|Abstract: non-representational - abstract concept, expression of something non-objective - how to demarcate from concrete objects? How to differentiate between abstract entities and concepts, ultimately words.|
|Quine, Willard Van Orman
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Abstract/Concrete: independent from stimulus meaning.
I 212 ff
Abstract terms: alleged names of properties - "roundness": "F"/"round":"a" in "Fa" - should not be used unhesitatingly without metaphysical definition - would be too non-binding - every abstract singular term provides an abstract general term.
Not all abstract objects are properties: numbers, classes, functions, geometrical figures, ideas, possibilities - giving up or re-tracing abstract objects - faithfully distinguish them from concrete ones by use of "-ness".
Plural: abstract singular term: "lions are dying out" -Disposition: "eats mice" (31).
Intensional abstraction: "the act of being a dog", "the act of baking a cake", "the act of erring".
Class abstraction attributed to singular descriptions: (iy)(x)(x from y iff ..x..) - instead of: x^(..x..) - is not possible for intensional abstraction.
Difference classes/Properties: classes identical, with the same elements - properties not quite identical if they are attributed to the same things.
Abstraction of relations, propositions and properties: opaque (planets).
Class abstraction: transparent, - intensional abstraction: opaque.
Abstract general term: relative clause: "Y is a class X such that FX" - new: these are classes of classes. Normal relative clause: = general term: "y is a thing x such that Fx".
Concrete/abstract/Quine: by pointing to a square we do not assume identity with others - "squareness" is shared by other objects, but we do not need to insinuate entities like "attributes" - we do not point to the "attributes" (as an entity) nor do we need it in reference to the word "square".
Abstract singular term/Quine: like names - philosophically revolutionary: setting abstract entities - (unlike general term).
Abstract entities/Quine: classes and truth values may be accepted abstract entities - only statements and predicates should not be regarded as names of these and other entities, i.e. "p", "q"p,"F" etc. should not be bindable (quantifiable) variables (>2nd order logic) - (E.g.)(x is a dog. x is white.) does not commit X to "dogness" or to the class of white things as universals. - Solution: explicit form: belonging to two classes: (Ex)(xεy.xεz). - Of course, there are names for abstract entities: singular term: "dogness" "class of white things" (as names ((s) it does not imply existence).
Wort und Gegenstand Stuttgart 1980
Theorien und Dinge Frankfurt 1985
Grundzüge der Logik Frankfurt 1978
Mengenlehre und ihre Logik Wiesbaden 1967
Die Wurzeln der Referenz Frankfurt 1989
Unterwegs zur Wahrheit Paderborn 1995
From a logical point of view Cambridge, Mass. 1953
Bezeichnung und Referenz
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982
Philosophie der Logik Bamberg 2005
Ontologische Relativität Frankfurt 2003