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It is plausible to suppose that that the truth value of a proposition such as (i) or (ii) depends on the existence of something distinct from that proposition.
A neuron's response can represent the truth value of a proposition.
A truth function defines the truth value of a proposition composed by connectives (conjunction, disjunction, negation) in terms of the truth values of its components.
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Formally, this means that in the Leibnizian semantics the truth-value of a proposition only depends on the Leibnizian time.
Equivalently, there cannot be a difference in the truth-value of a proposition without a difference in its subject matter.
I suggest that shi is a verum focus marker, which focuses the truth values of a proposition (Höhle 1992; Schaffar and Chen 2001).
This paper introduces a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures, and the truth value of a quantified proposition is evaluated by using Sugeno's integral.
MacFarlane (2011b) articulates the relativist solution: Sandra and I disagree about the truth-value of a single proposition, the proposition that Susan might be at the store.
Except for uncertain inference, the uncertain set has also been used to uncertain logic (Liu [18]) as a tool to calculate the truth value of an uncertain proposition.
Third, the notion of "value" (Wert) here clearly means the truth-value of a whole proposition, not its propositional content specifically, which explains why a modal predicate "contributes nothing to the content of a judgment," i.e., it contributes nothing to the specific content of a judgment over and above its truth-value.
According to Russell, it is unnecessary to suppose that there exists any special sort of fact corresponding to molecular propositions; the truth-value of a molecular proposition could be entirely derivative on the truth-values of its constituents (PLA, 209).
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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