16 ideas
| 12302 | Definitions formed an abstract hierarchy for Aristotle, as sets do for us [Fine,K] |
| 14266 | Aristotle sees hierarchies in definitions using genus and differentia (as we see them in sets) [Fine,K] |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| 14181 | Validity is where either the situation or the interpretation blocks true premises and false conclusion [Etchemendy, by Read] |
| 14180 | Etchemendy says fix the situation and vary the interpretation, or fix interpretations with varying situations [Etchemendy, by Read] |
| 14268 | Maybe bottom-up grounding shows constitution, and top-down grounding shows essence [Fine,K] |
| 14267 | There is no distinctive idea of constitution, because you can't say constitution begins and ends [Fine,K] |
| 14264 | Is there a plausible Aristotelian notion of constitution, applicable to both physical and non-physical? [Fine,K] |
| 14265 | The components of abstract definitions could play the same role as matter for physical objects [Fine,K] |