Combining Philosophers
Ideas for Friedrich Schlegel, John Stuart Mill and Theophrastus
expand these ideas

start again

choose
another area for these philosophers
display all the ideas for this combination of philosophers
17 ideas
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
5201

Mill says logic and maths is induction based on a very large number of instances [Mill, by Ayer]

9360

If two black and two white objects in practice produced five, what colour is the fifth one? [Lewis,CI on Mill]

9888

Mill mistakes particular applications as integral to arithmetic, instead of general patterns [Dummett on Mill]

9796

Things possess the properties of numbers, as quantity, and as countable parts [Mill]

9794

There are no such things as numbers in the abstract [Mill]

9795

Numbers have generalised application to entities (such as bodies or sounds) [Mill]

9797

'2 pebbles and 1 pebble' and '3 pebbles' name the same aggregation, but different facts [Mill]

9798

Different parcels made from three pebbles produce different actual sensations [Mill]

9799

3=2+1 presupposes collections of objects ('Threes'), which may be divided thus [Mill]

9803

We can't easily distinguish 102 horses from 103, but we could arrange them to make it obvious [Mill]

9802

Numbers denote physical properties of physical phenomena [Mill]

9804

Arithmetical results give a mode of formation of a given number [Mill]

9805

12 is the cube of 1728 means pebbles can be aggregated a certain way [Mill]

8741

Numbers must be of something; they don't exist as abstractions [Mill]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
12411

Mill is too imprecise, and is restricted to simple arithmetic [Kitcher on Mill]

5656

Empirical theories of arithmetic ignore zero, limit our maths, and need probability to get started [Frege on Mill]

6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
9624

Numbers are a very general property of objects [Mill, by Brown,JR]
