The cognitive history of deduction: the theory of Reviel Netz and the notion of Vygotsky's psychological instrument

Reviel Netz has proposed a cognitive history to explain how deduction was shaped in Greek mathematics. The point of his book is that deduction emerged from practices of those first mathematicians. That practices were built using two essential cognitive tools: the lettered diagram and a very specific kind of language. The deductive principles of necessity and generality associated with deduction were too built in those practices. Netz suggest that cognitive history is necessary to explain what Fodor says is out of scope for cognitive science: central processes. He argues that if central processes are out of scope of scientific research on cognition, then what must be done is to study reasoning in some concrete historical circumstances. Here, nevertheless, we suggest that what Netz offers as an example of cognitive history is all about a beautiful example of some ideas from Vygotsky. Using some symbolic tools externalizes, make explicits and permits control about deductive processes of thinking. Using psychological tools was the basic mechanism that Vygotsky defended to explain the development from basic to more advanced psychological processes. The history of deduction that Netz proposes is, we suggest, a very fitting and clear example of that theory.