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Being the pioneer of modern logic, Frege, with his quantification theory, was the pioneer of not only first-order logic, but also second-order logic. But today, as it may be seen from the recent pedagogical works clearly, learning modern logic has become almost equivalent to learning first-order logic. In the other words, first-order logic appears as the most natural, paradigmatic and central system of logic. However second-order logic either doesn’t appear in recent pedagogical works or appears as an interesting detail of the history of logic. Moreover, today even the logicality of second-order logic has become controversial. In this controversy, two of the criticisms against the logicality of second-order logic have become more apparent than the others: (1) the logical incompleteness criticism, and (2) the ontological commitments criticism. In this study, these two criticisms, which was put forward as a justification of the claim that second order logic is not a purely-logical system, and several responses to these criticisms are tried to be clarified in a simple and untechnical manner. Additionally it is argued that, while these two criticisms are strong and justified, several responses to these criticisms are weak. Ozet Modern mantigin oncusu Frege niceleme kuramiyla, yalnizca birinci seviye mantigin degil, ayni zamanda ikinci seviye mantigin da oncusuydu. Ancak gunumuz pedagojik yapitlarinda da acikca gorulebilecegi gibi bugun modern mantigi ogrenmek bunlardan birinci seviye mantigi ogrenmekle esdeger hale gelmistir. Diger bir deyisle birinci seviye mantik, mantigin en dogal, paradigmatik ve merkezi sistemi olarak kendini gostermektedir. Diger taraftan ikinci seviye mantik ise gunumuz pedagojik yapitlarinda ya yer almamakta ya da bu yapitlarda mantik tarihinin ilginc bir ayrintisi olarak yer almaktadir. Dahasi bugun ikinci seviye mantigin mantiksalligi dahi tartismali hale gelmistir. Bu tartismalarda ikinci seviye mantigin mantiksalligina getirilen elestirilerden ikisi digerlerine gore daha belirgin hale gelmistir. (1) Mantik sistemsel eksiklik elestirisi ve (2) gizli ontolojik kabuller elestirisi. Bu calismada ikinci seviye mantigin saf-mantiksal bir sistem olmadigi iddiasina gerekce olarak ileri surulen bu iki elestiri ve bu elestirilere getirilen cesitli yanitlar, basit ve teknik olmayan bir dille acik kilinmaya calisilmistir. Ek olarak bu iki elestirinin guclu ve hakli elestiriler oldugu ve bu elestirilere getirilen cesitli yanitlarin ise gucsuz oldugu savunulmustur.

uluslararası i̇nsan bilimleri dergisi

Logicality of second-order logic: A critical inquiry on the related debates&lt;p&gt;İkinci seviye mantığın mantıksallığı: İlgili tartışmalar üzerine eleştirel bir değerlendirme