77 ideas
2930 | The main aim of philosophy must be to determine the order of rank among values [Nietzsche] |
20143 | Scientific knowledge is nothing without a prior philosophical 'faith' [Nietzsche] |
23722 | Objectivity is not disinterestedness (impossible), but the ability to switch perspectives [Nietzsche] |
4417 | Only that which has no history is definable [Nietzsche] |
23715 | Psychologists should be brave and proud, and prefer truth to desires, even when it is ugly [Nietzsche] |
13689 | 'Theorems' are formulas provable from no premises at all [Sider] |
13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
13711 | System B introduces iterated modalities [Sider] |
13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider] |
13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider] |
13714 | We can treat modal worlds as different times [Sider] |
13720 | Converse Barcan Formula: □∀αφ→∀α□φ [Sider] |
13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider] |
13723 | System B is needed to prove the Barcan Formula [Sider] |
13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
13680 | Maybe logical consequence is a primitive notion [Sider] |
13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider] |
13700 | A 'total' function must always produce an output for a given domain [Sider] |
13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
13688 | Good axioms should be indisputable logical truths [Sider] |
13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
13685 | Natural deduction helpfully allows reasoning with assumptions [Sider] |
13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |
13697 | Valuations in PC assign truth values to formulas relative to variable assignments [Sider] |
13684 | The semantical notion of a logical truth is validity, being true in all interpretations [Sider] |
13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider] |
13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider] |
13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider] |
13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
13683 | A relation is a feature of multiple objects taken together [Sider] |
13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
13709 | Logical truths must be necessary if anything is [Sider] |
13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider] |
13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider] |
13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider] |
4421 | Philosophers have never asked why there is a will to truth in the first place [Nietzsche] |
23719 | Forgetfulness is a strong positive ability, not mental laziness [Nietzsche] |
4420 | There is only 'perspective' seeing and knowing, and so the best objectivity is multiple points of view [Nietzsche] |
4414 | Philosophers invented "free will" so that our virtues would be permanently interesting to the gods [Nietzsche] |
4419 | People who think in words are orators rather than thinkers, and think about facts instead of thinking facts [Nietzsche] |
4411 | It is a delusion to separate the man from the deed, like the flash from the lightning [Nietzsche] |
3793 | We must question the very value of moral values [Nietzsche] |
4408 | The concept of 'good' was created by aristocrats to describe their own actions [Nietzsche] |
23716 | A strong rounded person soon forgets enemies, misfortunes, and even misdeeds [Nietzsche] |
20129 | All animals strive for the ideal conditions to express their power, and hate any hindrances [Nietzsche] |
3259 | Nietzsche rejects impersonal morality, and asserts the idea of living well [Nietzsche, by Nagel] |
4409 | Only the decline of aristocratic morality led to concerns about "egoism" [Nietzsche] |
4416 | Basic justice is the negotiation of agreement among equals, and the imposition of agreement [Nietzsche] |
4418 | A masterful and violent person need have nothing to do with contracts [Nietzsche] |
4407 | Plato, Spinoza and Kant are very different, but united in their low estimation of pity [Nietzsche] |
4415 | Guilt and obligation originated in the relationship of buying and selling, credit and debt [Nietzsche] |
23718 | If we say birds of prey could become lambs, that makes them responsible for being birds of prey [Nietzsche] |
23717 | Modern nihilism is now feeling tired of mankind [Nietzsche] |
23721 | Old tribes always felt an obligation to the earlier generations, and the founders [Nietzsche] |
20142 | The state begins with brutal conquest of a disorganised people, not with a 'contract' [Nietzsche] |
22971 | In moving from capitalism to communism a revolutionary dictatorship of the proletariat is needed [Marx] |
22969 | People who only have their labour power are the slaves of those permitting them to work [Marx] |
22970 | Freedom is making the state subordinate to its society [Marx] |
22000 | From each according to his ability, to each according to his need [Marx] |
22972 | Bourgeois 'freedom of conscience' just tolerates all sorts of religious intolerance [Marx] |
23720 | Punishment makes people harder, more alienated, and hostile [Nietzsche] |
4410 | The truly great haters in world history have always been priests [Nietzsche] |