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Answer for the clue "The logical analysis of mathematical reasoning ", 15 letters:
metamathematics

Word definitions for metamathematics in dictionaries

Wikipedia Word definitions in Wikipedia
Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories , which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the term itself) ...

Wiktionary Word definitions in Wiktionary
n. A branch of mathematics dealing with mathematical systems and their nature.

Douglas Harper's Etymology Dictionary Word definitions in Douglas Harper's Etymology Dictionary
1890, from meta- + mathematics .

WordNet Word definitions in WordNet
n. the logical analysis of mathematical reasoning

Usage examples of metamathematics.

It lies in a widespread lack, at that time, of the required epistemological attitude toward metamathematics and toward non-finitary reasoning.