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Title Transcription
スウガク キョウイク ニ オケル キゴウ ヒョウゲン ノ モンダイ 2 ロンリ キゴウ コウ ソノ1
Title Alternative (English)
Problems in Mathematical Symbolism(II) : Investigations of the Logical Symbols(1)
File
language
jpn
Author
Mino, Eiji
Description
In this paper, I investigate the sources and the developments on the "Logical Symbols", through adaptations of logical thoughts, within our school mathematics.
Giuseppe Peano, a mathematician in Italy, carried out an important part in symbolism of logic, because logical symbols we use generally are led by him. His ideas was expressed by uses of ε, C , = , ∩, ∪, ~, Λ. as the primitive ideas. (Still, he introduced the existence-quantifier Ea in 1897.)
His symbolism-formal language does not symbolize a contraction, an abbreviation, and a substance in short hand. That is, it does not mean "words", but "expressions of ideas".
B. Russell has developed the ideas and the symbols of Peano. The other side, D. Hilbert adopted his own symbols which he formulated and systematized logical ideas from a mathematical standpoint. For instance, he deviced p^^ ̄ in place of the negation -p, p & q in place of the conjunction p・q, p→q in place of the implication p⊃q, p~q (→←,⇔) in place of the equivalence (logical connective) p≡q, and (Ex) in splace of (Ex) etc. His symbol (Ex) represent "Es gibt ein x von . . . . . . . ".
Further, A. Heyting (and G. Gentzen) adopted ¬p as the negation, G. Gentzen adopted (Ax) as the all-quantifier, and Skolem, Hermes, and Freudenthal use ∧x, ∨x, the recent symbols, as the quantifiers.
Journal Title
Memoirs of the Faculty of Education, Shimane University. Educational science
Volume
8
Start Page
13
End Page
25
ISSN
0287251X
Published Date
1974-12-25
NCID
AN0010792X
Publisher
島根大学教育学部
Publisher Aalternative
The Faculty of Education Shimane University
NII Type
Departmental Bulletin Paper
OAI-PMH Set
Faculty of Education
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