Meaning and Proscription in Formal Logic by Thomas Macaulay Ferguson

Author:Thomas Macaulay Ferguson
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

4.3.1 Ill-Formedness

We have observed in foregoing sections (e.g., Sects. 2.​2 and 3.​2.​3) the coincidence of the themes of meaningfulness and possibility implicit within the context of logics of nonsense . If we recall the remarks made by Åqvist while describing his own system of nonsense logic , who concedes in [1, p. 151] that there are circumstances in which the doctrine of the predominance of the atheoretical element clearly holds. In labeling ill-formed formulae ‘statements’ and professing that they exhibit a particular type of semantical behavior, Åqvist may be interpreted as suggesting that ill-formed formulae constitute paradigmatic examples of syntactical objects that, while meaningless, still demand a logical analysis. Indeed, Åqvist’s rejection of this doctrine is due only to the intuition that the class of ill-formed formulae does not exhaust the class of meaningless statements.

We may try to apply Åqvist’s comment associating meaningfulness with well-formedness to shine light on the interpretation of disjunction in and . Before judging some string of symbols to be true (or false), one must determine that the string is in fact a well-formed formula and this demands that all its components must be surveyed. Otherwise, there exists an open invitation to error.

We can employ a concrete illustration—along the lines of the treatment of conjunction in [34]—to demonstrate that there is something intuitively correct about this picture. Suppose for a moment that merely securing the truth of the first disjunct were sufficient to establish the truth of a disjunction. Then, for example, we could design an algorithm to evaluate a string of symbols interpreted as positive disjunctive formulae as represented in Fig. 4.3.

Fig. 4.3McCarthy-style algorithm interpreting disjunction

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