56 ideas
16227 | Philosophers are good at denying the obvious [Hawley] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
16216 | Part of the sense of a proper name is a criterion of the thing's identity [Hawley] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
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] |
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] |
16239 | To decide whether something is a counterpart, we need to specify a relevant sortal concept [Hawley] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
16218 | On any theory of self, it is hard to explain why we should care about our future selves [Hawley] |
7441 | Experiences are defined by their causal role, and causal roles belong to physical states [Lewis] |
7442 | 'Pain' contingently names the state that occupies the causal role of pain [Lewis] |
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] |