85 ideas
16512 | Semantic facts are preferable to transcendental philosophical fiction [Wiggins] |
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] |
17529 | Maybe the concept needed under which things coincide must also yield a principle of counting [Wiggins] |
17530 | The sortal needed for identities may not always be sufficient to support counting [Wiggins] |
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] |
5062 | First: there must be reasons; Second: why anything at all?; Third: why this? [Leibniz] |
19377 | A monad and its body are living, so life is everywhere, and comes in infinite degrees [Leibniz] |
16523 | Realist Conceptualists accept that our interests affect our concepts [Wiggins] |
16524 | Conceptualism says we must use our individuating concepts to grasp reality [Wiggins] |
16526 | Animal classifications: the Emperor's, fabulous, innumerable, like flies, stray dogs, embalmed…. [Wiggins] |
16492 | Individuation needs accounts of identity, of change, and of singling out [Wiggins] |
16493 | Individuation can only be understood by the relation between things and thinkers [Wiggins] |
16496 | Singling out extends back and forward in time [Wiggins] |
16495 | The only singling out is singling out 'as' something [Wiggins] |
16501 | In Aristotle's sense, saying x falls under f is to say what x is [Wiggins] |
16506 | Every determinate thing falls under a sortal, which fixes its persistence [Wiggins] |
9806 | Whatever is made up of parts is made up of parts of those parts [Mill] |
16509 | Natural kinds are well suited to be the sortals which fix substances [Wiggins] |
11156 | The essence is that without which a thing can neither be, nor be conceived to be [Mill] |
16514 | Artefacts are individuated by some matter having a certain function [Wiggins] |
16510 | Nominal essences don't fix membership, ignore evolution, and aren't contextual [Wiggins] |
16503 | 'What is it?' gives the kind, nature, persistence conditions and identity over time of a thing [Wiggins] |
16499 | A restored church is the same 'church', but not the same 'building' or 'brickwork' [Wiggins] |
16515 | A thing begins only once; for a clock, it is when its making is first completed [Wiggins] |
16517 | Priests prefer the working ship; antiquarians prefer the reconstruction [Wiggins] |
16498 | Identity cannot be defined, because definitions are identities [Wiggins] |
16497 | Leibniz's Law (not transitivity, symmetry, reflexivity) marks what is peculiar to identity [Wiggins] |
16502 | Identity is primitive [Wiggins] |
16521 | A is necessarily A, so if B is A, then B is also necessarily A [Wiggins] |
16505 | By the principle of Indiscernibility, a symmetrical object could only be half of itself! [Wiggins] |
16494 | We want to explain sameness as coincidence of substance, not as anything qualitative [Wiggins] |
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] |
16522 | It is hard or impossible to think of Caesar as not human [Wiggins] |
19353 | 'Perception' is basic internal representation, and 'apperception' is reflective knowledge of perception [Leibniz] |
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] |
16525 | Our sortal concepts fix what we find in experience [Wiggins] |
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] |
5061 | Animals are semi-rational because they connect facts, but they don't see causes [Leibniz] |
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] |
16518 | We conceptualise objects, but they impinge on us [Wiggins] |
16511 | A 'conception' of a horse is a full theory of what it is (and not just the 'concept') [Wiggins] |
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] |
5063 | Music charms, although its beauty is the harmony of numbers [Leibniz] |
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] |