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Single Idea 14284

[filed under theme 10. Modality / B. Possibility / 6. Probability ]

Full Idea

If (and only if) an argument is valid, then in no probability distribution does the improbability of its conclusion exceed the sum of the improbabilities of its premises. We can call this the Probability Preservation Principle.

Gist of Idea

Conclusion improbability can't exceed summed premise improbability in valid arguments

Source

Dorothy Edgington (Conditionals (Stanf) [2006], 3.2)

Book Ref

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.14

A Reaction

[Ernest Adams is credited with this] This means that classical logic is in some way probability-preserving as well as truth-preserving.

The 14 ideas from 'Conditionals (Stanf)'

14270 Simple indicatives about past, present or future do seem to form a single semantic kind [Edgington]
14269 Maybe forward-looking indicatives are best classed with the subjunctives [Edgington]
14274 Inferring conditionals from disjunctions or negated conjunctions gives support to truth-functionalism [Edgington]
14271 Non-truth-functionalist say 'If A,B' is false if A is T and B is F, but deny that is always true for TT,FT and FF [Edgington]
14272 I say "If you touch that wire you'll get a shock"; you don't touch it. How can that make the conditional true? [Edgington]
14273 Conditional Proof is only valid if we accept the truth-functional reading of 'if' [Edgington]
14276 The truth-functional view makes conditionals with unlikely antecedents likely to be true [Edgington]
14275 Truth-function problems don't show up in mathematics [Edgington]
14278 Truth-functionalists support some conditionals which we assert, but should not actually believe [Edgington]
14282 On the supposition view, believe if A,B to the extent that A&B is nearly as likely as A [Edgington]
14281 A thing works like formal probability if all the options sum to 100% [Edgington]
14284 Conclusion improbability can't exceed summed premise improbability in valid arguments [Edgington]
14287 Does 'If A,B' say something different in each context, because of the possibiites there? [Edgington]
14290 Doctor:'If patient still alive, change dressing'; Nurse:'Either dead patient, or change dressing'; kills patient! [Edgington]