So what if we can't see it or prove it? Doesn't mean it doesn't exist. I can't see heaven either am I right to dismiss it as nonsense? Why should we assume that we can see everything? Seems arrogant to me.
So what if we can't see God or prove God? Doesn't mean He doesn't exist. I can't see heaven either am I right to dismiss it as nonsense? Why should we assume that we can see everything? Seems arrogant to me.
You've asked for it...
Most people have heard of evolutionary biology. But the term evolution is often applied in a broader sense (gradual, naturalistic changes over long ages) to other fields of study. Some people study geology or astronomy from an evolutionary perspective. But has anyone ever studied evolutionary mathematics? What would an evolutionist mathematician study? Can the existence of numbers and mathematical laws be explained by a time-and-chance naturalistic origin?
Lets consider first the naturalistic, or evolutionary, view. In this way of thinking, people attempt to explain the characteristics of a modern object by considering how it gradually evolved over millions or billions of years from something less complex. If we applied this concept to mathematics, we would ask, From what did numbers evolve? What were numbers before they were numbers? When did the physical universe begin obeying mathematical laws?
Just take one number as a token case. From what simpler number did the number 7 evolve? Was 7 once 3? Did 3 have to transition through 4, 5, and 6 before it became 7? When did the negative numbers evolve? Or how about the irrational numbers? When did these numbers begin obeying mathematical laws? Did laws of mathematics evolve first, and then numbers later? Or was it the reverse?
If these sorts of questions sound silly, it is because they are. The evolution of numbers makes no sense whatsoever. 7 has always been 7, just as 3 has always been 3. Likewise, the expression 2+3=5 was as true at the beginning of time as it is today. Mathematical laws and the numbers they govern are invariantthey do not change with time and, therefore, cannot have evolved from anything!
The secularist is truly stuck when it comes to mathematics. He knows that mathematical truths existed before human beings discovered them. For example, the orbits of the planets around the sun were described by the mathematical formulae expressed in Keplers laws before human beings existed. And yet laws of mathematics are conceptual in nature. Concepts exist in a mind; they are objects of thought. So how can a conceptual entity like math exist before any mind is around to think it?
You tell me.