Outline I: Historical/Metaphysical Backgrounds: early Greek philosophy/science
These summary notes based primarily on:
with additional references to
Individual philosophers are further linked to History of Ancient and Medieval Philosophy (PHIL 301) web materials, based primarily on W.T. Jones A History of Western Philosophy and additional texts as noted. See the Overview for additional information.]
A. Thales - the nature of explanation (ca. 600 B.C.E.)
B. Pythagoras - mysticism and the discovery of number (580-500)
Begins with discovery that major musical intervals are expressible in simple numerical ratios of the first four integers (octave = 2:1 / fifth = 3:2 / fourth = 4:3). --> everything else is expressible as a number of a proportion --> all things are composed of number-unit-"atoms."
Not entirely a novel insight: Anaximander
(ca. 611-545) also described the sun, earth, and moon in terms of arithmetical
proportion.
1. Other contributions:
a. Kosmos - the orderliness found in the arrangement of the universe, an order that is ultimately numerical/mathematical and comprehensible to reason.
b. Theoria - "contemplation," namely of the ultimate order of things. (It is believed that such contemplation would lead to a katharsis, a purification of the individual soul that would allow the individual to escape the cycle of reincarnation and to attain true immortality.)
2. Problem: the belief in a fundamental correspondance between mathematics and reality is universalized from one example and is reinforced by what we take to be a religious faith. This points to the modern question: why should reality be ultimately mathematical in character?
C. Parmenides
- the discovery of Being, the denial of Void
1. Either a thing is, or is not.
That which is not by definition cannot be, nor can it be thought
Therefore, the void does not exist.
Therefore, only what is ("Being"), is and can be thought
Being must then be: single, entire, immovable, homogenous, continuous, and timeless.
2. Problem: results in radical dualism between "What is" (as known by reason) and appearances (as revealed by the senses to be a world of change). The effort to "save the appearances" - i.e., to avoid "explaining" the universe only by rejecting change/appearance as empty illusion - motivates the development of "Pluralism," including atomism.
D. Democritus
- Lucretius: the arguments for atomism
1. Other pluralists (Empedocles and Anaxagoras) attempted to provide accounts of the world based on qualitatively diverse roots. These fail because they result in an explanans (the explanation) as complicated as the explanandum (what it is we're trying to account for or explain). Atomism represents an insistence that:
a. An explanation must reduce the complexity of the explanandum to a simpler set of terms, processes, etc.;
b. we may do so more successfully if we shift to a quantitative basis for explanation - i.e., atoms which of themselves have no qualitative differences (e.g., color), but the constitution of which into particular forms results in such qualitative differences.
2. The concept of an atom (an "a-tom," un-cutable) is developed to further avoid Zeno's paradox: if reality can be cut into ever smaller pieces, reality will consist of infinitely small pieces -- but even an infinite number of infinitely small pieces is nothing (infinity X 0 = 0), - i.e., reality wouldn't exist. So if reality is to exist, it must consist of particles which may be very small, but still have extension.
3. Atoms take on many of the qualities of the Parmenidean Being - eternal, indestructible, uncreated, and indivisible (a-tom). At the same time, however, the atomists introduce the conception of the Void (or, we might say, space) as part of their explanation. Contrary to Parmenides argument, they argue (in effect) that "what is" may mean (a) a material something, or (b) the space in which material things move.
4. The appeal to experience to support an argument is very old in Greek philosophy/science: Anaximenes (?-499) supported his account of the relationship between heat/cold and expansion/contraction with an "empirical" observation. We find this same appeal to experience in Lucretius' poem - e.g., the transmission of heat and sound through solids, the compressibility of things, and various observable changes, as arguments for atoms and space (Singer, 158). In particular:
a. "...if the nature of color has not been granted to the first-beginnings [atoms]...you can most easily at once give account, why those things which were a little while before of black color, are able of a sudden to become of marble whiteness; as the sea, when mighty winds have stirred its level waters, is turned into white waves of shining marble. For you might say that when the substance of that which we often see black has been mingled up, and the order of its first-beginnings changed and certain things added and taken away, straightway it comes to pass that it is seen shining and white. But if the level waters of the ocean were made of sky-blue seeds, they could in no wise grow white. For in whatever way you were to jostle together seeds which are sky-blue, never can they pass into a marble color...." (Lucretius: On the Nature of Things, C. Bailey trans. (Clarendon Press, Oxford, 1924), cited in W.T. Jones, A History of Philosophy: The Classical Mind, 2nd ed. (Harcourt, Brace, New York, 1969), p. 89.)
5. At the same time - also true to Greek philosophy/science - there is much that is simple argument:
a. Nothing can be created - because if all things came to being from nothing, every kind of thing might be born any any other thing: there would be no order, especially in biological reproduction (Singer, p. 161)
b. Nothing is destroyed - if matter disappeared over time, the world would have disappeared by now (?), but it is here, so matter cannot disappear over time (Singer, pp. 159f.) (Cf. contemporary laws of conservation of matter/ energy)
c. Space is infinite: if space were finite, and you could stand at the limiting edge - if you threw a dart, wouldn't it go beyond the edge? (Cf. the "thought experiments" which become especially critical to quantum mechanics.)
1. Correspondance between mathematics//Reality
[Anaximander (ca. 611-545); Pythagoras (580-500)]
2. Universe is ordered (kosmos) - and that order is comprehensible to human reason
[An assumption found both in Greek myth and since the earliest beginnings of philosophy/science, i.e., Thales (600).]
3. In offering an explanation:
4. We arrive at our views:
5. Religious and tradition claims are ignored.
Cf. as well Lindberg's "The Achievement of Early Greek Philosophy"
***
Additional reading:
Herbert Butterfield, The Origins of Modern Science
Robert P. Crease and Charles C. Mann, The Second Creation
George Gamow, Mr. Thompkins in Paperback
Historical/Metaphysical Backgrounds (continued)
1. The Socratic turn: shift from "physics" (natural
science) to ethics is alleged to have slowed down the development
of natural science. But:
a. This shift began with the Sophists, to whom Socrates, and then Plato, address their arguments.
b. His view (?) that the body is a temporary habitat thrown off by the soul (which persists after death) allows for human dissection 100 years later. That is, this view encourages the development of anatomy at Alexandria (Singer).
2. As Oldroyd points out, Plato - especially through the analogy
of the line in the Republic - formalizes the model of knowledge
which has become definitive for the West. More carefully:
a. The doctrine of the forms ("ideas") begins with the recognition of the importance of mathematical entities (e.g., triangles) and definitions (triangle-ness). In fact, some of the strongest arguments for the existence of the forms rest on mathematics - e.g.:
(1) the definition of triangle cannot be embodied in a material entity (many triangles - only one definition of triangle-ness);
(2) we recognize that annihilation of all material triangles would not annihilate the definition: the definition thus seems to exist in a non-material way. In particular:
(a) material triangles come into being and disappear - in contrast with the definition, which seems eternal (cf. the definition of Being from Parmenides)
(b) material triangles are recognized to be imperfect - implying that we somehow have access to a standard of perfection (i.e., the definition) which must be non-material.
(3) if our senses only reveal a plurality (many) of triangles which are transient and imperfect - how could we ever make the leap to the conception of a unitary (one) definition of the perfect, eternal triangle? (N.B. This remains a major problem for any "empiricist" epistemology - and philosophy of science: as Oldroyd puts it, "How can one, starting from observation of the world, find the theoretical principles of a science?"[13]) It would seem, rather, that we must have access to the definition first in order to be able to recognize that a particular figure is a triangle (i.e. it imperfectly, transiently embodies or "participates in" "triangleness.")
b. The problem here is related ("backwards") to the problem raised by the Pythagoreans: why should mathematical descriptions correspond to Reality? (The Pythagorean "solution": this is a fundamentally religious claim, and hence needs no further justification.) The Platonic claim is that Reality is built upon the model of the forms - and hence corresponds to them.
c. The problem here is directly "the problem of the universals."
d. As Oldroyd points out, the doctrine of the forms further stands as an attempt to answer a difficult question: why are the axioms of geometry true? Without further grounding in "first principles," - such as the forms - there is no reason to believe that mathematical knowledge is genuine knowledge. Rather, it would stand as an arbitrary manipulation of symbols.
(In Oldroyd's terms, Plato is rightly pointed to the need for a cornerstone in the arch of knowledge.)
3. It is true that Plato's focus on the forms involves a shift away from the observation side of natural science: but we will see this to be an ongoing process/problem in the history of science.
Lindberg comments, however, with regard to Plato's account of the Demiurge in the Timaeus as a rational craftsman/mathematician who constructs the cosmos on geometrical principles, including Plato's "geometrical corpuscles" - a kind of mathematical atom made of one of the five regular geometrical solids:
...Plato's geometrical corpuscles represent a significant step
toward the mathematization of nature. Indeed, it is important
for us to see just how large a step it is. Plato's elements are
not material substance packaged as the regular solids; in such
a scheme matter would still be acknowledged as the fundamental
stuff. For Plato, the shape is all there is; corpuscles are entirely
reducible (without residue) to the regular solids, which are reducible
to plane geometrical figures. Water, air, and fire are not triangular;
they are simply triangles. The Pythagorean program of reducing
everything to matehmatical first principles has been fulfilled.
(41: emphasis added, CE)
(Cf. as well Lindberg's summary of "The Achievement of Early Greek Philosophy")
Moreover, Singer credits Plato with furthering the development
of mathematics as follows:
a. Through Plato, mathematics obtained and retained a place in education. (The study of mathematics was the doorway to philosophy.)
b. the body of mathematical knowledge owes its systematic structure and logical finish to his logical teaching. Euclid's Elements, essentially the mathematical textbook for the West until the invention of calculus (17th ct. A.D.) and the discovery of non-Euclidean geometries (19th ct.), are a product of Plato's thought and Plato's school.
c. astronomy -- Plato saw that the irregularities of planetary motion were inconsistent with his view of the perfection of the universe. [Note: keep this sort of discrepancy in mind when we read Galileo] These movements had to be explained as somehow compounded of simple circular movements - a concept that he derived from the Pythagoreans. His pupils were given the task of seeking out rules by which the movements of the heavenly bodies could be reduced to a system of circles and spheres: this was the main task of astronomers until Kepler (i.e., ca. 2000 years!). Here Copernicus and Kepler are pupils of Plato, as Plato is a pupil of Pythagoras.
[Pine will refer to this in ch. 5 as "Plato's Homework Problem" - i.e., precisely the problem at the heart of the Copernican Revolution, and with it, the "Scientific Revolution" that begins modern natural science.]
d. "the analytic method" -- Singer calls this "a positive contribution to science of first-class importance," i.e., the method of assuming that a problem is solved and working back from it until a statement is reached, the truth or falsehood is already known. In this way may be discovered whether the problem is, in fact, soluble, and indications may be forthcoming as to the general direction of the solution and whether there are any limitations to it. The best example of this is in the Meno - though it must also be pointed out that germs of this approach are in the Pythagoreans.
1. By codifying logic, Aristotle provides an "instrument" of reasoning for use in science (Oldroyd, 18).
Or, to say it differently, Aristotle begins to formalize the procedure for moving ("downward") by way of deduction from first principles to claims about the particular properties of things - and, thereby, for distinguishing between valid and invalid moves.
But, as Oldroyd points out, this sharpens the focus on the important of first principles as the beginning point of any such deductive move.
2. Aristotle's "methodology" is to determine the essences
of things - and to capture this essence in a definition.
Oldroyd's position is called (linguistic) nominalism, which assumes that the meaning of terms is arbitrary. He is right to point out that the question of the relationship between the definition of a thing and the properties one can deduce from that definition is a serious issue. But we will see that this remains a serious issue for any effort to use the Aristotelian framework [i.e. that struggles to define basic essences and to derive/deduce subsequent properties from these basic entities].
Also notice that this problem is simply a variation of the original
problem: how to establish first principles?
TANGENT--
Oldroyd's comments on the question of how to adequately define the essence of the genus containing both human and chimp point to a larger issue that will arise as a continuous theme in the history of modern science.
As Oldroyd points out, since Aristotle's time, the dispute has been "between those who thought that any system would do, no matter how artificial - provided that clear criteria could be given for the organisms in their various pigeon-holes in the taxonomic hierarchy - and those who believed that there was a natural system, which might be found by methodical examination of the data..."(20f.)
As he notes, this problem is further related to the realism/nominalism dispute. In still other terms, the problem here will emerge in the modern period as a dispute between the (scientific) realists (not to be confused with the linguistic realists) and instrumentalists. In this case, the realists believe in a correspondance theory of truth - and that scientific theory provides an accurate "map" of the external reality revealed by the senses. Instrumentalists, by contrast, hold that scientific theory is a conceptual instrument for allowing us to describe, predict, and control the world of sense-experience: but whether or not such theory accurately maps the ultimate underlying realities is an issue we neither can nor need to decide.
By way of anticipation, instrumentalism will be defended by Copernicus, the philosopher Kant, - and, generally, by the developers of (beginning with Einstein) and developments in quantum mechanics (e.g., the uncertainty principle.) I want you to be aware, however, that this issue is already a "live" issue, - one raised by and pointed to by the problems we are seeing with Aristotle as he attempts to nail science more securely in sense experience (and, in this way, to insure the realism of his account), - an attempt that is problematic because (as Plato would have told us) we don't appear to directly "see" the conceptual classifications (e.g., "genus") and definitions of things through the senses.
The questions, that is, are:
3. Any Other Difficulties?
4. Singer's comments --
a. distinguished between the terrestrial and celestial orders. Ironically, this astronomical/cosmological doctrine held sway for centuries, - and was wrong -, while his biological treatises, which contain surprisingly accurate observational details, were ignored until recent times.
b. the universe is limited in space, but unlimited in time.
c. contrary to modern tendencies to accuse Aristotle of impeding
astronomy (by divorcing terrestrial from celestial) and mechanics
(by assuming the distinction between 'natural' and 'unnatural'
motion), --
"While the philosophers developed the conception of a rational world, it was the physicians, typified by Hippocrates, who first put the rational conception to the test of experience. It was they who first consciously adopted the scientific procedure..." which we now call inductive and which at the time was called Hippocratic.
"...belief in the constant sequence of cause and effect as a 'religion,' essentially a matter of faith." In Hippocratic times there was as yet no large body of exact observations by which the operations of nature could be exactly forecasted, save only the astronomical record. Thus the regularity of the astronomical sequences was, by an act of faith, set forth as the type to which all nature should accord."