65 ideas
| 23027 | Ideals and metaphysics are practical, not imaginative or speculative [Green,TH, by Muirhead] |
| 3035 | Dialectic involves conversations with short questions and brief answers [Diog. Laertius] |
| 23030 | Truth is a relation to a whole of organised knowledge in the collection of rational minds [Green,TH, by Muirhead] |
| 10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
| 10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
| 18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
| 7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
| 10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
| 10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
| 13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
| 10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| 10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| 10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
| 10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| 10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| 13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
| 10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
| 10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
| 7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| 10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
| 10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
| 10833 | Many concepts can only be expressed by second-order logic [Boolos] |
| 10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
| 10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| 10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
| 10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
| 23044 | All knowledge rests on a fundamental unity between the knower and what is known [Green,TH, by Muirhead] |
| 1816 | Sceptics say demonstration depends on self-demonstrating things, or indemonstrable things [Diog. Laertius] |
| 23034 | The ultimate test for truth is the systematic interdependence in nature [Green,TH, by Muirhead] |
| 23029 | Knowledge is secured by the relations between its parts, through differences and identities [Green,TH, by Muirhead] |
| 1819 | Scepticism has two dogmas: that nothing is definable, and every argument has an opposite argument [Diog. Laertius] |
| 3064 | When sceptics say that nothing is definable, or all arguments have an opposite, they are being dogmatic [Diog. Laertius] |
| 3033 | Induction moves from some truths to similar ones, by contraries or consequents [Diog. Laertius] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 23035 | The good life aims at perfections, or absolute laws, or what is absolutely desirable [Green,TH] |
| 23032 | What is distinctive of human life is the desire for self-improvement [Green,TH, by Muirhead] |
| 1838 | Cyrenaic pleasure is a motion, but Epicurean pleasure is a condition [Diog. Laertius] |
| 1769 | Cynics believe that when a man wishes for nothing he is like the gods [Diog. Laertius] |
| 23033 | Hedonism offers no satisfaction, because what we desire is self-betterment [Green,TH, by Muirhead] |
| 23046 | States only have full authority if they heed the claims of human fellowship [Green,TH] |
| 23045 | Politics is compromises, which seem supported by a social contract, but express the will of no one [Green,TH] |
| 23050 | The ideal is a society in which all citizens are ladies and gentlemen [Green,TH] |
| 23052 | Enfranchisement is an end in itself; it makes a person moral, and gives a basis for respect [Green,TH] |
| 23036 | The good is identified by the capacities of its participants [Green,TH, by Muirhead] |
| 23039 | A true state is only unified and stabilised by acknowledging individuality [Green,TH, by Muirhead] |
| 23037 | People are improved by egalitarian institutions and habits [Green,TH] |
| 23051 | Equality also implies liberty, because equality must be of opportunity as well as possessions [Green,TH] |
| 23043 | All talk of the progress of a nation must reduce to the progress of its individual members [Green,TH] |
| 23038 | People only develop their personality through co-operation with the social whole [Green,TH, by Muirhead] |
| 23028 | The highest political efforts express our deeper social spirit [Green,TH, by Muirhead] |
| 23054 | Communism is wrong because it restricts the freedom of individuals to contribute to the community [Green,TH, by Muirhead] |
| 23047 | Original common ownership is securing private property, not denying it [Green,TH, by Muirhead] |
| 23042 | National spirit only exists in the individuals who embody it [Green,TH, by Muirhead] |
| 23048 | The ground of property ownership is not force but the power to use it for social ends [Green,TH, by Muirhead] |
| 23049 | Property is needed by all citizens, to empower them to achieve social goods [Green,TH] |
| 23040 | If something develops, its true nature is embodied in its end [Green,TH] |
| 23031 | God is the ideal end of the mature mind's final development [Green,TH] |
| 23041 | God is the realisation of the possibilities of each man's self [Green,TH] |