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The mother again responds with a short reiteration of the nurse's statement, functioning to confirm that the nurse's presupposition is correct 'Yes she's drinking some water'.
A correct theory of just how presuppositions are inherited from simple to complex sentences would solve the projection problem, and doing so seems to be required for a semantic account of presupposition.
However, this is not a direct disconfirmation (eg, Yes she is coughing), but instead the mother qualifies her response— not a constant cough, functioning to uphold the nurse's presupposition as at least partially correct.
It is in fact often quite easy to make out fallacies and to correct them; but such corrections must remain incomplete without sufficient information about Plato's conception of the good life and its moral presuppositions.
Likewise, Carnap had not been prompted do so some thirty years earlier by Neurath (1931b, 1932a) who argued that such a type of rational reconstruction traded on objectionable counterfactual presuppositions (methodological solipsism did not provide a correct description of the reasoning involved in cognitive commerce with the world around us).
Assuming that Strawson's observations are correct, should we say (a) that non-topical definites are non-presuppositional, or (b) that they do have presuppositions, whose failure happens not to affect speakers' truth-value judgments?
The presupposition is fantastical.
Presupposition and Implicature: Laurence R. Horn.
Presupposition (D.I. Beaver).
This alone constitutes the presupposition of love.
DANIEL ROTHSCHILD Presupposition Projection and Logical Equivalence.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com