IRRATIONAL LOGICS TESTS

{A} An example of logical metatheory would be giving a proof, in English, that a certain logical system is sound and com- Preliminaries plete, i.e., that every inference its deductive system allows is valid according to its semantics, and vice versa. Since... More

{A} An example of logical metatheory would be giving a proof, in English, that a certain logical system is sound and com- Preliminaries plete, i.e., that every inference its deductive system allows is valid according to its semantics, and vice versa. Since the proof is about a logical system, the proof is not given A.1 Some Vocabulary within that logical system, but within the metalanguage. An object language is a language under discussion or be- Though it is not our main emphasis, we will be doing a fair ing studied (the “object” of our study). amount of logical metatheory in this course. Our metalan- guage will be English, and to avoid confusion, we will use A metalanguage is the language used when discussing an English words like “if”, “and” and “not” rather than their object language. corresponding object language equivalents when work- In logic courses we often use English as a metalanguage ing in the metalanguage. We will, however, be employing when discussing an object language Less