88 ideas
7001 | If you begin philosophy with language, you find yourself trapped in it [Heil] |
7037 | Parsimony does not imply the world is simple, but that our theories should try to be [Heil] |
7038 | A theory with few fundamental principles might still posit a lot of entities [Heil] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
7004 | The view that truth making is entailment is misguided and misleading [Heil] |
9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
7035 | God does not create the world, and then add the classes [Heil] |
9605 | If a proposition is false, then its negation is true [Brown,JR] |
9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
9630 | The most brilliant formalist was Hilbert [Brown,JR] |
9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
7017 | The reductionist programme dispenses with levels of reality [Heil] |
7003 | There are levels of organisation, complexity, description and explanation, but not of reality [Heil] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
7045 | Realism says some of our concepts 'cut nature at the joints' [Heil] |
7065 | Anti-realists who reduce reality to language must explain the existence of language [Heil] |
7020 | Concepts don't carve up the world, which has endless overlooked or ignored divisions [Heil] |
7007 | I think of properties as simultaneously dispositional and qualitative [Heil] |
7015 | A predicate applies truly if it picks out a real property of objects [Heil] |
7042 | A theory of universals says similarity is identity of parts; for modes, similarity is primitive [Heil] |
7023 | Powers or dispositions are usually seen as caused by lower-level qualities [Heil] |
7025 | Are a property's dispositions built in, or contingently added? [Heil] |
7034 | Universals explain one-over-many relations, and similar qualities, and similar behaviour [Heil] |
7039 | How could you tell if the universals were missing from a world of instances? [Heil] |
7009 | Similarity among modes will explain everthing universals were for [Heil] |
7041 | Similar objects have similar properties; properties are directly similar [Heil] |
7032 | Objects join sets because of properties; the property is not bestowed by set membership [Heil] |
7008 | Trope theorists usually see objects as 'bundles' of tropes [Heil] |
7018 | Objects are substances, which are objects considered as the bearer of properties [Heil] |
7019 | Maybe there is only one substance, space-time or a quantum field [Heil] |
7046 | Rather than 'substance' I use 'objects', which have properties [Heil] |
7047 | Statues and bronze lumps have discernible differences, so can't be identical [Heil] |
7048 | Do we reduce statues to bronze, or eliminate statues, or allow statues and bronze? [Heil] |
7028 | If properties were qualities without dispositions, they would be undetectable [Heil] |
7029 | Can we distinguish the way a property is from the property? [Heil] |
7030 | Properties don't possess ways they are, because that just is the property [Heil] |
7051 | Objects only have secondary qualities because they have primary qualities [Heil] |
7044 | Secondary qualities are just primary qualities considered in the light of their effect on us [Heil] |
7052 | Colours aren't surface properties, because of radiant sources and the colour of the sky [Heil] |
7053 | Treating colour as light radiation has the implausible result that tomatoes are not red [Heil] |
7066 | If the world is just texts or social constructs, what are texts and social constructs? [Heil] |
18284 | Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper] |
7021 | If the world is theory-dependent, the theories themselves can't be theory-dependent [Heil] |
7026 | Science is sometimes said to classify powers, neglecting qualities [Heil] |
7060 | One form of explanation is by decomposition [Heil] |
7010 | Dispositionality provides the grounding for intentionality [Heil] |
7054 | Intentionality now has internalist (intrinsic to thinkers) and externalist (environment or community) views [Heil] |
7011 | Qualia are not extra appendages, but intrinsic ingredients of material states and processes [Heil] |
7061 | Philosophers' zombies aim to show consciousness is over and above the physical world [Heil] |
7063 | Zombies are based on the idea that consciousness relates contingently to the physical [Heil] |
7064 | Functionalists deny zombies, since identity of functional state means identity of mental state [Heil] |
7027 | Functionalists say objects can be the same in disposition but differ in quality [Heil] |
7062 | Functionalism cannot explain consciousness just by functional organisation [Heil] |
7059 | The 'explanatory gap' is used to say consciousness is inexplicable, at least with current concepts [Heil] |
7012 | If a car is a higher-level entity, distinct from its parts, how could it ever do anything? [Heil] |
7043 | Multiple realisability is actually one predicate applying to a diverse range of properties [Heil] |
7058 | Externalism is causal-historical, or social, or biological [Heil] |
7057 | Intentionality is based in dispositions, which are intrinsic to agents, suggesting internalism [Heil] |
9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
7013 | The Picture Theory claims we can read reality from our ways of speaking about it [Heil] |
9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
7002 | If propositions are states of affairs or sets of possible worlds, these lack truth values [Heil] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
7016 | The standard view is that causal sequences are backed by laws, and between particular events [Heil] |
7036 | The real natural properties are sparse, but there are many complex properties [Heil] |