129 ideas
19807 | Both nature and reason require that everything has a cause [Rousseau] |
10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
11011 | Same say there are positive, negative and neuter free logics [Read] |
11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
10986 | Not all validity is captured in first-order logic [Read] |
10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
10973 | A theory is logically closed, which means infinite premisses [Read] |
11007 | Quantifiers are second-order predicates [Read] |
10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
10988 | Any first-order theory of sets is inadequate [Read] |
10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
11016 | Would a language without vagueness be usable at all? [Read] |
11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
10989 | The standard view of conditionals is that they are truth-functional [Read] |
11017 | Some people even claim that conditionals do not express propositions [Read] |
10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
9567 | Maths deals with quantities of physical significance, ignoring irrelevant features [Geroch] |
11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
7235 | Without freedom of will actions lack moral significance [Rousseau] |
19791 | Natural mankind is too fragmented for states of peace, or of war and enmity [Rousseau] |
20501 | Rousseau assumes that laws need a people united by custom and tradition [Rousseau, by Wolff,J] |
7237 | The act of becoming 'a people' is the real foundation of society [Rousseau] |
19792 | To overcome obstacles, people must unite their forces into a single unified power [Rousseau] |
19812 | Human nature changes among a people, into a moral and partial existence [Rousseau] |
19814 | A state must be big enough to preserve itself, but small enough to be governable [Rousseau] |
19815 | Too much land is a struggle, producing defensive war; too little makes dependence, and offensive war [Rousseau] |
19822 | If the state enlarges, the creators of the general will become less individually powerful [Rousseau] |
19823 | If the population is larger, the government needs to be more powerful [Rousseau] |
7232 | Man is born free, and he is everywhere in chains [Rousseau] |
7234 | No man has any natural authority over his fellows [Rousseau] |
19816 | A state's purpose is liberty and equality - liberty for strength, and equality for liberty [Rousseau] |
7247 | The greatest social good comes down to freedom and equality [Rousseau] |
19838 | The measure of a successful state is increase in its population [Rousseau] |
19848 | The sovereignty does not appoint the leaders [Rousseau] |
20567 | Rousseau insists that popular sovereignty needs a means of expressing consent [Rousseau, by Oksala] |
19801 | Sovereignty is the exercise of the general will, which can never be delegated [Rousseau] |
19805 | Just as people control their limbs, the general-will state has total control of its members [Rousseau] |
19818 | Political laws are fundamental, as they firmly organise the state - but they could still be changed [Rousseau] |
19790 | Force can only dominate if it is seen as a right, and obedience as a duty [Rousseau] |
7233 | The social order is a sacred right, but based on covenants, not nature [Rousseau] |
19842 | The government is instituted by a law, not by a contract [Rousseau] |
7239 | The social pact is the total subjection of individuals to the general will [Rousseau] |
19793 | We need a protective association which unites forces, but retains individual freedom [Rousseau] |
7240 | To foreign powers a state is seen as a simple individual [Rousseau] |
19795 | The act of association commits citizens to the state, and the state to its citizens [Rousseau] |
19797 | Citizens must ultimately for forced to accept the general will (so freedom is compulsory!) [Rousseau] |
19796 | Individual citizens still retain a private will, which may be contrary to the general will [Rousseau] |
7244 | The general will is common interest; the will of all is the sum of individual desires [Rousseau] |
19802 | The general will is always right, but the will of all can err, because it includes private interests [Rousseau] |
19803 | If the state contains associations there are fewer opinions, undermining the general will [Rousseau] |
19804 | If a large knowledgeable population votes in isolation, their many choices will have good results [Rousseau] |
19808 | The general will changes its nature when it focuses on particulars [Rousseau] |
7246 | The general will is always good, but sometimes misunderstood [Rousseau] |
7250 | Laws are authentic acts of the general will [Rousseau] |
19844 | Assemblies must always confirm the form of government, and the current administration [Rousseau] |
19846 | The more unanimous the assembly, the stronger the general will becomes [Rousseau] |
19817 | Citizens should be independent of each other, and very dependent on the state [Rousseau] |
19840 | A citizen is a subject who is also sovereign [Rousseau] |
19839 | The flourishing of arts and letters is too much admired [Rousseau] |
19798 | Ancient monarchs were kings of peoples; modern monarchs more cleverly rule a land [Rousseau] |
19831 | The highest officers under a monarchy are normally useless; the public could choose much better [Rousseau] |
19833 | Hereditary monarchy is easier, but can lead to dreadful monarchs [Rousseau] |
19834 | Attempts to train future kings don't usually work, and the best have been unprepared [Rousseau] |
19829 | Natural aristocracy is primitive, and hereditary is dreadful, but elective aristocracy is best [Rousseau] |
7249 | Natural aristocracy is primitive, hereditary is bad, and elective aristocracy is the best [Rousseau] |
19830 | Large states need a nobility to fill the gap between a single prince and the people [Rousseau] |
19827 | Law makers and law implementers should be separate [Rousseau] |
19820 | The state has a legislature and an executive, just like the will and physical power in a person [Rousseau] |
19821 | I call the executive power the 'government', which is the 'prince' - a single person, or a group [Rousseau] |
19824 | Large populations needs stronger control, which means power should be concentrated [Rousseau] |
19826 | Democracy for small states, aristocracy for intermediate, monarchy for large [Rousseau] |
19837 | If inhabitants are widely dispersed, organising a revolt is much more difficult [Rousseau] |
19843 | The state is not bound to leave civil authority to its leaders [Rousseau] |
19825 | If the sovereign entrusts government to at least half the citizens, that is 'democracy' [Rousseau] |
19832 | Democratic elections are dangerous intervals in government [Rousseau] |
7243 | Silence of the people implies their consent [Rousseau] |
7251 | The English are actually slaves in between elections [Rousseau] |
7238 | Minorities only accept majority-voting because of a prior unanimous agreement [Rousseau] |
19828 | Democracy leads to internal strife, as people struggle to maintain or change ways of ruling [Rousseau] |
19835 | When ministers change the state changes, because they always reverse policies [Rousseau] |
19849 | In early theocracies the god was the king, and there were as many gods as nations [Rousseau] |
19841 | Sometimes full liberty is only possible at the expense of some complete enslavement [Rousseau] |
19847 | We can never assume that the son of a slave is a slave [Rousseau] |
7242 | Appetite alone is slavery, and self-prescribed laws are freedom [Rousseau] |
19800 | The social compact imposes conventional equality of rights on people who may start unequally [Rousseau] |
7248 | No citizen should be rich enough to buy another, and none so poor as forced to sell himself [Rousseau] |
19794 | If we all give up all of our rights together to the community, we will always support one another [Rousseau] |
7241 | In society man loses natural liberty, but gains a right to civil liberty and property [Rousseau] |
19806 | We alienate to society only what society needs - but society judges that, not us [Rousseau] |
19799 | Private property must always be subordinate to ownership by the whole community [Rousseau] |
19819 | The state ensures liberty, so civil law separates citizens, and binds them to the state [Rousseau] |
7245 | Natural justice, without sanctions, benefits the wicked, who exploit it [Rousseau] |
19809 | We accept the death penalty to prevent assassinations, so we must submit to it if necessary [Rousseau] |
19810 | A trial proves that a criminal has broken the social treaty, and is no longer a member of the state [Rousseau] |
19811 | Only people who are actually dangerous should be executed, even as an example [Rousseau] |
7236 | War gives no right to inflict more destruction than is necessary for victory [Rousseau] |
23607 | Wars are between States, not people, and the individuals are enemies by accident [Rousseau] |
19850 | By separating theological and political systems, Jesus caused divisions in the state [Rousseau] |
19852 | Civil religion needs one supreme god, an afterlife, justice, and the sanctity of the social contract [Rousseau] |
19853 | All religions should be tolerated, if they tolerate each other, and support citizenship [Rousseau] |
19851 | Every society has a religion as its base [Rousseau] |
19836 | The amount of taxation doesn't matter, if it quickly circulates back to the citizens [Rousseau] |
7252 | A tyrant exploits Christians because they don't value this life, and are made to be slaves [Rousseau] |