Deduction and ampliativity: a critical appraisal

The ampliativity of deduction has been defended in several ways—such as the semi-decidability of the theories, the surprise of unexpected consequences, the need of new individuals in deduction, or ampliative inference as deduction with suppressed premises (Dummett, Frege. Philosophy of mathematics. Duckworth, London, 1991; Hintikka, Logic, language-games and information. Oxford University Press, Oxford, 1973; Musgrave, Imre Lakatos and theories of scientific change. Kluwer, Boston, 1989; Rota, Indiscrete thoughts. Birkhäuser, Boston, 1997). These lines of defensive arguments fail if we characterize ampliativity in a strong way, that is, in terms of ‘novelty’ stricto sensu, as an inferential process producing genuinely 13 new pieces of information in the conclusion of a reasoning (Cellucci, Rethinking logic. Springer, Dordrecht, 2013; Ippoliti, Heuristic reasoning. Springer, Basel, 2015). Nevertheless, it is possible to defend a weaker stance of the ampliativity of deduction and its usefulness. This requires interpreting novelty more loosely, that is, as the inferential production of new relations among known entities. This stance maintains that, in this sense, deduction can provide us with new knowledge. Thus, a typical deductive activity, as re-proving theorems, can be thought as heuristic and ampliative because it establishes new relations between known elements (e.g. between given axioms or properties and the statement of the theorem). I argue 22 that also this line of defence is defective for it does not account for the necessity and usefulness of reproving theorems. In particular, a foundationalist, axiomatic-deductive viewpoint does not fully account for the usefulness and the weak ampliative power of deduction.