Ancient vs. Modern Atomism
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This very compelling world-view has given rise to a mechanistic, deterministic, point of view that has been even more popular in modern times than it was in ancient times. (Contemporary problems about deterministic physics arising from quantum mechanics have considerably weakened the support for this point of view. The classical Newtonian view that quantum theory has replaced is basically Democritean.)
The ancient atomists may appear to have provided a brilliant anticipation of a much later scientific theory. But is this picture accurate? Our enthusiasm for the achievements of the ancient atomists must be tempered by a closer look at the basis of their view.
- An anonymous cleric filed a report with the Inquisition in which he claimed the first citation to show that Galileo was an atomist and the second to be in conflict with the Council of Trent's pronunciations on the Eucharist. The report did not lead to any action against Galileo.
- Atomism definition, the theory that minute, discrete, finite, and indivisible elements are the ultimate constituents of all matter.
Their impetus did not come from physical inquiries, but from the logical and metaphysical positions of Parmenides and Zeno. As Barnes says (Presocratics, p. 346: “the first atoms came from Elea.” Atoms were postulated in response to the Eleatic view that a truly real entity must be one and indivisible. So we must ask: In what sense were Democritus’s atoms indivisible? Democritus might have meant either of the following:
- It is physically impossible to divide an atom.
- It is logically or conceptually impossible to divide an atom.
If (a) is the Democritean position, then it would make sense to talk about the parts of an atom - there might even be such parts - although it would not be physically possible to separate the parts.
If (b) is what Democritus maintained, then this sort of talk makes no sense. The very idea of “splitting an atom” would represent not just a technological difficulty (or even a technological impossibility) but a conceptual absurdity.
- In favor of (a) are
- Burnet (EGP, p. 336):
We must observe that the atom is not mathematically indivisible, for it has magnitude; it is however physically indivisible, because, like the One of Parmenides, it contains no empty space.
- KRS, p. 415:
[An atom] is presumably only physically, not notionally, indivisible, since for example atoms differ in size.
- Burnet (EGP, p. 336):
- In favor of (b) are
- Guthrie (vol. 2, p. 396):
Democritus held that his atoms, being not only very small but the smallest possible particles of matter, were not only too small to be divided physically but also logically indivisible.
- Furley: I will give a quick sketch of the case he makes for (b).
- Guthrie (vol. 2, p. 396):
- Aristotle says that atoms were postulated to meet (what he called) Zeno’s “Dichotomy Argument.” This would be either the paradox of the race course, or the paradox of plurality.
- But, as we have seen, both of these arguments of Zeno’s are meant to show that infinite divisibility (whether physical or theoretical) leads to absurd results. Hence,
- The atomists would not be meeting Zeno’s argument unless they conceived of atoms as both physically and theoretically indivisible. Furley (p. 510):
A theoretically divisible atom would not answer either of Zeno’s arguments. [The plurality paradox] would show that an atom theoretically divisible to infinity must be infinite in magnitude; and [the race course] would show that such an atom could never be traversed - that is, if one starts imagining it, one can never imagine the whole of it.
Furley’s conclusion is supported by further evidence from Aristotle, who claims that atomism conflicts with mathematics (De Caelo 303a20):
They must be in conflict with mathematics when they say there are indivisible bodies.
But an atom that is (merely) physically unsplittable would not conflict with mathematics.
If this interpretation is correct, and atoms are theoretically indivisible, then the differences between the Democritean view and modern scientific atomism are greater than the similarities.
Objections to theoretically indivisible Democritean atoms.
- According to Simplicius, Democritus thought that atoms had size and shape:
5=A37: For some of them are rough, some are hooked, others concave and others convex, while yet others have innumerable other differences.
27=A14: These atoms, which are separate from one another in the infinite void and differ in shape and size and position and arrangement, move in the void . . . .
- But it is hard to see how someone could conceive of atoms as having size and shape, and still being theoretically indivisible. For it would seem that, for any size x, we can always think of something that is only half that size: we can always divide x by 2.
This very compelling world-view has given rise to a mechanistic, deterministic, point of view that has been even more popular in modern times than it was in ancient times. (Contemporary problems about deterministic physics arising from quantum mechanics have considerably weakened the support for this point of view. The classical Newtonian view that quantum theory has replaced is basically Democritean.)
The ancient atomists may appear to have provided a brilliant anticipation of a much later scientific theory. But is this picture accurate? Our enthusiasm for the achievements of the ancient atomists must be tempered by a closer look at the basis of their view.
Their impetus did not come from physical inquiries, but from the logical and metaphysical positions of Parmenides and Zeno. As Barnes says (Presocratics, p. 346: “the first atoms came from Elea.” Atoms were postulated in response to the Eleatic view that a truly real entity must be one and indivisible. So we must ask: In what sense were Democritus’s atoms indivisible? Democritus might have meant either of the following:
- It is physically impossible to divide an atom.
- It is logically or conceptually impossible to divide an atom.
If (a) is the Democritean position, then it would make sense to talk about the parts of an atom - there might even be such parts - although it would not be physically possible to separate the parts.
If (b) is what Democritus maintained, then this sort of talk makes no sense. The very idea of “splitting an atom” would represent not just a technological difficulty (or even a technological impossibility) but a conceptual absurdity.
- In favor of (a) are
- Burnet (EGP, p. 336):
We must observe that the atom is not mathematically indivisible, for it has magnitude; it is however physically indivisible, because, like the One of Parmenides, it contains no empty space.
- KRS, p. 415:
[An atom] is presumably only physically, not notionally, indivisible, since for example atoms differ in size.
- Burnet (EGP, p. 336):
- In favor of (b) are
- Guthrie (vol. 2, p. 396):
Democritus held that his atoms, being not only very small but the smallest possible particles of matter, were not only too small to be divided physically but also logically indivisible.
- Furley: I will give a quick sketch of the case he makes for (b).
- Guthrie (vol. 2, p. 396):
- Aristotle says that atoms were postulated to meet (what he called) Zeno’s “Dichotomy Argument.” This would be either the paradox of the race course, or the paradox of plurality.
- But, as we have seen, both of these arguments of Zeno’s are meant to show that infinite divisibility (whether physical or theoretical) leads to absurd results. Hence,
- The atomists would not be meeting Zeno’s argument unless they conceived of atoms as both physically and theoretically indivisible. Furley (p. 510):
A theoretically divisible atom would not answer either of Zeno’s arguments. [The plurality paradox] would show that an atom theoretically divisible to infinity must be infinite in magnitude; and [the race course] would show that such an atom could never be traversed - that is, if one starts imagining it, one can never imagine the whole of it.
Atomistic
Furley’s conclusion is supported by further evidence from Aristotle, who claims that atomism conflicts with mathematics (De Caelo 303a20):
They must be in conflict with mathematics when they say there are indivisible bodies.
But an atom that is (merely) physically unsplittable would not conflict with mathematics.
If this interpretation is correct, and atoms are theoretically indivisible, then the differences between the Democritean view and modern scientific atomism are greater than the similarities.
Objections to theoretically indivisible Democritean atoms.
Atomistic Simulation
- According to Simplicius, Democritus thought that atoms had size and shape:
5=A37: For some of them are rough, some are hooked, others concave and others convex, while yet others have innumerable other differences.
27=A14: These atoms, which are separate from one another in the infinite void and differ in shape and size and position and arrangement, move in the void . . . .
- But it is hard to see how someone could conceive of atoms as having size and shape, and still being theoretically indivisible. For it would seem that, for any size x, we can always think of something that is only half that size: we can always divide x by 2.