[Guille]

As a first thread to this forum, I want all of us to keep the high level of abstraction that Robert asks in his introductory thread. I believe that the theme I have chosen is perfect to begin an overal view on the nature of mathematics.

Probably you know that the basis of mathematics is logic. But, how exactly does mathematics relate to logic? Is it logic's language, or just a type of use of it?

Well, In my opinion, mathematics is the language that humans use in doing science to study nature. And all of science has a core which is pure logic. But science is the study of nature. Not the study of logic or the study of the relationship between mathematics and logic. This arises a question in my mind: If the logicists of the 20th century were correct when they said that humanity was (and still is) going through a des-philosophicalization and intro-scientification, then, will there be a science one day that studies mathematics itself, and the relation of mathematics to logic, or of mathematics to science? In theory, the answer should be yes, but this doesn't make sense to our minds. It dosn't make sense because the actual fact of questioning and considering the relationship between the study of nature (science) and the language of the study of nature (mathematics) is itself philosophical. Now, coming back to the top of tis paragraph, well, mathematics is thus a kind of logic, or beter said, a way of using logic. So mathematics is not the language of logic. Mathematics is the study of mathematical logic, and the language of mathematical logic, but not of logic itself. A way of understanding the idfference between mathematical logic and logic itself is by studying human beings: each has a logic, that has been created in the mind by their experiences in their lifes. But these logics differ: differ first inside the same human, who can change of logic by a stron expirience, differs between humans, and, of course, differes to mathematical logic. But it's still logic. Now that we have clear that there are different kinds of logics, a question arises: Are there independent languages for each kind or type of logic, or can a language be created to represent the LOGIC itself, of any kind? The answer depends absolutelly in one property: if the types of logics all have a connection of the type that they can be different but still proccessed in the same way, then they can share a language, but if they don't have a connection of the type that they can be different but still proccessed in the same way, then there can be no language for all, because they are porcessed in different ways. I cannot determine the correct answer myself. But I believe it's more possible that no lanugage exists for all the logics, because we, humans, have invented a laungage for mathematical logic, but we don't manage to invent a language for the logic of our minds. We still odn't understand how it works, and this is because we study mind logic by mathematical logic, but, if mind logic can't be related with mathematical logic, then it must happen that they are processed in different ways, and, thus, that there can be no shared language.

I will continue to expose my porfound thoughts in this thread now, I give you all the opportunity to consider my thoughts and discuss them, and expose yours.