Hausman and MacPherson (2006, Introduction) provide a more detailed discussion of all three of these objections and answers to them.
1: Values are not scientifically meaningful because they do not correspond to any observable phenomena. [“independent of sense experience” - Ayer]
The positivist idea that facts must be verifiable by confrontation with direct experience ran into trouble with gravitational fields, charges on electrons, and many other theoretical entities which could not be parsed out of existence as being convenient shorthand descriptions of sensory data. Mathematical concepts are meaningful even though they do not correspond to any observable entities, and are not analytic in the sense that the positivists sought to show. Putnam (2002) provides a sophisticated philosophical discussion, while Hausman and McPherson (2006) provide an intuitive approach. The upshot is that concepts like charges, cruelty, alienation and exploitation can be meaningful without having any direct connection with observable entities. Indeed, the charge of ambiguity and meaninglessness applied to ethical values can be reversed; Putnam and Walsh (2010, draft) cite an observation of White that the concept of “stealing” seems crystal clear, when compared with the central positivist idea of “observability,” which has been critiqued and re-defined many times and continues to be controversial.
2: A moral judgment is an imperative – a demand for action, or an expression of “ought” – which cannot be assessed for truth or falsity. [“do not come under the category of truth or falsehood.” -- Ayer]
The positivist conception of knowledge as statements to which the binary attribute of true/false is applicable is too narrow. Consider for example, alternative strategies for treating cancer, which have different implications on longevity and quality of life during and after treatment. Like choices among lifestyles, comparative statements like “strategy A is preferable to strategy B” may not have truth values, but nonetheless fall within the scope of scientific investigation. Subjective evaluation of relative tolerance of different potential side effects must be combined with gathering data on past comparable cases, and making inferences to potential probabilities of different outcomes. A more striking example arises from the Gödel undecidability of the continuum hypothesis (CH); see Cohen (1967) for a lucid presentation. Both CH and its negation are consistent with the Zermelo-Fraenkel axioms for set theory, and therefore neither true nor false. Both Cohen and Gödel came to the view that choice among the two must be based on intuitive grounds.
The naïve view that empirical and objective issues can be isolated, and studied in separation from the value based and subjective issues can be challenged on many grounds. Some aspects of the complex interdependence between preference, beliefs, welfare, and normative policy choices are explored in Hausman and McPherson (1994, and also 2006 Section 8.3.1.).
3. Value judgments are subjective, arbitrary and cannot be discussed rationally. There is no way to resolve disagreements. [“unverifiable … as a cry of pain” -- Ayer]
To refute these positivist views, widely echoed in popular economics textbooks, it is enough to cite Sen (1987), Putnam (2002), as well as Hausman and McPherson (2006) both as counterexamples (rational discussions of value judgments) and refutations (they show how to discuss value judgments rationally). This positivist idea is predicated on the possibility of sharp separation of facts and values. Mongin (2006) and Putnam (2002) give several examples of statements which generate substantial controversy regarding whether they should be classified as facts or values. At the same time, it is easy to give examples of value judgments which command substantially greater consensus.