A logical solution to Goldbach's hypothesis – (reformulation).
As is well known, mathematics poses a philosophical obstacle, because it teaches us things about reality, on the one hand, but it seems to derive from intellectual ability alone. That is why Kant called this field 'a priori synthetic'. Synthetic – which teaches something about reality. And a priori – before the data of the senses, or – pure intellect.
But such a position poses a challenge to the empiricist conception that all our knowledge is given from the data of the senses. The only one who claimed that mathematics is indeed learned from the senses is the philosopher Mill.
On this background, attempts arose to base mathematics on logic. At first it was Frege with his pioneering experience, and later the ones who mainly operated in this field are Russell and Whitehead in their book 'Principia Mathematica'.
The basic principle by which the two operated was groups theory. That is, the number eight, for example, is the group of things that counts eight items.
But this project is generally considered a failure. The paradox presented to Russell is well known – 'what about the group of all groups that does not contain itself as an organ', which supposedly collapses its entire enterprise.
But paradoxes are extreme cases in logic, requiring discussion on their own. But they never interfered with putting forward scientific theories. Thus, for example, Zeno's paradoxes about motion never received an appropriate answer, and in any case the science of physics continued to advance, with reference to motion and rest.
The same should happen in this case, in my opinion. And to show how the foundation of mathematics on logic, and in particular on groups theory, is effective, I will show how it provides a solution to an unresolved ancient mathematical riddle, which is the Goldbach conjecture.
I have written this things before and I bring them again:
The Goldbach conjecture is a conjecture in number theory, according to which any even number greater than 2 can be represented as the sum of two prime numbers.
To date they have failed to prove this claim.
And lo and behold, in my opinion this is simply a linguistic-logical problem and the sentence is tautological. After all, what is a number that is divided by 2 if not a division into two parts, each of which is defined as a whole unit, just like the definition of the prime number?
And this is not a vain argument but has a mathematical implication: following it I argue that even any number divided by 3 can be represented as the sum of three prime numbers and so on and so on.
Note: I refer to number 1 as a prime number. Or alternatively the limit 'greater than 2' should be applied here as well, and say – 'greater than 3', and so on.
For example: 6 = 3 + 2 + 1, or: 6 = 2 + 2 + 2, 9 = 3 + 3 + 3, 12 = 5 + 5 + 2, and so on.
check and argue and correct me if I am wrong.