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The limits of the body seem well defined enough as definitions go, but definitions seldom go far.

 

Samuel(novelistButler

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Rules for Demonstrations. I. Not to undertake to demonstrate any thing that is so evident of itself that nothing can be given that is clearer to prove it. II. To prove all propositions at all obscure, and to employ in their proof only very evident maxims or propositions already admitted or demonstrated. III. To always mentally substitute definitions in the place of things defined, in order not to be misled by the ambiguity of terms which have been restricted by definitions.

 

Blaise Pascal

 

Rules necessary for definitions. Not to leave any terms at all obscure or ambiguous without definition; Not to employ in definitions any but terms perfectly known or already explained.

 

Blaise Pascal

 

Necessity may be defined in two ways, conformably to the two definitions of cause, of which it makes an essential part. It consists either in the constant conjunction of like objects, or in the inference of the understating from one object to another.

 

David Hume

 

If we wish to express our ideas in terms of the concepts synthetic and analytic, we would have to point out that these concepts are applicable only to sentences that can be either true of false, and not to definitions. The mathematical axioms are therefore neither synthetic nor analytic, but definitions. ...Hence the question of whether axioms are a priori becomes pointless since they are arbitrary.

 

Hans Reichenbach

 

Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other, and also stand in exact relationships, ordered by definitions, to those concepts which have previously been introduced and are already at hand and established. In particular, in the introduction of new numbers, it is only obligated to give definitions of them which will bestow such a determinacy and, in certain circumstances, such a relationship to the other numbers that they can in any given instance be precisely distinguished. As soon as a number satisfies all these conditions, it can and must be regarded in mathematics as existent and real.

 

Georg Cantor