61 ideas
| 16227 | Philosophers are good at denying the obvious [Hawley] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 16216 | Part of the sense of a proper name is a criterion of the thing's identity [Hawley] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 16211 | A homogeneous rotating disc should be undetectable according to Humean supervenience [Hawley] |
| 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] |
| 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] |
| 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] |
| 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] |
| 16205 | The stages of Stage Theory seem too thin to populate the world, or to be referred to [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] |
| 16225 | If two things might be identical, there can't be something true of one and false of the other [Hawley] |
| 16239 | To decide whether something is a counterpart, we need to specify a relevant sortal concept [Hawley] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 16218 | On any theory of self, it is hard to explain why we should care about our future selves [Hawley] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 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] |