109 ideas
| 19023 | Slippery slope arguments are challenges to show where a non-arbitrary boundary lies [Vetter] |
| 19033 | Deontic modalities are 'ought-to-be', for sentences, and 'ought-to-do' for predicates [Vetter] |
| 19032 | S5 is undesirable, as it prevents necessities from having contingent grounds [Vetter] |
| 19036 | The Barcan formula endorses either merely possible things, or makes the unactualised impossible [Vetter] |
| 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] |
| 9912 | There are no such things as numbers [Benacerraf] |
| 9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
| 9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
| 13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
| 17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
| 17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
| 9801 | Numbers must be assumed to have identical units, as horses are equalised in 'horse-power' [Mill] |
| 9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
| 17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
| 9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
| 8742 | The only axioms needed are for equality, addition, and successive numbers [Mill, by Shapiro] |
| 9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
| 9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
| 9800 | Arithmetic is based on definitions, and Sums of equals are equal, and Differences of equals are equal [Mill] |
| 8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
| 8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
| 9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
| 9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
| 9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
| 9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
| 9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
| 8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
| 9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
| 9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
| 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] |
| 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] |
| 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] |
| 9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
| 9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
| 19034 | The world is either a whole made of its parts, or a container which contains its parts [Vetter] |
| 19015 | Grounding can be between objects ('relational'), or between sentences ('operational') [Vetter] |
| 19012 | The Humean supervenience base entirely excludes modality [Vetter] |
| 19024 | A determinate property must be a unique instance of the determinable class [Vetter] |
| 19021 | I have an 'iterated ability' to learn the violin - that is, the ability to acquire that ability [Vetter] |
| 19016 | We should think of dispositions as 'to do' something, not as 'to do something, if ....' [Vetter] |
| 19017 | Nomological dispositions (unlike ordinary ones) have to be continually realised [Vetter] |
| 19014 | How can spatiotemporal relations be understood in dispositional terms? [Vetter] |
| 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] |
| 19030 | Why does origin matter more than development; why are some features of origin more important? [Vetter] |
| 19040 | We take origin to be necessary because we see possibilities as branches from actuality [Vetter] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 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] |
| 19008 | The modern revival of necessity and possibility treated them as special cases of quantification [Vetter] |
| 19029 | It is necessary that p means that nothing has the potentiality for not-p [Vetter] |
| 19028 | Possibilities are potentialities of actual things, but abstracted from their location [Vetter] |
| 19010 | All possibility is anchored in the potentiality of individual objects [Vetter] |
| 19013 | Possibility is a generalised abstraction from the potentiality of its bearer [Vetter] |
| 19019 | Potentiality is the common genus of dispositions, abilities, and similar properties [Vetter] |
| 19022 | Water has a potentiality to acquire a potentiality to break (by freezing) [Vetter] |
| 23705 | A potentiality may not be a disposition, but dispositions are strong potentialities [Vetter, by Friend/Kimpton-Nye] |
| 19009 | Potentiality does the explaining in metaphysics; we don't explain it away or reduce it [Vetter] |
| 19027 | Potentiality logic is modal system T. Stronger systems collapse iterations, and necessitate potentials [Vetter] |
| 19031 | There are potentialities 'to ...', but possibilities are 'that ....'. [Vetter] |
| 19025 | Potentialities may be too weak to count as 'dispositions' [Vetter] |
| 19011 | If worlds are sets of propositions, how do we know which propositions are genuinely possible? [Vetter] |
| 19037 | Are there possible objects which nothing has ever had the potentiality to produce? [Vetter] |
| 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] |
| 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] |
| 19018 | Explanations by disposition are more stable and reliable than those be external circumstances [Vetter] |
| 19020 | Grounding is a kind of explanation, suited to metaphysics [Vetter] |
| 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] |
| 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] |
| 19039 | The view that laws are grounded in substance plus external necessity doesn't suit dispositionalism [Vetter] |
| 19038 | Dispositional essentialism allows laws to be different, but only if the supporting properties differ [Vetter] |
| 19026 | If time is symmetrical between past and future, why do they look so different? [Vetter] |
| 19041 | Presentists explain cross-temporal relations using surrogate descriptions [Vetter] |