69 ideas
4194 | Metaphysics is concerned with the fundamental structure of reality as a whole [Lowe] |
4214 | Maybe such concepts as causation, identity and existence are primitive and irreducible [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] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
4229 | An infinite series of tasks can't be completed because it has no last member [Lowe] |
4240 | It might be argued that mathematics does not, or should not, aim at truth [Lowe] |
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] |
12215 | The existence of numbers is not a matter of identities, but of constituents of the world [Fine,K] |
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] |
4241 | If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects [Lowe] |
12211 | It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K] |
12209 | The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K] |
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] |
12214 | 'Exists' is a predicate, not a quantifier; 'electrons exist' is like 'electrons spin' [Fine,K] |
12212 | Just as we introduced complex numbers, so we introduced sums and temporal parts [Fine,K] |
4239 | Nominalists deny abstract objects, because we can have no reason to believe in their existence [Lowe] |
12216 | Real objects are those which figure in the facts that constitute reality [Fine,K] |
12218 | Being real and being fundamental are separate; Thales's water might be real and divisible [Fine,K] |
4202 | Change can be of composition (the component parts), or quality (properties), or 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] |
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] |
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] |
12217 | For ontology we need, not internal or external views, but a view from outside reality [Fine,K] |
12213 | Ontological claims are often universal, and not a matter of existential quantification [Fine,K] |
4196 | The main categories of existence are either universal and particular, or abstract and concrete [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] |
4197 | The category of universals can be sub-divided into properties and relations [Lowe] |
4232 | Nominalists believe that only particulars exist [Lowe] |
4205 | 'Is non-self-exemplifying' is a predicate which cannot denote a property (as it would be a contradiction) [Lowe] |
4233 | If 'blueness' is a set of particulars, there is danger of circularity, or using universals, in identifying the set [Lowe] |
4206 | Conventionalists see the world as an amorphous lump without identities, but are we part of the lump? [Lowe] |
4204 | Statues can't survive much change to their shape, unlike lumps of bronze, which must retain material [Lowe] |
4200 | If old parts are stored and then appropriated, they are no longer part of the original (which is the renovated ship). [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] |
4203 | Identity of Indiscernibles (same properties, same thing) ) is not Leibniz's Law (same thing, same properties) [Lowe] |
4195 | It is impossible to reach a valid false conclusion from true premises, so reason itself depends on possibility [Lowe] |
4207 | We might eliminate 'possible' and 'necessary' in favour of quantification over possible worlds [Lowe] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
4223 | Unfalsifiability may be a failure in an empirical theory, but it is a virtue in metaphysics [Lowe] |
4193 | The behaviour of persons and social groups seems to need rational rather than causal explanation [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] |
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] |
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] |
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] |
4228 | If space is entirely relational, what makes a boundary, or a place unoccupied by physical objects? [Lowe] |