|Mill, John Stuart
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|Numbers||Thiel I 15
Numbers/John Stuart Mill: mathematical objects, especially the numbers, are abstractions taken from concrete experience, that is, the most general properties or characteristics of reality. By generalizing the observation, we arrive at definitions for mathematical objects. They express facts about the totality of physical objects. (Mill: "aggregates").
Each proposition based on this asserts that a definite totality could have been formed by combining certain other totals, or by withdrawing them.
Each numeral sign "2", "3", etc. denotes for Mill a physical phenomenon, a property which belongs to the totality of things that we describe with the numeral signs.
FregeVsMill: drastic counterexamples: Doubtfulness in the case of 0 and 1, but also for very large numbers. Who should have ever observed the fact for the definition of 777 865? Mill could have defended himself. That his position seems to be more suited to the justification of our number and form than for the justification of arithmetic.
J. St. Mill
Utilitarianism: 1st (First) Edition Oxford 1998
Philosophie und Mathematik Darmstadt 1995