Hello, thank you for sharing the paper. This is an interesting philosophical point; however, I have the impression that your conclusion is not true for all the possible value functions.
All the examples in your paper assume that the value of a commodity is linear in the amount of it (for example, Plutonium costs 5$/mg). But what happens if the value of a commodity increases with time? For example, a never-ending plutonium speculation bubble could make 1 mg of plutonium cost 1$ x exp(kt), for some k.
I feel that you have a point, but I think that you should axiomatize what properties the “value” function fulfills. If I do not want to sell my stuffed toy for any price, does it mean that it has an infinite price? Does your argument still hold if we replace “value” with “beauty” or any other undefined concept, or is this an argument specific for economic value? If yes, what is your definition of an “economic value” functional?
Maybe you have already answered to this kind of objection and I did not notice it.
“All the examples in your paper assume that the value of a commodity is linear in the amount of it” No, this is only assumed for the economic value, and does not change the finitude of the value. Also see the discussion about exponential versus polynomial growth.
”If I do not want to sell my stuffed toy for any price” See the discussion of lexicographic utility.
You are saying that you can always redefine the value function to be finite, while maintaining the lexicographic order.
Fair enough, but then your “value” is no longer a measurement of the amount of effort/money/resources you would be willing to pay for something. It is just a real function with the same order relationship on the set of objects.
It is certainly is possible to construct a “value” function which is finite over all the possible states of the universe, I totally agree. But is this class of functions the only logically possible choice?
>then your “value” is no longer a measurement of the amount of effort/money/resources you would be willing to pay for something
No, that’s exactly what I’m saying isn’t true. If the preference order for bundles of goods (which include effort/money/etc.) doesn’t change, no decision—including tradeoffs between effort/money/resources—will change.
Hello, thank you for sharing the paper. This is an interesting philosophical point; however, I have the impression that your conclusion is not true for all the possible value functions.
All the examples in your paper assume that the value of a commodity is linear in the amount of it (for example, Plutonium costs 5$/mg). But what happens if the value of a commodity increases with time? For example, a never-ending plutonium speculation bubble could make 1 mg of plutonium cost 1$ x exp(kt), for some k.
I feel that you have a point, but I think that you should axiomatize what properties the “value” function fulfills. If I do not want to sell my stuffed toy for any price, does it mean that it has an infinite price? Does your argument still hold if we replace “value” with “beauty” or any other undefined concept, or is this an argument specific for economic value? If yes, what is your definition of an “economic value” functional?
Maybe you have already answered to this kind of objection and I did not notice it.
“All the examples in your paper assume that the value of a commodity is linear in the amount of it” No, this is only assumed for the economic value, and does not change the finitude of the value. Also see the discussion about exponential versus polynomial growth.
”If I do not want to sell my stuffed toy for any price” See the discussion of lexicographic utility.
You are saying that you can always redefine the value function to be finite, while maintaining the lexicographic order.
Fair enough, but then your “value” is no longer a measurement of the amount of effort/money/resources you would be willing to pay for something. It is just a real function with the same order relationship on the set of objects.
It is certainly is possible to construct a “value” function which is finite over all the possible states of the universe, I totally agree. But is this class of functions the only logically possible choice?
>then your “value” is no longer a measurement of the amount of effort/money/resources you would be willing to pay for something
No, that’s exactly what I’m saying isn’t true. If the preference order for bundles of goods (which include effort/money/etc.) doesn’t change, no decision—including tradeoffs between effort/money/resources—will change.
Ok, now I get it.