65 ideas
| 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] |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| 6919 | Absolute thought remains in another world from being [Feuerbach] |
| 19457 | Being is what is undetermined, and hence indistinguishable [Feuerbach] |
| 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] |
| 6908 | Consciousness is absolute reality, and everything exists through consciousness [Feuerbach] |
| 6932 | Ideas arise through communication, and reason is reached through community [Feuerbach] |
| 6935 | In man the lowest senses of smell and taste elevate themselves to intellectual acts [Feuerbach] |
| 6925 | The new philosophy thinks of the concrete in a concrete (not a abstract) manner [Feuerbach] |
| 7357 | People who control others with fluent language often end up being hated [Kongzi (Confucius)] |
| 7358 | All men prefer outward appearance to true excellence [Kongzi (Confucius)] |
| 6924 | Plotinus was ashamed to have a body [Feuerbach] |
| 7362 | Humans are similar, but social conventions drive us apart (sages and idiots being the exceptions) [Kongzi (Confucius)] |
| 6927 | If you love nothing, it doesn't matter whether something exists or not [Feuerbach] |
| 7360 | Do not do to others what you would not desire yourself [Kongzi (Confucius)] |
| 7359 | Excess and deficiency are equally at fault [Kongzi (Confucius)] |
| 7363 | The virtues of the best people are humility, maganimity, sincerity, diligence, and graciousness [Kongzi (Confucius)] |
| 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] |
| 7361 | Men of the highest calibre avoid political life completely [Kongzi (Confucius)] |
| 23393 | Confucianism assumes that all good developments have happened, and there is only one Way [Norden on Kongzi (Confucius)] |
| 6913 | God's existence cannot be separated from essence and concept, which can only be thought as existing [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] |
| 6902 | Catholicism concerns God in himself, Protestantism what God is for man [Feuerbach] |
| 6905 | Absolute idealism is the realized divine mind of Leibnizian theism [Feuerbach] |