The phrase "God created the natural numbers, all else is the work of man" is a famous quote by the 19th-century German mathematician Leopold Kronecker.

You can basically read it as: the moment one has axiomatized mathematics to the point it supports natural numbers, the rest implicitly follows. The natural numbers (positive integers) are closed for addition, multiplication, ...

One can perfectly model the integers with a pair of naturals: < M, N > ~ (M-N)

Now we can have any < M1, N1 > and subtract < M2, N2 > without needing the ability to subtract natural numbers:

< M1 , N1 > - < M2, N2> ~ (M1-N1) - (M2 - N2)

= < M1 + N2 , M2 + N1 > ~ (M1+N2) - (M1+N1)

We can similarily define addition of such tuples, or test equivalence without access to subtraction of naturals:

< M1, N1 > == < M2, N2 > <=> M1 + N2 == M2 + N1

~ (M1-N1) == (M2-N2) <=> (M1+N2)=(M2+N1)

we can also still multiply such tuples:

< M1, N1 > x < M2, N2 > = < M1*M2+N1*N2, M1*N2+M2*N1>

Similarily, even though these newly defined integers (which can be positive or negative) don't support division, the same trick can be used to make a new compound tuple of integers closed for division, by only using multiplications.

Probability is a branch of mathematics (probability already exists embedded in mathematics implicitly, probability theory involves the addition of eliminable definitions, syntactic sugar. The patterns are already there, just less explicitly manifest.

Mathematics is itself a branch of logic.

Do you reject like all of logic, and if so, what would you like us to evaluate the sentences you write to? You want us to evaluate your expressions as "true" or as "false"?