[Guille]

Now that we have clarified the relationships between mathematics logic and science, and we have adetermined that mathematics is not the language f logic itself but a kind of logic, we can proceed to describing what the relatioships between mathematics and logic are. Well, the branche of matheamtics that studies logic, which is wrongly called logic, has tried to make a logical foundation of mathematics by not using mathematics but describing it in matheatical forms. And this is, in my opinion, a mistake. A mistake, because by describing with mathematical language the mathematical study of logic, we are making logic itself mathematical, and thus, it makes logic go further and further away form nature. For example, we say that 1+1=2 which in number theory is ok, but transforme dinto logic, it's wrong: because 2 is the set of all the numbers between 0 and 1.9999... not just of 1 and 1. But of course, the logicla connection "and" is very different from the mathematical sing "+". Another mayor error is that whiles in number theory 2 is a complete new number separate from the 1s, well, in logic, 2 would not be a "new" set in that sense:: it woudl be a new name, but it would just be the adition of the previosu sets, the group of 1 and the other 1 is set 2, so set 2 is not really new.

This, we can conclude that mathematics is not equal to or good enough to describe logic. Morever, we can say that mathematical logic is not completely logical, which is a very basic principle into starting to understand the differences between "logic itself" and mathematical logic.