All of physics, except constants, is possible to deduce by a mad-dog rationalist

 As I said here, I think the ultimate goal of physics is the theoretical determination of constants, for it is possible by metaphysical considerations similar to that of Descartes and Spinoza's to determine which quantities are going to be constant: God put a finite amount of energy in universe when creating it (conservation of energy). This implies energy varies in a compact domain. Via my proposals $$E=\frac{lc^4}{G},$$ $$E=\frac{tc^5}{G},$$

and conservation of energy, length and time would have to have minimums and maximums, which are of course Planck units, $$l_P\leq l \leq l_{\text{max}},$$ $$t_P\leq t \leq t_{\text{max}},$$ where l_P is Planck length and t_P Planck time. I shall attend to the issue of maximums elsewhere. 

With this I can deliver on my earlier promise of a `historical thought experiment': Suppose you are a genius living in Newton's time. One day after reading the Principia it is solely revealed to you by Spinoza's God that there is a fundamental constant of Nature which is a speed. God wouldn't tell you the value at all. Nevertheless you still can fully construct Special Relativity. 

With the above reasoning, you would not need the revelation of God anymore; only conservation of energy: $$ \text{min}\ v= \frac{l_P}{t_P} := c.$$

I am aware there is a possible charge of circularity for I have used the energy equivalent of space (length) and time above, which explicitly involve c. But that was only to make things quantified. Descartes does not need that, if he takes his res extensa and quantity of motion synonymous. As he supposes there is no vacuum, through his corporeal extension notion of vacuum, he would reach the same conclusion. 

This gives us kinematics of classical mechanics. What about dynamics? Note that $$F=ma$$ is possible to get by Descartes law of inertia, all free particles move on straight lines. A generalization of this would be Hamilton Principle $$\delta S=0,$$ thanks to Leibniz. 

This even gives us the dynamics of gravitational field, $$\nabla^2 \phi=0,$$ as this (Laplace equation for gravity) is the geodesic equation, only in a different space (not spacetime). 

From this, employing a method familiar to a mathematical mind (which is derivable from Descartes' methods, as I show here), it is easy to arrive at the Poisson equation $$\nabla^2 \phi= 4\pi G \rho,$$

in which G is a constant. This is the farthest Descartes and Spinoza, and for that matter all physics, can get: up to a constant in the simplest possible laws.

These all testify my tweet: 

All of physics, except constants, is possible to arrive at by a mad-dog rationalist. 

I have done similar reasoning for quantum mechanics so I do not repeat them here. 

How do we proceed to determine these constants? As constants like Planck length and time, have units, and thus their numerical value not independent of the system of units, we shall focus on a simpler problem. We should try to find the numerical value of the only constant of physics that is dimensionless; a pure number, 

$$\alpha^{-1}=\left(\frac{q_P}{e}\right)^2;$$

the Fine-structure constant. 

We must again give the God a choice and read his mind: Choose a real number, dear God. I will try to read God's mind in an upcoming post. Stay tuned!