If Austrian economics is based on deductive logic, has anyone ever attempted to write out the chain of assumptions and propositions without all the extra explanatory material in e.g. Mises or Rothbard? Shouldn't you be able to write out a numbered step-by-step verbal proof of any proposition? If not, why not?

I've pondered over this exact same question. I know what you're talking about is different, but I've analyzed one tiny deduction in one of my Menger posts:

the existence of requirements for goods of higher order is dependent upon the corresponding goods of lower order having economic character.

If goods of lower order do not have economic character, then there would be no need to produce more of them (there are already plenty), and therefore, there is no requirement for the higher order goods used to produce them. And a good with no requirements necessarily can have no economic character, since quantities necessarily exceed requirements. Therefore...

the economic character of goods of higher order depends upon the economic character of the goods of lower order for whose production they serve. In other words, no good of higher order can attain economic character or maintain it unless it is suitable for the production of some economic good of lower order.

This is a nice, simple example of Menger's use of formal logic, and how Menger's method (like all good economics) is deductive. Let the following letters represent the following corresponding terms:

A: Higher order goods with non-economic corresponding lower order goods B: Goods with no requirements C: Goods with more available quantities than requirements D. Non-economic goods

What Menger is saying is basically the following syllogism: All A's are B's. All B's are C's. All C's are D's. Therefore, all A's are D's.

"the obligation to justice is founded entirely on the interests of society, which require mutual abstinence from property" -David Hume

I've thought of doing this myself. I've found in my reading however that the textual context is often more important, as it helps guide one through to seeing the validity of the theorems. I originally thought of using symbolic logic as well, however, I think such a simplistic form is not possible due to the nontrivial nature of many of the statements of Austrian Economics.

I'll mention this to the professors at MisesU as well, and try to get off my backside and actually compile the notes I've made from Human Action so far.

"When the King is far the people are happy." Chinese proverb

For Alexander Zinoviev and the free market there is a shared delight:

If Austrian economics is based on deductive logic, has anyone ever attempted to write out the chain of assumptions and propositions without all the extra explanatory material in e.g. Mises or Rothbard? Shouldn't you be able to write out a numbered step-by-step verbal proof of any proposition? If not, why not?

This would be possible if the proofs were analytic (requiring formal logic only) such as in mathematics.

1 + 1 = 2.

1 + 2 = 3.

Therefore 1 + 1 + 1 = 3.

However, most of the deductions are synthetic (requiring intuitive insight from our understanding). The fact that action presupposes the passage of time is not a matter of simple logical deduction. We have to understand what it means to act and what time is, to understand the connection.

At most, you could diagram the deductions in a chart which shows which concept implies other concepts. Step by step, numbered proof is inappropriate in this case and would only create confusion in a subject that cannot be logically formalized, but must be understood intuitively.

Realize that mathematical "proofs" do not contain any information that did not previously exist. That is, a deductive "proof" does not contain any information that cannot be merely written in ordinary natural language. Therefore, you do not need to contain logical symbols that are unintelligible to the layman to be logically precise.

One of the goals of many of the Austrian economists is to present information that is both self-contained and can be understood by the intelligent layman. Logical symbolism would detract from that goal.

However, I do believe that one of the main focus's of the Austrian tradition is to more greatly explicitize the arguments. For example, "Man, Economy, and State" seems much more explicit than "Human Action". That is, in "MES", Rothbard explicitly announces that he is presenting a new assumption or explicitly announces that a certain implication follows directly from a certain axiom more often than Mises does in "HA".

I believe that the arguments can and will become more explicit and therefore more precisely presented in the Austrian treatises that will appear in this generation.

If I wrote it more than a few weeks ago, I probably hate it by now.

Also, I would like to post a passage from page 75 of "MES":

"The suggestion has been made that, since praxeology and economics are logical chains of reasoning based on a few universally known premises, to be really scientific it should be elaborated according to the symbolic notations of mathematical logic.[44] This represents a curious misconception of the role of mathematical logic, or “logistics.” In the first place, it is the great quality of verbal propositions that each one is meaningful. On the other hand, algebraic and logical symbols, as used in logistics, are not in themselves meaningful. Praxeology asserts the action axiom as true, and from this (together with a few empirical axioms—such as the existence of a variety of resources and individuals) are deduced, by the rules of logical inference, all the propositions of economics, each one of which is verbal and meaningful. If the logistic array of symbols were used, each proposition would not be meaningful. Logistics, therefore, is far more suited to the physical sciences, where, in contrast to the science of human action, the conclusions rather than the axioms are known. In the physical sciences, the premises are only hypothetical, and logical deductions are made from them. In these cases, there is no purpose in having meaningful propositions at each step of the way, and therefore symbolic and mathematical language is more useful.

Simply to develop economics verbally, then to translate into logistic symbols, and finally to retranslate the propositions back into English, makes no sense and violates the fundamental scientific principle of Occam’s razor, which calls for the greatest possible simplicity in science and the avoidance of unnecessary multiplication of entities or processes.

Contrary to what might be believed, the use of verbal logic is not inferior to logistics. On the contrary, the latter is merely an auxiliary device based on the former. For formal logic deals with the necessary and fundamental laws of thought, which must be verbally expressed, and logistics is only a symbolic system that uses this formal verbal logic as its foundation. Therefore, praxeology and economics need not be apologetic in the slightest for the use of verbal logic—the fundamental basis of symbolic logic, and meaningful at each step of the route.[45]"[1]

[1] http://mises.org/rothbard/mes/chap1d.asp

If I wrote it more than a few weeks ago, I probably hate it by now.

However, most of the deductions are synthetic (requiring intuitive insight from our understanding). The fact that action presupposes the passage of time is not a matter of simple logical deduction. We have to understand what it means to act and what time is, to understand the connection.

Couldn't the intuitive bits be treated as axioms which 99% of the readers will not dispute? And most of the intuition is only at the beginning of the chain of inference. Most of the logical steps are fairly straightforward deductions.

"the obligation to justice is founded entirely on the interests of society, which require mutual abstinence from property" -David Hume

However, most of the deductions are synthetic (requiring intuitive insight from our understanding). The fact that action presupposes the passage of time is not a matter of simple logical deduction. We have to understand what it means to act and what time is, to understand the connection.

As Lilburne mentioned above, the "intuitive insight from our understanding" should be mentioned as the axioms. I do not know why you believe that the basic unpentrable "givens" of our understanding cannot be written explicitly as axioms.

If I wrote it more than a few weeks ago, I probably hate it by now.

One of the goals of many of the Austrian economists is to present information that is both self-contained and can be understood by the intelligent layman. Logical symbolism would detract from that goal.

I agree it shouldn't be the focus, just as charts and graphics shouldn't be. But a small measure of these approaches have their uses. For example, with a numbered chain of deductions, we could respond to critics who respect that sort of thing, with, "Okay so you don't like our conclusions, but exactly which number in this chain of deductions do you dispute?" That would have the effect of focusing the debate quickly upon the true bone of contention, and quite possibly efficiently delivering our opponents a "blank out" moment, when they realize they can't reasonably dispute any of our inferences. Of course positivists won't have any of it, but not every non-Austrian is a hard-core positivist.

"the obligation to justice is founded entirely on the interests of society, which require mutual abstinence from property" -David Hume

Now, I believe I misread you. I thought you were referring to outlined, numbered chains of deduction. But I realize now you were referring to formal symbols.

"the obligation to justice is founded entirely on the interests of society, which require mutual abstinence from property" -David Hume

I agree it shouldn't be the focus, just as charts and graphics shouldn't be. But a small measure of these approaches have their uses. For example, with a numbered chain of deductions, we could respond to critics who respect that sort of thing, with, "Okay so you don't like our conclusions, but exactly which number in this chain of deductions do you dispute?" That would have the effect of focusing the debate quickly upon the true bone of contention, and quite possibly efficiently delivering our opponents a "blank out" moment, when they realize they can't reasonably dispute any of our inferences. Of course positivists won't have any of it, but not every non-Austrian is a hard-core positivist.

I agree. However, those explicit deductive sequences should be written in ordinary language rather than logistics. For example:

Lilburne:

1. Increases in productivity come from more effective production processes.

2. More effective production processes involve more roundabout production methods.

3. More roundabout production methods require more capital.

4. Additional capital requires additional savings.

5. Additional savings require a lower time preference.

And your conclusion is that an increase of productivity implies an increase of average time preference.

If I wrote it more than a few weeks ago, I probably hate it by now.

Now, I believe I misread you. I thought you were referring to outlined, numbered chains of deduction. But I realize now you were referring to formal symbols.

Ah, yes. As Rothbard explained, it would be a worthless and roundabout translation to utilize formal logistic symbols. I am not sure that I completely understand his explanation; I believe that his explanation was somewhat . . . underdeveloped. Can any one here expand it or comment on it?

If I wrote it more than a few weeks ago, I probably hate it by now.

I am much too tired right now to compose a proper response to any of the previous comments, so I'll just point out a distinction concerning the present topic I think is being overlooked (which people make take or leave as they like, depending on how useful they find it).

Anyway, the idea of a mathematical deduction, as opposed to any other sort of deduction, is that it is independent of however one might intuit its premises; this is precisely what makes it characteristically mathematical. On the other hand, the arguments in praxeology up to now rely almost exclusively on one's intuition of its notions.

This in itself says nothing about the mathematizability of praxeology or the utility of doing so. My point is merely that it is extremely simplistic to say that "praxeology (in its present form) is deductive, just like math" when the two are quite unalike.

Anyway, the idea of a mathematical deduction, as opposed to any other sort of deduction, is that it is independent of however one might intuit its premises; this is precisely what makes it characteristically mathematical. On the other hand, the arguments in praxeology up to now rely almost exclusively on one's intuition of its notions.

Indeed. This is crucial. The dfference is much bigger than most Austrians realize.