157 ideas
7950 | Philosophy tries to explain how the actual is possible, given that it seems impossible [Macdonald,C] |
7923 | 'Did it for the sake of x' doesn't involve a sake, so how can ontological commitments be inferred? [Macdonald,C] |
5082 | Reason grasps generalities, while the senses grasp particulars [Aristotle] |
17774 | Definitions make our intuitions mathematically useful [Mayberry] |
17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
7933 | Don't assume that a thing has all the properties of its parts [Macdonald,C] |
17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
17803 | Limitation of size is part of the very conception of a set [Mayberry] |
13270 | Are a part and whole one or many? Either way, what is the cause? [Aristotle] |
17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
9790 | Geometry studies naturally occurring lines, but not as they occur in nature [Aristotle] |
22962 | Two is the least number, but there is no least magnitude, because it is always divisible [Aristotle] |
17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
18090 | Without infinity time has limits, magnitudes are indivisible, and numbers come to an end [Aristotle] |
17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
22929 | Aristotle's infinity is a property of the counting process, that it has no natural limit [Aristotle, by Le Poidevin] |
22930 | Lengths do not contain infinite parts; parts are created by acts of division [Aristotle, by Le Poidevin] |
18833 | A continuous line cannot be composed of indivisible points [Aristotle] |
17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
9974 | Ten sheep and ten dogs are the same numerically, but it is not the same ten [Aristotle] |
5105 | The incommensurability of the diagonal always exists, and so it is not in time [Aristotle] |
16115 | Change is the implied actuality of that which exists potentially [Aristotle] |
22960 | The sophists thought a man in the Lyceum is different from that man in the marketplace [Aristotle] |
17262 | Aristotle's formal and material 'becauses' [aitiai] arguably involve grounding [Aristotle, by Correia/Schnieder] |
7944 | Reduce by bridge laws (plus property identities?), by elimination, or by reducing talk [Macdonald,C] |
16656 | The separation from here to there is not the same as the separation from there to here [Aristotle] |
7938 | Relational properties are clearly not essential to substances [Macdonald,C] |
7967 | Being taller is an external relation, but properties and substances have internal relations [Macdonald,C] |
16644 | The features of a thing (whether quality or quantity) are inseparable from their subjects [Aristotle] |
7965 | Does the knowledge of each property require an infinity of accompanying knowledge? [Macdonald,C] |
7934 | Tropes are abstract (two can occupy the same place), but not universals (they have locations) [Macdonald,C] |
7958 | Properties are sets of exactly resembling property-particulars [Macdonald,C] |
7972 | Tropes are abstract particulars, not concrete particulars, so the theory is not nominalist [Macdonald,C] |
7959 | How do a group of resembling tropes all resemble one another in the same way? [Macdonald,C] |
7960 | Trope Nominalism is the only nominalism to introduce new entities, inviting Ockham's Razor [Macdonald,C] |
5117 | Heavy and light are defined by their tendency to move down or up [Aristotle] |
7951 | Numerical sameness is explained by theories of identity, but what explains qualitative identity? [Macdonald,C] |
7964 | How can universals connect instances, if they are nothing like them? [Macdonald,C] |
7971 | Real Nominalism is only committed to concrete particulars, word-tokens, and (possibly) sets [Macdonald,C] |
7955 | Resemblance Nominalism cannot explain either new resemblances, or absence of resemblances [Macdonald,C] |
17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
7961 | A 'thing' cannot be in two places at once, and two things cannot be in the same place at once [Macdonald,C] |
7926 | We 'individuate' kinds of object, and 'identify' particular specimens [Macdonald,C] |
17041 | Natural objects include animals and their parts, plants, and the simple elements [Aristotle] |
7936 | Unlike bundles of properties, substances have an intrinsic unity [Macdonald,C] |
16172 | Substance is not predicated of anything - but it still has something underlying it, that originates it [Aristotle] |
16623 | We only infer underlying natures by analogy, observing bronze of a statue, or wood of a bed [Aristotle] |
7930 | The bundle theory of substance implies the identity of indiscernibles [Macdonald,C] |
7932 | A phenomenalist cannot distinguish substance from attribute, so must accept the bundle view [Macdonald,C] |
7937 | When we ascribe a property to a substance, the bundle theory will make that a tautology [Macdonald,C] |
7939 | Substances persist through change, but the bundle theory says they can't [Macdonald,C] |
7940 | A substance might be a sequence of bundles, rather than a single bundle [Macdonald,C] |
16174 | A nature is related to a substance as shapeless matter is to something which has a shape [Aristotle] |
7948 | A statue and its matter have different persistence conditions, so they are not identical [Macdonald,C] |
17043 | Form, not matter, is a thing's nature, because it is actual, rather than potential [Aristotle] |
16970 | A thing's form and purpose are often the same, and form can be the initiator of change too [Aristotle] |
16104 | Unity of the form is just unity of the definition [Aristotle] |
11255 | In feature-generation the matter (such as bronze) endures, but in generation it doesn't [Aristotle, by Politis] |
7929 | A substance is either a bundle of properties, or a bare substratum, or an essence [Macdonald,C] |
7941 | Each substance contains a non-property, which is its substratum or bare particular [Macdonald,C] |
7942 | The substratum theory explains the unity of substances, and their survival through change [Macdonald,C] |
7943 | A substratum has the quality of being bare, and they are useless because indiscernible [Macdonald,C] |
9071 | We first sense whole entities, and then move to particular parts of it [Aristotle] |
16791 | There is no whole except for the parts [Aristotle] |
16972 | The four explanations are the main aspects of a thing's nature [Aristotle, by Moravcsik] |
5084 | A thing's nature is what causes its changes and stability [Aristotle] |
16173 | Coming to be is by shape-change, addition, subtraction, composition or alteration [Aristotle] |
17042 | Natural things are their own source of stability through change [Aristotle] |
16691 | A day, or the games, has one thing after another, actually and potentially occurring [Aristotle] |
16574 | Coming-to-be may be from nothing in a qualified way, as arising from an absence [Aristotle] |
7927 | At different times Leibniz articulated three different versions of his so-called Law [Macdonald,C] |
7928 | The Identity of Indiscernibles is false, because it is not necessarily true [Macdonald,C] |
11254 | Matter is potentiality [Aristotle, by Politis] |
13110 | Intrinsic cause is prior to coincidence, so nature and intelligence are primary causes, chance secondary [Aristotle] |
13106 | Maybe there is no pure chance; a man's choices cause his chance meetings [Aristotle] |
13108 | Chance is a coincidental cause among events involving purpose and choice [Aristotle] |
8331 | To know something we need understanding, which is grasp of the primary cause [Aristotle] |
5080 | We know a thing if we grasp its first causes, principles and basic elements [Aristotle] |
16969 | Science refers the question Why? to four causes/explanations: matter, form, source, purpose [Aristotle] |
11250 | Four Explanations: the essence and form; the matter; the source; and the end [Aristotle, by Politis] |
12045 | Aristotle's four 'causes' are four items which figure in basic explanations of nature [Aristotle, by Annas] |
16968 | There are as many causes/explanations as there are different types of why-question [Aristotle] |
13109 | Chance is inexplicable, because we can only explain what happens always or usually [Aristotle] |
7947 | In continuity, what matters is not just the beginning and end states, but the process itself [Macdonald,C] |
9789 | You can't abstract natural properties to make Forms - objects and attributes are defined together [Aristotle] |
9788 | Mathematicians study what is conceptually separable, and doesn't lead to error [Aristotle] |
5107 | Predicates are substance, quality, place, relation, quantity and action or affection [Aristotle] |
20042 | We assign the cause of someone's walking when we say why they are doing it [Aristotle] |
5110 | Goodness is when a thing (such as a circle) is complete, and conforms with its nature [Aristotle] |
5111 | All moral virtue is concerned with bodily pleasure and pain [Aristotle] |
5092 | Nature is a principle of change, so we must understand change first [Aristotle] |
5113 | Nothing natural is disorderly, because nature is responsible for all order [Aristotle] |
5085 | 'Nature' refers to two things - form and matter [Aristotle] |
5089 | Nature has purpose, and aims at what is better. Is it coincidence that crops grow when it rains? [Aristotle] |
5086 | The nature of a thing is its end and purpose [Aristotle] |
5087 | A thing's purpose is ambiguous, and from one point of view we ourselves are ends [Aristotle] |
5091 | Teeth and crops are predictable, so they cannot be mere chance, but must have a purpose [Aristotle] |
5108 | Is ceasing-to-be unnatural if it happens by force, and natural otherwise? [Aristotle] |
5095 | The heavens seem to be infinite, because we cannot imagine their end [Aristotle] |
5093 | Continuity depends on infinity, because the continuous is infinitely divisible [Aristotle] |
16762 | Matter desires form, as female desires male, and ugliness desires beauty [Aristotle] |
17464 | When Aristotle's elements compound they are stable, so why would they ever separate? [Weisberg/Needham/Hendry on Aristotle] |
11252 | The 'form' of a thing explains why the matter constitutes that particular thing [Aristotle, by Politis] |
11253 | A 'material' cause/explanation is the form of whatever is the source [Aristotle, by Politis] |
13107 | Causes produce a few things in their own right, and innumerable things coincidentally [Aristotle] |
8332 | The four causes are the material, the form, the source, and the end [Aristotle] |
9787 | Scientists must know the essential attributes of the things they study [Aristotle] |
20063 | Motion fulfils potentiality [Aristotle] |
5114 | If movement can arise within an animal, why can't it also arise in the universe? [Aristotle] |
5116 | When there is unnatural movement (e.g. fire going downwards) the cause is obvious [Aristotle] |
5099 | The universe as a whole is not anywhere [Aristotle] |
5097 | If everything has a place, this causes an infinite regress, because each place must have place [Aristotle] |
5098 | Place is not shape, or matter, or extension between limits; it is the limits of a body [Aristotle] |
20920 | If there were many cosmoses, each would have its own time, giving many times [Aristotle] |
5106 | Would there be time if there were no mind? [Aristotle] |
22967 | It is unclear whether time depends on the existence of soul [Aristotle] |
8590 | Time does not exist without change [Aristotle] |
22965 | Time measures rest, as well as change [Aristotle] |
22885 | For Aristotle time is not a process but a means for measuring processes [Aristotle, by Bardon] |
22959 | Time is not change, but the number we associate with change [Aristotle] |
22964 | Change only exists in time through its being temporally measure [Aristotle] |
5104 | Time is an aspect of change [Aristotle] |
22956 | How can time exist, when it is composed of what has ceased to be and is yet to be? [Aristotle] |
5102 | If all of time has either ceased to exist, or has not yet happened, maybe time does not exist [Aristotle] |
5103 | Time is not change, but requires change in our minds to be noticed [Aristotle] |
22961 | The present moment is obviously a necessary feature of time [Aristotle] |
22916 | Unlike time, change goes at different rates, and is usually localised [Aristotle, by Le Poidevin] |
16693 | Time has parts, but the now is not one of them, and time is not composed of nows [Aristotle] |
22958 | Nows can't be linked together, any more than points on a line [Aristotle] |
22968 | Circular motion is the most obvious measure of time, and especially the celestial sphere [Aristotle] |
22963 | We measure change by time, and time by change, as they are interdefined [Aristotle] |
22966 | The present moment is a link (of past to future), and also a limit (of past and of future) [Aristotle] |
22957 | We can't tell whether the changing present moment is one thing, or a succession of things [Aristotle] |
5083 | Do things come to be from what is, or from what is not? Both seem problematical. [Aristotle] |
5119 | The source of all movement must be indivisible and have no magnitude [Aristotle] |