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Single Idea 9078

[filed under theme 18. Thought / E. Abstraction / 1. Abstract Thought ]

Full Idea

The metaphysical inquiry into the nature and composition of what have been called Abstract Ideas, or in other words, of the notions which answer in the mind to classes and to general names, belongs not to Logic, but to a different science.

Gist of Idea

The study of the nature of Abstract Ideas does not belong to logic, but to a different science

Source

John Stuart Mill (System of Logic [1843], 4.2.1)

Book Ref

Mill,John Stuart: 'System of Logic (9th ed, 2 vols)' [Longmans, Green etc 1875], p.195

A Reaction

He doesn't name the science, but the point here seems to be precisely what Frege so vigorously disagreed with. I would say that the state of being 'abstract' has logical aspects, and can be partly described by logic, but that Mill is basically right.

The 51 ideas from 'System of Logic'

4944 Mill says names have denotation but not connotation [Mill, by Kripke]
7762 Proper names are just labels for persons or objects, and the meaning is the object [Mill, by Lycan]
8625 What physical facts could underlie 0 or 1, or very large numbers? [Frege on Mill]
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]
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]
17086 Surprisingly, empiricists before Mill ignore explanation, which seems to transcend experience [Mill, by Ruben]
17091 Explanation is fitting of facts into ever more general patterns of regularity [Mill, by Ruben]
8345 A cause is the total of all the conditions which inevitably produce the result [Mill]
10391 Causes and conditions are not distinct, because we select capriciously from among them [Mill]
17895 Combining two distinct assertions does not necessarily lead to a single 'complex proposition' [Mill]
11156 The essence is that without which a thing can neither be, nor be conceived to be [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]
9798 Different parcels made from three pebbles produce different actual sensations [Mill]
9797 '2 pebbles and 1 pebble' and '3 pebbles' name the same aggregation, but different facts [Mill]
9799 3=2+1 presupposes collections of objects ('Threes'), which may be divided thus [Mill]
9800 Arithmetic is based on definitions, and Sums of equals are equal, and Differences of equals are equal [Mill]
9801 Numbers must be assumed to have identical units, as horses are equalised in 'horse-power' [Mill]
16845 The whole theory of induction rests on causes [Mill]
14547 The strict cause is the total positive and negative conditions which ensure the consequent [Mill]
14545 A cause is an antecedent which invariably and unconditionally leads to a phenomenon [Mill]
12190 Necessity is what will be, despite any alternative suppositions whatever [Mill]
16805 Causal inference is by spotting either Agreements or Differences [Mill, by Lipton]
16835 The Methods of Difference and of Agreement are forms of inference to the best explanation [Mill, by Lipton]
16843 Mill's methods (Difference,Agreement,Residues,Concomitance,Hypothesis) don't nail induction [Mill, by Lipton]
9806 Whatever is made up of parts is made up of parts of those parts [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]
9417 What are the fewest propositions from which all natural uniformities could be inferred? [Mill]
8377 Causation is just invariability of succession between every natural fact and a preceding fact [Mill]
16860 Inductive generalisation is more reliable than one of its instances; they can't all be wrong [Mill]
16859 Most perception is one-tenth observation and nine-tenths inference [Mill]
9079 We can focus our minds on what is common to a whole class, neglecting other aspects [Mill]
9078 The study of the nature of Abstract Ideas does not belong to logic, but to a different science [Mill]
9080 General conceptions are a necessary preliminary to Induction [Mill]
9081 We don't recognise comparisons by something in our minds; the concepts result from the comparisons [Mill]
9082 Clear concepts result from good observation, extensive experience, and accurate memory [Mill]
9624 Numbers are a very general property of objects [Mill, by Brown,JR]
4773 Mill's regularity theory of causation is based on an effect preceded by a conjunction of causes [Mill, by Psillos]
8741 Numbers must be of something; they don't exist as abstractions [Mill]
4775 In Mill's 'Method of Agreement' cause is the common factor in a range of different cases [Mill, by Psillos]
4776 In Mill's 'Method of Difference' the cause is what stops the effect when it is removed [Mill, by Psillos]
10427 All names are names of something, real or imaginary [Mill]
22623 Necessity can only mean what must be, without conditions of any kind [Mill]
8742 The only axioms needed are for equality, addition, and successive numbers [Mill, by Shapiro]