Philosophy of Mathematics Handbook

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Oneofthe moststrikingfeatures ofmathematicsis the fact that we aremuch
morecertainaboutwhatmathematicalknowledgewe havethan aboutwhatmath
ematicalknowledgeis knowledgeof. Mathematicalknowledgeisgenerallyaccepted
tobemorecertainthananyotherbranchofknowledge;butunlikeotherscientific
disciplines,the subjectmatterofmathematicsremains controversial.
Inthescienceswemaynotbesureourtheories arecorrect,butatleast weknow
whatit is we arestudying. Physicsis the studyofmatterandits motionwithin
spaceandtime. Biologyis the studyofliving organismsandhowthey react and
interact withtheir environment. Chemistryis the studyofthe structureof,and
interactions between,the elements. Whenmanfirst beganspeculatingaboutthe
natureofthe Sunandthe Moon,he maynothave beensure his theories were
correct,butatleast hecouldpointwithconfidencetothe objectsaboutwhichhe
wastheorizing. Inall ofthese casesandothersweknowthat the objectsunder
investigation - physicalmatter,living organisms,the knownelements,the Sun
andthe M

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Philosophy of Mathematics Handbook