13 ideas
7661 | Truth is the opinion fated to be ultimately agreed by all investigators [Peirce] |
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] |
19089 | Our whole conception of an object is its possible practical consequences [Peirce] |
7660 | We are aware of beliefs, they appease our doubts, and they are rules of action, or habits [Peirce] |
14906 | Non-positivist verificationism says only take a hypothesis seriously if it is scientifically based and testable [Ladyman/Ross on Peirce] |
15998 | Perfect love is not in spite of imperfections; the imperfections must be loved as well [Kierkegaard] |