After thinking more about: Daniel Dennett's concept of free will as an equation of state?
I am super confused about the linguistics concerning mathematics. For example, "take the limit of x to 0 and then then limit of y to infinity; else the equation will diverge"
Notice the subtleties:
Firstly, it is natural for us to put something like a notion of time in our language (then). Secondly, our style of doing math assumes we can think of math as an equation of state with degrees of freedom possibly because of Dennett's freewill (see the first link).
Daniel Dennett's concept of free will, in which he argues that our choices are the result of complex computations that take into account our desires, beliefs, and goals, as well as the external world. I realized that the nature of these computations would not be modeled by what physicists call a time evolution equation but, rather, an equation of state.*
*To elaborate a bit more: Consider the ideal gas law - PV = NRT. I understand the relationship between pressure and, let's say, temperature. Notice that I do not know the time evolution of the system. However, I can say, "If I increase the pressure, the temperature will change." Regardless of whether a time evolution equation for "me" + "gas in a box" exists (or whether the degree of freedom of "if" exists), I can perform this computation.
**Note: When I say "as an equation of state" I'm not thinking the mind is actually putting in numbers but rather it is doing an activity which can be mapped to that. Consider this example: I am asked the time signature of a pop song. I can do so by merely headbanging and instinctively knowing it's 4/4 or I can count. Both activities can be mapped to same output and inputs.
Math is an abstraction! One which can be abstracted a particular way or does our notion of freewill obstruct that of Plato's heaven we can access? In other words is there an extension of mathematics we cannot access because of our notion of will?