A Bridge to Advanced Mathematics

Amongprobabilitytheorists,abittercontroversyhasragedfordecadesbetweentheadherentsofJohnMaynardKeynes\'ATreatiseonProbability(1921)andthoseofRichardvonMises\'\"GrundlagenderWahrscheinlichkeitsrechnung\"(1919).Keynesdeclaredthatprobabilitiesmeasuretheextenttowhichaso-calledevidencepropositionsupportsanothersentence.VonMisesinsistedthattheymeasuretherelativefrequencywithwhichthemembersofaso-calledreferencesetbelongtoanotherset.StatisticalandInductiveProbabilitiesoffersanevenhandedtreatmentofthisissue,assertingthatbothstatisticalandinductiveprobabilitiesmaybetreatedassentence-theoreticmeasurements,andthatthelatterqualifyasestimatesoftheformer.Beginningwithasurveyoftheessentialsofsentencetheoryandofsettheory,authorHuguesLeblancexaminesstatisticalprobabilities(whichareallottedtosetsbyvonMises\'followers),showingthatstatisticalprobabilitiesmaybepassedontosentences,andtherebyqualifyastruth-values.Leblancconcludeswithanexplorationofinductiveprobabilities(whichKeynes\'followersallottosentences),demonstratingtheirreinterpretationasestimatesoftruth-values.Eachchapterisprecededbyasummaryofitscontents.Illustrationsaccompanymostdefinitionsandtheorems,andfootnoteselucidatetechnicalitiesandbibliographicalreferences.