The falsity of the labour theory of value

Marx’s argument—as set out in the first chapter of Das Kapital—for the labour theory of value is based on three false claims.  The first is:

The utility of a thing makes it a use value. But this utility is not a thing of air. Being limited by the physical properties of the commodity, it has no existence apart from that commodity.

This is wrong, for utility is utility to someone. The utility comes from its connection to their purposes. So, the utility of a thing does have existence apart from that commodity, it exists in the relation of the thing to the purposes of anyone who has a use for it.

The second is:

…[commodities of equal value] must, as exchange values, be replaceable by each other, or equal to each other. Therefore, first: the valid exchange values of a given commodity express something equal; secondly, exchange value, generally, is only the mode of expression, the phenomenal form, of something contained in it, yet distinguishable from it.

Which is equally wrong,…