33 ideas
24032 | Clever scholars can obscure things which are obvious even to peasants [Descartes] |
24033 | Most scholastic disputes concern words, where agreeing on meanings would settle them [Descartes] |
24024 | The secret of the method is to recognise which thing in a series is the simplest [Descartes] |
24018 | One truth leads us to another [Descartes] |
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] |
24035 | Unity is something shared by many things, so in that respect they are equals [Descartes] |
24036 | I can only see the proportion of two to three if there is a common measure - their unity [Descartes] |
24029 | Among the simples are the graspable negations, such as rest and instants [Descartes] |
24030 | 3+4=7 is necessary because we cannot conceive of seven without including three and four [Descartes] |
24019 | If we accept mere probabilities as true we undermine our existing knowledge [Descartes] |
24020 | We all see intuitively that we exist, where intuition is attentive, clear and distinct rational understanding [Descartes] |
24031 | When Socrates doubts, he know he doubts, and that truth is possible [Descartes] |
24025 | Clear and distinct truths must be known all at once (unlike deductions) [Descartes] |
24022 | Our souls possess divine seeds of knowledge, which can bear spontaneous fruit [Descartes] |
24034 | If someone had only seen the basic colours, they could deduce the others from resemblance [Descartes] |
24021 | The method starts with clear intuitions, followed by a process of deduction [Descartes] |
24027 | Nerves and movement originate in the brain, where imagination moves them [Descartes] |
24026 | Our four knowledge faculties are intelligence, imagination, the senses, and memory [Descartes] |
24028 | The force by which we know things is spiritual, and quite distinct from the body [Descartes] |
24023 | All the sciences searching for order and measure are related to mathematics [Descartes] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |