41 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] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 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] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 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] |
| 22137 | Observation can force rejection of some part of the initial set of claims [Duhem, by Boulter] |
| 18197 | Experiments only test groups of hypotheses, and can't show which one is wrong [Duhem] |
| 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] |
| 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] |