Section 1 reviews Strawson’s logic of presuppositions. Strawson’s justification is critiqued and a new justification proposed. Section 2 extends the logic of presuppositions to cases when the subject class is necessarily empty, such as (x)((Px & ~Px) → Qx) . The strong similarity of the resulting logic with Richard Diaz’s truth-relevant logic is pointed out. Section 3 further extends the logic of presuppositions to sentences with many variables, and a certain valuation is proposed. It is noted that, given this valuation, Gödel’s sentence becomes neither true nor false. The similarity of this outcome with Goldstein and Gaifman’s solution of the Liar paradox, which is discussed in section 4, is emphasized. Section 5 returns to the definition of meaningfulness; the meaninglessness of certain sentences with empty subjects and of the Liar sentence is discussed. The objective of this paper is to show how all of the above-mentioned concepts are interrelated.
Keywords Strawson  Diaz  Gaifman  Goldstein  Gödel  meaning  presuppositions  truth-relevant logic  liar paradox
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On Referring.P. F. Strawson - 1950 - Mind 59 (235):320-344.
Introduction to Logical Theory.Christopher Blake - 1953 - Journal of Symbolic Logic 18 (3):273-276.

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