68 ideas
| 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] |
| 17518 | Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers] |
| 17516 | If counting needs a sortal, what of things which fall under two sortals? [Ayers] |
| 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] |
| 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] |
| 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] |
| 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] |
| 17520 | Events do not have natural boundaries, and we have to set them [Ayers] |
| 17519 | To express borderline cases of objects, you need the concept of an 'object' [Ayers] |
| 17510 | Speakers need the very general category of a thing, if they are to think about it [Ayers] |
| 17522 | We use sortals to classify physical objects by the nature and origin of their unity [Ayers] |
| 17515 | Seeing caterpillar and moth as the same needs continuity, not identity of sortal concepts [Ayers] |
| 17511 | Recognising continuity is separate from sortals, and must precede their use [Ayers] |
| 17517 | Could the same matter have more than one form or principle of unity? [Ayers] |
| 594 | Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle] |
| 17513 | If there are two objects, then 'that marble, man-shaped object' is ambiguous [Ayers] |
| 9806 | Whatever is made up of parts is made up of parts of those parts [Mill] |
| 17523 | Sortals basically apply to individuals [Ayers] |
| 11156 | The essence is that without which a thing can neither be, nor be conceived to be [Mill] |
| 17521 | You can't have the concept of a 'stage' if you lack the concept of an object [Ayers] |
| 17514 | Temporal 'parts' cannot be separated or rearranged [Ayers] |
| 17509 | Some say a 'covering concept' completes identity; others place the concept in the reference [Ayers] |
| 17512 | If diachronic identities need covering concepts, why not synchronic identities too? [Ayers] |
| 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] |
| 16860 | Inductive generalisation is more reliable than one of its instances; they can't all be wrong [Mill] |
| 16843 | Mill's methods (Difference,Agreement,Residues,Concomitance,Hypothesis) don't nail induction [Mill, by Lipton] |
| 16845 | The whole theory of induction rests on causes [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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 2632 | Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero] |