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Translation/formal language/Mates: a translation of everyday language in the artificial language is meaningless as long as the artificial language is not interpreted - "minimum translation": translated true in true and false in false statements.
Translation/meaning/sense/interpretation/Mates: to know whether something is a satisfactory translation (of a formal language), we need not only to know the meaning (reference), but also the sense - otherwise we can obtain various everyday language translations - sense: cannot be stated in a list as meaning - meaning/Mates: gives the non-logical constants truth conditions: E.g. 2 < 3 is true, if the smallest prime number is less than 3 - sense/Mates: provides the content: that the smallest ... is smaller - reference/Mates: provides truth conditions: true, if .. - sense: content: that it is true.
Translation/variables/Mates: the translation is not affected by the substitution of the variables, but only by the substitution of the constants.
Translation/summary/Mates: 1. meaningless without interpretation. (Assignment of objects to the individual constants) - 2. If an interpretation is given, one can get a "standard translation" for every formal statement, and this by means of the definition of "true in interpretation I" - Problem: if the same interpretation is given in various ways (E.g. 2 = "smallest prime" or "sole even prime number") one can obtain several non-synonymous translations - two formal statements may be equivalent, without being equally good translations - conversely possible: that two statements are adequate but not equivalent - (only for ambiguity).
Elementare Logik Göttingen 1969