Necessity and sufficiency From Wikipedia, the free encyclopedia Contents 1 Abductive reasoning 1 1.1 History ................................................. 1 1.2 Deduction, induction, and abduction ................................. 1 1.3 Formalizations of abduction ...................................... 2 1.3.1 Logic-based abduction .................................... 2 1.3.2 Set-cover abduction ...................................... 2 1.3.3 Abductive validation ..................................... 3 1.3.4 Probabilistic abduction .................................... 3 1.3.5 Subjective logic abduction .................................. 4 1.4 History ................................................. 4 1.4.1 1867 ............................................. 6 1.4.2 1878 ............................................. 6 1.4.3 1883 ............................................. 6 1.4.4 1902 and after ......................................... 6 1.4.5 Pragmatism .......................................... 7 1.4.6 Three levels of logic about abduction ............................. 7 1.4.7 Other writers ......................................... 8 1.5 Applications .............................................. 8 1.6 See also ................................................ 9 1.7 References ............................................... 10 1.8 Notes ................................................. 11 1.9 External links ............................................. 14 2 Condition (philosophy) 15 2.1 References ............................................... 17 3 Deductive reasoning 18 3.1 Simple example ............................................ 18 3.2 Law of detachment .......................................... 18 3.3 Law of syllogism ........................................... 19 3.4 Law of contrapositive ......................................... 19 3.5 Validity and soundness ........................................ 20 3.6 History ................................................ 20 i ii CONTENTS 3.7 Education ............................................... 20 3.8 See also ................................................ 20 3.9 References ............................................... 21 3.10 Further reading ............................................ 21 3.11 External links ............................................. 22 4 Inductive reasoning 23 4.1 Description .............................................. 23 4.2 Inductive vs. deductive reasoning ................................... 24 4.3 Criticism ................................................ 24 4.3.1 Biases ............................................. 24 4.4 Types ................................................. 25 4.4.1 Generalization ......................................... 25 4.4.2 Statistical syllogism ...................................... 25 4.4.3 Simple induction ....................................... 26 4.4.4 Causal inference ....................................... 26 4.4.5 Prediction ........................................... 26 4.5 Bayesian inference ........................................... 26 4.6 Inductive inference .......................................... 27 4.7 See also ................................................ 27 4.8 References ............................................... 28 4.9 Further reading ............................................ 28 4.10 External links ............................................. 29 5 Inference 30 5.1 Examples ............................................... 30 5.1.1 Example for definition #2 ................................... 31 5.2 Incorrect inference ........................................... 31 5.3 Automatic logical inference ...................................... 32 5.3.1 Example using Prolog ..................................... 32 5.3.2 Use with the semantic web .................................. 32 5.3.3 Bayesian statistics and probability logic ............................ 32 5.3.4 Nonmonotonic logic[2] .................................... 33 5.4 See also ................................................ 33 5.5 References ............................................... 34 5.6 Further reading ............................................ 34 5.7 External links ............................................. 35 6 Logic 36 6.1 The study of logic ........................................... 36 6.1.1 Logical form ......................................... 36 6.1.2 Deductive and inductive reasoning, and abductive inference ................. 37 CONTENTS iii 6.1.3 Consistency, validity, soundness, and completeness ...................... 38 6.1.4 Rival conceptions of logic ................................... 38 6.2 History ................................................. 38 6.3 Types of logic ............................................. 40 6.3.1 Syllogistic logic ........................................ 40 6.3.2 Propositional logic (sentential logic) ............................. 40 6.3.3 Predicate logic ........................................ 40 6.3.4 Modal logic .......................................... 41 6.3.5 Informal reasoning ...................................... 41 6.3.6 Mathematical logic ...................................... 42 6.3.7 Philosophical logic ...................................... 42 6.3.8 Computational logic ...................................... 42 6.3.9 Bivalence and the law of the excluded middle; non-classical logics ............. 43 6.3.10 “Is logic empirical?" ..................................... 44 6.3.11 Implication: strict or material? ................................ 44 6.3.12 Tolerating the impossible ................................... 44 6.3.13 Rejection of logical truth ................................... 44 6.4 See also ................................................ 45 6.5 Notes and references ......................................... 46 6.6 Bibliography .............................................. 48 6.7 External links ............................................. 48 7 Necessity and sufficiency 50 7.1 Definitions ............................................... 50 7.2 Necessity ............................................... 50 7.3 Sufficiency ............................................... 52 7.4 Relationship between necessity and sufficiency ............................ 53 7.5 Simultaneous necessity and sufficiency ................................ 53 7.6 See also ................................................ 54 7.6.1 Argument forms involving necessary and sufficient conditions ................ 54 7.7 References ............................................... 54 7.8 External links ............................................. 54 8 Occam’s razor 55 8.1 History ................................................. 56 8.1.1 Formulations before Ockham ................................. 56 8.1.2 Ockham ............................................ 57 8.1.3 Later formulations ...................................... 57 8.2 Justifications .............................................. 58 8.2.1 Aesthetic ........................................... 58 8.2.2 Empirical ........................................... 58 8.2.3 Practical considerations and pragmatism ........................... 58 iv CONTENTS 8.2.4 Mathematical ......................................... 59 8.2.5 Other philosophers ...................................... 60 8.3 Applications .............................................. 61 8.3.1 Science and the scientific method ............................... 61 8.3.2 Biology ............................................ 62 8.3.3 Medicine ........................................... 63 8.3.4 Religion ............................................ 64 8.3.5 Penal ethics .......................................... 65 8.3.6 Probability theory and statistics ................................ 65 8.4 Controversial aspects of the razor ................................... 66 8.5 Anti-razors .............................................. 66 8.6 See also ................................................ 67 8.7 Notes ................................................. 68 8.8 References ............................................... 68 8.9 Further reading ............................................ 71 8.10 External links ............................................. 72 8.11 Text and image sources, contributors, and licenses .......................... 73 8.11.1 Text .............................................. 73 8.11.2 Images ............................................ 76 8.11.3 Content license ........................................ 77 Chapter 1 Abductive reasoning “Abductive” redirects here. For other uses, see Abduction (disambiguation). Abductive reasoning (also called abduction,[1] abductive inference[2] or retroduction[3]) is a form of logical inference that goes from an observation to a hypothesis that accounts for the observation, ideally seeking to find the simplest and most likely explanation. In abductive reasoning, unlike in deductive reasoning, the premises do not guarantee the conclusion. One can understand abductive reasoning as “inference to the best explanation”.[4] The fields of law,[5] computer science, and artificial intelligence research[6] renewed interest in the subject of abduc- tion. Diagnostic expert systems frequently employ abduction. 1.1 History The American philosopher Charles Sanders Peirce (1839–1914) first introduced the term as “guessing”.[7] Peirce said that to abduce a hypothetical explanation a from an observed circumstance b is to surmise that a may be true because then