35 ideas
| 19335 | Reasonings have a natural ordering in God's understanding, but only a temporal order in ours [Leibniz] |
| 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] |
| 14775 | Numbers are just names devised for counting [Peirce] |
| 14776 | That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce] |
| 14770 | Reasoning is based on statistical induction, so it can't achieve certainty or precision [Peirce] |
| 14774 | Innate truths are very uncertain and full of error, so they certainly have exceptions [Peirce] |
| 14773 | A truth is hard for us to understand if it rests on nothing but inspiration [Peirce] |
| 14772 | If we decide an idea is inspired, we still can't be sure we have got the idea right [Peirce] |
| 14771 | Only reason can establish whether some deliverance of revelation really is inspired [Peirce] |
| 14769 | Only imagination can connect phenomena together in a rational way [Peirce] |
| 19367 | Saying we must will whatever we decide to will leads to an infinite regress [Leibniz] |
| 19351 | Perfections of soul subordinate the body, but imperfections of soul submit to the body [Leibniz] |
| 19331 | Will is an inclination to pursue something good [Leibniz] |
| 19346 | Most people facing death would happily re-live a similar life, with just a bit of variety [Leibniz] |
| 19340 | Metaphysical evil is imperfection; physical evil is suffering; moral evil is sin [Leibniz] |
| 19366 | You can't assess moral actions without referring to the qualities of character that produce them [Leibniz] |
| 19326 | God must be intelligible, to select the actual world from the possibilities [Leibniz] |
| 19327 | The intelligent cause must be unique and all-perfect, to handle all the interconnected possibilities [Leibniz] |
| 19344 | God prefers men to lions, but might not exterminate lions to save one man [Leibniz] |
| 19330 | If justice is arbitrary, or fixed but not observed, or not human justice, this undermines God [Leibniz] |
| 19325 | God is the first reason of things; our experiences are contingent, and contain no necessity [Leibniz] |
| 19329 | The laws of physics are wonderful evidence of an intelligent and free being [Leibniz] |
| 19437 | Prayers are useful, because God foresaw them in his great plan [Leibniz] |
| 19337 | How can an all-good, wise and powerful being allow evil, sin and apparent injustice? [Leibniz] |
| 19345 | Being confident of God's goodness, we disregard the apparent local evils in the visible world [Leibniz] |