112 ideas
16000 | Fixed ideas should be tackled aggressively [Kierkegaard] |
7578 | I conceived it my task to create difficulties everywhere [Kierkegaard] |
22087 | Philosophy fails to articulate the continual becoming of existence [Kierkegaard, by Carlisle] |
22047 | Wherever there is painless contradiction there is also comedy [Kierkegaard] |
18859 | Metaphysics is a quest for truthmakers [Tallant] |
16012 | Philosophy can't be unbiased if it ignores language, as that is no more independent than individuals are [Kierkegaard] |
18861 | Maybe number statements can be paraphrased into quantifications plus identities [Tallant] |
22092 | Kierkegaard's truth draws on authenticity, fidelity and honesty [Kierkegaard, by Carlisle] |
15999 | Pure truth is for infinite beings only; I prefer endless striving for truth [Kierkegaard] |
22094 | Subjective truth can only be sustained by repetition [Kierkegaard, by Carlisle] |
16005 | I recognise knowledge, but it is the truth by which I can live and die that really matters [Kierkegaard] |
5651 | Traditional views of truth are tautologies, and truth is empty without a subject [Kierkegaard, by Scruton] |
20313 | The highest truth we can get is uncertainty held fast by an inward passion [Kierkegaard] |
18866 | Maybe only 'positive' truths need truth-makers [Tallant] |
18860 | A truthmaker is the minimal portion of reality that will do the job [Tallant] |
18863 | What is the truthmaker for a possible new power? [Tallant] |
18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
17824 | The master science is physical objects divided into sets [Maddy] |
8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
18182 | The extension of concepts is not important to me [Maddy] |
18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
10718 | A natural number is a property of sets [Maddy, by Oliver] |
18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
16007 | I assume existence, rather than reasoning towards it [Kierkegaard] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
18864 | The wisdom of Plato and of Socrates are not the same property [Tallant] |
18865 | Substance must have two properties: individuation, and property-bearing [Tallant] |
16013 | Nothing necessary can come into existence, since it already 'is' [Kierkegaard] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
20742 | The real subject is ethical, not cognitive [Kierkegaard] |
16002 | The self is a combination of pairs of attributes: freedom/necessity, infinite/finite, temporal/eternal [Kierkegaard] |
18862 | Are propositions all the thoughts and sentences that are possible? [Tallant] |
22098 | Socrates neglects the gap between knowing what is good and doing good [Kierkegaard, by Carlisle] |
22086 | The most important aspect of a human being is not reason, but passion [Kierkegaard, by Carlisle] |
15998 | Perfect love is not in spite of imperfections; the imperfections must be loved as well [Kierkegaard] |
16003 | If people marry just because they are lonely, that is self-love, not love [Kierkegaard] |
7579 | While big metaphysics is complete without ethics, personal philosophy emphasises ethics [Kierkegaard] |
7581 | Speculative philosophy loses the individual in a vast vision of humanity [Kierkegaard] |
22090 | For me time stands still, and I with it [Kierkegaard, by Carlisle] |
22096 | Anxiety is not a passing mood, but a response to human freedom [Kierkegaard, by Carlisle] |
22097 | The ultimate in life is learning to be anxious in the right way [Kierkegaard] |
21909 | Ultimate knowledge is being anxious in the right way [Kierkegaard] |
20758 | Anxiety is staring into the yawning abyss of freedom [Kierkegaard] |
21910 | Our destiny is the highest pitch of world-weariness [Kierkegaard] |
9305 | The plebeians bore others; only the nobility bore themselves [Kierkegaard] |
5650 | Reason is just abstractions, so our essence needs a subjective 'leap of faith' [Kierkegaard, by Scruton] |
22095 | There are aesthetic, ethical and religious subjectivity [Kierkegaard, by Carlisle] |
20314 | People want to lose themselves in movements and history, instead of being individuals [Kierkegaard] |
7582 | Becoming what one is is a huge difficulty, because we strongly aspire to be something else [Kierkegaard] |
20747 | What matters is not right choice, but energy, earnestness and pathos in the choosing [Kierkegaard] |
16001 | Life may be understood backwards, but it has to be lived forwards [Kierkegaard] |
22093 | Life is a repetition when what has been now becomes [Kierkegaard] |
16009 | When we seek our own 'freedom' we are just trying to avoid responsibility [Kierkegaard] |
22091 | Kierkegaard prioritises the inward individual, rather than community [Kierkegaard, by Carlisle] |
7586 | God does not think or exist; God creates, and is eternal [Kierkegaard] |
16006 | Either Abraham rises higher than universal ethics, or he is a mere murderer [Kierkegaard] |
7577 | Abraham was willing to suspend ethics, for a higher idea [Kierkegaard] |
20312 | God cannot be demonstrated objectively, because God is a subject, only existing inwardly [Kierkegaard] |
7580 | Pantheism destroys the distinction between good and evil [Kierkegaard] |
16008 | The best way to be a Christian is without 'Christianity' [Kierkegaard] |
20735 | We need to see that Christianity cannot be understood [Kierkegaard] |
22088 | Faith is like a dancer's leap, going up to God, but also back to earth [Kierkegaard, by Carlisle] |
7583 | Faith is the highest passion in the sphere of human subjectivity [Kierkegaard] |
7584 | Without risk there is no faith [Kierkegaard] |