Review, Part #4
Ontology
The question dealing with an existence of general concepts belongs to the part of philosophy, which is called ontology, where base-elements and structures of the reality will be examined. Willard V. Quine (1908-2000) express the base-question of ontology in form: "What exists?"; according to his answer separate concept-systems contains different (depending on value-propositions of variables which are bound by two quantors) existence-hypothesis's - ontological commitments - which have to accept by them who are using this system. So, in realistic systems is made stronger "commitments" than in nominalistic systems.
Karl Popper (1902-1993) have represented an apparently easy solution to ontological problems. He separates from the others a world 1 consisting of physical objects, a world 2 consisting of a consciousness and thoughts and a world 3 consisting of (among other things) propositions, numbers and creations of human mind. So can man place all ontologically problematic cases to third basket consisting of the 3rd world: (at least most) general concepts, meanings, propositions, numbers/digits, classes, poems, symphonies, values, norms etc. Then is forming as a problem to characterize satisfied relation(s) between these three "worlds". The separate existence of a "world 3" is obviously in conflict with nominalism and conceptualism. According to the platonic realism, a world 3 exists without depending worlds 1 and 2. Popper adopted however a view of constructivism which differs so from a realism, a nominalism as from a conceptualism.
Frege and Mathematics
Gottlob Frege (1848-1925) attempted - in his The Foundations of Arithmetic (Grundlagen der Arithmetik, 1884) and Fundamental Laws of Arithmetic (1893-1903) - to make arithmetic secure by deriving it from the laws of logic: his philosophy grows out of the problems which that attempt engenders. His problems are "technical", therefore , in the sense in which so much recent philosophy is technical. We can understand how the traditional subjective-objective antithesis can be overcome, Frege argues, once we realize that number are applied to "concepts" - a "concept" understood not as an "idea", an image in an individual mind, but as an "object of Reason".
