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Single Idea 9576

[filed under theme 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units ]

Full Idea

Multiplicity in general is no more than something and something and something, etc.; ..or more briefly, one and one and one, etc.

Gist of Idea

Multiplicity in general is just one and one and one, etc.

Source

Edmund Husserl (Philosophy of Arithmetic [1894], p.85), quoted by Gottlob Frege - Review of Husserl's 'Phil of Arithmetic'

Book Ref

-: 'Mind July 1972' [-], p.323


A Reaction

Frege goes on to attack this idea fairly convincingly. It seems obvious that it is hard to say that you have seventeen items, if the only numberical concept in your possession is 'one'. How would you distinguish 17 from 16? What makes the ones 'multiple'?


The 7 ideas from 'Philosophy of Arithmetic'

Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck]
We clarify concepts (e.g. numbers) by determining their psychological origin [Husserl, by Velarde-Mayol]
Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl]
Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl]
0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett]
Husserl identifies a positive mental act of unification, and a negative mental act for differences [Husserl, by Frege]
Multiplicity in general is just one and one and one, etc. [Husserl]