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(METHODO)LOGICAL PRESUPPOSITIONS IN THE WORK OF LEIBNIZ 19<br />

Consequently, an equivalent formulation of the above <strong>de</strong>finition<br />

reads:<br />

Definition. A statement (proposition) P has as its logical<br />

presupposition the statement (proposition) Q if and only if, for all the<br />

possible circumstances (contexts) w, if Q is false in w, then P is<br />

neither true, nor false (P has no value of truth) in w.<br />

Thus it becomes obvious, given the consi<strong>de</strong>rations above, that Q<br />

ceases to constitute a logical presupposition for P as soon as a<br />

circumstance (context) w can be i<strong>de</strong>ntified, in which P has no value of<br />

truth and Q is false.<br />

Sandu (1997) consi<strong>de</strong>rs that the philosophical justification for this<br />

type of presuppositions resi<strong>de</strong>s in Frege’s theory on meaning and<br />

signification.<br />

In the example:<br />

(i) The queen of England is (not) very popular<br />

(ii) There is a (unique) queen of England,<br />

the statement (i) logically presupposes the statement (ii) precisely<br />

because, if the proposition that (i) expresses has a value of truth, then its<br />

correspon<strong>din</strong>g function has a value, so it follows it also has an argument.<br />

The existence of the argument indicates that the subject-term “the queen<br />

of England” has both meaning and signification. Consequently, it is<br />

necessary that the object that the concept <strong>de</strong>notes exist. Therefore, (ii) is<br />

true.<br />

Still, there are cases in which the subject-term has meaning, but it<br />

lacks signification, as in the following example:<br />

(iii) The king of France is a bold man.<br />

The proposition has no value of truth, because the function that<br />

corresponds to the predicate “is a bold man” lacks argument for the object<br />

that “the king of France” <strong>de</strong>notes (there is no such object). Thus,<br />

(iv) There is a (unique) king of France<br />

does not constitute a logical presupposition for (iii), because there is at<br />

least one context (the current one) in which (iv) is false and for which (iii)<br />

has no truth-value.<br />

Sandu specifies that it has been established (Soames; 1989) that<br />

there are situations that do not sustain Frege’s theory:

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