In Chapter 5 of ''Word and Object'' Quine proposes a system of regimentation: the paraphrasing of sentences into a ‘canonical notation’, that we can use to understand how reference works in a language. Since we use language for science, the reductions that we make in the complicitycomplexity of the structure of sentences will also simplify the conceptual schema of science. In the canonical notation, a sentence S is paraphrased as S’. S’ is a paraphrase of S that should clarify its reference, which means that it often resolves ambiguities, and is therefore by definition not synonymous with S. However, S’ should express the intended meaning of the speaker. Therefore, it should always be the original speaker who does the paraphrasing. The canonical notation consists of: atomic sentences (sentences that do not have sentences as a part) that have a general term in the predicate position, with one or more variables: ‘Fa’ or ‘Fab,’ etc. Non-atomic sentences are built from atomic sentences by using truth functions, quantifiers, and some other devices, like the four variable-binding operators. Quine drops tense, and instead uses the present as temporally neutral. We can express time with the use of ‘a at t’, where x is a spatiotemporal object. In his canonical notation, Quine has eliminated all singular terms other than variables. This greatly simplifies his logical theory, in the sense that there is economy in the roots of the theory: there is a very limited number of elements. In some situations, however, short paraphrases are very useful, for example in mathematic deductions. For these cases, Quine introduces ''definitions'': we can define singular terms relative to the canonical notation. In that way, we can still use singular terms, without having to include them in our theory.
