96 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] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 19906 | All countries are in a mutual state of nature [Locke] |
| 19882 | We are not created for solitude, but are driven into society by our needs [Locke] |
| 19864 | In nature men can dispose of possessions and their persons in any way that is possible [Locke] |
| 19865 | There is no subjection in nature, and all creatures of the same species are equal [Locke] |
| 19866 | The rational law of nature says we are all equal and independent, and should show mutual respect [Locke] |
| 19872 | The animals and fruits of the earth belong to mankind [Locke] |
| 19907 | There is a natural right to inheritance within a family [Locke] |
| 19863 | Politics is the right to make enforceable laws to protect property and the state, for the common good [Locke] |
| 5654 | The Second Treatise explores the consequences of the contractual view of the state [Locke, by Scruton] |
| 19888 | A society only begins if there is consent of all the individuals to join it [Locke] |
| 6702 | If anyone enjoys the benefits of government (even using a road) they give tacit assent to its laws [Locke] |
| 19909 | A politic society is created from a state of nature by a unanimous agreement [Locke] |
| 19910 | A single will creates the legislature, which is duty-bound to preserve that will [Locke] |
| 19893 | Anyone who enjoys the benefits of a state has given tacit consent to be part of it [Locke] |
| 19894 | You can only become an actual member of a commonwealth by an express promise [Locke] |
| 19892 | Children are not born into citizenship of a state [Locke] |
| 19885 | Absolute monarchy is inconsistent with civil society [Locke] |
| 19886 | The idea that absolute power improves mankind is confuted by history [Locke] |
| 19903 | Despotism is arbitrary power to kill, based neither on natural equality, nor any social contract [Locke] |
| 19905 | People stripped of their property are legitimately subject to despotism [Locke] |
| 19904 | Legitimate prisoners of war are subject to despotism, because that continues the state of war [Locke] |
| 19895 | Even the legislature must be preceded by a law which gives it power to make laws [Locke] |
| 19900 | The executive must not be the legislature, or they may exempt themselves from laws [Locke] |
| 19902 | Any obstruction to the operation of the legislature can be removed forcibly by the people [Locke] |
| 19908 | Rebelling against an illegitimate power is no sin [Locke] |
| 19911 | If legislators confiscate property, or enslave people, they are no longer owed obedience [Locke] |
| 19901 | The people have supreme power, to depose a legislature which has breached their trust [Locke] |
| 19887 | Unanimous consent makes a united community, which is then ruled by the majority [Locke] |
| 19913 | A master forfeits ownership of slaves he abandons [Locke] |
| 19883 | Slaves captured in a just war have no right to property, so are not part of civil society [Locke] |
| 19870 | If you try to enslave me, you have declared war on me [Locke] |
| 19871 | Freedom is not absence of laws, but living under laws arrived at by consent [Locke] |
| 19880 | All value depends on the labour involved [Locke] |
| 19873 | We all own our bodies, and the work we do is our own [Locke] |
| 19884 | There is only a civil society if the members give up all of their natural executive rights [Locke] |
| 19879 | A man owns land if he cultivates it, to the limits of what he needs [Locke] |
| 6580 | Locke (and Marx) held that ownership of objects is a natural relation, based on the labour put into it [Locke, by Fogelin] |
| 20520 | Locke says 'mixing of labour' entitles you to land, as well as nuts and berries [Wolff,J on Locke] |
| 19875 | A man's labour gives ownership rights - as long as there are fair shares for all [Locke] |
| 19874 | If a man mixes his labour with something in Nature, he thereby comes to own it [Locke] |
| 19877 | Fountain water is everyone's, but a drawn pitcher of water has an owner [Locke] |
| 19876 | Gathering natural fruits gives ownership; the consent of other people is irrelevant [Locke] |
| 19878 | Mixing labour with a thing bestows ownership - as long as the thing is not wasted [Locke] |
| 19898 | Soldiers can be commanded to die, but not to hand over their money [Locke] |
| 19881 | The aim of law is not restraint, but to make freedom possible [Locke] |
| 19868 | It is only by a law of Nature that we can justify punishing foreigners [Locke] |
| 19867 | Reparation and restraint are the only justifications for punishment [Locke] |
| 19912 | Self-defence is natural, but not the punishment of superiors by inferiors [Locke] |
| 19869 | Punishment should make crime a bad bargain, leading to repentance and deterrence [Locke] |
| 19899 | The consent of the people is essential for any tax [Locke] |