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By A. R. D. Mathias, H. Rogers

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Additional resources for Cambridge Summer School in Mathematical Logic, Cambridge, 1971

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Example: 'pious' sense: [pious] significance: Ill. Which of the following terms lacks denotation and significance? bridesmaid mermaid sea cow sea squirrel N. To what attributes, if any, do the following characterizations correpond? BEING A BACHELOR BEING A MARRIED BACHELOR BEING A MERMAID ****************************************************************** Reasoning 17 11. Statement Meaning Statements and terms are the two basic kinds of material expressions. Terms are used for characterizing things in the world.

40 An Invitation to Formal Reasoning 10. Logical Syntax Syntax or sentence structure is of special concern to grammarians and to logicians. The logician's concern with sentence structure differs from the linguist's or grammarian's in two ways. In the first place the logician restricts himself to sentence forms that are appropriate to statements. In practice the exclusive concern with statementsentences restricts the logician to the consideration ofelementary sentences that are declarative or indicative in fonn.

However, not all STATES can be represented graphically and the actual use of Venn diagrams for logical purposes is rather limited. As students of logic we want to learn how to infer conclusions from given premises. And we want techniques for checking the validity of a wide range of arguments. For example, we might wish to see whether an argument like 'every noncitizen is an alien, hence, anyone who arrests a non-alien arrests a citizen' is valid. ) For arguments of this kind the method of checking validity by means of state diagrams will not work.

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