..."
e. and they describe different sized orbits because: -"..at the great separations from Jupiter two planets could never be seen united.." -"[while]...near Jupiter two, three, and occasionally four planets are found crowded together..."
f. and that the satellites describing smaller orbits are traveling faster because: -"..the stars closer to Jupiter are often seen to the east when the previous day they appeared to the west, and vice versa, while from a careful examination...the planet traversing the largest orb appears to have a semi-monthly period."
g. Conclusion: The argument that: -the earth could not move like other planets since the moon would not be able to keep up with it is clearly false because here were Jupiter's planets doing exactly that! (and the Copernican system is thereby further supported)
SUGGESTION: -construct a schema like Galileo's in which you label the Galilean satellites (I, II, III, IV) for the nights of Jan. 7-Jan. 13- I've done it, it's not too tricky.
-state for each satellite whether it is moving east or west (for each of the six nights).
-from the exercise, determine the rank-order of the satellites' orbits from smallest to largest.
The Letter to the Grand Dutchess of Tuscany
Bachelors and Masters of Arts who do not follow Aristotle's philosophy are subject to a fine of 5 shillings for each point of divergence. Fourteenth-century Statute of Oxford University (barrow 205)
1. To put Galileo's achievement in perspective, we must recognize that just prior to the modern age we knew less about the universe than Archimedes in the third century B.C.E (Arendt 261). Galileo had his work cut out for him -- nothing less than to overturn the Aristotelian world view which had been held for 2,000 years..
2. As Hannah Arendt writes, "What Galileo did and what nobody had done before was to use the telescope in such a way that the secrets of the universe were delivered to human cognition 'with the certainty of sense perception"(259-260).
3. As Cardinal Ballarmine declared, there was a considerable difference between speculation through hypothesizing about the movement of the earth and actually demonstrating it. Copernicus could be dismissed but not Galileo. In other words, the Copernican system was looked upon by the church as no more than the addition of some new insight to "save the appearance" of the order of the universe -- well-meaning but mere conjecture.
4. Notice the subtitle -- "Concerning the use of Biblical Quotations in Matters of Science". Galileo means to directly confront the church with an argument that takes many twists and turns. Let's examine a few quotes (note: page numbers refer to the small numbers of the actual text):
Galileo states the challenge he confronts when he writes, "Since the Bible cannot err, it follows as a necessary consequence that anyone takes an erroneous and heretical position who maintains that the sun is inherently motionless and the earth movable" (181).
Appeal to the senses
Referring to his critics: "Showing a great fondness for their own opinions than for truth, they sought to deny and disprove the new things which, if they had cared to look for themselves, their own senses would have demonstrated to them" (175).
"...they would have us altogether abandon reason and the evidence of our senses in favor of some biblical passage" (179).
Appeal to Scientific Authorities
"Men who were well-grounded in astronomical and physical science were persuaded as soon as they received my first message" (176).
"...mathematics is written for mathematicians, by whom, if I am not deceived, these labors of mine will be recognized as contributing something to their domain..."(180).
"...before a physical proposition is condemned it must be shown to be not rigorously demonstrated..."(195).
Galileo lists those ancient Greeks who held the heliocentric view: Pythagoras, Heraceides of Pontus, Philolaus, Plato, Aristarchus, Seleucus, and Nicetas.(187-88).
Appeal to Religious Authorities
"[Copernicus] was not only a Catholic, but a priest and a canon..[whose book, On the Celestial Revolutions] was accepted by the holy Church" (178).
"...the Bible can never speak untruth -- whenever its true meaning is understood..."(181).
A quote from Cardinal Baronius: 'That the intention of the Holy Ghost is to teach us how one goes to heaven, not how heaven goes'(186).
Science and Religion are separate areas of human inquiry
"...it does not become the dignity of theology to stoop to the investigation of fallacies in the subordinate sciences..."(192).
"[theologians] should not arrogate to themselves the authority to decide on controversies in professions which they have neither studied nor practiced"(193).
"...I have no doubt that where human reasoning cannot reach -- and where consequently we can have no science but only opinion and faith -- it is necessary in piety to comply absolutely with the strict sense of Scripture" (197).
and finally (in cases where science and religion conflict) --
"...in questions of nature which are not matters of faith it is first to be considered whether anything is demonstrated beyond doubt or known by sense-experience, or whether such knowledge or proof is possible; if it is, then, being the gift of God, it ought to be applied to find out the true senses of holy Scripture in those passages which superficially might seem to declare differently" (199).
In a nutshell, Galileo is stating that the Bible subordinates every other human inquiry, unless it is wrong (i.e., science shows otherwise), in which case it must have been initially misunderstood because it cannot be wrong.
Arendt argues that this separation of religion and science (pried apart by instrumentation) set the stage for René Descartes and what Nietzsche called "the school of suspicion" or the idea of Cartesian doubt.
Sir Francis Bacon
1620 Novum Organum: The Great Instauration
1627 The New Atlantis
Setting the historical stage
If you wanted to pick moments and places in history that you would at all costs prefer to avoid, the period from 1590 to 1650 in Europe should be at the top of the list. Europeans were experiencing rapidly rising food prices, a severe economic depression, incredible poverty, starvation, and disease. Wealth was concentrated in the hands of a few powerful landowners. The so-called "Little Ice Age" in the 1590s caused harvest failures, food riots and the Great Death. Population actually declined during the 17th c. -- the only time after the 14th c. -- and there was a permanent war condition from 1551 to 1650, highlighted by the Thirty Year's War (1618-48).
Major Points and Concepts
1. Ten years after Sidereus Nuncius had been published and nine years after Johannes Kepler perfected the microscope, Sir Francis Bacon set about transforming the philosophy of knowledge acquisition. The academies of learning had to be turned upside down. The telescope and microscope, both inventions of the 17th century, created a certain shock and awe. Bacon was "... astounded at the precision of nature revealed under the microscope..." and Pascal declared, The eternal silence of these infinite spaces frightens me" as he examined space through the telescope (Sennett 196).
"... the entire fabric of human reason which we employ in the inquisition of nature, is badly put together and built up, and like some magnificent structure without any foundation. For while men are occupied in admiring and applauding the false powers of the mind, they pass by and throw away those true powers, which, if it be supplied with the proper aids and can itself be content to wait upon nature instead of vainly affecting to overrule her, are within its reach. There was but one course left, therefore,---to try the whole thing anew upon a better plan, and to commence a total reconstruction of sciences, arts, and all human knowledge, raised upon the proper foundations" (The Great Instauration 2).
And part of this process required an attack on the thought experiments and syllogistic reasoning of Aristotle and those schools of thought that continued to follow his methods of acquiring knowledge:
a. Regarding the whole of the arts and sciences: "And for its value and utility it must be plainly avowed that that wisdom which we have derived principally from the Greeks is but like the boyhood of knowledge ... it can talk, but it cannot generate, for it is fruitful of controversies but barren of works"(8).
b. "... those who have given the first place to Logic, supposing that the surest helps to the sciences were to be found in that ... have ... [correctly] perceived that the human intellect left to its own course is not to be trusted ... [but this Logic]... is not nearly subtle enough to deal with nature ..." (12).
c. "I on the other hand reject demonstration by syllogism, as acting too confusedly, letting nature slip out of its hands. For although no one can doubt that things which agree in a middle term agree with one another ... yet it leaves an opening for deception; which is this. The syllogism consists of propositions; propositions of words; and words are the tokens and signs of notions. Now if the very notions of the mind (which are as the soul of words and the basis for the whole structure) be improperly and overhastily abstracted from facts, vague, and not sufficiently definite, faulty in short in many ways, the whole edifice tumbles" (22.
Bacon is here calling into question the relationship between words or signs and that which they intend to signify. From the seventeenth century on, until the modern period, Foucault writes, "The profound kinship of language with the world was thus dissolved. The primacy of the written word went into abeyance" (43). Elsewhere Foucault expands on this, "...[Words and images cannot] be reduced to the other's terms: it is in vain that we say what we see; what we see never resides in what we say. And it is in vain that we attempt to show, by the use of images, metaphors, or similes, what we are saying; the space where they achieve their splendour is not that deployed by our eyes but that defined by the sequential elements of syntax" (9).
A True Priest of the Sense
2. Bacon appears to be fascinated by the act of discovery, the art of invention, that moment when a breakthrough has occurred. To accomplish this one must be absolutely unbiased, avoid appealing to authority or popular opinion; make use of technological aids, employ experimentation and the inductive method of reasoning, and not be captive to what seems to be elegant or fitting.
"For all those who before me have applied themselves to the invention of arts have but cast a glance or two upon facts and examples and experience, and straightaway proceeded, as if invention were nothing more than an exercise of thought, to invoke their own spirits to give them oracles. I, on the contrary, dwelling purely and constantly among the facts of nature, withdraw my intellect from them no further than may suffice to let the images and rays of natural objects meet in a point, as they do in the sense of vision; whence it follows that the strength and excellency of the wit has but little to do in the matter" (14).
Recall in Tinker at Pilgrim Creek when Dillard fantasizes about what it would be like to be a one-celled organism completely open to all stimuli or a newly-sighted person seeing the world in a state absolutely unfiltered by prior experience (26-32). This is seemingly what Bacon is getting at. And it seems a completely impossible goal.
3. Bacon takes a parting shot at Aristotle (without mentioning his name) when he declares, "...I suppose that I have established forever a true and lawful marriage between the empirical and the rational faculty, the unkind and ill-starred divorce and separation of which has thrown into confusion all the affairs of the human family" (15). Reread "Metaphysics" in the Anthology (12-13) for Aristotle's views on the difference between Art and Experience and which is the path to wisdom.
4. Moreover, with an undoubted reference to Ptolemy he remarks, "... I humbly pray that things human may not interfere with things divine [and that we may] give to faith that which is faith's" (15).
What is Knowledge for?
1. Bacon is charting a course (or at least recognizing a human course that has already begun) for the continuous accumulation of knowledge or, as Arendt states, linking the past through the present to the future in a long chain of scientists who "step by step through contributions of generations of explorers building upon and gradually amending the findings of their predecessors" (The Life of the Mind 152).
Bacon is the first to fully develop this notion of human progress as "a vast cooperative drive", Arendt notes, during a period when scientific knowledge was advancing at a rate that made "the previous centuries since antiquity appear as sheer stagnation by comparison" (The Life of the Mind ibid).
But why do we do it? Here he initially gives Aristotle his due on a number of points but fundamentally redirects the human experiment:
"[humans should seek] the true ends of knowledge ... not either for pleasure of the mind, or for contention, or for superiority to others, or for profit, or fame, or power, or any of these inferior things; but for the benefit and use of life (italics added); and that they perfect and govern it in charity" (16).
So, as with Aristotle, profit, fame and power are still out but along with that are pleasures of the mind (it's not just knowledge for the sake of knowledge, i.e. pleasing us, satisfying our natural curiosity) or for superiority over others (those artisans and slaves -- the ordinary folk) but we should acquire knowledge for the sake of human benefit and utility. Bacon is seeking the secularization of knowledge. You can almost hear the commercial jingle "G.E., we bring good things to life".
René Descartes
1637 The Discourse on the Method of Rightly Conducting the Reason and Seeking for the Truth in the Sciences
Galileo stirred things up by establishing the truth of the Copernican system through the use of the telescope, thereby demonstrating the inherent difficulty of relying upon the unaided human senses. Descartes saw this as a sign that there needed to be a new order, a new method of thinking about the relationship between humans and the world around them.
Cartesian Duality
"...to enable the animal spirits, contained in the body, to have the power to move its limbs, ... even though they are no longer alive;" Further, Descartes muses about the process by which ideas occur through our senses and, again, about how "our own bodies can move without the will conducting them." These involuntary or instinctual processes are machine-like (clocks, telescopes, microscopes, gears, pulleys of all kinds were profoundly affecting human thought) and essentially dumb.
"... if there were such machines which had the appearance of a monkey ... we would have no means of recognizing that they were not of exactly the same nature as animals..." So, the lower order of animals are essentially machines. But a machine could never be mistaken for a human because machines "...could never use words or other signs, composing them as we do to declare our thoughts to others." We are separate and superior to other animals because we "act through knowledge" rather than simply through "the disposition of [our] organs."
We are further removed from nature in that "...our soul is of a nature entirely independent of the body, and that, consequently, it is not subject to die with it." Whereas, a "reasonable soul" ... could not in any way be derived from the power of matter" and therefore animals, which operate on the basis of pure matter, have no souls.
Descartes has separated human existence from that of the natural world. We're on our own and everything else is "otherness". Science is free to operate (dissecting, experimenting etc) on the natural world as if it were just another machine. But as the Theologian John F. Haught writes, "Scientists animated by the purpose of proving that they are purposeless constitute an interesting subject for study" (Haught). Embedded in all of this new thinking is doubt about the human capacity to perceive reality. The beginning of the seventeenth century was the era of trompe-l' æil (fool the eye) painting, comic illusion, and would have to anticipate the age of reason that would follow (Foucault 51).
References
Arendt, Hannah. The Human Condition. The University of Chicago Press. 1998.
____________ The Life of the Mind. Harcourt-Brace-Javanovich. 1978.
Barrow, J.D. Pi in the Sky: Counting, Thinking and Being. Little, Brown & Co. 1992.
Drake, S. Discoveries and Opinions of Galileo. Anchor Books. 1957
Foucault, M. The Order of Things: An Archaeology of the Human Sciences. Vintage Books. 1970.
Lear, Jonathan. Aristotle: The Desire to Understand. Cambridge U. Pr. 1988
Sennett, Richard. The Craftsman. Yale University Press. 2008.