87 ideas
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] |
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] |
5937 | The goodness of opinions depends on their grounds, and corresponding degrees of conviction [Ross] |
3570 | Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M] |
5936 | Knowledge is superior to opinion because it is certain [Ross] |
5927 | I prefer the causal theory to sense data, because sensations are events, not apprehensions [Ross] |
2748 | A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J] |
5940 | Two goods may be comparable, although they are not commensurable [Ross] |
5924 | Identical objects must have identical value [Ross] |
5933 | Aesthetic enjoyment combines pleasure with insight [Ross] |
5928 | Beauty is neither objective nor subjective, but a power of producing certain mental events [Ross] |
5911 | Moral duties are as fundamental to the universe as the axioms of mathematics [Ross] |
5926 | The beauty of a patch of colour might be the most important fact about it [Ross] |
7259 | Ross said moral principles are self-evident from the facts, but not from pure thought [Ross, by Dancy,J] |
5913 | The moral convictions of thoughtful educated people are the raw data of ethics [Ross] |
5920 | Value is held to be either a quality, or a relation (usually between a thing and a mind) [Ross] |
5923 | The arguments for value being an objective or a relation fail, so it appears to be a quality [Ross] |
5918 | The thing is intrinsically good if it would be good when nothing else existed [Ross] |
5930 | All things being equal, we all prefer the virtuous to be happy, not the vicious [Ross] |
5922 | An instrumentally good thing might stay the same, but change its value because of circumstances [Ross] |
5921 | We can ask of pleasure or beauty whether they are valuable, but not of goodness [Ross] |
5932 | The four goods are: virtue, pleasure, just allocation of pleasure, and knowledge [Ross] |
5910 | The three intrinsic goods are virtue, knowledge and pleasure [Ross] |
5898 | 'Right' and 'good' differ in meaning, as in a 'right action' and a 'good man' [Ross] |
5899 | If there are two equally good acts, they may both be right, but neither a duty [Ross] |
5904 | In the past 'right' just meant what is conventionally accepted [Ross] |
5919 | Goodness is a wider concept than just correct ethical conduct [Ross] |
5941 | Motives decide whether an action is good, and what is done decides whether it was right [Ross] |
5938 | Virtue is superior to pleasure, as pleasure is never a duty, but goodness is [Ross] |
5931 | All other things being equal, a universe with more understanding is better [Ross] |
5939 | Morality is not entirely social; a good moral character should love truth [Ross] |
5905 | We clearly value good character or understanding, as well as pleasure [Ross] |
5929 | No one thinks it doesn't matter whether pleasure is virtuously or viciously acquired [Ross] |
5906 | Promise-keeping is bound by the past, and is not concerned with consequences [Ross] |
18622 | Promises create a new duty to a particular person; they aren't just a strategy to achieve well-being [Ross] |
5908 | Prima facie duties rest self-evidently on particular circumstance [Ross] |
5917 | People lose their rights if they do not respect the rights of others [Ross] |
5900 | We should do our duty, but not from a sense of duty [Ross] |
5942 | We like people who act from love, but admire more the people who act from duty [Ross] |
5909 | Be faithful, grateful, just, beneficent, non-malevolent, and improve yourself [Ross, by PG] |
5914 | An act may be described in innumerable ways [Ross] |
5912 | We should use money to pay debts before giving to charity [Ross] |
5916 | Rights were originally legal, and broadened to include other things [Ross] |
5915 | Rights can be justly claimed, so animals have no rights, as they cannot claim any [Ross] |