65 ideas
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 14650 | Maybe proper names involve essentialism [Plantinga] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 14648 | Could I name all of the real numbers in one fell swoop? Call them all 'Charley'? [Plantinga] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 14664 | Necessary beings (numbers, properties, sets, propositions, states of affairs, God) exist in all possible worlds [Plantinga] |
| 16435 | Plantinga proposes necessary existent essences as surrogates for the nonexistent things [Plantinga, by Stalnaker] |
| 14655 | The 'identity criteria' of a name are a group of essential and established facts [Plantinga] |
| 14647 | Surely self-identity is essential to Socrates? [Plantinga] |
| 14658 | 'Being Socrates' and 'being identical with Socrates' characterise Socrates, so they are among his properties [Plantinga] |
| 13132 | A snowball's haecceity is the property of being identical with itself [Plantinga, by Westerhoff] |
| 14666 | Socrates is a contingent being, but his essence is not; without Socrates, his essence is unexemplified [Plantinga] |
| 14656 | Does Socrates have essential properties, plus a unique essence (or 'haecceity') which entails them? [Plantinga] |
| 14646 | An object has a property essentially if it couldn't conceivably have lacked it [Plantinga] |
| 14654 | Properties are 'trivially essential' if they are instantiated by every object in every possible world [Plantinga] |
| 14653 | X is essentially P if it is P in every world, or in every X-world, or in the actual world (and not ¬P elsewhere) [Plantinga] |
| 14660 | If a property is ever essential, can it only ever be an essential property? [Plantinga] |
| 14661 | Essences are instantiated, and are what entails a thing's properties and lack of properties [Plantinga] |
| 14657 | Does 'being identical with Socrates' name a property? I can think of no objections to it [Plantinga] |
| 14642 | Expressing modality about a statement is 'de dicto'; expressing it of property-possession is 'de re' [Plantinga] |
| 14643 | 'De dicto' true and 'de re' false is possible, and so is 'de dicto' false and 'de re' true [Plantinga] |
| 14649 | Can we find an appropriate 'de dicto' paraphrase for any 'de re' proposition? [Plantinga] |
| 14652 | 'De re' modality is as clear as 'de dicto' modality, because they are logically equivalent [Plantinga] |
| 14659 | We can imagine being beetles or alligators, so it is possible we might have such bodies [Plantinga] |
| 11984 | Asserting a possible property is to say it would have had the property if that world had been actual [Plantinga] |
| 14662 | Possible worlds clarify possibility, propositions, properties, sets, counterfacts, time, determinism etc. [Plantinga] |
| 18383 | Plantinga says there is just this world, with possibilities expressed in propositions [Plantinga, by Armstrong] |
| 16472 | Plantinga's actualism is nominal, because he fills actuality with possibilia [Stalnaker on Plantinga] |
| 11980 | A possible world is a maximal possible state of affairs [Plantinga] |
| 14651 | What Socrates could have been, and could have become, are different? [Plantinga] |
| 11982 | If possible Socrates differs from actual Socrates, the Indiscernibility of Identicals says they are different [Plantinga] |
| 11983 | It doesn't matter that we can't identify the possible Socrates; we can't identify adults from baby photos [Plantinga] |
| 11985 | If individuals can only exist in one world, then they can never lack any of their properties [Plantinga] |
| 11891 | Possibilities for an individual can only refer to that individual, in some possible world [Plantinga, by Mackie,P] |
| 11986 | The counterparts of Socrates have self-identity, but only the actual Socrates has identity-with-Socrates [Plantinga] |
| 11987 | Counterpart Theory absurdly says I would be someone else if things went differently [Plantinga] |
| 6356 | Maybe a reliable justification must come from a process working with its 'proper function' [Plantinga, by Pollock/Cruz] |
| 9086 | The idea of abstract objects is not ontological; it comes from the epistemological idea of abstraction [Plantinga] |
| 9087 | Theists may see abstract objects as really divine thoughts [Plantinga] |
| 16469 | Plantinga has domains of sets of essences, variables denoting essences, and predicates as functions [Plantinga, by Stalnaker] |
| 16470 | Plantinga's essences have their own properties - so will have essences, giving a hierarchy [Stalnaker on Plantinga] |
| 14663 | Are propositions and states of affairs two separate things, or only one? I incline to say one [Plantinga] |
| 9085 | If propositions are concrete they don't have to exist, and so they can't be necessary truths [Plantinga] |
| 9084 | Propositions can't just be in brains, because 'there are no human beings' might be true [Plantinga] |
| 20704 | A possible world contains a being of maximal greatness - which is existence in all worlds [Plantinga, by Davies,B] |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| 1474 | Moral evil may be acceptable to God because it allows free will (even though we don't see why this is necessary) [Plantinga, by PG] |
| 1475 | It is logically possible that natural evil like earthquakes is caused by Satan [Plantinga, by PG] |