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

Word definitions for metamathematics in dictionaries

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

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

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) ...

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

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.