68 ideas
16519 | No one can conceive of a possible substance, apart from those which God has created [Arnauld] |
8625 | What physical facts could underlie 0 or 1, or very large numbers? [Frege on Mill] |
17895 | Combining two distinct assertions does not necessarily lead to a single 'complex proposition' [Mill] |
10427 | All names are names of something, real or imaginary [Mill] |
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] |
9801 | Numbers must be assumed to have identical units, as horses are equalised in 'horse-power' [Mill] |
8742 | The only axioms needed are for equality, addition, and successive numbers [Mill, by Shapiro] |
9800 | Arithmetic is based on definitions, and Sums of equals are equal, and Differences of equals are equal [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] |
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] |
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] |
8741 | Numbers must be of something; they don't exist as abstractions [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] |
9624 | Numbers are a very general property of objects [Mill, by Brown,JR] |
9806 | Whatever is made up of parts is made up of parts of those parts [Mill] |
11156 | The essence is that without which a thing can neither be, nor be conceived to be [Mill] |
1350 | Continuity is needed for existence, otherwise we would say a thing existed after it ceased to exist [Reid] |
21322 | We treat slowly changing things as identical for the sake of economy in language [Reid] |
21320 | Identity is familiar to common sense, but very hard to define [Reid] |
1367 | Identity can only be affirmed of things which have a continued existence [Reid] |
12190 | Necessity is what will be, despite any alternative suppositions whatever [Mill] |
22623 | Necessity can only mean what must be, without conditions of any kind [Mill] |
16859 | Most perception is one-tenth observation and nine-tenths inference [Mill] |
9082 | Clear concepts result from good observation, extensive experience, and accurate memory [Mill] |
23644 | Without memory we could have no concept of duration [Reid] |
23643 | We all trust our distinct memories (but not our distinct imaginings) [Reid] |
16860 | Inductive generalisation is more reliable than one of its instances; they can't all be wrong [Mill] |
16845 | The whole theory of induction rests on causes [Mill] |
16843 | Mill's methods (Difference,Agreement,Residues,Concomitance,Hypothesis) don't nail induction [Mill, by Lipton] |
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] |
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] |
1356 | A person is a unity, and doesn't come in degrees [Reid] |
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] |
1359 | Personal identity is the basis of all rights, obligations and responsibility [Reid] |
21319 | I can hardly care about rational consequence if it wasn't me conceiving the antecedent [Reid] |
21323 | The identity of a thief is only known by similarity, but memory gives certainty in our own case [Reid] |
21321 | Memory reveals my past identity - but so does testimony of other witnesses [Reid] |
21324 | If consciousness is transferable 20 persons can be 1; forgetting implies 1 can be 20 [Reid] |
21325 | Boy same as young man, young man same as old man, old man not boy, if forgotten! [Reid] |
21327 | If a stolen horse is identified by similitude, its identity is not therefore merely similitude [Reid] |
1366 | If consciousness is personal identity, it is continually changing [Reid] |
1352 | Thoughts change continually, but the self doesn't [Reid] |
9080 | General conceptions are a necessary preliminary to Induction [Mill] |
9078 | The study of the nature of Abstract Ideas does not belong to logic, but to a different science [Mill] |
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] |
14547 | The strict cause is the total positive and negative conditions which ensure the consequent [Mill] |
8377 | Causation is just invariability of succession between every natural fact and a preceding fact [Mill] |
14545 | A cause is an antecedent which invariably and unconditionally leads to a phenomenon [Mill] |
4773 | Mill's regularity theory of causation is based on an effect preceded by a conjunction of causes [Mill, by Psillos] |
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] |
9417 | What are the fewest propositions from which all natural uniformities could be inferred? [Mill] |