In my prior criticism of Austrian economics (https://steemit.com/libertarian/@seanbrown/the-fatal-flaw-of-austrian-economics), I noted how you cannot reason your way to meaningful conclusions entirely a priori. That does not, however, mean that you cannot deduce certain economic principles by simply starting with a few simple observations and working up from there. Regardless, this line of reasoning would still be considered a posteriori.
Hans Hermann-Hoppe elaborated on what is elsewhere called "Robinson Crusoe Economics" to generate extremely insightful observations about the nature of opportunity cost, savings, investment, and more. In this fictionalized, one-man economy, there are indeed many useful insights. But this thought experiment is not purely a priori, since it must have at least observed the world in order to note its total, unbending scarcity in its every facet, including that of time itself.
This is still an improvement over strict a priori derivation, however, since we are merely noting what the necessary conditions are to achieve certain outcomes. For example, the concept of scarcity alone is enough to deduce that in order for a man to deliberately to produce an advancement in technology, he must have accumulated some form of savings on which to support himself -- or even to invest in the actual development of his new technology -- while he is devoting more of his scarce time to innovation and less of it to collecting resources for himself and his immediate needs. This is purely logical conclusion, and it is a very much true one, but it required the observation of scarcity, which is very much a posteriori.
In essence, the fault of Austrian economics is its assertion that the whole of economics can be derived in total isolation from reality or knowledge of the world. This is not true. Note that in my example of technological advancement, nowhere does it assume that the man wishes to advance his technology; it simply posits that he must engage in certain general activities if he wants to advance his technology, simply as a result of scarcity. This is not praxeology; this is simply deductive reasoning.
"Mainstream economics" does not totally reject the concept of logical derivation of economic principles, and neither does it totally embrace statistical modeling. The Production Possibilities Curve, for example, is one such deductive concept; it nowhere assumes the behavior of individuals but instead merely makes observations about the state of the world, and then logically extends those purely factual -- and not predictive in the least -- observations. But only Austrian economics carries the notion of logical economic theorizing to philosophically and practically useless extremes.
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