From: Julio Huato
Subject: dialectics of nature
Andy: <<anyone who recognises that dialectical forms are manifested in history and asserts that such laws are not manifested in other aspects of nature, has the onus of showing why this is so>>
I agree. Now, Flora's point, "the dialectic does not exist outside human consciousness" is of a different type. What I read here is that there is NO objective dialectics, which begs the question of how dialectics got into our minds in the first place, etc.
If I understand correctly, by alluding Vygotsky and Piaget, Andy tries to show how the objective world exhibits an objective "logic" (eg, a "formal" logic, but not only that) that imprints in our brains during our development. If the subjective rules of (formal, etc.) logic are of any practical utility in our interaction with the world, it is because they are a reflection of the way the objective world actually works. And then he makes the case for dialectics (as a more comprehensive logic).
As to mathematics, I have more questions than answers. In its current format, mathematics is exposed axiomatically. That is, from a set of definitions, primitive concepts, and axioms, a whole set of theorems is derived by strictly following the rules of logic. Even though mathematicians seem remarkably unconcerned with the "intuitive" (a term that, IMO, is used to refer in a skewed way to "objective" as greasped sensorially) standing of their definitions and axioms. And then, those theorems (deductions implied by those axioms) turn out to be, as E. Wigner says, "unreasonably effective in science" and industry!! Why? IMO, they wouldn't be so effective if the axioms and logical rules weren't somewhat objective in content. But then, shouldn't we take the mathematicians apparent disregard for the objectivity of their axioms at face value? Are the foundations of mathematics objective despite the claims of the most outstanding mathematicians?
Now, Kol'man & Yanovskaya (IMO) advocate for a conversion of mathematics from a formal science with a special status (as they see Hegel perceiving it) into a concrete science, its object being the "quantity" aspect of the world. But, concrete sciences refer to the the *empirical* world at every important step of the way. Why Andy's distinction between "empirical" and "objective" is pertinent here? So, all the "objectivity" needed in mathematics is injected by making sure definitions, axioms, and rules are objective reflections of the world out there? If so, K&Y miss the point and mathematics retains the special status perceived by Hegel.