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There is a certain passage by Karl Marx I remember in which he talks about the assumptions behind the meaning of the number 1.

Marx points out that when we add together two items, such as apples (not sure if that's the example he used), that each of those items is inevitably different. He goes on to say (as I remember it) that we must assume that different things are in some way the same in order to do simple operations like addition and counting.

I'm not very knowledgeable about Marx's writings and searches for this passage have turned up nothing.

Can anyone tell me where I can find this passage? Or if I just imagined it?

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    It is a well known "philosophical" doubt: how can two things be identical? For phisical things: they can't. But numbers are abstracts.
    – Mauro ALLEGRANZA
    Commented Feb 22, 2022 at 18:46
  • @MauroALLEGRANZA Are you saying physical things cannot be identical?
    – Sandejo
    Commented Feb 22, 2022 at 22:41
  • @Sandejo physical things cannot be identical in every aspect - e.g. even "identical" particles by the definition in this article cannot occupy the same position in space, so they differ in at least one quality.
    – Mack
    Commented Feb 23, 2022 at 5:57
  • @Mack That is only true for fermions, not bosons. Even then, you cannot say that "particle A" is in state 1, and "particle B" is in state 2. You can only label the particles by there states, but you cannot tell if the two particles are swapped.
    – Sandejo
    Commented Feb 23, 2022 at 6:07
  • Maybe useful Hubert Kennedy, Karl Marx and the foundations of differential calculus, HistMath (1977) and Mathematical manuscripts of Karl Marx
    – Mauro ALLEGRANZA
    Commented Feb 23, 2022 at 8:22

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This strikes me as something from early in "Das Kapital". I skimmed the first four chapters without finding an exact match. The closest I found was this:

Let us take two commodities, e.g., corn and iron. The proportions in which they are exchangeable, whatever those proportions may be, can always be represented by an equation in which a given quantity of corn is equated to some quantity of iron: e.g., 1 quarter corn = x cwt. iron. What does this equation tell us? It tells us that in two different things – in 1 quarter of corn and x cwt. of iron, there exists in equal quantities something common to both. The two things must therefore be equal to a third, which in itself is neither the one nor the other. Each of them, so far as it is exchange value, must therefore be reducible to this third. (paragraph 6 of chapter I)

I suggest you look through those chapters and see if you can find more precisely what you're looking for.

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    I think the passage is spot on. As a side note: Marx goes on to argue that this comparable quality inherent to all goods -- indeed, the only such quality -- is the amount of labor "congealed" in them, and that the labor (basically, in hours) therefore defines the price. I always took issue with this argument because quite obviously the labor on the production side has an equivalent in the use, or usefulness, on the consumption side. This usefulness is an equally shared and comparable quality. The synthesis of both makes the price: Items nobody wants are worthless, regardless of any labor.
    – Peter - Reinstate Monica
    Commented Feb 23, 2022 at 1:11
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    @Peter-ReinstateMonica in fact it's wrong even before that... the ratio of equivalence is different for every different person you ask, depending on the uses they have for iron, or for corn. Values are subjective and goods are never really fungible except when viewed from a very long distance. But in any case the passage identification seems right.
    – hobbs
    Commented Feb 23, 2022 at 2:39
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    @hobbs: I think you've missed the essence of commodification, which obscures both use-value and labor-value under abstract and generalized exchange-value.
    – Ted Wrigley
    Commented Feb 23, 2022 at 5:14
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    @Peter-ReinstateMonica "Items nobody wants are worthless, regardless of any labor." - and exactly this happened in countries trying to implement marxist economics: factories produced a lot of things nobody wanted (but it looked good in statistics how much productivity has gone up) and there was always a dire shortage of essential products.
    – vsz
    Commented Feb 23, 2022 at 5:30

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