30 ideas
8093 | Seek wisdom rather than truth; it is easier [Joubert] |
8095 | We must think with our entire body and soul [Joubert] |
8107 | The love of certainty holds us back in metaphysics [Joubert] |
8099 | The truths of reason instruct, but they do not illuminate [Joubert] |
8098 | Truth consists of having the same idea about something that God has [Joubert] |
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
8101 | To know is to see inside oneself [Joubert] |
8094 | The imagination has made more discoveries than the eye [Joubert] |
7444 | Type-type psychophysical identity is combined with a functional characterisation of pain [Lewis] |
7445 | The application of 'pain' to physical states is non-rigid and contingent [Lewis] |
7443 | A theory must be mixed, to cover qualia without behaviour, and behaviour without qualia [Lewis, by PG] |
8103 | A thought is as real as a cannon ball [Joubert] |
8100 | Where does the bird's idea of a nest come from? [Joubert] |
8096 | He gives his body up to pleasure, but not his soul [Joubert] |
8104 | What will you think of pleasures when you no longer enjoy them? [Joubert] |
8097 | Virtue is hard if we are scorned; we need support [Joubert] |
8106 | In raising a child we must think of his old age [Joubert] |
8105 | We can't exactly conceive virtue without the idea of God [Joubert] |
8102 | We cannot speak against Christianity without anger, or speak for it without love [Joubert] |