The Dialogical Roots of Deduction

"Despite quite some variation in its numerous manifestations, three core features of deductive reasoning seem to stand out. They are aptly captured in the following definition of a mathematical proof, taken from the 1989 guideline of the National Council of Teachers of Mathematics (and quoted in (Balacheff, 1991) (p. 177)): a mathematical proof is "a careful sequence of steps with each step following logically from an assumed or previously proved statement and from previous steps." So a deductive argument is a (i) stepwise process, (ii) where each step 'follows logically' (iii) from assumed or previously established statements. In the remainder of the book, it will be further argued that focusing on these three aspects offers an adequate vantage point to investigate deduction in its many facets. Here they are presented in decreasing order of general recognition of their centrality for the notion of deduction"--