▁of ▁prov ability ▁pred ic ates ▁had ▁been ▁obtained ▁earlier ▁using ▁very ▁different ▁methods ▁by ▁Sol omon ▁Fe fer man . ▁ ▁Bool os ▁was ▁an ▁authority ▁on ▁the ▁ 1 9 th - century ▁German ▁math ematic ian ▁and ▁phil os opher ▁Gott lob ▁Fre ge . ▁Bool os ▁proved ▁a ▁conject ure ▁due ▁to ▁Cris pin ▁Wright ▁( and ▁also ▁proved , ▁independently , ▁by ▁others ), ▁that ▁the ▁system ▁of ▁Fre ge ' s ▁Grund ges et ze , ▁long ▁thought ▁v iti ated ▁by ▁Russell ' s ▁par ado x , ▁could ▁be ▁fre ed ▁of ▁incons ist ency ▁by ▁replacing ▁one ▁of ▁its ▁ax i oms , ▁the ▁not orious ▁Basic ▁Law ▁V ▁with ▁H ume ' s ▁Princi ple . ▁The ▁resulting ▁system ▁has ▁since ▁been ▁the ▁subject ▁of ▁inten se ▁work . ▁ ▁Bool os ▁argued ▁that ▁if ▁one ▁reads ▁the ▁second - order ▁variables ▁in ▁mon adic ▁second - order ▁logic ▁pl ur ally , ▁then ▁second - order ▁logic ▁can ▁be ▁interpreted ▁as ▁having ▁no ▁ont ological ▁commit ment ▁to ▁entities ▁other ▁than ▁those ▁over ▁which ▁the ▁first - order ▁variables ▁range . ▁The ▁result ▁is ▁pl ural ▁quant ification . ▁David ▁Lewis ▁employed ▁pl ural ▁quant ification ▁in ▁his ▁Part s ▁of ▁Class es ▁to ▁derive ▁a ▁system ▁in ▁which ▁Z erm elo – F ra enk el ▁set ▁theory ▁and ▁the ▁Pe ano ▁ax i oms ▁were ▁all ▁the or ems . ▁While ▁Bool os ▁is ▁usually ▁cred ited ▁with ▁pl ural