Hykel Hosni (2016). Review of ‘Analogies and Theories: Formal Models of Reasoning’ Economics and Philosophy, 32, pp 373-381. doi:10.1017/S0266267116000122.
Induction and analogy have long been considered indispensable items in the uncertain reasoner’s toolbox, and yet their formal relation to probability has never been less than puzzling. One of the first mathematically well-informed attempts at gripping the problem can be found in the penultimate chapter of Laplace’s Essai philosophique sur les probabilités. There, a key contributor to the construction of the theories of mathematical probability and statistics, argues that analogy and induction, along with a “happy tact”, provide the principal means for “approaching certainty” when the probabilities involved are “impossible to submit to calculus”. Laplace then hastens to warn the reader against the subtleties of reasoning by induction and the difficulties of pinning down the right “similarity” between causes and effects which is required for the sound application of analogical reasoning. Two centuries on, reasoning about the kind of uncertainty which resists clear-cut probabilistic representations remains, theoretically, pretty much uncharted territory.
Analogies and Theories: Formal Models of Reasoning is theattempt of I. Gilboa, L. Samuelson and D. Schmeidler to put those vexed epistemological questions on a firm decision-theoretic footing.