245 ideas
13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
13477 | The problems are the monuments of philosophy [Hart,WD] |
9414 | Metaphysics is the mapping of possibilities [Lowe, by Mumford] |
16414 | Science needs metaphysics to weed out its presuppositions [Lowe, by Hofweber] |
13917 | Metaphysics aims to identify categories of being, and show their interdependency [Lowe] |
4194 | Metaphysics is concerned with the fundamental structure of reality as a whole [Lowe] |
8282 | Only metaphysics can decide whether identity survives through change [Lowe] |
16127 | Metaphysics tells us what there could be, rather than what there is [Lowe] |
4214 | Maybe such concepts as causation, identity and existence are primitive and irreducible [Lowe] |
13919 | Philosophy aims not at the 'analysis of concepts', but at understanding the essences of things [Lowe] |
13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
4222 | If all that exists is what is being measured, what about the people and instruments doing the measuring? [Lowe] |
4217 | It is more extravagant, in general, to revise one's logic than to augment one's ontology [Lowe] |
16539 | A definition of a circle will show what it is, and show its generating principle [Lowe] |
16540 | Defining an ellipse by conic sections reveals necessities, but not the essence of an ellipse [Lowe] |
16548 | An essence is what an entity is, revealed by a real definition; this is not an entity in its own right [Lowe] |
16549 | Simple things like 'red' can be given real ostensive definitions [Lowe] |
8262 | How can a theory of meaning show the ontological commitments of two paraphrases of one idea? [Lowe] |
18351 | Propositions are made true, in virtue of something which explains its truth [Lowe] |
13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
8315 | Maybe facts are just true propositions [Lowe] |
8319 | One-to-one correspondence would need countable, individuable items [Lowe] |
13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
8309 | A set is a 'number of things', not a 'collection', because nothing actually collects the members [Lowe] |
13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
8322 | I don't believe in the empty set, because (lacking members) it lacks identity-conditions [Lowe] |
13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
8312 | It is better if the existential quantifier refers to 'something', rather than a 'thing' which needs individuation [Lowe] |
6653 | Syntactical methods of proof need only structure, where semantic methods (truth-tables) need truth [Lowe] |
13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
4229 | An infinite series of tasks can't be completed because it has no last member [Lowe] |
13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
9117 | The smallest heap has four objects: three on the bottom, one on the top [Hart,WD, by Sorensen] |
4240 | It might be argued that mathematics does not, or should not, aim at truth [Lowe] |
13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
8297 | Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe] |
8266 | Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe] |
8302 | Fs and Gs are identical in number if they one-to-one correlate with one another [Lowe] |
8298 | Sets are instances of numbers (rather than 'collections'); numbers explain sets, not vice versa [Lowe] |
8311 | If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2 [Lowe] |
4241 | If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects [Lowe] |
8310 | Does the existence of numbers matter, in the way space, time and persons do? [Lowe] |
13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
8321 | All possible worlds contain abstracta (e.g. numbers), which means they contain concrete objects [Lowe] |
4239 | Nominalists deny abstract objects, because we can have no reason to believe in their existence [Lowe] |
8300 | Perhaps possession of causal power is the hallmark of existence (and a reason to deny the void) [Lowe] |
4202 | Change can be of composition (the component parts), or quality (properties), or substance [Lowe] |
15541 | Maybe particles are unchanging, and intrinsic change in things is their rearrangement [Lowe, by Lewis] |
8281 | Heraclitus says change is new creation, and Spinoza that it is just phases of the one substance [Lowe] |
4201 | Four theories of qualitative change are 'a is F now', or 'a is F-at-t', or 'a-at-t is F', or 'a is-at-t F' [Lowe, by PG] |
8270 | Events are changes or non-changes in properties and relations of persisting objects [Lowe] |
4219 | Numerically distinct events of the same kind (like two battles) can coincide in space and time [Lowe] |
4221 | Maybe modern physics requires an event-ontology, rather than a thing-ontology [Lowe] |
8308 | Events are ontologically indispensable for singular causal explanations [Lowe] |
4220 | Maybe an event is the exemplification of a property at a time [Lowe] |
4225 | Events are changes in the properties of or relations between things [Lowe] |
13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
8314 | Are facts wholly abstract, or can they contain some concrete constituents? [Lowe] |
8316 | Facts cannot be wholly abstract if they enter into causal relations [Lowe] |
8318 | The problem with the structured complex view of facts is what binds the constituents [Lowe] |
8323 | It is whimsical to try to count facts - how many facts did I learn before breakfast? [Lowe] |
8313 | Facts are needed for truth-making and causation, but they seem to lack identity criteria [Lowe] |
8258 | Two of the main rivals for the foundations of ontology are substances, and facts or states-of-affairs [Lowe] |
8301 | Some abstractions exist despite lacking causal powers, because explanation needs them [Lowe] |
8283 | Ontological categories are not natural kinds: the latter can only be distinguished using the former [Lowe] |
8284 | The top division of categories is either abstract/concrete, or universal/particular, or necessary/contingent [Lowe] |
13122 | Lowe divides things into universals and particulars, then kinds and properties, and abstract/concrete [Lowe, by Westerhoff] |
4196 | The main categories of existence are either universal and particular, or abstract and concrete [Lowe] |
18353 | Modes are beings that are related both to substances and to universals [Lowe] |
8273 | Is 'the Thames is broad in London' relational, or adverbial, or segmental? [Lowe] |
8285 | I prefer 'modes' to 'tropes', because it emphasises their dependence [Lowe] |
4234 | Trope theory says blueness is a real feature of objects, but not the same as an identical blue found elsewhere [Lowe] |
4235 | Maybe a cushion is just a bundle of tropes, such as roundness, blueness and softness [Lowe] |
4236 | Tropes seem to be abstract entities, because they can't exist alone, but must come in bundles [Lowe] |
8286 | Tropes cannot have clear identity-conditions, so they are not objects [Lowe] |
8294 | How can tropes depend on objects for their identity, if objects are just bundles of tropes? [Lowe] |
8295 | Why cannot a trope float off and join another bundle? [Lowe] |
8296 | Does a ball snug in plaster have one trope, or two which coincide? [Lowe] |
18352 | Tropes have existence independently of any entities [Lowe] |
8288 | Sortal terms for universals involve a substance, whereas adjectival terms do not [Lowe] |
4197 | The category of universals can be sub-divided into properties and relations [Lowe] |
8293 | Real universals are needed to explain laws of nature [Lowe] |
8307 | Particulars are instantiations, and universals are instantiables [Lowe] |
4232 | Nominalists believe that only particulars exist [Lowe] |
7720 | Two things can only resemble one another in some respect, and that may reintroduce a universal [Lowe] |
4205 | 'Is non-self-exemplifying' is a predicate which cannot denote a property (as it would be a contradiction) [Lowe] |
8967 | Not all predicates can be properties - 'is non-self-exemplifying', for example [Lowe] |
4233 | If 'blueness' is a set of particulars, there is danger of circularity, or using universals, in identifying the set [Lowe] |
8267 | Perhaps concrete objects are entities which are in space-time and subject to causality [Lowe] |
8265 | Our commitment to the existence of objects should depend on their explanatory value [Lowe] |
8275 | Objects are entities with full identity-conditions, but there are entities other than objects [Lowe] |
16130 | To be an object at all requires identity-conditions [Lowe] |
7783 | Bodies, properties, relations, events, numbers, sets and propositions are 'things' if they exist [Lowe] |
8263 | An object is an entity which has identity-conditions [Lowe] |
8965 | Neither mere matter nor pure form can individuate a sphere, so it must be a combination [Lowe] |
8268 | Some things (such as electrons) can be countable, while lacking proper identity [Lowe] |
8303 | Criteria of identity cannot individuate objects, because they are shared among different types [Lowe] |
8292 | Diversity of two tigers is their difference in space-time; difference of matter is a consequence [Lowe] |
8291 | Individuation principles identify what kind it is; identity criteria distinguish items of the same kind [Lowe] |
4206 | Conventionalists see the world as an amorphous lump without identities, but are we part of the lump? [Lowe] |
16128 | A 'substance' is an object which doesn't depend for existence on other objects [Lowe] |
7712 | On substances, Leibniz emphasises unity, Spinoza independence, Locke relations to qualities [Lowe] |
4204 | Statues can't survive much change to their shape, unlike lumps of bronze, which must retain material [Lowe] |
16545 | The essence of lumps and statues shows that two objects coincide but are numerically distinct [Lowe] |
16546 | The essence of a bronze statue shows that it could be made of different bronze [Lowe] |
13918 | Holes, shadows and spots of light can coincide without being identical [Lowe] |
8279 | The identity of composite objects isn't fixed by original composition, because how do you identify the origin? [Lowe] |
16551 | Grasping an essence is just grasping a real definition [Lowe] |
13921 | All things must have an essence (a 'what it is'), or we would be unable to think about them [Lowe] |
16542 | Explanation can't give an account of essence, because it is too multi-faceted [Lowe] |
13922 | Knowing an essence is just knowing what the thing is, not knowing some further thing [Lowe] |
16552 | If we must know some entity to know an essence, we lack a faculty to do that [Lowe] |
6618 | A 'substance' is a thing that remains the same when its properties change [Lowe] |
8271 | An object 'endures' if it is always wholly present, and 'perdures' if different parts exist at different times [Lowe] |
8272 | How can you identify temporal parts of tomatoes without referring to tomatoes? [Lowe] |
4198 | If 5% replacement preserves a ship, we can replace 4% and 4% again, and still retain the ship [Lowe] |
4199 | A renovation or a reconstruction of an original ship would be accepted, as long as the other one didn't exist [Lowe] |
4200 | If old parts are stored and then appropriated, they are no longer part of the original (which is the renovated ship). [Lowe] |
8305 | A clear idea of the kind of an object must precede a criterion of identity for it [Lowe] |
8290 | One view is that two objects of the same type are only distinguished by differing in matter [Lowe] |
13920 | Each thing has to be of a general kind, because it belongs to some category [Lowe] |
4203 | Identity of Indiscernibles (same properties, same thing) ) is not Leibniz's Law (same thing, same properties) [Lowe] |
15079 | 'Conceptual' necessity is narrow logical necessity, true because of concepts and logical laws [Lowe] |
16533 | Logical necessities, based on laws of logic, are a proper sub-class of metaphysical necessities [Lowe] |
16063 | Metaphysical necessity is logical necessity 'broadly construed' [Lowe, by Lynch/Glasgow] |
16531 | 'Metaphysical' necessity is absolute and objective - the strongest kind of necessity [Lowe] |
8260 | Logical necessity can be 'strict' (laws), or 'narrow' (laws and definitions), or 'broad' (all logical worlds) [Lowe] |
16131 | The metaphysically possible is what acceptable principles and categories will permit [Lowe] |
4195 | It is impossible to reach a valid false conclusion from true premises, so reason itself depends on possibility [Lowe] |
16532 | 'Epistemic' necessity is better called 'certainty' [Lowe] |
16543 | If an essence implies p, then p is an essential truth, and hence metaphysically necessary [Lowe] |
16544 | Metaphysical necessity is either an essential truth, or rests on essential truths [Lowe] |
4207 | We might eliminate 'possible' and 'necessary' in favour of quantification over possible worlds [Lowe] |
8320 | Does every abstract possible world exist in every possible world? [Lowe] |
16538 | We could give up possible worlds if we based necessity on essences [Lowe] |
6635 | Causal theories of belief make all beliefs true, and can't explain belief about the future [Lowe] |
6619 | Perhaps 'I' no more refers than the 'it' in 'it is raining' [Lowe] |
6643 | 'Ecological' approaches say we don't infer information, but pick it up directly from reality [Lowe] |
8280 | While space may just be appearance, time and change can't be, because the appearances change [Lowe] |
13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
8276 | Properties or qualities are essentially adjectival, not objectual [Lowe] |
6638 | One must be able to visually recognise a table, as well as knowing its form [Lowe] |
6644 | Computationalists object that the 'ecological' approach can't tell us how we get the information [Lowe] |
6647 | Comparing shapes is proportional in time to the angle of rotation [Lowe] |
6639 | The 'disjunctive' theory of perception says true perceptions and hallucinations need have nothing in common [Lowe] |
7710 | Perception is a mode of belief-acquisition, and does not involve sensation [Lowe] |
7711 | Science requires a causal theory - perception of an object must be an experience caused by the object [Lowe] |
6640 | A causal theorist can be a direct realist, if all objects of perception are external [Lowe] |
6645 | If blindsight shows we don't need perceptual experiences, the causal theory is wrong [Lowe] |
6637 | How could one paraphrase very complex sense-data reports adverbially? [Lowe] |
16534 | 'Intuitions' are just unreliable 'hunches'; over centuries intuitions change enormously [Lowe] |
6667 | There are memories of facts, memories of practical skills, and autobiographical memory [Lowe] |
6642 | Psychologists say illusions only occur in unnatural and passive situations [Lowe] |
4223 | Unfalsifiability may be a failure in an empirical theory, but it is a virtue in metaphysics [Lowe] |
8968 | If the flagpole causally explains the shadow, the shadow cannot explain the flagpole [Lowe] |
4193 | The behaviour of persons and social groups seems to need rational rather than causal explanation [Lowe] |
6641 | Externalists say minds depend on environment for their very existence and identity [Lowe] |
6617 | The main questions are: is mind distinct from body, and does it have unique properties? [Lowe] |
6626 | 'Phenomenal' consciousness is of qualities; 'apperceptive' consciousness includes beliefs and desires [Lowe] |
6646 | The brain may have two systems for vision, with only the older one intact in blindsight [Lowe] |
8966 | Properties are facets of objects, only discussable separately by an act of abstraction [Lowe] |
6665 | Persons are selves - subjects of experience, with reflexive self-knowledge [Lowe] |
6670 | If my brain could survive on its own, I cannot be identical with my whole body [Lowe] |
6671 | It seems impossible to get generally applicable mental concepts from self-observation [Lowe] |
7714 | Personal identity is a problem across time (diachronic) and at an instant (synchronic) [Lowe] |
6666 | All human languages have an equivalent of the word 'I' [Lowe] |
8289 | The idea that Cartesian souls are made of some ghostly 'immaterial' stuff is quite unwarranted [Lowe] |
6625 | If qualia are causally inert, how can we even know about them? [Lowe] |
6621 | You can only identify behaviour by ascribing belief, so the behaviour can't explain the belief [Lowe] |
6654 | A computer program is equivalent to the person AND the manual [Lowe] |
6623 | Functionalism can't distinguish our experiences in spectrum inversion [Lowe] |
6628 | Functionalism only discusses relational properties of mental states, not intrinsic properties [Lowe] |
6629 | Functionalism commits us to bizarre possibilities, such as 'zombies' [Lowe] |
6622 | Non-reductive physicalism accepts token-token identity (not type-type) and asserts 'supervenience' of mind and brain [Lowe] |
6634 | Physicalists must believe in narrow content (because thoughts are merely the brain states) [Lowe] |
6630 | Eliminativism is incoherent if it eliminates reason and truth as well as propositional attitudes [Lowe] |
6648 | Some behaviourists believe thought is just suppressed speech [Lowe] |
6652 | 'Base rate neglect' makes people favour the evidence over its background [Lowe] |
6651 | People are wildly inaccurate in estimating probabilities about an observed event [Lowe] |
7715 | Mentalese isn't a language, because it isn't conventional, or a means of public communication [Lowe] |
6655 | The 'Frame Problem' is how to program the appropriate application of general knowledge [Lowe] |
6657 | Computers can't be rational, because they lack motivation and curiosity [Lowe] |
6656 | The Turing test is too behaviourist, and too verbal in its methods [Lowe] |
6636 | The naturalistic views of how content is created are the causal theory and the teleological theory [Lowe] |
6633 | Twin Earth cases imply that even beliefs about kinds of stuff are indexical [Lowe] |
16535 | A concept is a way of thinking of things or kinds, whether or not they exist [Lowe] |
13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
8299 | Abstractions are non-spatial, or dependent, or derived from concepts [Lowe] |
4238 | The centre of mass of the solar system is a non-causal abstract object, despite having a location [Lowe] |
4237 | Concrete and abstract objects are distinct because the former have causal powers and relations [Lowe] |
8306 | You can think of a direction without a line, but a direction existing with no lines is inconceivable [Lowe] |
7722 | If meaning is mental pictures, explain "the cat (or dog!) is NOT on the mat" [Lowe] |
16550 | Direct reference doesn't seem to require that thinkers know what it is they are thinking about [Lowe] |
6632 | The same proposition provides contents for the that-clause of an utterance and a belief [Lowe] |
6631 | If propositions are abstract entities, how can minds depend on their causal powers? [Lowe] |
6659 | The three main theories of action involve the will, or belief-plus-desire, or an agent [Lowe] |
6661 | Libet gives empirical support for the will, as a kind of 'executive' mental operation [Lowe] |
6662 | We feel belief and desire as reasons for choice, not causes of choice [Lowe] |
6663 | People's actions are explained either by their motives, or their reasons, or the causes [Lowe] |
4210 | If the concept of a cause says it precedes its effect, that rules out backward causation by definition [Lowe] |
4215 | It seems proper to say that only substances (rather than events) have causal powers [Lowe] |
4209 | The theories of fact causation and event causation are both worth serious consideration [Lowe] |
8317 | To cite facts as the elements in causation is to confuse states of affairs with states of objects [Lowe] |
4211 | Causal overdetermination is either actual overdetermination, or pre-emption, or the fail-safe case [Lowe] |
4213 | Causation may be instances of laws (seen either as constant conjunctions, or as necessities) [Lowe] |
4212 | Hume showed that causation could at most be natural necessity, never metaphysical necessity [Lowe] |
14581 | The normative view says laws show the natural behaviour of natural kind members [Lowe, by Mumford/Anjum] |
16745 | No one even knows the nature and properties of a fly - why it has that colour, or so many feet [Bacon,R] |
16547 | H2O isn't necessary, because different laws of nature might affect how O and H combine [Lowe] |
4208 | 'If he wasn't born he wouldn't have died' doesn't mean birth causes death, so causation isn't counterfactual [Lowe] |
4224 | If motion is change of distance between objects, it involves no intrinsic change in the objects [Lowe] |
8269 | Points are limits of parts of space, so parts of space cannot be aggregates of them [Lowe] |
4227 | Surfaces, lines and points are not, strictly speaking, parts of space, but 'limits', which are abstract [Lowe] |
4228 | If space is entirely relational, what makes a boundary, or a place unoccupied by physical objects? [Lowe] |