Did you by any chance mean nonempty?
“If we can equate nothing with the empty set and something with a non-empty set, (not a trivial assumption, given that mathematics extends beyond set theory), then it is significant to note that whilst every set contains the empty set as a subset, the converse certainly isn't true.”
“Clearly the intersections of sex with both toothpaste and orange juice should be non-empty.”
“The ones who get hosed by the present system are those with no bargaining power and non-empty pockets.”
“However, this resemblance is merely apparent, because empty nouns are genuine names and can always be decomposed into non-empty genuine names (e.g., "round square").”
“An inclusive or exclusive disjunction of two propositions s1 and s2 is interpreted by Bolzano as a proposition which attributes to the idea [a true proposition belonging to the collection consisting of s1 and s2] the property of being non-empty or singular, respectively (WL II, 204 f., 228 f.).”
“A propositional form F is universally valid iff at least one member of F is true, and every member of F with a non-empty subject idea is true; F is universally contravalid iff every member of F is false.”
“If all i-variants of a proposition s with an non-empty subject idea are true, Bolzano will say that s is universally valid with respect to i.”
“If all variants of s with respect to i with non-empty subject ideas are true,”
“In a sentence of the form ˜There is at least one A™ we attribute, according to Bolzano, not a property to A itself but to [A], i.e., the idea of A, namely the property of being non-empty.”
“A propositional form F is logically valid iff F is a logical propositional form that is universally valid, i.e., at least one of its members is true, and all of its members with non-empty subject ideas are true.”
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