Confusion about labor supply and wages?

I just finished reading George Reisman’s Classical Economics Versus the Exploitation Theory and found it very insightful. However, I found one confusion that I hope somebody can clear up for me.

Here is a link to the PDF, and the paragraph in question isthe last complete one on page 11:

In this he seems to say that wages are not reliant on the quantity of labor, but rather the supply of labor. Aren’t both the same thing? It seems to be a contradiction, but maybe I am reading it incorrectly. Thanks for the help.

Supply vs. Quantity Supplied

The labor theory of value asserts that all prices are determined by some objective measure of labor-time required to produce such commodities (for Marx it was SNLT). At the same time, though, labor-power (supplied by laborers) is also a commodity, and the price of it is wages. The labor theory of value, therefore, if it is to universally explain the formation of market prices, must also explain the determination of wages. This is clearly impossible, which is why Reisman claims that the LTV can only explain the objective exchange value (market price) of reproducible commodities (labor is not a reproducible commodity).