52 ideas
| 1922 | Spiritual qualities only become advantageous with the growth of wisdom [Plato] |
| 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] |
| 9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
| 10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
| 11259 | How can you seek knowledge of something if you don't know it? [Plato] |
| 8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
| 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] |
| 18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
| 8757 | The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H] |
| 18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
| 10261 | The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro] |
| 18218 | Hilbert explains geometry, by non-numerical facts about space [Field,H] |
| 9623 | Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H] |
| 18215 | It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H] |
| 18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
| 18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
| 18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
| 24029 | Among the simples are the graspable negations, such as rest and instants [Descartes] |
| 18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
| 8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
| 18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
| 24030 | 3+4=7 is necessary because we cannot conceive of seven without including three and four [Descartes] |
| 20219 | True opinions only become really valuable when they are tied down by reasons [Plato] |
| 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] |
| 5985 | Seeking and learning are just recollection [Plato] |
| 5986 | The slave boy learns geometry from questioning, not teaching, so it is recollection [Plato] |
| 24034 | If someone had only seen the basic colours, they could deduce the others from resemblance [Descartes] |
| 1923 | As a guide to action, true opinion is as good as knowledge [Plato] |
| 24021 | The method starts with clear intuitions, followed by a process of deduction [Descartes] |
| 1919 | You don't need to learn what you know, and how do you seek for what you don't know? [Plato] |
| 18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
| 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] |
| 9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
| 1913 | Is virtue taught, or achieved by practice, or a natural aptitude, or what? [Plato] |
| 1921 | If virtue is a type of knowledge then it ought to be taught [Plato] |
| 1927 | It seems that virtue is neither natural nor taught, but is a divine gift [Plato] |
| 1918 | How can you know part of virtue without knowing the whole? [Plato] |
| 1916 | Even if virtues are many and various, they must have something in common to make them virtues [Plato] |
| 24023 | All the sciences searching for order and measure are related to mathematics [Descartes] |
| 18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
| 18220 | Both philosophy and physics now make substantivalism more attractive [Field,H] |
| 18219 | Relational space is problematic if you take the idea of a field seriously [Field,H] |