I 286
Intensional abstraction means "the act of being a dog", "the act of baking a cake", "the act of erring".
I 289
Class abstraction re-traced to singular descriptions: (iy)(x)(x from y iff
..x..) - instead of: x^(..x..) - is not possible for intensional abstraction.
I 295
Abstraction of relations, propositions and properties is opaque (E.g. of the planet).
I 322
Property abstraction (elimination) instead of "a = x(..x..)". New is the irreducible two-digit Operator "0": "a0x(..x..)". Variables are the only thing that remains. The pronoun has primacy.
IX 12ff
Class Abstraction/Quine: class abstraction "{x:Fx}" refers to "the class of all objects x with Fx". In the eliminable combination that we have in mind "ε" appears only in front of a class abstraction term and class abstraction terms appear only after "ε". The whole combination "y ε {x: Fx}" is then reduced according to a law:
Concretization Law/Quine: reduces "y ε {x: Fx}" to "Fy".
Existence/Ontology: thus no indication remains that such a thing as the class {x:Fx} exists at all.
Introduction: it would be a mistake, e.g. to write "*(Fx)" for "x = 1 and EyFy". Because it would be wrong to conclude "*(F0) *(F1)" from "F0 F1". Therefore we have to mistrust our definition 2.1 which has "Fx" in the definiendum, but does not have it in the definiens.
IX 16
Relations Abstraction/Relation Abstraction/Quine: "{xy:Fxy}" is to represent the relationship of a certain x to a certain y such that Fxy.
Relation/Correctness/Quine: parallel to the element relationship there is the concept of correctness for relations. Definition concretization law for relations/Quine: is also the definition correctness/relation: "z{xy: Fxy}w stands for "Fzw".
IX 52
Function Abstraction/lambda operator/Quine: before terms one must generate terms (expressions). (Frege/Church: is here also valid of statements and thus a second time class abstraction, but both group statements are under terms and classes under functions (QuineVsFrege,QuineVsChurch).
Definition lambda operator/Quine: if "...x..." contains x as a free variable, λx (...x...) is that function whose value is ...x... for each argument x - therefore λx(x²) the function "the "square of" - general: "λx(...x...)" stands for "{ : y = ...x...}" - identity: λx x{: y = x } = λ. - λx {z: Fxy} = {: y = {z: Fxz}} -. "λx a" stands for "{: y = a}". The equal sign now stands between variable and a class abstraction term.
IX 181
Abstraction/Order/Quine: the order of the abstracting expression must not be less than that of the free variables.