April 15 – Induction

Readings:

• John Vickers, “The Problem of Induction”, The Stanford Encyclopedia of Philosophy (Spring 2013 Edition), Edward N. Zalta (ed.)
  • This article more or less identifies induction with ampliative reasoning (reasoning that adds to what we can derive from our knowldge). “Deduction on the other hand is explicative. Deduction orders and rearranages our knowledge without adding to its content” (section 1). In the class sessions, I am distinguishing between induction as a from of generalization and/or projection from instances into new rules or instances, on one hand, and abductive inference as another ampliative form of reasoning, from what we observe to possible causes or explanations. The latter forms the topic of the next session, on “Scientific Explanation”, but on Vickers’ account it is part of induction.
• Joshua B. Tenenbaum, Charles Kemp, Thomas L. Griffiths and Noah D. Goodman, “How to Grow a Mind: Statistics, Structure, and Abstraction”,  Science 331(6022):1279-1285, 2011
  • The article ends by relating the HBM approach to the late MIT AI researcher David Marr’s levels of analysis for information processing systems: computational, algorithmic, and implementational. Marr’s levels correspond roughly to what the philosopher Daniel Dennett calls the “intentional stance”, the “design stance”, and the “physical stance”. The first two levels roughly correspond to Allen Newell’s knowledge level and symbol level; to Herbert Simon’s “substantive” and “procedural rationality”; to Marvin Minksy’s “content” and “form”; and to John McCarthy’s and Patrick Hayes’s “epistemological” and “heuristic adequacy”.

Slides for this session are at http://www.stanford.edu/class/symsys130/SymSys130-4-15-2013.pdf. Some notes:

• The theory of induction has evolved, since Hume defined the problem of induction, from justifying the assumption that the future will be like the past (which is not justified in general) to distinguishing between good and bad generalizations and predictions based on instances. What helps us make this distinction is background knowledge that tells us whether the inferences we are drawing are reliable or spurious.
• Proofs of the theorems about probability are given here, along with examples and behavioral experiments that test whether human judgment obeys the axioms of probability.