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This last puzzle, presented as a series of questions about the application of the predicate 'is bald', was originally known as the falakros puzzle.
The degree of change between adjacent members of the series relative to which 'F' is soritical would seem too small to make any difference to the application of the predicate 'F'.
In some cases of ontological reduction of Ks to K*s, we withhold application of the predicate 'K' to the K*s because not enough of what we ordinarily take to be true of the Ks is preserved by the reduction.
The difference of one grain would seem to be too small to make any difference to the application of the predicate; it is a difference so negligible as to make no apparent difference to the truth-values of the respective antecedents and consequents.
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The sorites paradox is the name given to a class of paradoxical arguments, also known as little-by-little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved.
First of all, in a setting where sentences are context dependent, the natural formulation of a truth claim is always in terms of expressing a true proposition, or some related semantically careful application of the truth predicate.
Basically, if the sufficient condition for the application of the reason predicate (the condition given by the antecedent of the principle corresponding to the reason) includes such a free-agent variable then the reason is agent-relative; otherwise it is agent-neutral.
The former is cast in terms of whether a reason for one agent must also be a reason for anyone else while the latter is cast in terms of the occurrence of free agent variables in the sufficient condition for the application of the reason predicate corresponding to the reason.
The only difference is that for Nagel the relevant back-reference is to be found in the general form of the reason (which turns out to be a universally quantified principle giving a sufficient condition for the application of the reason predicate) whereas for Pettit the relevant back-reference is to be found in a full statement of the reason itself.
We use behavioural manifestations of the mind as criteria for the application of these predicates, for 'mental phenomena' are expressed in behaviour.
Mental predicates therefore presuppose the mentality that creates them: mentality cannot consist simply in the applicability of the predicates themselves.
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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