128 ideas
| 19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
| 16227 | Philosophers are good at denying the obvious [Hawley] |
| 1575 | For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle] |
| 1589 | Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle] |
| 10237 | Coherence is a primitive, intuitive notion, not reduced to something formal [Shapiro] |
| 8200 | Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine] |
| 4385 | Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson] |
| 10204 | An 'implicit definition' gives a direct description of the relations of an entity [Shapiro] |
| 10206 | Modal operators are usually treated as quantifiers [Shapiro] |
| 10208 | Axiom of Choice: some function has a value for every set in a given set [Shapiro] |
| 10252 | The Axiom of Choice seems to license an infinite amount of choosing [Shapiro] |
| 10207 | Anti-realists reject set theory [Shapiro] |
| 13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
| 10259 | The two standard explanations of consequence are semantic (in models) and deductive [Shapiro] |
| 10257 | Intuitionism only sanctions modus ponens if all three components are proved [Shapiro] |
| 10253 | Either logic determines objects, or objects determine logic, or they are separate [Shapiro] |
| 10251 | The law of excluded middle might be seen as a principle of omniscience [Shapiro] |
| 4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
| 10212 | Classical connectives differ from their ordinary language counterparts; '∧' is timeless, unlike 'and' [Shapiro] |
| 10209 | A function is just an arbitrary correspondence between collections [Shapiro] |
| 16216 | Part of the sense of a proper name is a criterion of the thing's identity [Hawley] |
| 10268 | Maybe plural quantifiers should be understood in terms of classes or sets [Shapiro] |
| 10235 | A sentence is 'satisfiable' if it has a model [Shapiro] |
| 10239 | The central notion of model theory is the relation of 'satisfaction' [Shapiro] |
| 10240 | Model theory deals with relations, reference and extensions [Shapiro] |
| 10214 | Theory ontology is never complete, but is only determined 'up to isomorphism' [Shapiro] |
| 10238 | The set-theoretical hierarchy contains as many isomorphism types as possible [Shapiro] |
| 10234 | Any theory with an infinite model has a model of every infinite cardinality [Shapiro] |
| 10201 | Virtually all of mathematics can be modeled in set theory [Shapiro] |
| 10213 | Real numbers are thought of as either Cauchy sequences or Dedekind cuts [Shapiro] |
| 18243 | Understanding the real-number structure is knowing usage of the axiomatic language of analysis [Shapiro] |
| 18245 | Cuts are made by the smallest upper or largest lower number, some of them not rational [Shapiro] |
| 10236 | There is no grounding for mathematics that is more secure than mathematics [Shapiro] |
| 10256 | For intuitionists, proof is inherently informal [Shapiro] |
| 10202 | Natural numbers just need an initial object, successors, and an induction principle [Shapiro] |
| 10205 | Mathematics originally concerned the continuous (geometry) and the discrete (arithmetic) [Shapiro] |
| 10222 | Mathematical foundations may not be sets; categories are a popular rival [Shapiro] |
| 10218 | Baseball positions and chess pieces depend entirely on context [Shapiro] |
| 10224 | The even numbers have the natural-number structure, with 6 playing the role of 3 [Shapiro] |
| 10228 | Could infinite structures be apprehended by pattern recognition? [Shapiro] |
| 10230 | The 4-pattern is the structure common to all collections of four objects [Shapiro] |
| 10249 | The main mathematical structures are algebraic, ordered, and topological [Shapiro] |
| 10273 | Some structures are exemplified by both abstract and concrete [Shapiro] |
| 10276 | Mathematical structures are defined by axioms, or in set theory [Shapiro] |
| 10270 | The main versions of structuralism are all definitionally equivalent [Shapiro] |
| 10221 | Is there is no more to structures than the systems that exemplify them? [Shapiro] |
| 10248 | Number statements are generalizations about number sequences, and are bound variables [Shapiro] |
| 10220 | Because one structure exemplifies several systems, a structure is a one-over-many [Shapiro] |
| 10223 | There is no 'structure of all structures', just as there is no set of all sets [Shapiro] |
| 8703 | Shapiro's structuralism says model theory (comparing structures) is the essence of mathematics [Shapiro, by Friend] |
| 10274 | Does someone using small numbers really need to know the infinite structure of arithmetic? [Shapiro] |
| 10200 | We distinguish realism 'in ontology' (for objects), and 'in truth-value' (for being either true or false) [Shapiro] |
| 10210 | If mathematical objects are accepted, then a number of standard principles will follow [Shapiro] |
| 10215 | Platonists claim we can state the essence of a number without reference to the others [Shapiro] |
| 10233 | Platonism must accept that the Peano Axioms could all be false [Shapiro] |
| 10244 | Intuition is an outright hindrance to five-dimensional geometry [Shapiro] |
| 10280 | A stone is a position in some pattern, and can be viewed as an object, or as a location [Shapiro] |
| 10254 | Can the ideal constructor also destroy objects? [Shapiro] |
| 10255 | Presumably nothing can block a possible dynamic operation? [Shapiro] |
| 10279 | Can we discover whether a deck is fifty-two cards, or a person is time-slices or molecules? [Shapiro] |
| 16211 | A homogeneous rotating disc should be undetectable according to Humean supervenience [Hawley] |
| 10227 | The abstract/concrete boundary now seems blurred, and would need a defence [Shapiro] |
| 10226 | Mathematicians regard arithmetic as concrete, and group theory as abstract [Shapiro] |
| 10262 | Fictionalism eschews the abstract, but it still needs the possible (without model theory) [Shapiro] |
| 10277 | Structuralism blurs the distinction between mathematical and ordinary objects [Shapiro] |
| 16219 | Non-linguistic things cannot be indeterminate, because they don't have truth-values at all [Hawley] |
| 16223 | Maybe for the world to be vague, it must be vague in its foundations? [Hawley] |
| 16226 | Epistemic vagueness seems right in the case of persons [Hawley] |
| 16208 | Supervaluation refers to one vaguely specified thing, through satisfaction by everything in some range [Hawley] |
| 16221 | Supervaluationism takes what the truth-value would have been if indecision was resolved [Hawley] |
| 16230 | Maybe the only properties are basic ones like charge, mass and spin [Hawley] |
| 16232 | An object is 'natural' if its stages are linked by certain non-supervenient relations [Hawley] |
| 10272 | The notion of 'object' is at least partially structural and mathematical [Shapiro] |
| 16200 | Are sortals spatially maximal - so no cat part is allowed to be a cat? [Hawley] |
| 16237 | The modal features of statue and lump are disputed; when does it stop being that statue? [Hawley] |
| 16238 | Perdurantists can adopt counterpart theory, to explain modal differences of identical part-sums [Hawley] |
| 10275 | A blurry border is still a border [Shapiro] |
| 16220 | Vagueness is either in our knowledge, in our talk, or in reality [Hawley] |
| 16222 | Indeterminacy in objects and in properties are not distinct cases [Hawley] |
| 13276 | The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki] |
| 13277 | The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki] |
| 16228 | The constitution theory is endurantism plus more than one object in a place [Hawley] |
| 16229 | Constitution theory needs sortal properties like 'being a sweater' to distinguish it from its thread [Hawley] |
| 14492 | If the constitution view says thread and sweater are two things, why do we talk of one thing? [Hawley] |
| 16193 | 'Adverbialism' explains change by saying an object has-at-some-time a given property [Hawley] |
| 16195 | Presentism solves the change problem: the green banana ceases, so can't 'relate' to the yellow one [Hawley] |
| 16202 | The problem of change arises if there must be 'identity' of a thing over time [Hawley] |
| 16192 | Endurance theory can relate properties to times, or timed instantiations to properties [Hawley] |
| 16196 | Endurance is a sophisticated theory, covering properties, instantiation and time [Hawley] |
| 16197 | How does perdurance theory explain our concern for our own future selves? [Hawley] |
| 16191 | Perdurance needs an atemporal perspective, to say that the object 'has' different temporal parts [Hawley] |
| 16199 | If an object is the sum of all of its temporal parts, its mass is staggeringly large! [Hawley] |
| 16201 | Perdurance says things are sums of stages; Stage Theory says each stage is the thing [Hawley] |
| 16240 | If a life is essentially the sum of its temporal parts, it couldn't be shorter or longer than it was? [Hawley] |
| 16203 | Stage Theory seems to miss out the link between stages of the same object [Hawley] |
| 16204 | Stage Theory says every stage is a distinct object, which gives too many objects [Hawley] |
| 16212 | An isolated stage can't be a banana (which involves suitable relations to other stages) [Hawley] |
| 16213 | Stages of one thing are related by extrinsic counterfactual and causal relations [Hawley] |
| 16206 | Stages must be as fine-grained in length as change itself, so any change is a new stage [Hawley] |
| 16205 | The stages of Stage Theory seem too thin to populate the world, or to be referred to [Hawley] |
| 16225 | If two things might be identical, there can't be something true of one and false of the other [Hawley] |
| 10258 | Logical modalities may be acceptable, because they are reducible to satisfaction in models [Shapiro] |
| 10266 | Why does the 'myth' of possible worlds produce correct modal logic? [Shapiro] |
| 16239 | To decide whether something is a counterpart, we need to specify a relevant sortal concept [Hawley] |
| 5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
| 11239 | The notion of a priori truth is absent in Aristotle [Aristotle, by Politis] |
| 23312 | Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M] |
| 16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
| 16971 | Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik] |
| 11243 | Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis] |
| 3320 | Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA] |
| 12000 | Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung] |
| 10203 | We apprehend small, finite mathematical structures by abstraction from patterns [Shapiro] |
| 16218 | On any theory of self, it is hard to explain why we should care about our future selves [Hawley] |
| 23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
| 10229 | Simple types can be apprehended through their tokens, via abstraction [Shapiro] |
| 10217 | We can apprehend structures by focusing on or ignoring features of patterns [Shapiro] |
| 9554 | We can focus on relations between objects (like baseballers), ignoring their other features [Shapiro] |
| 10231 | Abstract objects might come by abstraction over an equivalence class of base entities [Shapiro] |
| 11240 | The notion of analytic truth is absent in Aristotle [Aristotle, by Politis] |
| 6559 | Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin] |
| 11150 | It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle] |
| 3037 | Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius] |
| 8660 | There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend] |
| 12058 | Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins] |
| 16215 | Causation is nothing more than the counterfactuals it grounds? [Hawley] |
| 16207 | Time could be discrete (like integers) or dense (rationals) or continuous (reals) [Hawley] |
| 22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |