121 ideas
19441 | All philosophies presuppose their historical moment, and arise from it [Feuerbach] |
19456 | Philosophy is distinguished from other sciences by its complete lack of presuppositions [Feuerbach] |
19442 | I don't study Plato for his own sake; the primary aim is always understanding [Feuerbach] |
6928 | Only that which can be an object of religion is an object of philosophy [Feuerbach] |
6918 | Philosophy should not focus on names, but on the determined nature of things [Feuerbach] |
6904 | Modern philosophy begins with Descartes' abstraction from sensation and matter [Feuerbach] |
6931 | Empiricism is right about ideas, but forgets man himself as one of our objects [Feuerbach] |
6933 | The laws of reality are also the laws of thought [Feuerbach] |
19444 | Each proposition has an antithesis, and truth exists as its refutation [Feuerbach] |
19445 | A dialectician has to be his own opponent [Feuerbach] |
19443 | Truth forges an impersonal unity between people [Feuerbach] |
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] |
21382 | Things get smaller without end [Anaxagoras] |
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] |
481 | Nothing is created or destroyed; there is only mixing and separation [Anaxagoras] |
6919 | Absolute thought remains in another world from being [Feuerbach] |
19457 | Being is what is undetermined, and hence indistinguishable [Feuerbach] |
21822 | Anaxagoras's concept of supreme Mind has a simple First and a multiple One [Anaxagoras, by Plotinus] |
6920 | Being posits essence, and my essence is my being [Feuerbach] |
6921 | Particularity belongs to being, whereas generality belongs to thought [Feuerbach] |
6926 | The only true being is of the senses, perception, feeling and love [Feuerbach] |
17995 | Basic is the potentially perceptible, then comes the contrary qualities, and finally the 'elements' [Anaxagoras] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
19446 | To our consciousness it is language which looks unreal [Feuerbach] |
6908 | Consciousness is absolute reality, and everything exists through consciousness [Feuerbach] |
19447 | The Absolute is the 'and' which unites 'spirit and nature' [Feuerbach] |
6932 | Ideas arise through communication, and reason is reached through community [Feuerbach] |
20802 | Snow is not white, and doesn't even appear white, because it is made of black water [Anaxagoras, by Cicero] |
6935 | In man the lowest senses of smell and taste elevate themselves to intellectual acts [Feuerbach] |
13257 | The senses are too feeble to determine the truth [Anaxagoras] |
22761 | We reveal unreliability in the senses when we cannot discriminate a slow change of colour [Anaxagoras, by Sext.Empiricus] |
13256 | Nous is unlimited, self-ruling and pure; it is the finest thing, with great discernment and strength [Anaxagoras] |
13784 | Mind is self-ruling, pure, ordering and ubiquitous [Anaxagoras, by Plato] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
5118 | Anaxagoras says mind remains pure, and so is not affected by what it changes [Anaxagoras, by Aristotle] |
19451 | When absorbed in deep reflection, is your reason in control, or is it you? [Feuerbach] |
6925 | The new philosophy thinks of the concrete in a concrete (not a abstract) manner [Feuerbach] |
6924 | Plotinus was ashamed to have a body [Feuerbach] |
6927 | If you love nothing, it doesn't matter whether something exists or not [Feuerbach] |
19450 | Reason, love and will are the highest perfections and essence of man - the purpose of his life [Feuerbach] |
19458 | Egoism is the only evil, love the only good; genuine love produces all the other virtues [Feuerbach] |
18231 | Anaxagoras said a person would choose to be born to contemplate the ordered heavens [Anaxagoras] |
6934 | Man is not a particular being, like animals, but a universal being [Feuerbach] |
6936 | The essence of man is in community, but with distinct individuals [Feuerbach] |
631 | For Anaxagoras the Good Mind has no opposite, and causes all movement, for a higher reason [Anaxagoras, by Aristotle] |
22727 | Mind creates the world from a mixture of pure substances [Anaxagoras, by ] |
550 | Anaxagoras said that the number of principles was infinite [Anaxagoras, by Aristotle] |
21383 | The ultimate constituents of reality are the homoeomeries [Anaxagoras, by Vlastos] |
13208 | Anaxagoreans regard the homoeomeries as elements, which compose earth, air, fire and water [Anaxagoras, by Aristotle] |
367 | Anaxagoras says mind produces order and causes everything [Anaxagoras, by Plato] |
21381 | Germs contain microscopic organs, which become visible as they grow [Anaxagoras] |
19448 | Consciousness is said to distinguish man from animals - consciousness of his own species [Feuerbach] |
22726 | When things were unified, Mind set them in order [Anaxagoras] |
2629 | Anaxagoras was the first to say that the universe is directed by an intelligence [Anaxagoras, by Cicero] |
19454 | A God needs justice, kindness and wisdom, but those concepts don't depend on the concept of God [Feuerbach] |
6913 | God's existence cannot be separated from essence and concept, which can only be thought as existing [Feuerbach] |
480 | Past, present and future, and the movements of the heavens, were arranged by Mind [Anaxagoras] |
19452 | The nature of God is an expression of human nature [Feuerbach] |
6903 | If God is only an object for man, then only the essence of man is revealed in God [Feuerbach] |
6923 | God is what man would like to be [Feuerbach] |
6911 | God is for us a mere empty idea, which we fill with our own ego and essence [Feuerbach] |
19453 | If love, goodness and personality are human, the God who is their source is anthropomorphic [Feuerbach] |
7488 | Anaxagoras was the first recorded atheist [Anaxagoras, by Watson] |
5956 | Anaxagoras was charged with impiety for calling the sun a lump of stone [Anaxagoras, by Plutarch] |
6902 | Catholicism concerns God in himself, Protestantism what God is for man [Feuerbach] |
19449 | Religion is the consciousness of the infinite [Feuerbach] |
6905 | Absolute idealism is the realized divine mind of Leibnizian theism [Feuerbach] |
19455 | Today's atheism will tomorrow become a religion [Feuerbach] |