The first part of the book is a defense of the labor theory of (exchange) value: First, that labor creates economic value, and second, that the exchange value of a commodity is the amount of socially necessary labor time to create that commodity. This theory stands in opposition to the subjective theory of value, that the exchange value of a commodity is determined by subjective use-value, and the scarcity theory of value, that the exchange value of a commodity is determined by the scarcity of its supply relative to the demand. There's also the marginal theory of value, but that's a topic for another post.
The subjective theory of value seems hard to make falsifiable: how do you quantify the subjective perception of value independently of the actual exchange price. The scarcity theory applies even in theory only when supply is inelastic, but it's fairly obvious that the production of most commodities — food, oil automobiles, DVD players, computers, buildings, etc — is elastic; the most significant inelastic item of value is real estate.
However, Carson makes an enormous philosophical error:
As Mises wrote, the variables of the market are so many that no laws can be induced from mere observation, without the aid of valid starting assumptions established on an a priori basis. ...It's just bullshit to be concerned with the after-the-fact interpretive value of a theory.
If an adequate theory of value requires a high degree of predictive value concerning concrete prices, then both the labor theory and subjective theory fall apart equally. On the other hand, if value theory in the sense of an empirical rule for predicting concrete prices is impossible because the variables are too many, then both theories are likewise on equally untenable ground. But like Mises' subjective theory of value, our version of the labor theory is a set of a priori axioms and the deductions from them, which can be used to more usefully interpret market data
after the fact. [emphasis original] [pp. 75-76]
It is a fallacy of naive empiricism that one must "induce" laws from mere observation. All scientific laws are not a priori assumptions, but hypotheses from which we derive empirical predictions; if the predictions match the observations, the theory is supported; if not, it must be somehow revised. Empirical observation is the context of justification, not the context of discovery.
The Labor Theory of Value makes several empirical predictions about concrete prices. Most importantly, there should be a substantial correlation between measurable socially necessary labor time and actual prices in any economy. Furthermore the correlation should become when we control for independently determinable variables representing externalities, such as physical and socially constructed inelasticity. (We could also independently determine differences in external variables when two unrelated commodities had similar labor times but very different prices, or similar prices but different labor times.)
The Labor Theory of Value makes dynamic predictions. Assuming we were to find a correlation between labor time and price, we can then determine a general average correlation over many unrelated commodities. The Labor Theory of Value predicts the supply of commodities that had a price/time ratio lower than average would fall over time, and the price/time ratio would increase; likewise the supply of commodities that had a price/time ratio lower than the general average would rise over time, and the price/time ratio decrease.
Scientists and statisticians — especially biologists and ecologists — have figured out a lot of ways to test hypotheses under conditions with a lot of interacting variables. There's simply no reason not to apply these tools and techniques to the Labor Theory of Value.
Carson does note the Positivist fallacy of the Austrian school of economics:
The Austrians have made a closely related argument: that equilibrium price is an imaginary construct that can never be observed in the real marketplace. [p. 76]We don't need to directly observe anything for it to have scientific validity: it just has to be an ineluctable component of a theory that overall matches what we can directly observe. Furthermore, we can actually observe some sort of equilibrium: all similar DVD players, tomatoes, automobiles, etc. all cost about the same from store to store and from day to day, even though there is (usually) no collusion or intentionality to keep prices stabile.