28 ideas
10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
10185 | Set theory is the standard background for modern mathematics [Burgess] |
10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
19855 | The purpose of society is to protect the rights of liberty, property, security and resistance [Mirabeau/committee] |
19856 | The law expresses the general will, and all citizens can participate [Mirabeau/committee] |
19861 | There is only a constitution if rights are assured, and separation of powers defined [Mirabeau/committee] |
19858 | No one should be molested for their opinions, if they do not disturb the established order [Mirabeau/committee] |
19859 | Free speech is very precious, and everyone may speak and write freely (but take responsibility for it) [Mirabeau/committee] |
19857 | All citizens are eligible for roles in the state, purely on the basis of merit [Mirabeau/committee] |
19862 | Property is a sacred right, breached only when essential, and with fair compensation [Mirabeau/committee] |
19860 | Everyone must contribute to the state's power and administration, in just proportion [Mirabeau/committee] |