81 ideas
19073 | True philosophy aims at absolute unity, while our understanding sees only separation [Hegel] |
15624 | Free thinking has no presuppositions [Hegel] |
15631 | The ideal of reason is the unification of abstract identity (or 'concept') and being [Hegel] |
15612 | Older metaphysics naively assumed that thought grasped things in themselves [Hegel] |
21768 | Logic is metaphysics, the science of things grasped in thoughts [Hegel] |
21984 | We must break up the rigidity that our understanding has imposed [Hegel] |
22081 | Let thought follow its own course, and don't interfere [Hegel] |
15626 | Categories create objective experience, but are too conditioned by things to actually grasp them [Hegel] |
15616 | If truth is just non-contradiction, we must take care that our basic concepts aren't contradictory [Hegel] |
15615 | Older metaphysics became dogmatic, by assuming opposed assertions must be true and false [Hegel] |
21767 | Dialectic is seen in popular proverbs like 'pride comes before a fall' [Hegel] |
15638 | Dialectic is the moving soul of scientific progression, the principle which binds science together [Hegel] |
15639 | Socratic dialectic is subjective, but Plato made it freely scientific and objective [Hegel] |
17774 | Definitions make our intuitions mathematically useful [Mayberry] |
17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
19070 | Superficial truth is knowing how something is, which is consciousness of bare correctness [Hegel] |
5644 | In Hegel's logic it is concepts (rather than judgements or propositions) which are true or false [Hegel, by Scruton] |
19072 | In the deeper sense of truth, to be untrue resembles being bad; badness is untrue to a thing's nature [Hegel] |
19071 | The deeper sense of truth is a thing matching the idea of what it ought to be [Hegel] |
17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
17803 | Limitation of size is part of the very conception of a set [Mayberry] |
17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
21595 | Excluded middle is the maxim of definite understanding, but just produces contradictions [Hegel] |
17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
15628 | The idea that contradiction is essential to rational understanding is a key modern idea [Hegel] |
15629 | Tenderness for the world solves the antinomies; contradiction is in our reason, not in the essence of the world [Hegel] |
15630 | Antinomies are not just in four objects, but in all objects, all representations, all objects and all ideas [Hegel] |
17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
22078 | Even simple propositions about sensations are filled with categories [Hegel] |
15634 | Thought about particulars is done entirely through categories [Hegel] |
17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
21981 | The one substance is formless without the mediation of dialectical concepts [Hegel] |
15637 | Essence is the essential self-positing unity of immediacy and mediation [Hegel] |
15613 | Real cognition grasps a thing from within itself, and is not satisfied with mere predicates [Hegel] |
15636 | The Cogito is at the very centre of the entire concern of modern philosophy [Hegel] |
22300 | Existence is just a set of relationships [Hegel] |
15609 | The sensible is distinguished from thought by being about singular things [Hegel] |
15625 | Sense perception is secondary and dependent, while thought is independent and primitive [Hegel] |
15619 | Empiricism made particular knowledge possible, and blocked wild claims [Hegel] |
15620 | Empiricism contains the important idea that we should see knowledge for ourselves, and be part of it [Hegel] |
15622 | Empiricism unknowingly contains and uses a metaphysic, which underlies its categories [Hegel] |
15621 | Empiricism of the finite denies the supersensible, and can only think with formal abstraction [Hegel] |
15632 | The Humean view stops us thinking about perception, and finding universals and necessities in it [Hegel] |
15623 | Humean scepticism, unlike ancient Greek scepticism, accepts the truth of experience as basic [Hegel] |
15617 | In abstraction, beyond finitude, freedom and necessity must exist together [Hegel] |
15608 | The act of thinking is the bringing forth of universals [Hegel] |
21986 | Hegel's system has a vast number of basic concepts [Hegel, by Moore,AW] |
15607 | We don't think with concepts - we think the concepts [Hegel] |
15610 | Active thought about objects produces the universal, which is what is true and essential of it [Hegel] |
6012 | We must choose in which of the virtues we wish to excel [Panaetius] |
6013 | Panaetius said we should live according to our natural starting-points [Panaetius, by Asmis] |
6014 | Panaetius identified courage with great-mindedness, preferring civic courage to military [Panaetius, by Asmis] |
15614 | Old metaphysics tried to grasp eternal truths through causal events, which is impossible [Hegel] |
15635 | The older conception of God was emptied of human features, to make it worthy of the Infinite [Hegel] |
21980 | God is the absolute thing, and also the absolute person [Hegel] |
15618 | If God is the abstract of Supremely Real Essence, then God is a mere Beyond, and unknowable [Hegel] |
15633 | We establish unification of the Ideal by the ontological proof, deriving being from abstraction of thinking [Hegel] |
5888 | Souls are born, since they are sensitive and inherited, so they must perish [Panaetius, by Cicero] |