90 ideas
| 21970 | Philosophy attains its goal if one person feels perfect accord between their system and experience [Fichte] |
| 17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
| 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] |
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| 17751 | Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki] |
| 8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| 9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
| 21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
| 9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
| 10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
| 22017 | Normativity needs the possibility of negation, in affirmation and denial [Fichte, by Pinkard] |
| 10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
| 10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
| 17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
| 10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
| 19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
| 17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
| 10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
| 17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
| 10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
| 18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| 10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
| 10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
| 13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
| 17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
| 10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| 10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
| 9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
| 11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
| 10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
| 10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
| 10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
| 10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
| 10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
| 10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
| 10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
| 10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by 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] |
| 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] |
| 6027 | From the fact that some men die, we cannot infer that they all do [Philodemus] |
| 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] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 22061 | Judgement is distinguishing concepts, and seeing their relations [Fichte, by Siep] |
| 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] |
| 22241 | Don't fear god or worry about death; the good is easily got and the terrible easily cured [Philodemus] |
| 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] |