104 ideas
| 24047 | An account is either a definition or a demonstration [Aristotle] |
| 24052 | From one thing alone we can infer its contrary [Aristotle] |
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| 15130 | If a property is possible, there is something which can have it [Williamson] |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| 18107 | A 'proper class' cannot be a member of anything [Bostock] |
| 18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
| 18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
| 18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| 18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
| 18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
| 1729 | We perceive number by the denial of continuity [Aristotle] |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
| 18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
| 18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
| 18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
| 18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
| 18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
| 18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
| 18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
| 18097 | The Peano Axioms describe a unique structure [Bostock] |
| 18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
| 18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
| 18149 | There are many criteria for the identity of numbers [Bostock] |
| 18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
| 18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
| 18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| 18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
| 18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
| 18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| 18140 | The best version of conceptualism is predicativism [Bostock] |
| 18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
| 18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
| 18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
| 18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
| 18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
| 18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
| 24057 | What is prior is always potentially present in what is next in order [Aristotle] |
| 16752 | Sight is the essence of the eye, fitting its definition; the eye itself is just the matter [Aristotle] |
| 24058 | The substance is the cause of a thing's being [Aristotle] |
| 24055 | Matter is potential, form is actual [Aristotle] |
| 24040 | Scientists explain anger by the matter, dialecticians by the form and the account [Aristotle] |
| 5051 | The intellect has potential to think, like a tablet on which nothing has yet been written [Aristotle] |
| 16723 | Perception of sensible objects is virtually never wrong [Aristotle] |
| 1724 | Perception necessitates pleasure and pain, which necessitates appetite [Aristotle] |
| 1730 | Why do we have many senses, and not just one? [Aristotle] |
| 17711 | Our minds take on the form of what is being perceived [Aristotle, by Mares] |
| 1725 | Why can't we sense the senses? And why do senses need stimuli? [Aristotle] |
| 1732 | Sense organs aren't the end of sensation, or they would know what does the sensing [Aristotle] |
| 1728 | Many objects of sensation are common to all the senses [Aristotle] |
| 1727 | Some objects of sensation are unique to one sense, where deception is impossible [Aristotle] |
| 1734 | In moral thought images are essential, to be pursued or avoided [Aristotle] |
| 1726 | We may think when we wish, but not perceive, because universals are within the mind [Aristotle] |
| 16647 | Demonstration starts from a definition of essence, so we can derive (or conjecture about) the properties [Aristotle] |
| 24048 | Demonstrations move from starting-points to deduced conclusions [Aristotle] |
| 16646 | To understand a triangle summing to two right angles, we need to know the essence of a line [Aristotle] |
| 1714 | Mind involves movement, perception, incorporeality [Aristotle] |
| 5507 | Aristotle led to the view that there are several souls, all somewhat physical [Aristotle, by Martin/Barresi] |
| 24051 | Soul is seen as what moves, or what is least physical, or a combination of elements [Aristotle] |
| 12086 | Psuché is the form and actuality of a body which potentially has life [Aristotle] |
| 16754 | The soul is the cause or source of movement, the essence of body, and its end [Aristotle] |
| 24046 | Understanding is impossible, if it involves the understanding having parts [Aristotle] |
| 1717 | If the soul is composed of many physical parts, it can't be a true unity [Aristotle] |
| 24053 | If a soul have parts, what unites them? [Aristotle] |
| 1721 | What unifies the soul would have to be a super-soul, which seems absurd [Aristotle] |
| 1735 | In a way the soul is everything which exists, through its perceptions and thoughts [Aristotle] |
| 24061 | If we divide the mind up according to its capacities, there are a lot of them [Aristotle] |
| 24062 | Self-moving animals must have desires, and that entails having imagination [Aristotle] |
| 1710 | Emotion involves the body, thinking uses the mind, imagination hovers between them [Aristotle] |
| 24056 | The soul (or parts of it) is not separable from the body [Aristotle] |
| 24039 | All the emotions seem to involve the body, simultaneously with the feeling [Aristotle] |
| 24050 | If soul is separate from body, why does it die when the body dies? [Aristotle] |
| 24049 | Thinkers place the soul within the body, but never explain how they are attached [Aristotle] |
| 1514 | Early thinkers concentrate on the soul but ignore the body, as if it didn't matter what body received the soul [Aristotle] |
| 2683 | Aristotle has a problem fitting his separate reason into the soul, which is said to be the form of the body [Ackrill on Aristotle] |
| 1718 | Does the mind think or pity, or does the whole man do these things? [Aristotle] |
| 13275 | The soul and the body are inseparable, like the imprint in some wax [Aristotle] |
| 1733 | Thinking is not perceiving, but takes the form of imagination and speculation [Aristotle] |
| 23307 | Aristotle makes belief a part of reason, but sees desires as separate [Aristotle, by Sorabji] |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| 24060 | Self-controlled follow understanding, when it is opposed to desires [Aristotle] |
| 4376 | Pleasure and pain are perceptions of things as good or bad [Aristotle] |
| 1740 | Nature does nothing in vain [Aristotle] |
| 1739 | If all movement is either pushing or pulling, there must be a still point in between where it all starts [Aristotle] |
| 24045 | Movement is spatial, alteration, withering or growth [Aristotle] |
| 1738 | Practical reason is based on desire, so desire must be the ultimate producer of movement [Aristotle] |
| 24044 | Movement can be intrinsic (like a ship) or relative (like its sailors) [Aristotle] |
| 24064 | If something is pushed, it pushes back [Aristotle] |
| 24063 | What is born has growth, a prime, and a withering away [Aristotle] |