20 ideas
2661 | Dialectic is speech cast in the form of logical argument [Cicero] |
2673 | There cannot be more than one truth [Cicero] |
13030 | Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen] |
13032 | Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen] |
13033 | Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen] |
13037 | Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen] |
13038 | Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen] |
13034 | Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen] |
13039 | Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen] |
13036 | Choice: ∀A ∃R (R well-orders A) [Kunen] |
13029 | Set Existence: ∃x (x = x) [Kunen] |
13031 | Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen] |
13040 | Constructibility: V = L (all sets are constructible) [Kunen] |
2669 | Dialectic assumes that all statements are either true or false, but self-referential paradoxes are a big problem [Cicero] |
10558 | Abstract objects are actually constituted by the properties by which we conceive them [Zalta] |
2664 | If we have complete healthy senses, what more could the gods give us? [Cicero] |
2665 | How can there be a memory of what is false? [Cicero] |
20800 | Every true presentation can have a false one of the same quality [Cicero] |
10557 | Abstract objects are captured by second-order modal logic, plus 'encoding' formulas [Zalta] |
2672 | Virtues must be very detached, to avoid being motivated by pleasure [Cicero] |