In response to Mason's first question, this is my understanding of Mises'
view of math and logic:

Mises refers to his own method of constructing theories of human action as
"praxeology."  It is different from both purely logical reasoning and math.

"Logic and mathematics deal with an ideal system of thought. The relations
and implications of their system are coexistent and interdependent.  We may
say as well that they are synchronous or that they are out of time.  A
perfect mind could grasp them all in one thought.  Man's inability to
accomplish this makes thinking itself an action, proceeding step by step
from the less satisfactory state of insufficient cognition to the more
satisfactory state of better insight.  But the temporal order in which
knowledge is acquired must not be confused with the logical simultaneity of
all parts of an aprioristic deductive system.  Within such a system the
notions of anteriority and consequence are metaphorical only.  They do not
refer to the system, but to our action in grasping it.  The system itself
implies neither the category of time nor that of causality There is
functional correspondence between elements, but there is neither cause nor
effect.
"What distinguishes epistemologically the praxeological system from the
logical system is precisely that it implies the categories both of time and
of causality.  The praxeological system too is aprioristic and deductive.
As a system it is out of time.  But change is one of its elements....So is
the irreversibility of events.  In the frame of the praxeological system any
reference to functional correspondence is no less metaphorical and
misleading than is the reference to anteriority and consequence in the frame
of the logical system."  (pp. 99-100, Human Action, 1966 ed.)

My understanding of Mises's claim is that economic theorizing must always
include the time dimension as a part of the actor's choice context because
human action itself always takes place in real time and involves cause and
effect.  In understanding acting in the temporal order, and deriving
principles of action, there must be a theoretical role for inconsistency--in
contrast to both math and logic, where consistency can occur because of the
assumed simultaneity of all parts of the argument.

In many other places Mises argued that math functions are useless in
economic theorizing because there are no constant relations between
variables in human action.  Math is confined to simple pedagogical uses as a
shorthand to present theory in simpler form.

In answer to Mason's second question, I'm not sure that it is quite fair to
say that the people at the Mises Institute "write in Mises' name." They
apply their understandings of Mises, Rothbard, and others' theories to
specific policies set in an historical context like the people at Brookings,
AEI, Heritage, etc.  Those who believe that "theory" must always reflect the
historical context and personal characteristics (psychology, culture, sex,
etc.) of specific acting human beings are never going to accept the
application of any "general" theory, whether it is that of Mises, Keynes,
Stiglitz or Marx.

Samuel Bostaph