Crucial to DesCartes' argument for dualism, is that matter and mind are different because matter has extension and thoughts don't. Matter can be divided (infinitely?) into smaller parts, which will still be themselves matter, while thoughts aren't divisible, and hence lack spatial extension. Since matter and though have different properties, by Leibniz' identity principle, they are not the same thing.

Two developments have occurred since DesCartes' time:

  • Matter turned out to be divisible only up to a certain point, after which we arrive at indivisible elementary particles (quarks, super strings).
  • Logical atomism (Russell, Wittgenstein) provided a frame work through which ideas can be divided into basic logical atoms and mapped to facts about the outside world.

Given these 2 developments, does DesCartes' proposition that ideas lack extension because they are indivisible still hold?

  • If you're asking for my personal position, I'm not trying to 'beat' dualism. I actually want dualism to be true, but so far haven't found any reason to believe that this is the case. philosophy.stackexchange.com/questions/21983/… Oct 29, 2015 at 20:45
  • There are no "indivisible particles", nor even particles for that matter, these are only figures of speech. States in QFT are distributed superpositions, and "particles" are placeholders in Feynman diagrams used in perturbative calculations. They are neither divisible nor indivisible, classical notion of "division" is simply meaningless in this context. Logical atomism was heavily criticized by holists, including late Wittgenstein himself, and even granting it why would linguistic division have anything to do with "dividing" the mental.
    – Conifold
    Oct 30, 2015 at 0:05
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    @AlexanderSKing If it helps, while I have found it hard to "prove dualism," I have had decent luck demonstrating that under certain conditions, it is impossible to distinguish between functional phyisicalism and dualism from empirical evidence alone. Those conditions are not all that unreasonable. Trying to demonstrate something contentious like dualism "may not be wrong" is far easier than demonstrating that it is "right."
    – Cort Ammon
    Oct 30, 2015 at 0:31
  • @CortAmmon you're actually hinting at another question I have been struggling with: Dualism might never be proven, because the moment it is proven, it just becomes the new materialism. If we can make any testable and falsifiable statements about the mind substance, then that substance comes into the domain of science, and we just have to update materialism/physicalism to take it into account. I will have to post a separate question on that. Oct 30, 2015 at 3:44

4 Answers 4


Since strings and even quarks, are highly inferential, I do not believe we have any confirmation as to their "indivisibility" one way or another. Trends suggest otherwise. We have not reached some unambiguous limit of extensional "divisibility." Quite the opposite, we reach the limits of instrumentation and funding.

Logical atomism, I believe, foundered on qualia, definitions, and other problems. The logical positivist "mapping" of Carnap and others was largely abandoned as a failure. At least, this is my own understanding. This is not to say that the work did not have technological value.

I carry no torch for Cartesian dualism or 'essentialism," but I cannot accept your question "given these two developments...." Though we do not need to return to Descartes, divisibility and issues of infinite regress have not been slain and may indeed pose problems for any mathematization of "mind."

  • Actually, indivisibility is more of consequence of Heisenberg's uncertainty principle than of any experimental proof of quarks or super strings - I only mention them because they are the current candidates for fundamental particle. That result is on much more solid footing. I explained elsewhere why I think infinite regress is not a problem. I ask these question out of a desire to understand DesCartes and dualism, not some heroic effort to bring dualism down through a series of piercing SE posts. Oct 29, 2015 at 21:16
  • Well, it is a question worth pursuing. I'm not sure what to make of Heisenberg's principle as "indivisibility." Doesn't strike me as right. Just seems the very concept of "division" diverges into "entanglement" or whatever. Oct 29, 2015 at 21:53
  • Heisenberg does not imply atomicity. A smallest size of change does not result in a single set of smallest particles, especially if the quanta being changed are of sizes that are not themselves integer multiples of something -- How many red light waves per blue light wave? That varies continuously depending on the shade of each. Meanwhile strings split and join and in the process change the number of strings present and their sizes. Is that atomicity?
    – user9166
    Oct 29, 2015 at 23:37
  • @jobermark Quantization, discreteness seem to me to imply atomicity to me. The planck scale is the limit no matter how strings or quarks behave. I might have to do more research, mu knowledge is mostly basic QM, QC and semiconductors. Strings split and join, but they don't get split into anything smaller. In the same way the thought 'red' can be changed into 'color' or split into 'sensation' + 'electromagnetic radiation' but never not split into anything more fundamental. The way you describe, you're just confirming my analogy. Oct 30, 2015 at 3:32
  • Quantization does not equal discreteness in the atomistic sense. The boundary between discrete and continuous is not as clear as you imagine. Since matter is energy, it is neither discrete or continuous, but a mixture of both.
    – user9166
    Oct 30, 2015 at 16:04

There is no need to invoke modern science, the argument fails on other grounds. The evening star appears in the evening, the morning star appears in the morning, if the Leibniz's principle applied they can not be identical. Yet they are. Genome can not be a molecule, because one is a functional term, and the other a material term. Yet it is.

The whole simplicity/divisibility divide, along with other "category error" objections, are based on equivocating "identity". When a materialist says that mental is physical they mean it the same way as heat is Brownian motion, they are different ways of representing/talking about the same thing, the identity is understood de dicto. For Leibniz's principle to apply the identity must be understood de re, there is no substitutivity for de dicto identities. How do we know that simplicity and divisibility of mind/matter are de re metaphysical properties, as opposed to our de dicto ways of representing/talking about things? We don't. Assuming so begs the question against a materialist. Applying "simplicity" to matter and "divisibility" to mind strains the meaning of words, one has to make sense of them metaphorically. This wouldn't be the case if the identity was understood de re. If a neural pattern is found, which if induced in a human brain produces the perception of red we will say that the pattern is mental redness, "category error" notwithstanding.


As Conifold points out, there are lots of weaknesses in Descartes. You are just focussed on the wrong points as weaknesses.

All told, from late modern (or later) perspectives, true atomism is a non-starter in both domains.

Logical atomism failed, and we ended up with "the other" Wittgenstein, and later deSassure, Lacan and other back-and-forth/round-and-round definitions of language that involve interacting constructions, instead of atomic bases. An 'elementary' idea depends more strongly upon usage and intention the more basic it is. And the usage and intention, of course, depend upon agreement between the definitions of elementary ideas...

And someone one hundred years ago would have proposed we have reached physical atomism, as you do, only with different basic particles. They were wrong, then. So why would they be right now?

Strings themselves are not atoms, because they do not keep themselves together as unified wholes: they split and join, and are not integral multiples of some minimal element.

But more in keeping with the other realm, folks in string theory are already looking at a string as something whose outside is also an inside (see Greene's The Elegant Universe and the discussion of the Planck length) so at root physics may have the same problem as language -- there being two different perspectives, each subdivisible, where larger in one is smaller in the other.

In both cases, you can't choose atoms because when stuff gets small enough, it starts getting bigger. So as continue subdividing, you are eventually multiplying. There is a 'most definite' place, a smallest piece, but those bits are not self-contained and fixed in content, or even in the number of them before or after an interaction.

There is a minimal width of a color difference, but that does not mean the number of different colors are fixed, or that two people who agree on a single shade and a minimal difference have the same set of shades. Two strings can cross, and the short ends become one string while the long ends become another, and he middle bit ends up as a loop. Basic elements recombine in different sizes, shapes and numbers.

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    Has Logical Atomism really failed? I see it all around me everyday in my job as a programmer in both code and functional specs. Most legal documents seem to subscribe to some form of Logical Atomism to make them clear and unambiguous as well. At some point, people realized, that like all theoretical tools, its domain is limited, and that it wasn't the universal solve all that Russell originally hoped it to be. Oct 30, 2015 at 3:26
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    You see physical atomism of literal atoms, too. But that is not any kind of ultimate reality description. Logical atomism is very useful, so is atomism as the basis of Chemistry. But both have to fall back on something else when certain special cases arise (overlapping covalent bonds, for instance, require you to map orbital geometry, to break down atoms and orbitals into something less precise, but more realistic. Likewise when via the 1st Amendment religion affects law). So in the sense you want it to matter more basically, for you to use it for or against Descartes, it failed.
    – user9166
    Oct 30, 2015 at 15:54
  • @Alexander S King Logical atomism was unsuccessful as an account of scientific theories and natural languages. But formal languages and digital computers were largely engineered to its specifications, which would make it circular to have it bear on the nature of minds. Neural networks on the other hand are not atomistic, to alter a stored pattern requires adjustment of weights, which in turn alters it, and other stored patterns, as wholes. Perhaps this is the kind of "indivisibily" dualists have in mind, and the reason why it implies little on mind vs. matter divide.
    – Conifold
    Oct 30, 2015 at 18:00
  • @Conifold , unless someone disproves the Church-Turing thesis (or Deutsch's stronger physical version), which is very very unlikely, neural networks and Turing machines are computationally equivalent, and any neural pattern can be expressed in formal logic. To your point however, expressing certain neural patterns in formal logic might be intractable (i.e. NP-Complete or NP-hard) which I guess, assuming NP != P, does imply a weak form of non-reducibility. Oct 30, 2015 at 18:18
  • Even stronger results from "Control Theory" suggest that if we assume limited chaos, so that neural nets generally use transitions that are fairly differentiable, even the differences in complexity can't get too far out of hand. Compactness comes to the rescue, you make bounding approximations and they become good. To presume we actually evolved as systems that productively use chaotic dynamics seems a bit far-fetched to me. So the odds are neural nets can join the family of equivalent computers.
    – user9166
    Oct 30, 2015 at 18:55

That there is or is not a limit to the divisibility of matter, and of - conjecturally - space and time makes no real difference to how Descarte concieved the essence (for Spinoza - the essential attribute) of bodies - as extension; for we don't have to go down to the limit of divisibility to see that we can break up a chair into pieces, or a table - or to mark it with a pen and measure out a length.

But straight away we see this isn't possible with mind or thought; I can't divide my mind in two and have myself live two different lives - as much as I might devoutly wish to - and yet, and at the same time, be the same person; and this isn't something that we need think of only in theoretical terms: it's empirically valid, as the statement above of breaking tables apart is.

The thought that Russell and Wittgenstein mapped into logical atoms is the sense (sinn) of Frege; and not mind with its unitary sense of self, it's qualia, it's quiddity and haecitty.

For propositions can be written in many different ways:

Socrates is a man

Sokratis eina enas anthropos

Socrates est homo

Socrates est un homme

Socrates ek purush

And there is behind all these written or expressed propositions, a single thought.

But not as I now think it, and not also seperable from my thinking; or my self.

When I tell you, or some acquaintance this fact - I haven't broken of a piece of myself to give him this thought; whereas if I tell him I will give him half this bar of chocolate - he won't have it until he actually and physically holds it.

  • Split personalities are not unheard of, but that is beside the point, "dividing" is clearly used in two different senses when applied to tables and minds. Moreover, it makes no sense to "divide" heat, but it does dividing moving molecules that "create" it into two groups. Dualism may or may not be adequate to describe the mental, but this particular argument for it is a non-sequitur.
    – Conifold
    Oct 29, 2015 at 23:53
  • @conifold: I don't follow you... Oct 30, 2015 at 14:20
  • In the first two paragraphs you equivocate on "divide" as applied to mind and matter. Even accepting your meaning of "divide" mind can in fact get divided, as in DID patients. Even assuming that it could not your conclusion still does not follow because there is no reason why the types of division you picked for mind and matter have to correspond to each other even if mind and matter do. You equally can not divide a collective state of a neural network into pieces, it does not make it non-material however. I am not necessarily disputing the conclusion, only that the argument works.
    – Conifold
    Oct 30, 2015 at 23:02

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