98 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] |
10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
11011 | Same say there are positive, negative and neuter free logics [Read] |
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
10986 | Not all validity is captured in first-order logic [Read] |
10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
10973 | A theory is logically closed, which means infinite premisses [Read] |
11007 | Quantifiers are second-order predicates [Read] |
13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
10988 | Any first-order theory of sets is inadequate [Read] |
10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
4229 | An infinite series of tasks can't be completed because it has no last member [Lowe] |
11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
4240 | It might be argued that mathematics does not, or should not, aim at truth [Lowe] |
11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
4241 | If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects [Lowe] |
4239 | Nominalists deny abstract objects, because we can have no reason to believe in their existence [Lowe] |
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] |
11016 | Would a language without vagueness be usable at all? [Read] |
11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
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] |
10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
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] |
11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
4195 | It is impossible to reach a valid false conclusion from true premises, so reason itself depends on possibility [Lowe] |
10989 | The standard view of conditionals is that they are truth-functional [Read] |
11017 | Some people even claim that conditionals do not express propositions [Read] |
10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
4207 | We might eliminate 'possible' and 'necessary' in favour of quantification over possible worlds [Lowe] |
10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
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] |
10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
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] |
11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
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] |