more on this theme
|
more from this thinker
Single Idea 9624
[filed under theme 6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
]
Full Idea
Mill held that numbers are a kind of very general property that objects possess.
Gist of Idea
Numbers are a very general property of objects
Source
report of John Stuart Mill (System of Logic [1843], Ch.4) by James Robert Brown - Philosophy of Mathematics
Book Ref
Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.55
A Reaction
Intuitively this sounds hopeless, because if you place one apple next to another you introduce 'two', but which apple has changed its property? Both? It seems to be a Cambridge change. It isn't a change that would bother the apples. Kitcher pursues this.
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]
|
17091
|
Explanation is fitting of facts into ever more general patterns of regularity
[Mill, by Ruben]
|
17086
|
Surprisingly, empiricists before Mill ignore explanation, which seems to transcend experience
[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]
|
9794
|
There are no such things as numbers in the abstract
[Mill]
|
9796
|
Things possess the properties of numbers, as quantity, and as countable parts
[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]
|
9802
|
Numbers denote physical properties of physical phenomena
[Mill]
|
9803
|
We can't easily distinguish 102 horses from 103, but we could arrange them to make it obvious
[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]
|
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]
|
9079
|
We can focus our minds on what is common to a whole class, neglecting other aspects
[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]
|