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Here it is relevant that (in at least one sense; see above) Nagel builds teleology into the logical form of the reason predicate, so that a reason is always understood as a reason to promote something.
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.
Similar(54)
This is the first of a two part examination of the relationship between the predicate and the reason.
The reason is that the unique one-place predicate of L′ divides the domain of a structure into those objects it satisfies and those it does not.
This criterion is satisfied if all instances of the predicate are pervaded by the reason, or in the given example, if all impermanent things are included among, or pervaded by, the category of things that are produced.
The final criterion is the counter pervasion (vyatirekavyāpti) and this is satisfied if there are no instances of the reason that are not also instances of the predicate.
The reason why this cannot be reproduced for Tr is that this predicate is always a predicate of a language (the metalanguage) different from the language of the sentences to which it applies (the object language).
The reason for this quandary is very simple and predicated upon the fact that their emotional state drives the average person's decision-making process.
The third criterion of a valid reason the proof of the counter pervasion (vyatirekavyāpti / ldog khyab / ldog khyab), or the proof that the reason is completely absent from the dissimilar instances of the predicate (vipakṣa / mi mthun phyogs)—hold because there are no instances of the predicate which are not instances of the reason.
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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