91 ideas
| 21970 | Philosophy attains its goal if one person feels perfect accord between their system and experience [Fichte] |
| 22024 | Fichte's subjectivity struggles to then give any account of objectivity [Pinkard on Fichte] |
| 6912 | For Fichte there is no God outside the ego, and 'our religion is reason' [Fichte, by Feuerbach] |
| 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] |
| 8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
| 8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
| 3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
| 8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
| 6627 | Radical pragmatists abandon the notion of truth [Stich, by Lowe] |
| 8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| 8694 | Free logic was developed for fictional or non-existent objects [Friend] |
| 8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
| 8672 | A 'powerset' is all the subsets of a set [Friend] |
| 8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
| 8666 | Infinite sets correspond one-to-one with a subset [Friend] |
| 8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
| 8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
| 22017 | Normativity needs the possibility of negation, in affirmation and denial [Fichte, by Pinkard] |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| 8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
| 8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
| 8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
| 8668 | The 'rational' numbers are those representable as fractions [Friend] |
| 8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
| 8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
| 8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
| 8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
| 8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
| 8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
| 8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
| 8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
| 8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
| 8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
| 8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
| 8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
| 8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
| 8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
| 8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
| 8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
| 8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
| 8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
| 8706 | Constructivism rejects too much mathematics [Friend] |
| 8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
| 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] |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| 22018 | Necessary truths derive from basic assertion and negation [Fichte, by Pinkard] |
| 22062 | Mental presentation are not empirical, but concern the strivings of the self [Fichte] |
| 22015 | The thing-in-itself is an empty dream [Fichte, by Pinkard] |
| 22064 | Fichte's logic is much too narrow, and doesn't deduce ethics, art, society or life [Schlegel,F on Fichte] |
| 21973 | Fichte believed in things-in-themselves [Fichte, by Moore,AW] |
| 21914 | We can deduce experience from self-consciousness, without the thing-in-itself [Fichte] |
| 23241 | I am myself, but not the external object; so I only sense myself, and not the object [Fichte] |
| 22032 | Fichte's key claim was that the subjective-objective distinction must itself be subjective [Fichte, by Pinkard] |
| 20951 | The absolute I divides into consciousness, and a world which is not-I [Fichte, by Bowie] |
| 21964 | Reason arises from freedom, so philosophy starts from the self, and not from the laws of nature [Fichte] |
| 21968 | Abandon the thing-in-itself; things only exist in relation to our thinking [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] |
| 22020 | We only see ourselves as self-conscious and rational in relation to other rationalities [Fichte] |
| 23240 | We can't know by sight or hearing without realising that we are doing so [Fichte] |
| 22060 | The Self is the spontaneity, self-relatedness and unity needed for knowledge [Fichte, by Siep] |
| 22066 | Novalis sought a much wider concept of the ego than Fichte's proposal [Novalis on Fichte] |
| 22016 | The self is not a 'thing', but what emerges from an assertion of normativity [Fichte, by Pinkard] |
| 23243 | Consciousness of external things is always accompanied by an unnoticed consciousness of self [Fichte] |
| 22019 | Consciousness of an object always entails awareness of the self [Fichte] |
| 22063 | Effective individuals must posit a specific material body for themselves [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] |
| 21965 | Spinoza could not actually believe his determinism, because living requires free will [Fichte] |
| 23230 | Nature contains a fundamental force of thought [Fichte] |
| 8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
| 4765 | Stich accepts eliminativism (labelled 'pragmatism') about rationality and normativity [Stich, by Engel] |
| 22061 | Judgement is distinguishing concepts, and seeing their relations [Fichte, by Siep] |
| 8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
| 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] |
| 22023 | Fichte's idea of spontaneity implied that nothing counts unless we give it status [Fichte, by Pinkard] |
| 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] |
| 22065 | Fichte reduces nature to a lifeless immobility [Schlegel,F on Fichte] |