The Logic of Names: One Thing Known Through Many Thoughts, and the Names of God

Orientation #

He refers back to “question two of the Summa, those of you who were there for the ones where Thomas speaks about the existence of God,” and to “that other distinction we met between the meaning of a word and what it stands for.” At the end he asks whether “we begin the fall again” and mentions he could come “the fourth of September.” The previous class treated ST I q. 43 a. 8 and the order of theological treatises.

The class, in order #

1. Why names matter (“Hallowed be thy name”) #

Point: talking about names may look like a comedown, but names are central to theology and to the beginning of logic.

• Augustine on the Our Father: it teaches not only what to ask for but what to desire; the petition put before all others is “hallowed be thy name,” and however you understand it “you can’t get name out of it.”
• The revised Decree of Indulgences (Second Vatican Council; his first edition) singles out six litanies: All Saints, Joseph, Mary, and three for Christ, one being the litany of the Holy Name.
• Dionysius’ book that Thomas admires is about the divine names.
• Logic begins with the logic of names: Thomas explains that the Isagoge (genus, difference, species, property, accident) can be taken as a complete division of the univocal name (he says he mentioned this before).

2. Three things in a name (“three is enough”) #

Point: to understand names you need three things, not two, as with change.

1. Aristotle (in logic, but more explicitly in Natural Hearing I): change is between contraries, but two contraries are not enough; a third thing, the subject, is needed, and then “three is enough.”
2. Likewise names: the vocal sound, the thing it signifies, and that through which it signifies, the thought. Names relate first to sensible things; the thought is the hidden third, like the subject of contraries.
3. Easiest sign that thoughts are involved: universal names, man, dog, cat, horse, not just Socrates and Plato. There is no “man” or “dog” as such, only this man, this dog, so the thought is what the universal name goes through.

3. The obvious cases (“No big deal”) #

Point: two combinations are what you expect.

• One name, one thing, one thought: square in geometry, one figure, through the one thought “equilateral right-angled quadrilateral.”
• Many names, many things, many thoughts: square, circle, triangle.

4. One name, many things, many thoughts: the equivocal name (“I see said the blind man”) #

Point: one name can signify many things through many thoughts; this has a name, equivocation.

• To see: the act of the eye; Hamlet’s “I see my father… in my mind’s eye” (imagination); his mother’s “I see said the blind man, but he couldn’t see at all” (understanding). Three things, and the thought differs in each.
• Subdivided into equivocal by chance and equivocal by reason (to see has a connection, so by reason). He will not go into the ways a name becomes equivocal by reason today.
• Aside: a guidebook story that James I in Lancaster knighted a loin of beef, “sirloin”; he means to check whether that is the origin.

5. Many names, one thing, one thought: synonyms (“we call them synonyms”) #

Point: the reverse of the expected many-many-many is possible and has a name.

• Translation: man and homo, different sound, same thing, same thought (Aristotle, Peri Hermeneias).
• Within one language: drying up and desiccation.
• He notes this is a little more unusual than many-many-many.

6. One name, one thing, many thoughts (“the most unusual of the cases so far”) #

Point: one name can signify one and the same thing through several thoughts, i.e. several definitions or notions. Examples, in his order:

• Point: Euclid, “that which has no parts” (perhaps completed with “but has position”); also the beginning of a line, and the end of a line. Aside on the student who asked “do points really exist?”: bodies don’t go on forever, so there is a surface (length and width, no depth); the surface ends, so a line; the line ends, and that end is the point. Three thoughts, one thing.
• Odd number: Euclid defines even as a number divisible into two equal parts (has a half), but gives two definitions of odd, a number without a half and a number differing from an even by one, and sometimes reasons from the second.
• Difference in Porphyry’s Isagoge: (a) a name said with one meaning of many things other in kind, signifying how they are what they are (equilateral said of square and rhombus, right-angled of square and oblong; the genus says what they are, the differences how they are what they are); (b) what the species has in addition to the genus; (c) a name separating species under the same genus. Three notions, one thing.
• Continuous: in the Categories chapter on quantity, that whose parts meet at a common boundary (parts of a line at a point, semicircles at a line, parts of a body at a surface); in Natural Hearing VI he recalls that and works out another, that which is divisible forever. He himself uses both to reason that the understanding is not continuous: parts of a definition do not meet at a common boundary; thoughts are not divisible forever. “That’s a student example.”
• Demonstration and definition (Posterior Analytics II): Aristotle says a definition can be the beginning of a demonstration, the end, or a demonstration in a different order; he defines demonstration first from its end (a syllogism making us know the cause, and that it is the cause, and that it cannot be otherwise), then from its matter (from necessary premises), and demonstrates the second from the first. Likewise definition: speech signifying or making known what a thing is (from its end), or speech composed of genus and differences (from its matter). Combining the two definitions gives a third thought.

7. Many names, one thing, many thoughts (“That’s a really subtle case”) #

Point: many names can signify one thing through many thoughts.

• The transcendentals, being and one. Plato’s Parmenides has being partake of one and one of being, as if they were two things; Aristotle says no, not two things signified by two names but one and the same. Thomas more explicitly: one means undivided being; it adds a negation, but a negation is a being of reason, so it adds nothing real to being, only in thought. “That’s extremely subtle.”
• Good means the desirable; being desired is nothing real in the thing but a relation of reason.
• Perhaps also acting upon and undergoing (Natural Hearing III): if I kick you, my kicking and your being kicked are not two things, but kicking is from me to you and being kicked is in you from me. Aristotle argues acting and undergoing are the same thing as the motion: pushing the glass, the glass changing place, its being pushed, my pushing it are one change looked at in itself, as from me to it, as in it from me. Aristotle’s road from Athens to Thebes and from Thebes to Athens; distance A to B and B to A: same thing, thought not the same.

8. Crisscrossing: which combinations are real? (“three is enough again”) #

Point: crisscrossing divisions can give four real possibilities or only three; the same happens here.

• Man/woman crossed with good/bad: four real squares (good men, “not too many, but there are some”).
• Aristotle’s parts of the plot: before-and-after is the middle, before-not-after the beginning, after-not-before the end; neither before nor after is no part of the plot. Only three.
• Can one name signify many things through one thought? He sets aside the angelic and divine mind. Warning: don’t confuse what a name signifies with what it is said of. Animal is said of dog, cat, horse, but they are not three meanings of animal; it signifies one thing, a living body with senses, and to think dog, cat and horse distinctly you need three more thoughts. So no: a real possibility only for angels and God.
• So with one name only three real possibilities: one-one-one; the equivocal (one, many, many); and “the oddest animal,” one name, one thing, many thoughts. Plato/Socrates: if I find a man who can see a one in a many I’ll walk in his footsteps as if he were a god; this last case is “a very interesting one in a million.”
• Aside: a famous article on the calculus says our mind is striving to be like an angel, seeing the circle as the limit of polygons (square, eighths, dividing forever, never reaching the circle), trying to know two things distinctly by one thought. God knows everything distinctly by one thought, angels by many thoughts, we are at the bottom, needing a separate thought for each; hence the problem of specialization.
• Can many names signify many things through one thought? Same problem: no. Careful: knowing what animal is, I know dog, cat, horse only in ability [ed.: potency], not distinctly, as knowing odd number is not knowing all odd numbers. So three real cases in each half.
• “This is fundamental to the whole of our thinking”: without seeing the third thing, the thought, you could not see the strange possibilities.

9. Application to the study of God (“these are not synonyms”) #

Point: the odd cases are exactly what theology uses.

• ST I q. 2: five proofs of the existence of one thing, God, but as unmoved mover, first efficient cause (first maker), being necessary of itself, most perfect being, and so on: one name signifying one thing through many thoughts.
• The substance of God: simple, perfect, unlimited, unchanging, one. Many names signifying one thing through many thoughts, not through one; hence Thomas says they are not synonyms, since synonyms need the same thing through one thought. Simple negates composition, unchanging negates change; both know God negatively but do not negate the same thing. “God is unchanging” and “God is eternal” do not say exactly the same.
• Richard’s phrasing, “the unchangeable eternity of God” and “the eternal unchangingness,” “the perfect eternity” and “eternal perfection”: good, because the thing is the same though the thought differs; useful for meditations.
• He ordered the cases from the most obvious; some want to do away with equivocal words (a debatable matter). Aside: a story of someone [unclear in recording] teaching the sacraments under the authority of John of St. Thomas, who “makes a mistake” making the word sign univocal; separate names for each thought would avoid the problems, but there is a big reason you can’t do that. Universal importance for philosophy and theology.
• In the Summa Contra Gentiles Thomas makes a separate argument that pure act exists (act is before potency, Aristotle, “ninth book of wisdom” [ed.: Metaphysics IX]); another thought of God, as is the harder proof that to-be-itself exists.

10. Student check and supposition (“stand for”) #

Point: a student asks whether, of the eight cases, only the fourth is invalid; he answers the fourth and the eighth (the two “one thought” cases), a limitation of our mind.

• Don’t mix up what a name signifies with what it stands for (the distinction met before between meaning and standing for). Supposition has always puzzled him; best English is “stand for.”
• John 1:1: “the word was towards God”; if towards something, not what you are towards, so the word is not God; then “the word was God.” There God stands for the Father; that is not another meaning of God, a mistake people are apt to make.
• Sophism: I am the son of a man, therefore not a man (relatives are a kind of opposite; nothing is beginning of itself). Man stands for his father, Victor Berquist. Likewise “I am the father of a man, so not a man”: man stands confusedly for either son (Paul Thomas in Afghanistan or Marcus Duane in Georgia), not a new meaning. Proper answer to the sophist: “Be gone.”
• When a name is said of many equivocally, the many are its meanings (to see: eye, imagining, understanding); said univocally (animal of dog, cat, horse) they are not. Students temporarily mix this up.
• The corruption of modern logic: substituting class for universal. A class is a multitude and cannot be said of anyone (“you are the class” only by hyperbole); student is universal and said of each one alone.
• Closing aside: scheduling for the fall, a wedding in Minnesota, possibly the fourth of September.

His words #

• Natural Hearing: his name for Aristotle’s Physics [ed.: Physics].
• name / thing / thought: the three things needed to understand names; names signify things through thoughts.
• equivocal name: one name signifying many things through many thoughts; by chance or by reason.
• synonyms: many names signifying one thing through one thought.
• difference (Porphyry): a name said with one meaning of many things other in kind, signifying how they are what they are.
• continuous: that whose parts meet at a common boundary; that which is divisible forever.
• demonstration: a syllogism making us know the cause, that it is the cause, and that it cannot be otherwise (from its end); a syllogism from necessary premises (from its matter).
• one: undivided being; adds a negation, a being of reason, nothing real.
• good: the desirable; a relation of reason.
• ability: his word for potency [ed.: potency].
• ninth book of wisdom: [ed.: Metaphysics IX].
• stand for: his rendering of supposition [ed.: suppositio].
• univocal: said of many with the same meaning in mind in each case.
• class vs. universal: a class is a multitude, not said of any one; a universal is said of each.

Texts #

Read in class (recalled and commented on, not read verbatim)

• Euclid, definitions of point, even number, odd number.
• Porphyry, Isagoge, three notions of difference.
• Aristotle, Categories, chapter on quantity (definition of continuous); Natural Hearing VI (divisible forever).
• Aristotle, Posterior Analytics II (definition and demonstration; two definitions of demonstration).
• Thomas, Summa Theologiae I q. 2 (five ways, as many thoughts of one thing).
• John 1:1 (“the word was towards God… and the word was God”).

Mentioned

• Augustine on the Our Father; Decree of Indulgences (litany of the Holy Name); Dionysius, Divine Names.
• Aristotle, Natural Hearing I (contraries and subject), III (acting and undergoing); Peri Hermeneias (translation); Metaphysics IX (act before potency); parts of the plot (Poetics, inferred).
• Plato, Parmenides; Plato/Socrates on seeing a one in a many.
• Shakespeare, Hamlet (“in my mind’s eye”).
• Thomas, Summa Contra Gentiles (argument that pure act exists).
• John of St. Thomas on sign as univocal; “a famous article on the calculus.”

His questions #

• Can one name signify many things through many thoughts? Yes: the equivocal name, e.g. to see.
• Can many names signify one thing through one thought? Yes: synonyms, e.g. man and homo.
• Can one name signify one thing through many thoughts? Yes: point, odd number, difference, continuous, demonstration.
• Can many names signify one thing through many thoughts? Yes: being and one, good; acting and undergoing.
• Can one name signify many things through one thought? No, for our mind; don’t confuse signifying with being said of.
• Can many names signify many things through one thought? No: the same problem; we know dog, cat, horse only in potency through animal.
• Are dog, cat and horse three meanings of the word animal? No; animal has one meaning and is said of them univocally.
• Why aren’t the divine names (simple, perfect, unchanging, one) synonyms? They signify one thing but through many thoughts; synonyms need one thought.
• Out of those eight cases, is it just the fourth that’s invalid? The fourth and the eighth.
• Is “God” in “the word was towards God” another meaning of the word God? No; there God stands for the Father.