| This question <96|96> overall <97|99> Hans: <89|99>. |
| Question 118: How does Marx's statement in 138:2/o that a commodity's value material “does not contain a single atom of physical matter” relate to his other statement in 177:3-4 that “no chemist has ever discovered exchange-value in pearl or diamond.” Do they say the same thing or something different? |
| [98] Hans: Brain twister. The first statement says: value is not something that consists of physical material. If a chemist were to put value under his microscope he would not find any physical material in it. This is the mirror image of the second statement. It is logically equivalent with the second statement, but it is not identical to the second statement. |
| Perhaps one can see it best if one formulates it mathematically. A is the commodity as a physical object, and B is the value of the commodity. |
| The first statement says: from x in B follows x not in A. |
| The second statement says: from x in A follows x not in B. |
| These two statements are not identical. However they are mathematically equivalent to each other. One has to use a proof by contradiction to see this. In order to show that the first statement implies the second statement one has to argue as follows: Assume the first statement is true and x is in A. Then x cannot be in B. Because if it were in B, then by the first statement it would follow that it is not in A. Which contradicts the assumption made that it is in A. In a similar way one can show that the second statement implies the first statement. Ergo the two statements are mathematically equivalent. A symmetric way of expressing both statements would be to say that the two sets A and B are disjoint, i.e., their intersection is empty. |
| Stuart [96] does not see the difference between these two statements because he uses an ambiguous re-formulation to make sense of the first statement: |
| “the physical properties of a commodity do not contribute to its value.” |
| This re-formulation signifies a movement from the physical properties of the commodity to its value, which could be taken to mean that the commodity as a physical body does not contain value (if one focuses on the origin of the movement), or that the value of the commodity does not contain anything physical (if one focuses on the target of the movement). |
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