338 ideas
| 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] |
| 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] |
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| 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] |
| 8315 | Maybe facts are just true propositions [Lowe] |
| 8319 | One-to-one correspondence would need countable, individuable items [Lowe] |
| 13439 | Venn Diagrams map three predicates into eight compartments, then look for the conclusion [Bostock] |
| 13520 | A 'tautology' must include connectives [Wolf,RS] |
| 13422 | 'Conjunctive Normal Form' is ensuring that no disjunction has a conjunction within its scope [Bostock] |
| 13421 | 'Disjunctive Normal Form' is ensuring that no conjunction has a disjunction within its scope [Bostock] |
| 13524 | Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS] |
| 13355 | 'Disjunction' says that Γ,φ∨ψ|= iff Γ,φ|= and Γ,ψ|= [Bostock] |
| 13350 | 'Assumptions' says that a formula entails itself (φ|=φ) [Bostock] |
| 13351 | 'Thinning' allows that if premisses entail a conclusion, then adding further premisses makes no difference [Bostock] |
| 13356 | The 'conditional' is that Γ|=φ→ψ iff Γ,φ|=ψ [Bostock] |
| 13352 | 'Cutting' allows that if x is proved, and adding y then proves z, you can go straight to z [Bostock] |
| 13353 | 'Negation' says that Γ,¬φ|= iff Γ|=φ [Bostock] |
| 13354 | 'Conjunction' says that Γ|=φ∧ψ iff Γ|=φ and Γ|=ψ [Bostock] |
| 13610 | A logic with ¬ and → needs three axiom-schemas and one rule as foundation [Bostock] |
| 13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
| 13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |
| 13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| 13846 | A 'free' logic can have empty names, and a 'universally free' logic can have empty domains [Bostock] |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| 8309 | A set is a 'number of things', not a 'collection', because nothing actually collects the members [Lowe] |
| 18107 | A 'proper class' cannot be a member of anything [Bostock] |
| 8322 | I don't believe in the empty set, because (lacking members) it lacks identity-conditions [Lowe] |
| 18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
| 13529 | Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS] |
| 18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
| 13526 | Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS] |
| 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] |
| 13534 | In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS] |
| 13535 | First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS] |
| 13346 | Truth is the basic notion in classical logic [Bostock] |
| 13545 | Elementary logic cannot distinguish clearly between the finite and the infinite [Bostock] |
| 13822 | Fictional characters wreck elementary logic, as they have contradictions and no excluded middle [Bostock] |
| 13623 | The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem' [Bostock] |
| 13347 | Validity is a conclusion following for premises, even if there is no proof [Bostock] |
| 13348 | It seems more natural to express |= as 'therefore', rather than 'entails' [Bostock] |
| 13349 | Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid' [Bostock] |
| 13614 | MPP: 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ' (omit Γs for Detachment) [Bostock] |
| 13617 | MPP is a converse of Deduction: If Γ |- φ→ψ then Γ,φ|-ψ [Bostock] |
| 13800 | |= α=α and α=β |= φ(α/ξ ↔ φ(β/ξ) fix identity [Bostock] |
| 13803 | If we are to express that there at least two things, we need identity [Bostock] |
| 13799 | The sign '=' is a two-place predicate expressing that 'a is the same thing as b' (a=b) [Bostock] |
| 13357 | Truth-functors are usually held to be defined by their truth-tables [Bostock] |
| 13812 | A 'zero-place' function just has a single value, so it is a name [Bostock] |
| 13811 | A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock] |
| 13360 | In logic, a name is just any expression which refers to a particular single object [Bostock] |
| 13361 | An expression is only a name if it succeeds in referring to a real object [Bostock] |
| 13813 | Definite descriptions don't always pick out one thing, as in denials of existence, or errors [Bostock] |
| 13814 | Definite desciptions resemble names, but can't actually be names, if they don't always refer [Bostock] |
| 13816 | Because of scope problems, definite descriptions are best treated as quantifiers [Bostock] |
| 13817 | Definite descriptions are usually treated like names, and are just like them if they uniquely refer [Bostock] |
| 13848 | We are only obliged to treat definite descriptions as non-names if only the former have scope [Bostock] |
| 13815 | Names do not have scope problems (e.g. in placing negation), but Russell's account does have that problem [Bostock] |
| 13438 | 'Prenex normal form' is all quantifiers at the beginning, out of the scope of truth-functors [Bostock] |
| 13818 | If we allow empty domains, we must allow empty names [Bostock] |
| 8312 | It is better if the existential quantifier refers to 'something', rather than a 'thing' which needs individuation [Lowe] |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| 13801 | An 'informal proof' is in no particular system, and uses obvious steps and some ordinary English [Bostock] |
| 13619 | Quantification adds two axiom-schemas and a new rule [Bostock] |
| 13622 | Axiom systems from Frege, Russell, Church, Lukasiewicz, Tarski, Nicod, Kleene, Quine... [Bostock] |
| 13615 | 'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock] |
| 13616 | The Deduction Theorem greatly simplifies the search for proof [Bostock] |
| 13620 | Proof by Assumptions can always be reduced to Proof by Axioms, using the Deduction Theorem [Bostock] |
| 13621 | The Deduction Theorem and Reductio can 'discharge' assumptions - they aren't needed for the new truth [Bostock] |
| 13753 | Natural deduction takes proof from assumptions (with its rules) as basic, and axioms play no part [Bostock] |
| 13755 | Excluded middle is an introduction rule for negation, and ex falso quodlibet will eliminate it [Bostock] |
| 13758 | In natural deduction we work from the premisses and the conclusion, hoping to meet in the middle [Bostock] |
| 13754 | Natural deduction rules for → are the Deduction Theorem (→I) and Modus Ponens (→E) [Bostock] |
| 18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
| 13757 | Unlike natural deduction, semantic tableaux have recipes for proving things [Bostock] |
| 13756 | A tree proof becomes too broad if its only rule is Modus Ponens [Bostock] |
| 13762 | Tableau rules are all elimination rules, gradually shortening formulae [Bostock] |
| 13611 | Tableau proofs use reduction - seeking an impossible consequence from an assumption [Bostock] |
| 13613 | A completed open branch gives an interpretation which verifies those formulae [Bostock] |
| 13612 | Non-branching rules add lines, and branching rules need a split; a branch with a contradiction is 'closed' [Bostock] |
| 13761 | In a tableau proof no sequence is established until the final branch is closed; hypotheses are explored [Bostock] |
| 13759 | Each line of a sequent calculus is a conclusion of previous lines, each one explicitly recorded [Bostock] |
| 13760 | A sequent calculus is good for comparing proof systems [Bostock] |
| 13364 | Interpretation by assigning objects to names, or assigning them to variables first [Bostock, by PG] |
| 6653 | Syntactical methods of proof need only structure, where semantic methods (truth-tables) need truth [Lowe] |
| 13821 | Extensionality is built into ordinary logic semantics; names have objects, predicates have sets of objects [Bostock] |
| 13362 | If an object has two names, truth is undisturbed if the names are swapped; this is Extensionality [Bostock] |
| 13519 | Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS] |
| 13533 | First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS] |
| 13531 | Model theory reveals the structures of mathematics [Wolf,RS] |
| 13532 | Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS] |
| 13537 | An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS] |
| 13539 | The LST Theorem is a serious limitation of first-order logic [Wolf,RS] |
| 13541 | For 'negation-consistent', there is never |-(S)φ and |-(S)¬φ [Bostock] |
| 13542 | A proof-system is 'absolutely consistent' iff we don't have |-(S)φ for every formula [Bostock] |
| 13540 | A set of formulae is 'inconsistent' when there is no interpretation which can make them all true [Bostock] |
| 13538 | If a theory is complete, only a more powerful language can strengthen it [Wolf,RS] |
| 13544 | Inconsistency or entailment just from functors and quantifiers is finitely based, if compact [Bostock] |
| 13618 | Compactness means an infinity of sequents on the left will add nothing new [Bostock] |
| 13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
| 4229 | An infinite series of tasks can't be completed because it has no last member [Lowe] |
| 18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
| 4240 | It might be argued that mathematics does not, or should not, aim at truth [Lowe] |
| 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] |
| 13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
| 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] |
| 13358 | Ordinary or mathematical induction assumes for the first, then always for the next, and hence for all [Bostock] |
| 13359 | Complete induction assumes for all numbers less than n, then also for n, and hence for all numbers [Bostock] |
| 8297 | Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe] |
| 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] |
| 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] |
| 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] |
| 13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 13543 | A relation is not reflexive, just because it is transitive and symmetrical [Bostock] |
| 13802 | Relations can be one-many (at most one on the left) or many-one (at most one on the right) [Bostock] |
| 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] |
| 8295 | Why cannot a trope float off and join another bundle? [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] |
| 8296 | Does a ball snug in plaster have one trope, or two which coincide? [Lowe] |
| 18352 | Tropes have existence independently of any entities [Lowe] |
| 4197 | The category of universals can be sub-divided into properties and relations [Lowe] |
| 8288 | Sortal terms for universals involve a substance, whereas adjectival terms do not [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] |
| 16130 | To be an object at all requires identity-conditions [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] |
| 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] |
| 8268 | Some things (such as electrons) can be countable, while lacking proper identity [Lowe] |
| 8965 | Neither mere matter nor pure form can individuate a sphere, so it must be a combination [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] |
| 13847 | If non-existent things are self-identical, they are just one thing - so call it the 'null object' [Bostock] |
| 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] |
| 13820 | The idea that anything which can be proved is necessary has a problem with empty names [Bostock] |
| 8260 | Logical necessity can be 'strict' (laws), or 'narrow' (laws and definitions), or 'broad' (all logical worlds) [Lowe] |
| 4195 | It is impossible to reach a valid false conclusion from true premises, so reason itself depends on possibility [Lowe] |
| 16131 | The metaphysically possible is what acceptable principles and categories will permit [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] |
| 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] |
| 6629 | Functionalism commits us to bizarre possibilities, such as 'zombies' [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] |
| 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] |
| 6651 | People are wildly inaccurate in estimating probabilities about an observed event [Lowe] |
| 6652 | 'Base rate neglect' makes people favour the evidence over its background [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] |
| 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] |
| 13363 | A (modern) predicate is the result of leaving a gap for the name in a sentence [Bostock] |
| 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] |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| 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] |
| 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] |
| 4227 | Surfaces, lines and points are not, strictly speaking, parts of space, but 'limits', which are abstract [Lowe] |
| 8269 | Points are limits of parts of space, so parts of space cannot be aggregates of them [Lowe] |
| 4228 | If space is entirely relational, what makes a boundary, or a place unoccupied by physical objects? [Lowe] |