Dividing to Reach the Beginnings: Kinds of Whole and Part, Universals, and Hegel's Error

Orientation #

He is working through the first group of six questions of Book III of Wisdom [ed.: Metaphysics], having just set out Plato’s two positions (prev. lecture). He closes by announcing that next time — two weeks from now — comes the second six: four on the one and the many, two on whether the beginnings are in ability or in act. The neighbouring classes continue the same commentary on Book III.

The class, in order #

1. The second pass at the four causes (“all parts… are like the kind of cause called matter”) #

Point: Aristotle, returning to the four causes a second time, shows how broadly each is taken — and all parts, as parts, are like matter, because the whole comes to be from them and they are in it.

• First pass: material cause is “that from which something comes to be, existing within it” — bronze/silver of the statue, wood of the chair.
• Second pass examples, all immaterial or quasi-material:
  • premises of a syllogism as matter of the conclusion: in every B is A, every C is B, therefore every C is A, the parts of the conclusion (subject and predicate) are in the premises — yet the syllogism is immaterial;
  • statement defined by end (“speech signifying the true or the false”) vs. defined by matter (“speech put together from a noun and a verb”);
  • definition defined by end (“speech making known what a thing is”) vs. by matter (“speech composed of genus and differences”);
  • mother and father as parts of the family; soldiers as parts (matter) of the army.

2. Beginning, cause, element — and distinction, division, definition (“beginnings, causes, and elements”) #

Point: two triads of decreasing generality, the second built in imitation of the first.

1. Aristotle’s triad (opening of the Natural Hearing [ed.: Physics]; also the first three words of Book V of Wisdom): beginning is more general than cause — every cause is a beginning in some way, but not every beginning is a cause (the point is the beginning of a line but not its cause); cause is more general than element — element is basically the material cause, and not every material cause but the most basic one.
2. His own triad: distinction — division — definition. Every definition is a division (going from “square” to “equilateral right-angled quadrilateral” breaks the confused notion apart), but not every division is a definition. Division in the strict sense is the distinction of the parts of some whole: so every division is a distinction, not every distinction a division.

• Why this matters, in theology: between Father and Son there is a real distinction — to deny it is heresy — but never division; to speak of dividing God into three would falsely imagine God as a whole with parts.
• Consequence: since Aristotle here uses three kinds of division to reach the beginnings of reality, each kind yields a different beginning.

3. The four senses of whole and part in Book V (“there are four central meanings of whole and part”) #

Point: kinds of division correspond to kinds of whole and part; Book V gives four, and the first question uses only three.

1. Quantitative (composed) whole — a line, a circle, but also our body divided into organs, since the body is quantified. Continuous quantity is defined as that whose parts meet at a common boundary, or as what is divisible forever; Thomas: quantity by its very nature has parts.
2. Universal whole — not put together from its parts but said of them; its parts are called particulars, from “part”. Greek katholou (whence “catholic”) is kata holou, “according to the whole”: so the word for general is taken from “whole”, the word for particular from “part”. Hence in the Physics Aristotle’s analogy: the general is to the particular as the whole to the parts — we know the whole before distinguishing parts, so we know the general before the particulars.
3. Definition and its parts — genus and differences: another composed whole, but not one whose parts meet at a boundary.
4. Matter and form.

• Two cross-divisions of the four: (a) three are composed wholes, one (universal) is a whole said of its parts; (b) quantitative and matter/form are wholes in things outside, universal and definition are in the mind.

4. Cat and act: matter and form as a strange kind of part (“what’s in the word cat besides those letters”) #

Point: the matter/form sense of part is real but hidden, and so it is the one people miss.

• Ask for the parts of the word “cat” and you say c, a, t — quantitative parts. But “cat” and “act” have the same letters: what differs is the order. So the word is put together from the letters and their order — a strange, un-obvious sense of part.
• Likewise your parts: we think head, arms, legs (quantitative); but you are composed of body and soul, parts in the sense of matter and form — “more like the order and the letters.” And that may be what is most important for knowing you.
• Boundary/objection (student): you can’t call the order a part. Reply: it is intrinsic, and in some way the word is made up of it. Cut the word into c, a, t and you still have the letters — where is the order? Not there. Like the materialist doctor: “I cut up all these bodies in the lab and never saw a soul.” You were looking for the wrong kind of part.
• In Physics I Aristotle uses the other senses to show we know confusedly before distinctly: a sensible whole (a symphony, a salad dressing — you don’t distinguish the parts at first); name before definition (a child says “square” before defining it); the sense-sequence “something on the hill — something moving — a dog — Joe’s dog”. But matter and form, which is what everything that changes is found to have and is more important than anything else, does not appear in the first chapter. “Very subtle” — and that’s the one people miss.

5. The first question: divide to the elements, or say what it is? (“are they the genera, or those into which each thing is divided”) #

Point: do you reach the beginnings of a thing by quantitative division into elements, or by saying what it is (the universal)?

• Do I know “cat” better by spelling it c-a-t, or by saying “cat is a word”? Socrates taught Plato to ask what is it — and you have begun to answer when you say “a word”.
• The materialist/chemist answer: water is H₂O, cat is C-A-T, that’s its formula. Plato: you haven’t told me what it is.
• Answering the what always ends in something universal.
• Historical holders of the divide-into-parts side: Empedocles — the four roots, earth, air, fire and water, under poetic names, hate dividing flesh and blood into them; Democritus — the thought-experiment (Einstein’s word): imagine a body divided in every way it can be divided; nothing would not be left, since you cut a thing up into what it is made out of, so you must end at the uncuttable, the atoms. (Aside: I might cut you into pieces too small to find, like Jimmy Hoffa, but not into nothing; Stalin couldn’t either.) All the chemists and all the chemistry departments in the country side with them.
• His judgment: neither side has the only way. “Man walks” — it is a noun and a verb, and Aristotle in the book on the statement does divide it so; but he also defines it as speech signifying the true or the false. Both belong to knowing it, and it is in some way better to say it is a statement.
• Note: genus and difference are a bit like matter and form, since the difference determines the genus as form determines matter.

6. The second question: dividing upward or downward among universals (“you end up with the most universal”) #

Point: granted the universal is the beginning, there are still two opposed ways of dividing, giving opposite termini.

1. Divide a genus into species and species into lower species: you end at the least universal.
2. Divide by defining, and define the parts of the definition: square → equilateral right-angled quadrilateral → quadrilateral = rectilineal plane figure contained by four sides → plane figure contained by straight lines → plane figure → line. You end at the most universal.

• So three possible answers to “what is the beginning of things”: quantitative parts, the least universal, the most universal.
• Hegel takes the second road: his whole system starts from being, being rises to its antithesis non-being, the two to becoming — see the map of the system at the back of Stace’s book (Dover reprint).
• But Aristotle will say later: as matter and form are fundamental to changing things, ability and act are fundamental to all things. The answer is not among the three.

7. Universal in causing vs. universal in predicating (“universale causando… universale praedicando”) #

Point: the deepest error of Plato and Hegel is confusing what is said of all with the cause of all.

• Shakespeare’s pun (Troilus and Cressida): Cressida is kissed by the general, and kissed in general — the downfall of Cressida. MacArthur is a general (universal cause moving the army); “soldier” is general (said of everyone in it). MacArthur causes the army’s movement; “soldier” causes no one.
• Christian example: “Christian” is said of all of us; Christ is the cause of all of us. The wise man knows both the cause of all and what is said of all; the cause of all is the more important, but both are to be known — what must be avoided is confusing them.
• Why the confusion arises: we cannot grasp a universal cause without knowing its extent, and we express the extent by what is said of that extent. King vs. general: the general’s causality extends to everyone of whom “soldier” is said, the king’s to everyone of whom “citizen” is said; “citizen” is said of more, and the king causes more. So said-of-more and cause-of-more run together — but are not the same.
• Hegel explicitly identifies the being said of all things, that most confused notion of our mind, with him who said “I am who am”; hence Shakespeare is the wiser. Thomas, in Summa Contra Gentiles I, after showing God is I-am-who-am, has a whole chapter arguing that God is not the being said of all things. Many in the German universities, including theological schools, still mix them, and end in pantheism.
• Plato makes the same mistake insofar as the separated forms, said of many, are made causes of many — as all the moral virtues partake of reason.
• Spinoza anticipates Hegel: the order in thoughts and the order in things is the same; then what is first in our thought is first in things — and what is first in our thought is the most confused.

8. Genus like matter: Anaxagoras and Locke (“all of these in ability, none of them in act”) #

Point: because the more universal is the less determined, people make about genus the same mistake they make about matter.

• Wood can be shaped into table, cabinet or bookcase: indetermination. So the more universal is less determined, determined by the difference — genus is a bit like matter.
• Anaxagoras tries to put into matter actually everything that is there only in ability, and so gets into difficulties. Modern physicists saying every particle is composed of all the rest run into the same trouble.
• Locke (the text given): the general idea of triangle is neither isosceles nor scalene but “all and none of these” — putting the particular ideas together into the general. Its parts are inconsistent; a student adds that you have to use a lot of force, violence.
• The resolution he can’t reach: are the lines of the triangle in general equal or unequal? All of these in ability, none of them in act — the very distinction, belonging to the matter/form kind of whole and part, that these men cannot make.
• Still: there are elements of truth in all these positions.

9. What comes next (“the next six questions will be a little more particular”) #

The second six, also split — but four first, two second: four on the one and the many, the multitude of these beginnings (are the causes one or many?); two on whether the beginnings are in ability or in act. “Very interesting, very unusual questions.”

His words #

• Wisdom — his name for Aristotle’s Metaphysics (“the fifth book of Wisdom”).
• Natural Hearing — his rendering of Physics.
• beginning / cause / element — decreasing generality; beginning [ed.: principle], element = the most basic material cause.
• distinction / division / definition — division = the distinction of the parts of some whole; definition a kind of division.
• composed whole — “composed” from the Latin for put together; quantitative, definitional and matter/form wholes are all composed.
• universal whole — not put together from but said of its parts, which are called particulars.
• katholou — Greek for general, from kata holou, “according to the whole”; whence “catholic”.
• ability and act — [ed.: potency and act]; the distinction answering the first two questions, parallel to matter and form.
• universale causando / universale praedicando — universal in causing vs. universal in being predicated; cause of all vs. said of all.
• thought experiment — Democritus’s imagined total division, “what Einstein calls a thought experiment”.

Texts #

Read in class / commented

• Aristotle, Metaphysics III, questions 1–2 of the first group (“are they the genera, or those into which each thing is divided, existing within?”).
• Aristotle, Metaphysics V, chapter on part and whole; chapter on beginning; opening words “beginnings, causes and elements”.
• Aristotle, Physics I, opening chapter (general before particular; confused before distinct) and later in Book I (matter and form in all change).
• Locke, on the general idea of the triangle, “all and none of these” (a text they had before them).
• Handout, “Second Road in our Knowledge”, p. 5 (read from in class).

Mentioned

• Aristotle, On Interpretation — “the book on the statement” (inferred).
• Thomas Aquinas, Summa Contra Gentiles I, chapter that God is not the being said of all.
• Shakespeare, Troilus and Cressida (Cressida kissed by/in general).
• W. T. Stace, The Philosophy of Hegel (Dover), with the map of the system.
• Empedocles, Democritus, Anaxagoras, Plato, Socrates, Hegel, Spinoza.

His questions #

• Which cause are the soldiers of the army? Matter — all parts, as parts, are like the material cause.
• Is every beginning a cause? Is every cause an element? No and no: the point is the beginning of a line but not its cause; element is only the most basic material cause.
• Is every division a distinction, and every distinction a division? Every division is a distinction; not conversely — hence real distinction, but not division, in the Trinity.
• How many central meanings of whole and part are there in Book V, and how many does Aristotle use here? Four (quantitative, universal, definition, matter/form); he uses only three, and leaves out the decisive one.
• Is the order of the letters a part of the word “cat”? Yes — in the matter/form sense; the man in the street says no because he thinks only of quantitative parts.
• Do I know “cat” better by dividing it into C, A, T, or by saying it is a word? Both belong to knowing it, but it is in some way better to say what it is.
• Dividing genus into species, and dividing by defining — where do they end? The first at the least universal, the second at the most universal; neither gives the true beginning.
• Are the lines in the definition of triangle in general equal or unequal? All of these in ability, none of them in act.
• Is the cause of all the same as what is said of all? No — Christ is the cause of all, “Christian” is said of all; confusing them is Hegel’s error and ends in pantheism.