I'll try to avoid using the word "science" in this thread (which of course, doesn't mean someone else can use it).

I hope you mean "which of course, doesn't mean someone else CAN'T use it", right?

Gee, you need a Frenchman to correct your English!

Still, I see you've been somewhat impressed by my discussion of why there is no science of logic. Not all in vain, then.

Anyways, about numbers and logic: why does a set of symbols, the Arabic numerals, have a logic that we can't write an explicit formula for--prime numbers--and why is primality defined by division or a set of divisors?

It's not essentially a deductive logic problem. There is no general algorithm for proving theorems. The method humans use for proving theorem relies on deductive logic but deductive logic is only one part of the method, and the other part can't be dispensed with.

So we can write: If n is prime, then the divisors of n are 1 and n, and no other numbers.

Since it's symmetric we also have: If n and 1 are the only divisors of n then n is prime.

It's the definition. You have to start with one and you always start with the definition. But then deductive logic can't tell you on its own what would be the general formula for finding primes.

This is more or less useless if we have a number, n, and want to know if it's prime. We need more logic!

Sure we need more logic, you're making my point, but it wouldn't be enough anyway. We would need something else altogether, something of a very different nature, not theoretical and abstract: brain power. Raw brain power.

Humans are not good at thinking. It's costly in terms of energy and time and if we all did it we would not be here at all to talk about it because humans wouldn't have the time to do the basic chores of life which are necessary for their survival and therefore to our existence today. This explains why there are relatively few thinkers and also therefore why we remember them. And nothing bad about not being a thinker. Most are crap anyway and we only remember the good ones and they are even less many. It's mostly a thankless job.

So, mathematicians do their best but they don't have the raw brain power anyway and most of them are not even good mathematicians. Most so-called mathematicians just repeat all their lives what they've learnt at "school", barely making a scratch on the Great Book of mathematics. So, instead, people do what they know, algorithms! Alleluia. Thinking? No, thanks, too bloody exhausting. A thankless job.

But why don't you do it? You've identified the problem. All that remains for you to do is to think about it and solve it. You don't need much logic. You just need brain power. You just need to think. You know, the thing which it is just so exhausting to do?

Go on, do it.

EB