92 ideas
23917 | Contrary statements can both be reasonable, if they are meant in two different ways [Aristotle] |
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] |
13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [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] |
13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
13680 | Maybe logical consequence is a primitive notion [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] |
13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
13688 | Good axioms should be indisputable logical truths [Sider] |
13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [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] |
13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [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] |
5869 | The thesis of the Form of the Good (or of anything else) is verbal and vacuous [Aristotle] |
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] |
22505 | The two right angles of a triangle necessitate that a quadrilateral has four [Aristotle] |
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] |
22513 | Knowing is having knowledge; understanding is using knowledge [Aristotle] |
23906 | Courage from spirit is natural and unconquerable, as seen in the young [Aristotle] |
20204 | Whether the mind has parts is irrelevant, since it obviously has distinct capacities [Aristotle] |
22506 | A man is the cause of what is within his power, and what he causes is in his power [Aristotle] |
22504 | Only a human being can be a starting point for an action [Aristotle] |
22510 | Some emotional states are too strong for human nature [Aristotle] |
23913 | Nearly all the good and bad states of character are concerned with feelings [Aristotle] |
7518 | If folk psychology gives a network of causal laws, that fits neatly with functionalism [Churchland,PM] |
7519 | Many mental phenomena are totally unexplained by folk psychology [Churchland,PM] |
7520 | Folk psychology never makes any progress, and is marginalised by modern science [Churchland,PM] |
23918 | Akrasia is the clash of two feelings - goodness and pleasure [Aristotle] |
22515 | Choice results when deliberation brings together an opinion with an inclination [Aristotle] |
22508 | Unlike in inanimate things, in animate things actions have more than one starting point [Aristotle] |
22514 | The deliberative part of the soul discerns explanatory causes [Aristotle] |
23319 | We are responsible if our actions reflect our motivation [Aristotle, by Frede,M] |
22507 | An action is voluntary when it is accompanied by thought of some kind [Aristotle] |
22512 | Acts are voluntary if done knowingly, by the agent, and in his power to avoid it [Aristotle] |
22509 | What is natural for us is either there at birth, or appears by normal processes [Aristotle] |
18230 | No one would choose life just for activities not done for their own sake [Aristotle] |
23909 | Wearing a shoe is its intrinsic use, and selling it (as a shoe) is its coincidental use [Aristotle] |
5870 | Everything seeks, not a single good, but its own separate good [Aristotle] |
5877 | We judge people from their deeds because we cannot see their choices (which matter more) [Aristotle] |
5868 | Horses, birds and fish are not happy, lacking a divine aspect to their natures [Aristotle] |
5865 | Happiness involves three things, of which the greatest is either wisdom, virtue, or pleasure [Aristotle] |
5876 | Virtue is different from continence [Aristotle] |
5872 | Excellence is the best state of anything (like a cloak) which has an employment or function [Aristotle] |
5875 | Character (éthos) is developed from habit (ethos) [Aristotle] |
5874 | Character virtues (such as courage) are of the non-rational part, which follows the rational part [Aristotle] |
22516 | Character is shown by what is or is not enjoyed, and virtue chooses the mean among them [Aristotle] |
22517 | We judge character not by their actions, but by their reasons for actions [Aristotle] |
23914 | People sometimes exhibit both extremes together, but the mean is contrary to both of them [Aristotle] |
23911 | Possessors of a virtue tend to despise what reason shows to be its opposite [Aristotle] |
23910 | Greatness of soul produces all the virtues - and vice versa [Aristotle] |
23908 | If someone just looks at or listens to beautiful things, they would not be thought intemperate [Aristotle] |
23905 | Courage follows reason, which tells us to choose what is noble [Aristotle] |
23912 | Honour depends on what it is for, and whether it is bestowed by worthy people [Aristotle] |
5871 | Goods in the soul are more worthy than those outside it, as everybody wants them [Aristotle] |
23920 | Decent people can be friends with base people [Aristotle] |
23919 | Friendship cannot be immediate; it takes time, and needs testing [Aristotle] |
23915 | The main function of politics is to produce friendship [Aristotle] |
23916 | The best cure for mutual injustice is friendship [Aristotle] |
5866 | It is folly not to order one's life around some end [Aristotle] |
5878 | Eyes could be used for a natural purpose, or for unnatural seeing, or for a non-seeing activity [Aristotle] |
5873 | Each thing's function is its end [Aristotle] |