Gregory Browne, in this essay, replies to criticism of his book Necessary Factual Truth, a work which attempts to combine Misesian apriorism with Randian scholasticism. Rand, argues Browne, essentially pursues the same rationalistic method as the Austrian economist Ludwig von Mises. She can do so "because Objectivists believe that all facts except those resulting from human free will choices are ... 'necessary' and that no truths [can be considered] 'non-factual' [i.e., the analytical-synthetic dichotomy is wrong]." This allows Rand to "do ethics the way she does" while harmonizing Rand's economics "with the Austrian economics of Ludwig von Mises."
As an exegesis of the Peikoff/Rand view of the analytical-synthetic dichotomy, Long's analysis is on target. Objectivists reject this dichotomy because they want to justify the rationalistic methodology whereby matters of fact are determined through the manipulation of logical structures. Despite Rand's and Peikoff's lip-service to empiricism and the scientific method, in their actual philosophical works, they tend toward a kind of scholastic rationalism. Hence the axioms, the definition-mongering, the claim that concept formation is at least in some respects analogous to algebra, and the headlong plunge into the dubious quicksands of Aristotelean essentialism.
Having not read Browne's book, I cannot say how convincing (or unconvincing) his defense of necessary factual truths. However, I would be surprised if any convincing arguments could be brought on behalf of the notion of necessary truth. The best that has been said on this issue was provided by George Santayana: "Tradition is rich in maxims called necessary truths, such as 2+2=4, that space and time are infinitely divisible, that everything has a cause, and that God, or the most real of beings, necessarily exists. Many such propositions may be necessary, by virtue of the definitions given to their terms; many may be true, in that the facts of nature confirm them; and some may be both necessary logically and true materially, but even then the necessity will come from one quarter and the truth from another."
In other words, nature (or, for theistically inclined, God) determines what is true, not logic! Here's the problem with logic: There are an infinite number of logical (i.e., necessary) truths only a small fraction of which are exemplified in reality. So how is anyone is supposed to distinguish between the factually true necessary truths and the factually untrue necessary truths? Answer: the best way to determine between the two is by consulting the relevant facts! Evidence, particularly scientific evidence, is the best way of determining factual truth (though not the only way).
What gives the sort of apriori or scholastic rationalism advocated by Rand and Mises the aura of plausibility is that in some circumstances, matters of facts are so complicated that they cannot be determined by the usual logico-experimental methods of science. This is where logical speculation, as long is it is controlled by a strong sense of the elemental facts, can prove useful. Hence the need for the sort of economic reasoning advocated by Mises and Frank Knight, among others. However, we must be aware of the important limitations of this method. Knight calls deductive economic reasoning "the method of successive approximations" and insists that "without empirical correction to real situations" economists are likely to run into trouble.