128 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] |
| 21634 | Metaphysics is (supposedly) first the ontology, then in general what things are like [Hofweber] |
| 15612 | Older metaphysics naively assumed that thought grasped things in themselves [Hegel] |
| 21768 | Logic is metaphysics, the science of things grasped in thoughts [Hegel] |
| 21666 | 'Fundamentality' is either a superficial idea, or much too obscure [Hofweber] |
| 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] |
| 15638 | Dialectic is the moving soul of scientific progression, the principle which binds science together [Hegel] |
| 21767 | Dialectic is seen in popular proverbs like 'pride comes before a fall' [Hegel] |
| 15639 | Socratic dialectic is subjective, but Plato made it freely scientific and objective [Hegel] |
| 15615 | Older metaphysics became dogmatic, by assuming opposed assertions must be true and false [Hegel] |
| 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] |
| 21640 | 'It's true that Fido is a dog' conjures up a contrast class, of 'it's false' or 'it's unlikely' [Hofweber] |
| 9535 | 'Contradictory' propositions always differ in truth-value [Lemmon] |
| 9509 | That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon] |
| 9508 | The sign |- may be read as 'therefore' [Lemmon] |
| 9514 | If A and B are 'interderivable' from one another we may write A -||- B [Lemmon] |
| 9511 | We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon] |
| 9512 | We write the 'negation' of P (not-P) as ¬ [Lemmon] |
| 9510 | That proposition that either P or Q is their 'disjunction', written P∨Q [Lemmon] |
| 9513 | We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P) [Lemmon] |
| 9516 | A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [Lemmon] |
| 9519 | A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [Lemmon] |
| 9529 | A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon] |
| 9534 | Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon] |
| 9517 | The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon] |
| 9528 | A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon] |
| 9530 | A wff is 'contingent' if produces at least one T and at least one F [Lemmon] |
| 9518 | A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon] |
| 9533 | A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon] |
| 9532 | 'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon] |
| 9531 | 'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon] |
| 9399 | ∧E: Given A∧B, we may derive either A or B separately [Lemmon] |
| 9401 | ∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon] |
| 9395 | MTT: Given ¬B and A→B, we derive ¬A [Lemmon] |
| 9396 | DN: Given A, we may derive ¬¬A [Lemmon] |
| 9393 | A: we may assume any proposition at any stage [Lemmon] |
| 9400 | ∨I: Given either A or B separately, we may derive A∨B [Lemmon] |
| 9402 | RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon] |
| 9397 | CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon] |
| 9398 | ∧I: Given A and B, we may derive A∧B [Lemmon] |
| 9394 | MPP: Given A and A→B, we may derive B [Lemmon] |
| 9522 | 'Modus ponendo tollens' (MPT) says P, ¬(P ∧ Q) |- ¬Q [Lemmon] |
| 9526 | We can change conjunctions into negated conditionals with P→Q -||- ¬(P → ¬Q) [Lemmon] |
| 9527 | The Distributive Laws can rearrange a pair of conjunctions or disjunctions [Lemmon] |
| 9523 | De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon] |
| 9524 | We can change conditionals into disjunctions with P→Q -||- ¬P ∨ Q [Lemmon] |
| 9525 | We can change conditionals into negated conjunctions with P→Q -||- ¬(P ∧ ¬Q) [Lemmon] |
| 9521 | 'Modus tollendo ponens' (MTP) says ¬P, P ∨ Q |- Q [Lemmon] |
| 9537 | Truth-tables are good for showing invalidity [Lemmon] |
| 9538 | A truth-table test is entirely mechanical, but this won't work for more complex logic [Lemmon] |
| 9536 | If any of the nine rules of propositional logic are applied to tautologies, the result is a tautology [Lemmon] |
| 9539 | Propositional logic is complete, since all of its tautologous sequents are derivable [Lemmon] |
| 13909 | Write '(∀x)(...)' to mean 'take any x: then...', and '(∃x)(...)' to mean 'there is an x such that....' [Lemmon] |
| 13902 | 'Gm' says m has property G, and 'Pmn' says m has relation P to n [Lemmon] |
| 13911 | The 'symbols' are bracket, connective, term, variable, predicate letter, reverse-E [Lemmon] |
| 13910 | Our notation uses 'predicate-letters' (for 'properties'), 'variables', 'proper names', 'connectives' and 'quantifiers' [Lemmon] |
| 13904 | Universal Elimination (UE) lets us infer that an object has F, from all things having F [Lemmon] |
| 13901 | Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules [Lemmon] |
| 13903 | Universal elimination if you start with the universal, introduction if you want to end with it [Lemmon] |
| 13906 | With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro [Lemmon] |
| 13908 | UE all-to-one; UI one-to-all; EI arbitrary-to-one; EE proof-to-one [Lemmon] |
| 13905 | If there is a finite domain and all objects have names, complex conjunctions can replace universal quantifiers [Lemmon] |
| 13900 | 'Some Frenchmen are generous' is rendered by (∃x)(Fx→Gx), and not with the conditional → [Lemmon] |
| 21657 | Since properties can have properties, some theorists rank them in 'types' [Hofweber] |
| 9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
| 21595 | Excluded middle is the maxim of definite understanding, but just produces contradictions [Hegel] |
| 21653 | Maybe not even names are referential, but are just by used by speakers to refer [Hofweber] |
| 21636 | 'Singular terms' are not found in modern linguistics, and are not the same as noun phrases [Hofweber] |
| 21637 | If two processes are said to be identical, that doesn't make their terms refer to entities [Hofweber] |
| 21643 | The inferential quantifier focuses on truth; the domain quantifier focuses on reality [Hofweber] |
| 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] |
| 21644 | Numbers are used as singular terms, as adjectives, and as symbols [Hofweber] |
| 21646 | The Amazonian Piraha language is said to have no number words [Hofweber] |
| 21665 | The fundamental theorem of arithmetic is that all numbers are composed uniquely of primes [Hofweber] |
| 21649 | How can words be used for counting if they are objects? [Hofweber] |
| 21647 | Logicism makes sense of our ability to know arithmetic just by thought [Hofweber] |
| 21648 | Neo-Fregeans are dazzled by a technical result, and ignore practicalities [Hofweber] |
| 21664 | Supervenience offers little explanation for things which necessarily go together [Hofweber] |
| 21660 | Reality can be seen as the totality of facts, or as the totality of things [Hofweber] |
| 21661 | There are probably ineffable facts, systematically hidden from us [Hofweber] |
| 22078 | Even simple propositions about sensations are filled with categories [Hegel] |
| 15634 | Thought about particulars is done entirely through categories [Hegel] |
| 21652 | Our perceptual beliefs are about ordinary objects, not about simples arranged chair-wise [Hofweber] |
| 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] |
| 21663 | Counterfactuals are essential for planning, and learning from mistakes [Hofweber] |
| 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] |
| 21654 | The "Fido"-Fido theory of meaning says every expression in a language has a referent [Hofweber] |
| 21641 | Inferential role semantics is an alternative to semantics that connects to the world [Hofweber] |
| 21638 | Syntactic form concerns the focus of the sentence, as well as the truth-conditions [Hofweber] |
| 21658 | Properties can be expressed in a language despite the absence of a single word for them [Hofweber] |
| 21659 | 'Being taller than this' is a predicate which can express many different properties [Hofweber] |
| 21655 | Compositonality is a way to build up the truth-conditions of a sentence [Hofweber] |
| 21656 | Proposition have no content, because they are content [Hofweber] |
| 21635 | Without propositions there can be no beliefs or desires [Hofweber] |
| 21662 | Do there exist thoughts which we are incapable of thinking? [Hofweber] |
| 21645 | 'Semantic type coercion' is selecting the reading of a word to make the best sense [Hofweber] |
| 21639 | 'Background deletion' is appropriately omitting background from an answer [Hofweber] |
| 15614 | Old metaphysics tried to grasp eternal truths through causal events, which is impossible [Hegel] |
| 15618 | If God is the abstract of Supremely Real Essence, then God is a mere Beyond, and unknowable [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] |
| 15633 | We establish unification of the Ideal by the ontological proof, deriving being from abstraction of thinking [Hegel] |