Lexicon of Arguments

Philosophical and Scientific Issues in Dispute
 
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VII (d) 75ff
Attribute/Quine: an attribute may eventually be introduced in a second step: e.g. "squareness" according to geometrical definition, but then the name also requires substitutability, i.e. an abstract entity > Universals.
X 7ff
Attribute/Quine: an attribute corresponds to properties, predicates are not the same as attributes.
>Predicates/Quine.
IX 178ff
Attribute/(s): an attribute corresponds to the quantity of those x for which a particular condition applies: {x: x ε a} all objects that are mortal. Predicate: "x is mortal", is not a quantity, but a propositional function. The denomination forms refer "φx", "φ(x,y)" to the attribution.
>Propositional Function/Quine.
XII 38
Attributary Attitude/Quine: E.g. hunting, needing, catching, fearing, missing. Important to note here is that e.g. "lion hunt" does not require lions as individuals but as a species - > Introduction of properties.
IX 177
Attributes/Ontology/Russell: for Russell, the universe consisted of individuals, attributes and relations of them, attributes and relations of such attributes and relations, etc.
IX 178f
Extensionality/Quine: extensionality is what distinguishes attributes and classes. >Extensionality/Quine
So Russell has more to do with attributes than with classes.
Two attributes can be of different order and are therefore certainly different, and yet the things that each have one or the other attribute are the same.
For example the attribute "φ(φ^x <> φy) where "φ" has the order 1, an attribute only from y.
For example the attribute ∀χ(χ^x <> χy), where "χ" has order 2, again one attribute only from y, but one attribute has order 2, the other has order 3.
(> Classes/ >Quantities/ >Properties).
XIII 22
Class/set/property/Quine: whatever you say about a thing seems to attribute a property to it.
Property/Attribute/Tradition/Quine: in earlier times one used to say that an attribute is only called a property if it is specific to that thing. (a peculiarity of this object is...).
New: today these two expressions (attribute, property) are interchangeable.
"Attribute"/Quine: I do not use this term. Instead I use "property".
Identity/equality/difference/properties/Quine: if it makes sense to speak of properties, then it also makes sense to speak of their equality or difference.
Problem: but it does not make sense! Problem: if everything that has this one property, also has the other. Shall we say that it is simply the same quality? Very well. But people do not talk like that. For example to have a heart/kidney: is not the same, even if it also applies to the same living beings.
Coextensivity/Quine: two properties are not sufficient for their identity.
Identity/properties/possible solution: is there a necessary coextensiveness? >Coextensive/Quine
Vs: Necessity is too unclear as a term.
Properties/Quine: We only get along so well with the term property because identity is not so important for their identification or differentiation.
XIII 23
Solution/Quine: we are talking about classes instead of properties, then we have also solved the problem e.g. heart/kidneys.
Classes/Quine: are defined by their elements. That is the way of saying it, but unwisely, because the misunderstanding might arise that the elements cause the classes in a different way than objects cause their.
Def Singleton/Singleton/Single Class: class with only one element.
Def Class/Quine: (in useful use of the word): is simply a property in the everyday sense, without distinguishing coextensive cases.
XIII 24
Class/Russell/Quine: it struck like a bomb when Russell discovered the platitude that each containment condition (condition of containment, element relationship) establishes a class. (see paradoxes, see impredictiveness).
Russell's Paradox/Quine: applies to classes as well as to properties. It also shatters the platitude that anything said about a thing attributes a property.
Properties/Classes/Quine: all restrictions we impose on classes to avoid paradoxes must also be imposed on properties.
Property/Quine: we have to tolerate the term in everyday language.
Mathematics: here we can talk about classes instead, because coextensiveness is not the problem. (see Definition, > Numbers).
Properties/Science/Quine: in the sciences we do not talk about properties.

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