Hi everyone, welcome to another entry of our Short Attention Span Reading Group

The Text

We will study On Contradiction by Mao.

It is divided into 6 sections (7 if we count the very short conclusion), none of them will take you more than 20min to read (most will take less) :).

I think this essay can be summarized by its first sentence

The law of contradiction in things, that is, the law of the unity of opposites, is the basic law of materialist dialectics.

And this is all it studies, starting to what is the difference between dialectics and metaphysics, the law of contradiction, what are contradictions, how are they defined, what are their different types, and so on. And of course what it means for Marxism.

The biggest question I am left with after reading this essay is the place of Nature in materialist dialectics...

Supplementary material

  • On Practice by Mao Tse-tung. It is significantly shorter than On Contradiction, and they both go hand in hand.
  • ChaiTRex [none/use name]
    ·
    4 years ago

    Engels said, "Motion itself is a contradiction."

    How is motion itself a contradiction? What things contradict each other?

      • a_blanqui_slate [none/use name, any]
        3·
        4 years ago

        Motion itself is a contradiction even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it.

        The denial of a unique instantaneous position for a given time t flies in the face of pretty much all of kinematics.

        You literally could not write a displacement function (because multiple positions at time t indicates the relation is not a function), and thus couldn't calculate velocity or acceleration as the derivative of that displacement function.

          • a_blanqui_slate [none/use name, any]
            1·
            4 years ago

            idk how fair it is to judge those claims based on their usefulness to kinematics.

            That's true, but then I'm left to wonder how we're supposed to judge it's usefulness. If you're describing a model for the nature of motion, what are you after if not empirical adequacy?

        • ChaiTRex [none/use name]
          1·
          4 years ago

          The denial of a unique instantaneous position for a given time t flies in the face of pretty much all of kinematics.

          The linked essay has another example of a supposed impossibility, though the proof needs a bit of filling in:

          It is a contradiction that a negative quantity should be the square of anything, for every negative quantity multiplied by itself gives a positive square. The square root of minus one is therefore not only a contradiction, but even an absurd contradiction, a real absurdity. And yet square root of minus one is in many cases a necessary result of correct mathematical operations. Furthermore, where would mathematics — lower or higher — be, if it were prohibited from operation with square root of minus one?

          In its operations with variable quantities mathematics itself enters the field of dialectics, and it is significant that it was a dialectical philosopher, Descartes, who introduced this advance. ...

          It's correct that there are no real numbers that are the square root of negative real numbers. It's a real proof by contradiction if it's filled out properly.

          How would it have been if they'd said to Descartes that complex numbers flew in the face of pretty much all of arithmetic? Because I know that complex numbers had opposition after they were invented.

          (because multiple positions at time t indicates the relation is not a function)

          A function can in fact take a set of positions (or some other type of thing containing multiple positions) and produce a new set of positions. Perhaps it's merely a useful simplification to say that there's a unique position.

          We know that we can never find out exactly where a particle is due to the uncertainty principle and we know that we can't distinguish things that are separated by less than a Planck length, so is it possible even in principle to empirically determine for sure whether or not particles have a single instantaneous position?

          • a_blanqui_slate [none/use name, any]
            2·
            4 years ago

            It is a contradiction that a negative quantity should be the square of anything

            It's not though.

            It’s correct that there are no real numbers that are the square root of negative real numbers.

            Sure, but you're changing what he is saying. Saying that the "square root of negative integer is a real number" is a contradiction. Saying "the square root of -1 is an imaginary number" is not a contradiction, it's a stipulative definition of i.

            A function can in fact take a set of positions (or some other type of thing containing multiple positions) and produce a new set of positions. Perhaps it’s merely a useful simplification to say that there’s a unique position.

            Functions by definition produce a single unique output for a given input. To say that something is in two places at one is to say that you can't describe motion as a function of time, which is the opposite result of kinematics. See the second image in the linked section.

            We know that we can never find out exactly where a particle is due to the uncertainty principle

            That's not what Heisenberg's uncertainty relation says. And wouldn't matter anyway because epistemic uncertainty is different than ontological non-existence. Not knowing the exact position doesn't not proscribe the existence of an exact position.

            • ChaiTRex [none/use name]
              ·
              4 years ago

              Sure, but you’re changing what he is saying.

              Engels isn't a mathematician. To demand that he get correct every detail of a proof he may have heard once and that he has no training to reproduce is a bit overblown when the conclusion is correct and the true proof that he's obviously referencing would have been produced historically.

              Functions by definition produce a single unique output for a given input. To say that something is in two places at one is to say that you can’t describe motion as a function of time, which is the opposite result of kinematics. See the second image in the linked section.

              This is blatantly incorrect. Function outputs don't have to be unique. That's an injective function. If functions produce one output, that one output doesn't have to be a single number, it can be a single set of positions. You can have a function that takes in the starting set of positions and produces the resulting set of positions.

              That’s not what Heisenberg’s uncertainty relation says. And wouldn’t matter anyway because epistemic uncertainty is different than ontological non-existence. Not knowing the exact position doesn’t not proscribe the existence of an exact position.

              You must be having an argument with someone else in your head, because my point was that we can't know for sure whether or not particles have single positions, not that single positions are proscribed.

              • a_blanqui_slate [none/use name, any]
                ·
                4 years ago

                You're confused

                A function f from a set X to a set Y is defined by a set G of ordered pairs (x, y) such that x ∈ X, y ∈ Y, and every element of X is the first component of exactly one ordered pair in G.

                Function outputs must be unique for a given input. At time t, the position function must have a exactly one output. That can be a vector if you like, but it must always be the same vector for the same given t.

                You're confusing this with one-to-one, which would be to say the position at every time must be different than every other time. Which is not what I'm talking about, because I've always been focusing on some given time t

                my point was that we can’t know for sure whether or not particles have single positions

                Yeah, well your buddy Engels here knows they can't, because of dialectical gibberish. And you're still using a popscience misrepresentation of the inequality. The position of a quantum particle can be known to an arbitrary high position (i.e, as exactly as you want). That just has consequences for our knowledge of the momentum.

                • ChaiTRex [none/use name]
                  ·
                  4 years ago

                  You are apparently unaware that sets can contain sets, so the element of set Y in your definition can itself be a set, so the output of a function can be a set.

                  The position of an arbitrary particle can't empirically be known as exactly as you want because there are limitations to measuring devices, as you are apparently also unaware.

                  • a_blanqui_slate [none/use name, any]
                    ·
                    4 years ago

                    You are apparently unaware that sets can contain sets, so the element of set Y in your definition can itself be a set, so the output of a function can be a set.

                    Nope, like I said, it can be a vector, or a set, if you like. But it's always going to be the same unique set for a given input

                    limitations to measuring devices, as you are apparently also unaware.

                    Which has also nothing to do with the uncertainty principle; it's independent of any sort of technological limitations.

    • unperson [he/him]
      ·
      4 years ago

      I haven't read the relevant Engels work but I imagine he's invoking Aristotle's arrow paradox.