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By Ladislav Rieger

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An artificial international language. But this would not be entirely correct. Esperanto is, as a matter of fact, an artificial language built up so as to be (grammatically and syntactically) as simple as possible (to combine grammatical advantages of various languages and eliminate their complications), while resembling the main Indo-European languages by the diction of its words. Esperanto differs from natural languages also by the fact that — as far as I know — it is not the mother tongue of any children.

Then: Each of the expressions (X) v (7), (X)&(Y), (X) -► (7) assumes the meaning o/the corresponding compound statement or condition, this meaning being determined by the meaning of the components X, 7 and by the familiar meaning of the logical connectives v , &, -». The sentential expression "1 (X) acquires the meaning of the logical negation of the sentential meaning of the expression X. The sentential expression 3x (X) acquires the sentential meaning of the condition or assertion that, for a suitable choice of the meaning (in Ω) of the free individual indeterminate x in X, the sentential meaning of the expression X is true.

But this changes nothing in the fact that the names of sentences do not belong to the proper language of mathematics; actually they belong to its so-called metalanguage. For the time being, this is as much as need be said concerning the individual signs and symbolic expressions compiled from them. The introduction of abbrevia­ tions here has mostly practical reasons and it could be, "theoretically" at least, eliminated. *) Carnap [2] uses the term "autonyme Redeweise" to denote such a manner of exhibiting symbols.

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