Lexicon of Arguments

 

I 231
Ambiguity: The name Paul is not ambiguous. It is not a general term but a singular term with dissemination. Ambiguity Action/Habit: are ice skaters, delivery (action, object).
I 232
Truth is not ambiguous but general. A true confession is as true as math. Law: There is a difference between laws and confessions! Also, "existence" is not ambiguous.
I 233
Circumstances/Quine: circumstances are important for ambiguities.
I 236
Ambiguities: "a" (can be "any"). "Nothing" and "nobody" are undetermined singular terms (E.g. Polyphemus).
I 244
An ambiguous scope cannot be decided by parentheses. Undetermined singular terms are: a, any, every member - "not a"/"not every" - "I think one is so that ..." / "one is so that I think ... ".
IX 184
"Systematic (or type-wise) ambiguity/Russell: a solution for the problem are relations: the type is only fixed when we state the type of things from the left end of the range and from the right end of the range. There is one problem however: the two-dimensionality can add up to growths: E.g. type of a relation of things of type m to things of type n: (m, n). The type of a class of such relations should be called ((m, n)), then [((m,n))] is the type of a relation of such classes to such classes. Orders were obviously even worse.
IX 194
Systematic Ambiguity/theoretical terms/Quine: (context: polyvalent logic, 2nd order logic) Systematic ambiguity suppresses the indices and allows to stick to the simple quantifier logic. A formula like "∃y∀x(xεy)", which is treated as a type-wise ambiguous, can simply be equated with the scheme ∃y^{n + 1} ∀xⁿ (xⁿ ∃y^{n + 1}), where "n" is a schematic letter for any index. Its universality is the schematic universality that it stands for any of a number of formulas: ∃y1 "x0 (x0 ε Y1), ∃y2 "x1(x1 ε y2). It does not stand for the universality that consist in the fact that it is quantified undivided over an exhaustive universal class. A formula is meaningless if it cannot be equipped with indices that comply with the theoretical terms.
Problem: then also the conjunction of two meaningful formulas can become meaningless. Systematic ambiguity/theoretical terms: we can always reduce multiple variable types to a single one if we only take on suitable predicates. "Universal variables" that we restrict to the appropriate predicate are: "T_nx" expresses that x is of type n. The old formulae: "∀xⁿFxⁿ" and "∃xⁿFxⁿ". New is: "x(T_nx > Fx)", e.g.(T_nx u Fx).
>Indeterminacy/Quine.