Clarification: Bitcoin or any currency, asset or collectable doesn't literally "store value". Value is just a mental operation. 
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Great point. That deconstruction helps argue against the "shared illusion" "collective delusion" and "intersubjective" definitions of money.
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Folks too often confuse "subjective" with "illusion" or "arbitrary", when there is still tons of empirical and rational thinking out there informing subjective judgments. All intersubjective things (markets. etc.) fail if they don't ultimately reflect objective knowldge.
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Yes! A lot of people use AE to justify that all value is subjective. But value has both an objective and a subjective part. The thing is that economics only deals with the subjective part. The exception to that is money, and that's partly why monetary economics is so hard.
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Concrete example of objective value?
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Writing a text exactly about that! Coming soon!
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It imagine you are choosing between two types of gasoline to fuel your car. There’s an objective measure of use-value (octanes per volume, or something like that). You can objectively say that one is X better than the other. But you should talk to a chemical engineer.
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I think Menger used the term "utility" to designate this objective aspect, might be more appropriate term to make a clear distinction from the subjective concept of "value".
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I certainly have to dig deeper, but I think Menger used the word utility in a very different meaning from the one we do nowadays. The term utility was used by him as a property of any good (like air has utility). But only economic goods can have use-value.
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