Metaphysics IX: The Second Error, 'Everything Is Possible', and the Definition of the Possible

Orientation #

He opens “in the second part of this reading” — in the chapter division, the start of chapter four — the “second mistake” about the possible, which he says he had to finish “right before I break up” [unclear in recording]. The previous class treated the definition of the possible and of act in Book Theta; the next takes the fourth reading of Book IX on innate vs. acquired powers and rational vs. non-rational powers. Verified sources place this class in Aquinas’s lectio 3 on Metaphysics IX, with handout pages “The First Definition of Reason” p. 103 and “Texts for the Name Being” p. 10 in use.

The class, in order #

1. Thomas’s division and the two senses of “possible” (“the possible that includes the necessary”) #

Point: before reading the text he lays out Thomas’s division (two parts: Aristotle briefly states the error, then brings in the consequence about A and B) and the distinction Thomas needs.

• Distinction: possible opposed to necessary (what is able to be and able not to be) vs. possible that includes the necessary (what is not impossible). If the necessary were not possible in some sense it would be impossible — “obviously not”; so there must be two meanings of “possible” or “able”.
• Student asks whether the necessary gets its own name because it has “something significant” added. He agrees “partly”: things able to be divide into those also able not to be and those that must be; the second group has something worth talking about, so they get the new name “necessary”, while the first just keep the name “able” — that is why the narrower sense is the more known one. “Able not to be isn’t really an ability.”

2. The second error: everything is possible but some will never be (“something is possible, but will not be”) #

Point: he reads 1047b (inferred) — if the possible is as defined, it is not true to say something is possible but will not be — and uses Thomas to explain what is at stake.

1. The position: everything is possible, even the diagonal being commensurable with the side, “but it will never be”; this is how they escape admitting anything impossible. (He notes Aristotle “doesn’t say it clearly”, the diagonal being the famous Greek example everyone would know.)
2. Aristotle’s reply, going back to the definition: the possible is that which, when posited, results in nothing impossible. If you posit the diagonal measured with the side, something impossible happens. So it is not possible.
3. He stresses Aristotle’s point that the false and the impossible are not the same: false is what merely happens not to happen (“for you to stand now is false, but not impossible”); the impossible is another matter. So “possible but will never be” collapses false into impossible. Aside: he calls this position “kind of strange” and less probable than the first error (that of the Megarians, prev. lecture context implied).

3. Who says everything is possible, and why (“God can’t make a square circle”) #

Point: a digression on the sources of the second error, since Thomas gives no reason for it.

• Students: people say “anything’s possible”, “in some other world”; and people get upset if told God cannot make a square circle — “He can do all things, so it must be possible.”
• His diagnoses: it is the extreme opposite of “everything is necessary” — maybe they want to be free; maybe it comes from imagination. Test: you can imagine a gold mountain, a unicorn, a mermaid, but can you imagine a square circle? (Student: make it big enough and you can’t see the curve.) He concludes it “seems to come more from a weakness of mind”.
• Support from Metaphysics Book II: some want everything shown with mathematical certitude; others are bothered by certitude, either because they cannot follow it or because it seems illiberal. Shakespeare’s “stingy truth” in the sonnets: stinginess is opposed to liberality, and the truth seems stingy (praising a dinner but saying “that dish was not so good”). Thomas: to seek certitude is the sign of a good mind, unless sought where it cannot be found; so the weak mind cannot follow the rigour and cannot see that some things are impossible — hence everything is possible.
• Student: the incommensurable is a good example because at first it seems false — imagination always finds a small enough measure.
• Second source, the “mushy thinking” of technology: what we thought impossible (going to the moon, talking across the world, flying) became possible, so “even the impossible becomes possible”, and you don’t limit the models science might use.
• Comparison of the two errors: the first (everything necessary) is the mistake of the better mind, the second of the lesser mind; a scientist can make both — the first from mathematics, the second from technology. Asides: a student recalls someone teaching that at death each picks his own world (Mormons?).

4. The A and B argument as Aristotle states it (“if A is possible, then B must also be possible”) #

Point: he works through the text from about b14 (inferred; the recording gives “914”) to line 27, where the Greek is “kind of messed up”.

1. Premise: if A is so, then B is so, necessarily. (The truth of an if-then statement consists in the consequent following necessarily from the antecedent; it says nothing about whether antecedent or consequent is in fact so.)
2. Suppose A possible. By the definition, if A is posited nothing impossible follows. Posit A; then B is so; so B is not impossible. If B were impossible, then A would be impossible (or the if-then was not true).
3. Direction matters: from “B impossible” you may conclude “A impossible”, but not from “A impossible” to “B impossible”, since B could be so for some other reason. Example: if Socrates is a dog, he is an animal; it is impossible for him to be a dog, but that does not make animal impossible; whereas if animal were impossible, dog would be too.

• Further examples: “if 3 is 6, then 3 is half of 12” is a true if-then though 3 = 6 is impossible; “if a number is even it is not odd” plus “it is possible for a number to be even” gives “it is possible for a number to be not odd”.
• Student asks what “the first was impossible” (line 25) refers to; he explains the Greek there can be read “if impossible” or “if necessary”, the sense being: if B is impossible, it is necessary that A is impossible.
• Why Aristotle brings this in: the second error says “possible but it will never take place, and if it did, something impossible would happen” — you cannot have your cake and eat it.
• He reads the Greek (houtōs echontōn tōn A B, ei to A dynaton, anankē kai to B): as A is (so, or possible), so B must be.

5. The third admission: three statements that cannot stand together (“the third admission is a dangerous one”) #

Point: the form of Aristotle’s move is Socrates’s: two admissions may be harmless, the third gives a contradiction.

• The triad: (i) if A is so, B is so; (ii) A is possible; (iii) B is impossible. From (i)+(ii): B is possible, contradicting (iii). From (i)+(iii): A is impossible, contradicting (ii). So give up one: B not impossible, or A not possible, or the if-then not true.
• Slave boy (Meno, inferred): doubling the side doubles the square; 2×2 = 4, 4×4 = 16; but 16 is not double 4, so one of the three must go.
• His simplified classroom version: a rectangle with sides 2 and 3 and area 8 — either side-claim alone is harmless, the third “finishes you off”, since 2×3 ≠ 8, 8/2 ≠ 3, 8/3 ≠ 2.

6. Student objection: is “if A is possible, B is possible” a premise? (“mixing up the conclusion with the premise”) #

Point: a long exchange over whether Aristotle argues from a possibility-conditional, or only from the being-conditional.

• Student reads lines 26-27: “if when A is possible B must be possible, then if A is, necessarily B is” — and takes the possibility-statement as a premise. Berquist: he is “mixing up the conclusion with the premise”; the possibility-conditional is the conclusion, and Aristotle is “just putting the two together”. A conditional syllogism has one if-then, one simple statement, and a simple conclusion; stating the conclusion as an if-then is only a dramatic form.
• His account of the two statements: “if A is, B is” prescinds from possible/impossible; it is only a connection. From that necessary connection of being follows a connection of possibility. That is why you can argue: if B can’t be, A can’t be. If adding “possible” changed the forms of premises, this way of talking would make no sense.
• Test case put by a student: major “if A is possible, B is possible”, minor “A is”: can you conclude “B is”? He answers: no — you only get “B is possible” (or “B is not impossible”); “it could be that B is not, but it couldn’t be that B is impossible”. To conclude “B is” your premise must be “if A is, B is”.
• Student’s reconstruction via the definition: “A possible” means if A is, nothing impossible follows; posit A; then B; if B is impossible, something impossible follows from A being so, so A was not possible. He agrees: “that’s what he’s saying” — Aristotle makes the transition from “A is possible” to “let A be so” through the definition, by reduction to the absurd, not by a simple syllogism.
• He notes the two ways of reasoning from a conditional: affirm the antecedent, or deny the consequent; from the possibility-conditional you get “B possible” or “A not possible”, never “B is”.

7. What the argument shows against the second position (“everything’s possible, but it won’t take place”) #

Point: closing the reading. The second position says everything is possible though not all will take place; but among these are things impossible, and Aristotle takes it as evident from the meaning of “possible” that nothing impossible follows from positing the possible. If everything were possible, the strength of conditional arguments would be lost. The recording breaks off mid-sentence (“something can’t …”).

His words #

• able / possible — his rendering of dynaton; two senses: able to be and able not to be (opposed to necessary) vs. able in the broad sense (not impossible, includes necessary).
• necessary — “not able not to be”; gets a new name because it has something added.
• false vs. impossible — false: just does not happen to happen; impossible: cannot be.
• illiberal / stingy truth — certitude seen as illiberal (Metaphysics II); Shakespeare’s phrase for the truth as opposed to liberality.
• mushy thinking — the technological “everything’s possible”.
• if-then statement — its truth consists in the consequent following necessarily from the antecedent; conclusion of a conditional syllogism is always a simple statement.
• the third admission — Socrates’s point that two admissions can lead to contradiction with a third.
• houtōs echontōn tōn A B — “A and B having themselves in this way” (that if one is so the other is so).
• ei to A dynaton, anankē kai to B — if A is possible, necessarily B too.
• reduction to the absurd — how Aristotle gets from “A possible” to “let A be so” and then to the contradiction.

Texts #

Read in class

• Aristotle, Metaphysics IX ch. 4, opening (1047b, inferred; lines “38”, “14”, “23-27” cited from his text; Greek phrases read aloud).
• Thomas Aquinas, Commentary on Metaphysics IX, lectio 3 (verified source) — the division of the passage and the two senses of possible.
• Handouts: “The First Definition of Reason” p. 103; “Texts for the Name Being” p. 10 (verified sources; not named in the transcript).

Mentioned

• Aristotle, Metaphysics Book II — on those bothered by certitude.
• Thomas on seeking certitude as a sign of a good mind (locus not stated).
• Shakespeare, Sonnets — “stingy truth”.
• Plato, Meno (inferred) — Socrates and the slave boy doubling the square; “the third admission”.

His questions #

• Why must there be a sense of “possible” in which the necessary is possible? Because otherwise the necessary would be impossible, which is obviously not so.
• Do you find people who say everything’s possible, and do they mean it? Yes — “in some other world”, and those upset that God can’t make a square circle.
• Why do they think everything’s possible? Thomas gives no reason; he suggests imagination and, more, a weakness of mind that cannot follow rigour.
• Can you imagine a square circle? He thinks not; a student: make it big enough that you can’t see the curve.
• Can you argue from A impossible to B impossible? No — B could be so for some other reason; only from B impossible to A impossible.
• Can you admit all three: if A then B, A possible, B impossible? No; any two contradict the third, so one must be given up.
• If “if A is possible, B is possible” and “A is”, must you admit “B is”? No — only that B is possible / not impossible.
• Is there a way to work from the definition of possible to the conclusion? Yes: A possible means positing A yields nothing impossible; posit A, get B; if B impossible, A was not possible.