James,
My argument is not politics nor semantics. There is definitely a philosophical difference between “The maximum is infinity” and “There is no maximum”. Many people casually consider the two phases to say the same thing, which is clearly not so.
The phrase “The maximum is infinity” implies the maximum can reach a value of infinity. I cannot think of any real world variable that can attain a value of infinity, so the phrase makes no sense.
The phase “There is no maximum” means no single finite value is the maximum, and this applies to many things in the real world.
You asked me:
I have already given the example of the energy of a single photon.
Your other examples work too - the universe has no maximum voltage value, no maximum length value, no maximum volume, no maximum charge, no maximum pressure, no maximum gravitational pull, no maximum temperature.
By and large, finite maximum values are very rare. The universe seems to have only one finite maximum: the speed of light (c). Even then, you could argue that speeds faster than c exist as values, but just cannot be attained by anything real in this universe.
That is why Rational Metaphysics (RM) stands out with a claim that there is a maximum rate of change - the claim is asking for attention. If RM is ever published, this is going to be an easy target for critics. They will ask “Why does the rate of change at a point have a maximum value (like light), when most variables in the universe don’t have a maximum?”.
The choices to resolve this point are this:
(a) RM gives a logical argument why there must be a finite maximum rate of change at a point, or
(b) RM states an assumption that there is a finite maximum.
RM denies containing any assumptions, so RM needs to explain (a). This is not a waste of time - this is RM dealing with an issue that will be raised by many more than just me, especially academic philosophers and mathematicians.
If RM claims that “The maximum is infinity” means the same thing as “There is no maximum”, then RM is very vulnerable to being dismissed just on that claim. In comparison, making an assumption is OK - it just needs to be acknowledged.
Eugene Morrow