116 ideas
9414 | Metaphysics is the mapping of possibilities [Lowe, by Mumford] |
16414 | Science needs metaphysics to weed out its presuppositions [Lowe, by Hofweber] |
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] |
16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
16292 | An explicit definition enables the elimination of what is defined [Halbach] |
8262 | How can a theory of meaning show the ontological commitments of two paraphrases of one idea? [Lowe] |
16307 | Don't trust analogies; they are no more than a guideline [Halbach] |
16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach] |
16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach] |
16324 | Any definition of truth requires a metalanguage [Halbach] |
16293 | Traditional definitions of truth often make it more obscure, rather than less [Halbach] |
16301 | If people have big doubts about truth, a definition might give it more credibility [Halbach] |
8315 | Maybe facts are just true propositions [Lowe] |
8319 | One-to-one correspondence would need countable, individuable items [Lowe] |
16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
16337 | Disquotational truth theories are short of deductive power [Halbach] |
16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach] |
16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach] |
16326 | The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach] |
16311 | To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach] |
16318 | Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach] |
16299 | Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach] |
16340 | Truth axioms need a base theory, because that is where truth issues arise [Halbach] |
16305 | We know a complete axiomatisation of truth is not feasible [Halbach] |
16313 | A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG] |
16315 | The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach] |
16314 | Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach] |
16327 | Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach] |
16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach] |
16331 | The KF is much stronger deductively than FS, which relies on classical truth [Halbach] |
16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach] |
16320 | Some say deflationism is axioms which are conservative over the base theory [Halbach] |
16338 | Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach] |
16317 | The main problem for deflationists is they can express generalisations, but not prove them [Halbach] |
16316 | Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach] |
16319 | Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach] |
16335 | In Strong Kleene logic a disjunction just needs one disjunct to be true [Halbach] |
16334 | In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value [Halbach] |
8309 | A set is a 'number of things', not a 'collection', because nothing actually collects the members [Lowe] |
16309 | Every attempt at formal rigour uses some set theory [Halbach] |
8322 | I don't believe in the empty set, because (lacking members) it lacks identity-conditions [Lowe] |
16333 | The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach] |
16310 | A theory is some formulae and all of their consequences [Halbach] |
8312 | It is better if the existential quantifier refers to 'something', rather than a 'thing' which needs individuation [Lowe] |
16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach] |
16341 | Normally we only endorse a theory if we believe it to be sound [Halbach] |
16344 | Soundness must involve truth; the soundness of PA certainly needs it [Halbach] |
16347 | Many new paradoxes may await us when we study interactions between frameworks [Halbach] |
16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
16321 | The compactness theorem can prove nonstandard models of PA [Halbach] |
16343 | The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach] |
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] |
16312 | To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach] |
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] |
8310 | Does the existence of numbers matter, in the way space, time and persons do? [Lowe] |
16308 | Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach] |
8321 | All possible worlds contain abstracta (e.g. numbers), which means they contain concrete objects [Lowe] |
8300 | Perhaps possession of causal power is the hallmark of existence (and a reason to deny the void) [Lowe] |
8281 | Heraclitus says change is new creation, and Spinoza that it is just phases of the one substance [Lowe] |
8270 | Events are changes or non-changes in properties and relations of persisting objects [Lowe] |
8308 | Events are ontologically indispensable for singular causal explanations [Lowe] |
16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
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] |
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] |
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] |
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] |
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] |
8267 | Perhaps concrete objects are entities which are in space-time and subject to causality [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] |
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] |
16128 | A 'substance' is an object which doesn't depend for existence on other objects [Lowe] |
8279 | The identity of composite objects isn't fixed by original composition, because how do you identify the origin? [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] |
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] |
16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
15079 | 'Conceptual' necessity is narrow logical necessity, true because of concepts and logical laws [Lowe] |
16063 | Metaphysical necessity is logical necessity 'broadly construed' [Lowe, by Lynch/Glasgow] |
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] |
8320 | Does every abstract possible world exist in every possible world? [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] |
8289 | The idea that Cartesian souls are made of some ghostly 'immaterial' stuff is quite unwarranted [Lowe] |
8299 | Abstractions are non-spatial, or dependent, or derived from concepts [Lowe] |
8306 | You can think of a direction without a line, but a direction existing with no lines is inconceivable [Lowe] |
16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
8317 | To cite facts as the elements in causation is to confuse states of affairs with states of objects [Lowe] |
8269 | Points are limits of parts of space, so parts of space cannot be aggregates of them [Lowe] |
16713 | Philosophers are the forefathers of heretics [Tertullian] |
6610 | I believe because it is absurd [Tertullian] |