The statement is false just if it comes out false on at least one precisification.
But then some other intuitively true claim perhaps, 'Goliath and Lumpl (if they exist) are identical' will come out false.
On the ordinary English interpretation of Ω(mˆ), the quantifiers "see" these bijections, and so Ω(mˆ) comes out false.
The very process of trying to refute the induction step changes the context so that the instance will not come out false.
For instance, the liberal interpretations on which D1 comes out true ('Goliath and Lumpl exist') must, on pain of contradiction, make at least one of D2 through D4 come out false.
The demanding interpretations on which D1 comes out false do better than the liberal interpretations on this score, since they can make all of D2 through D4 come out true.
(Other claims, e.g., E3, will come out false for the same reason).[28] One might instead maintain that it is indeterminate which of various objects 'Theseus II' picks out.
Conversely, in the harmful style of disputation, the disputer distorts and twists the opponent's words, making them come out false or inconsistent or extending them in unintended ways.
With reference to artists' stipulative authority over the "features and boundaries" of their works, Sherri Irvin declares that "Any claim to the effect that all works belong to the same ontological category will thus come out false or uninformative" (2008, 1).
Thus there are not enough spatiotemporal entities to interpret set theory literally nor to make a structural interpretation of set theory non-vacuously true, and hence to ensure that set-theoretic falsehoods come out false rather than true.
If 'sugar' in this context referred to the various lumps and grains of sugar in a packet, then, if there are no more lumps or grains after the melting, then the set-equality, and hence the identity-claim, comes out false.
