30 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] |
10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
24036 | I can only see the proportion of two to three if there is a common measure - their unity [Descartes] |
24035 | Unity is something shared by many things, so in that respect they are equals [Descartes] |
24029 | Among the simples are the graspable negations, such as rest and instants [Descartes] |
14296 | Dispositions are physical states of mechanism; when known, these replace the old disposition term [Quine] |
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] |