45 ideas
| 23247 | The need to act produces consciousness, and practical reason is the root of all reason [Fichte] |
| 23232 | Sufficient reason makes the transition from the particular to the general [Fichte] |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 23227 | Each object has a precise number of properties, each to a precise degree [Fichte] |
| 23228 | The principle of activity and generation is found in a self-moving basic force [Fichte] |
| 23241 | I am myself, but not the external object; so I only sense myself, and not the object [Fichte] |
| 21966 | Self-consciousness is the basis of knowledge, and knowing something is knowing myself [Fichte] |
| 21967 | There is nothing to say about anything which is outside my consciousness [Fichte] |
| 21969 | Awareness of reality comes from the free activity of consciousness [Fichte] |
| 23231 | I immediately know myself, and anything beyond that is an inference [Fichte] |
| 23246 | Faith is not knowledge; it is a decision of the will [Fichte] |
| 23245 | Knowledge can't be its own foundation; there has to be regress of higher and higher authorities [Fichte] |
| 23242 | Consciousness has two parts, passively receiving sensation, and actively causing productions [Fichte] |
| 23240 | We can't know by sight or hearing without realising that we are doing so [Fichte] |
| 23243 | Consciousness of external things is always accompanied by an unnoticed consciousness of self [Fichte] |
| 23244 | Forming purposes is absolutely free, and produces something from nothing [Fichte] |
| 23237 | The capacity for freedom is above the laws of nature, with its own power of purpose and will [Fichte] |
| 23235 | I want independent control of the fundamental cause of my decisions [Fichte] |
| 23230 | Nature contains a fundamental force of thought [Fichte] |
| 23233 | The will is awareness of one of our inner natural forces [Fichte] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 23234 | I cannot change the nature which has been determined for me [Fichte] |
| 23239 | The self is, apart from outward behaviour, a drive in your nature [Fichte] |
| 23238 | If life lacks love it becomes destruction [Fichte] |
| 23236 | Freedom means making yourself become true to your essential nature [Fichte] |
| 23229 | Nature is wholly interconnected, and the tiniest change affects everything [Fichte] |