77 ideas
| 20801 | A wise man's chief strength is not being tricked; nothing is worse than error, frivolity or rashness [Zeno of Citium, by Cicero] |
| 1771 | When shown seven versions of the mowing argument, he paid twice the asking price for them [Zeno of Citium, by Diog. Laertius] |
| 20770 | Philosophy has three parts, studying nature, character, and rational discourse [Zeno of Citium, by Diog. Laertius] |
| 6022 | Someone who says 'it is day' proposes it is day, and it is true if it is day [Zeno of Citium, by Diog. Laertius] |
| 13689 | 'Theorems' are formulas provable from no premises at all [Sider] |
| 13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
| 13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
| 13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
| 13711 | System B introduces iterated modalities [Sider] |
| 13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider] |
| 13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider] |
| 13714 | We can treat modal worlds as different times [Sider] |
| 13720 | Converse Barcan Formula: □∀αφ→∀α□φ [Sider] |
| 13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider] |
| 13723 | System B is needed to prove the Barcan Formula [Sider] |
| 13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
| 13680 | Maybe logical consequence is a primitive notion [Sider] |
| 13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
| 13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
| 13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
| 13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
| 13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider] |
| 13700 | A 'total' function must always produce an output for a given domain [Sider] |
| 18935 | Semantic theory should specify when an act of naming is successful [Sawyer] |
| 18945 | Millians say a name just means its object [Sawyer] |
| 18934 | Sentences with empty names can be understood, be co-referential, and even be true [Sawyer] |
| 18938 | Frege's compositional account of truth-vaues makes 'Pegasus doesn't exist' neither true nor false [Sawyer] |
| 18947 | Definites descriptions don't solve the empty names problem, because the properties may not exist [Sawyer] |
| 13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
| 13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
| 13688 | Good axioms should be indisputable logical truths [Sider] |
| 13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
| 13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
| 13685 | Natural deduction helpfully allows reasoning with assumptions [Sider] |
| 13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |
| 13697 | Valuations in PC assign truth values to formulas relative to variable assignments [Sider] |
| 13684 | The semantical notion of a logical truth is validity, being true in all interpretations [Sider] |
| 13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider] |
| 13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider] |
| 13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider] |
| 13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
| 7555 | Zeno achieved the statement of the problems of infinitesimals, infinity and continuity [Russell on Zeno of Citium] |
| 13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
| 20860 | Whatever participates in substance exists [Zeno of Citium, by Stobaeus] |
| 13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
| 13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
| 13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
| 13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
| 13683 | A relation is a feature of multiple objects taken together [Sider] |
| 13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
| 13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
| 13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
| 13709 | Logical truths must be necessary if anything is [Sider] |
| 13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider] |
| 13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider] |
| 13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider] |
| 21397 | Perception an open hand, a fist is 'grasping', and holding that fist is knowledge [Zeno of Citium, by Long] |
| 20799 | A grasp by the senses is true, because it leaves nothing out, and so nature endorses it [Zeno of Citium, by Cicero] |
| 20797 | If a grasped perception cannot be shaken by argument, it is 'knowledge' [Zeno of Citium, by Cicero] |
| 21398 | A presentation is true if we judge that no false presentation could appear like it [Zeno of Citium, by Cicero] |
| 1770 | When a slave said 'It was fated that I should steal', Zeno replied 'Yes, and that you should be beaten' [Zeno of Citium, by Diog. Laertius] |
| 3799 | A dog tied to a cart either chooses to follow and is pulled, or it is just pulled [Zeno of Citium, by Hippolytus] |
| 21402 | Incorporeal substances can't do anything, and can't be acted upon either [Zeno of Citium, by Cicero] |
| 20816 | A body is required for anything to have causal relations [Zeno of Citium, by Cicero] |
| 1773 | A sentence always has signification, but a word by itself never does [Zeno of Citium, by Diog. Laertius] |
| 20841 | Zeno said live in agreement with nature, which accords with virtue [Zeno of Citium, by Diog. Laertius] |
| 1774 | Since we are essentially rational animals, living according to reason is living according to nature [Zeno of Citium, by Diog. Laertius] |
| 20863 | The goal is to 'live in agreement', according to one rational consistent principle [Zeno of Citium, by Stobaeus] |
| 2662 | Zeno saw virtue as a splendid state, not just a source of splendid action [Zeno of Citium, by Cicero] |
| 21395 | One of Zeno's books was 'That Which is Appropriate' [Zeno of Citium, by Long] |
| 5964 | Zeno says there are four main virtues, which are inseparable but distinct [Zeno of Citium, by Plutarch] |
| 20822 | There is no void in the cosmos, but indefinite void outside it [Zeno of Citium, by Ps-Plutarch] |
| 20811 | Since the cosmos produces what is alive and rational, it too must be alive and rational [Zeno of Citium] |
| 2648 | Things are more perfect if they have reason; nothing is more perfect than the universe, so it must have reason [Zeno of Citium] |
| 20810 | Rational is better than non-rational; the cosmos is supreme, so it is rational [Zeno of Citium] |
| 2649 | If tuneful flutes grew on olive trees, you would assume the olive had some knowledge of the flute [Zeno of Citium] |
| 20807 | The cosmos and heavens are the substance of god [Zeno of Citium, by Diog. Laertius] |