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Tuesday, March 25, 2014

What is Mathematics?

What is Mathematics?

By Jim J. McCrea

Some philosophers and scientists claim that mathematics is the ultimate reality - that it is from mathematical principle that all physical reality arises. They say that if we could find the ultimate equations governing reality, we would have an explanation for why the universe exists and why it is the way it is (thus ruling out God, or saying that mathematics is God).

However, this cannot be true if we look at what mathematics really is - that is, if we look at the essence of mathematics.

Mathematics, in its nature, is the necessary relationship of quantities. Some scholastic philosophers have called it the science of quantity.

Mathematical truths are abstract truths, rather than concrete objects as are physical things. When we say that 2+2=4 we are saying two of something over here and two of something over there give us four things when put together. We are considering the concepts of twoness and fourness without considering what particular two or four things they entail. This twoness is abstracted from all real and possible two things and this fourness is abstracted from all real and possible particular four things. As abstract concepts they are universals which transcend particular individuality, and 2+2=4 gives us the relationship between these abstract concepts.

Mathematics, in general, describes the necessary relationship between quantities such as length, area (which is length squared), volume (which is length cubed), force, mass, energy, power, voltage, time, luminosity, etc.

For example, the relationship between force, mass, and acceleration is given by the formula F=mXa - where 'F' is force in newtons, 'm' is mass in kilograms, and 'a' is acceleration in meters per second squared.

Geometry describes the necessary relationships between the measurements of shapes.

For example, the formula of a circle is r^2=x^2+y^2 - where '^2' is squared, 'r' is the radius of the circle, and (x,y) are the coordinates of any given point on the circle. This is true of all circles (in Euclidean geometry)

The interesting thing is, these mathematical statements are truth whether they pertain to actually existing things or potentially existing things. Mathematics has nothing to say about their actual vs. potential existence. It certainly does not cause things to exist, for that is not within the nature of mathematics. Mathematics are rules of quantitative logic, and the actual being vs. non-being to which they apply is not addressed by mathematics at all.

For example, with 2+2=4, we can say, if referring to something actual, that two existing things over here and two existing things over there give us four existing things when we total them; or we could say that it refers to two *potentially* existing things over here and two *potentially* existing things over there to give us four *potentially* existing things when we total them. With the equation  r^2=x^2+y^2 it can refer to a real circle or a circle potentially existing or existing merely as a concept in our understanding.

Given that mathematical truths are abstract truths that do not pertain to the individual in particular, and are indifferent to potential vs. actual existence, there must be *something else* that causes something to be actual rather than potential, as mathematics itself indicates the two possibilities of potential and actual for a given individual thing.

This something else that causes finite beings to exist is Being Itself or that which must exist because it is Existence Itself.

That which is Being Itself or Existence itself must be infinite as it must contain everything that being or existence implies.

That "it" is a Him and is the Judeo-Christian God, as that which contains everything possible about existence must contain the perfection of personhood (in fact, God has revealed Himself as three persons in one being). 

God's name is "I Am" as given in the Bible, in Exodus 3:14 - as He does not say "I am such and such." which means that He says that He does not have a qualifier which would be a limitation.


For a more detailed description of that which which is Being Itself, or God see here -  and which also explains why that which has everything that existence implies does not also contain evil.

And see here for and explanation of how God is three persons in one being.