84 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] |
18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
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] |
18819 | The idea that there are unrecognised truths is basic to our concept of truth [Rumfitt] |
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] |
18826 | 'True at a possibility' means necessarily true if what is said had obtained [Rumfitt] |
19071 | The deeper sense of truth is a thing matching the idea of what it ought to be [Hegel] |
18803 | Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt] |
18814 | 'Absolute necessity' would have to rest on S5 [Rumfitt] |
18798 | It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt] |
18799 | Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt] |
18830 | Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt] |
18843 | The iterated conception of set requires continual increase in axiom strength [Rumfitt] |
18836 | A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt] |
18837 | A set can be determinate, because of its concept, and still have vague membership [Rumfitt] |
18845 | If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt] |
18815 | Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt] |
18804 | The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt] |
18805 | Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt] |
18827 | If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt] |
18813 | Logical consequence is a relation that can extended into further statements [Rumfitt] |
18808 | Normal deduction presupposes the Cut Law [Rumfitt] |
18840 | When faced with vague statements, Bivalence is not a compelling principle [Rumfitt] |
21595 | Excluded middle is the maxim of definite understanding, but just produces contradictions [Hegel] |
18802 | In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt] |
18800 | Introduction rules give deduction conditions, and Elimination says what can be deduced [Rumfitt] |
18809 | Logical truths are just the assumption-free by-products of logical rules [Rumfitt] |
18807 | Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt] |
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] |
18842 | Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt] |
18834 | Infinitesimals do not stand in a determinate order relation to zero [Rumfitt] |
18846 | Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt] |
15634 | Thought about particulars is done entirely through categories [Hegel] |
22078 | Even simple propositions about sensations are filled with categories [Hegel] |
21981 | The one substance is formless without the mediation of dialectical concepts [Hegel] |
18839 | An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases [Rumfitt] |
18838 | The extension of a colour is decided by a concept's place in a network of contraries [Rumfitt] |
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] |
18816 | Metaphysical modalities respect the actual identities of things [Rumfitt] |
18825 | S5 is the logic of logical necessity [Rumfitt] |
18824 | Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right [Rumfitt] |
18828 | If two possibilities can't share a determiner, they are incompatible [Rumfitt] |
18821 | Possibilities are like possible worlds, but not fully determinate or complete [Rumfitt] |
18831 | Medieval logicians said understanding A also involved understanding not-A [Rumfitt] |
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] |
18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
22109 | The fullest knowledge places a conclusion within an accurate theory [Aquinas, by Kretzmann/Stump] |
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] |
18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |
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] |