This axiom, the proposition that humans act, fulfills the requirements precisely for a true synthetic a priori proposition.It cannot be denied that this proposition is true, since the denial would have to be categorized as an action and so the truth of the statement literally cannot be undone
(Hoppe, Economic Science and the Austrian Method, p. 22)
Clearly, the action axiom is a platitude. Hoppe could just as well have said, "This axiom, the proposition that economists use word processors, fulfills the requirements precisely for a true synthetic a priori proposition. It cannot be denied that this proposition is true, since the denial would have to be written on a word processor and so the truth of the statement literally cannot be undone."
Click here to learn what the term 'synthetic a priori' really means.


1) One's value scale is totally (linearly) ordered:

i) 
Transitive;

p q and q r imply p r 

ii) 
Reflexive;

p p 

iii) 
AntiSymmetric;

p q and q p imply p = q 

iv) 
Total;

p q or q p 
2) Marginal (diminishing) utility, u(s), is such that:

i) 
It is independent of firstunit demand.


ii) 
It is negative monotonic; that is, u'(s) < 0.


iii) 
The integral of u(s) from zero to infinity is finite.

3) Firstunit demand conforms to proportionate effect:

i) 
Value changes each day by a proportion (called 1+_{j}, with j denoting the day), of the previous day's value.


ii) 
In the long run, the _{j}'s may be considered random as they are not directly related to each other nor are they uniquely a function of value.


iii) 
The _{j}'s are taken from an unspecified distribution with a finite mean and a nonzero, finite variance.

(Aguilar, Axiomatic Theory of Economics, pp. xxiiixxiv) 