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Of course, "hardworking" – whether it is a predicate of "families" or "people" – is one of those glittering generalities that features regularly in political communications.
This means that for any predicate of any order, there is a predicate of the first-order level which is equivalent to it.
On this view, the logical form of "God exists" is not Exists (God)—where Exists is a predicate of individuals, but rather: The concept God applies to something, or Something possesses the property of being God).
Moreover, the first sentence contains what might be called an individuating predicate — it is a predicate of the form, a such and such, rather than of the form, such and such.
According to Kant, truth is a predicate of whole judgments, and not a predicate of the representational proper parts of judgments, i.e., intuitions/non-conceptual cognitions and concepts (A293/B350).
If (p) is a predicate of type (P(T_1 times cdots times T_k)), and for (1 le i le k), (t_i) is a term of type (T_i), then (p(t_1,ldots,t_k)) is an atomic formula (also called an atom).
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Metalinguistic descriptivism is commonly presented in a package with the view that proper nominals (see Syntax above) are metalinguistic predicates (so the nominal 'Alfred' is a predicate true of individuals that are so called).
Here, primitiveAction is a predicate characterizing all the actions of the domain.
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).
If existence is not a predicate of individuals, then one might suppose that neither is nonexistence.
Immanuel Kant took up Hume's idea and claimed that existence is not a "real predicate", a claim that is often interpreted as an anticipation of Gottlob Frege's famous doctrine that existence is not a predicate of individuals.
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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