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タイトルヨミ
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
日本語以外のタイトル
Problems in Mathematical Symbolism(II) : Investigations of the Logical Symbols(1)
ファイル
言語
日本語
著者
三野 栄治
内容記述(抄録等)
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.
掲載誌名
島根大学教育学部紀要. 教育科学
8
開始ページ
13
終了ページ
25
ISSN
0287251X
発行日
1974-12-25
NCID
AN0010792X
出版者
島根大学教育学部
出版者別表記
The Faculty of Education Shimane University
資料タイプ
紀要論文
部局
教育学部
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