The invention of concepts, or logical and mathematical conjectures through the shaping of new hypothesis.

The notion – itself abductive – comes from C.S. PEIRCE, who applied it to new concepts emerging in our mind from witnessing unusual or unprecedented situations in which neither induction nor deduction can be used. J. WARFIELD stresses these differences. According to him, the origin of newly invented concepts remains a mystery. KOESTLER proposed bisociation as a model for this type of creativity, which like all other types is a product of neural and cerebral networks activity.

G. KLIR considers the computer as a valuable instrument in the abduction process, because it makes it easier to look "for regularities and developing thus empirical support for a mathematical conjecture. When the support becomes convincing, it is appropriate to try to prove the conjuncture formally" (1991, p.103).

In fact, abduction precedes induction (and still more so, deduction). Ch S. PEIRCE observed that "induction has its role not in the forming of hypotheses, but (in certain fields) in testing the hypothesis arrived at by abductive inference" (as quoted by P.R. MASANI (1994, P. 45)

MASANI states for example that "statistical inference has to be abductive"(lbid)