91 ideas
| 23183 | Different abilities are needed for living in an incomplete and undogmatic system [Nietzsche] |
| 23188 | Bad writers use shapeless floating splotches of concepts [Nietzsche] |
| 23212 | A text has many interpretations, but no 'correct' one [Nietzsche] |
| 23199 | What is the search for truth if it isn't moral? [Nietzsche] |
| 23202 | Like all philosophers, I love truth [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] |
| 23196 | Logic is a fiction, which invents the view that one thought causes another [Nietzsche] |
| 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] |
| 23186 | Numbers enable us to manage the world - to the limits of counting [Nietzsche] |
| 13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
| 23211 | Events are just interpretations of groups of appearances [Nietzsche] |
| 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] |
| 23201 | The 'I' does not think; it is a construction of thinking, like other useful abstractions [Nietzsche] |
| 23207 | Appearance is the sole reality of things, to which all predicates refer [Nietzsche] |
| 23197 | Memory is essential, and is only possible by means of abbreviation signs [Nietzsche] |
| 23206 | Schematic minds think thoughts are truer if they slot into a scheme [Nietzsche] |
| 23209 | Each of our personal drives has its own perspective [Nietzsche] |
| 23184 | The mind is a simplifying apparatus [Nietzsche] |
| 23190 | Consciousness is our awareness of our own mental life [Nietzsche] |
| 23191 | Minds have an excluding drive to scare things off, and a selecting one to filter facts [Nietzsche] |
| 23213 | The greatest drive of life is to discharge strength, rather than preservation [Nietzsche] |
| 23210 | That all events are necessary does not mean they are compelled [Nietzsche] |
| 23192 | Concepts don’t match one thing, but many things a little bit [Nietzsche] |
| 23189 | Concepts are rough groups of simultaneous sensations [Nietzsche] |
| 23187 | Whatever their origin, concepts survive by being useful [Nietzsche] |
| 23205 | Thought starts as ambiguity, in need of interpretation and narrowing [Nietzsche] |
| 23198 | Aesthetics can be more basic than morality, in our pleasure in certain patterns of experience [Nietzsche] |
| 21233 | The beautiful is whatever it is intrinsically good to admire [Moore,GE] |
| 8039 | Moore tries to show that 'good' is indefinable, but doesn't understand what a definition is [MacIntyre on Moore,GE] |
| 11056 | The naturalistic fallacy claims that natural qualties can define 'good' [Moore,GE] |
| 22151 | The Open Question argument leads to anti-realism and the fact-value distinction [Boulter on Moore,GE] |
| 8033 | Moore cannot show why something being good gives us a reason for action [MacIntyre on Moore,GE] |
| 8032 | Can learning to recognise a good friend help us to recognise a good watch? [MacIntyre on Moore,GE] |
| 11050 | Moore's combination of antinaturalism with strong supervenience on the natural is incoherent [Hanna on Moore,GE] |
| 23726 | Despite Moore's caution, non-naturalists incline towards intuitionism [Moore,GE, by Smith,M] |
| 23208 | Caesar and Napoleon point to the future, when they pursue their task regardless of human sacrifice [Nietzsche] |
| 23193 | Napoleon was very focused, and rightly ignored compassion [Nietzsche] |
| 18676 | We should ask what we would judge to be good if it existed in absolute isolation [Moore,GE] |
| 11057 | It is always an open question whether anything that is natural is good [Moore,GE] |
| 5925 | The three main values are good, right and beauty [Moore,GE, by Ross] |
| 5902 | For Moore, 'right' is what produces good [Moore,GE, by Ross] |
| 5903 | 'Right' means 'cause of good result' (hence 'useful'), so the end does justify the means [Moore,GE] |
| 5907 | Relationships imply duties to people, not merely the obligation to benefit them [Ross on Moore,GE] |
| 23214 | For the strongest people, nihilism gives you wings! [Nietzsche] |
| 23203 | The great question is approaching, of how to govern the earth as a whole [Nietzsche] |
| 23200 | The controlling morality of aristocracy is the desire to resemble their ancestors [Nietzsche] |
| 23194 | People feel united as a nation by one language, but then want a common ancestry and history [Nietzsche] |
| 23204 | To be someone you need property, and wanting more is healthy [Nietzsche] |
| 23195 | Laws of nature are actually formulas of power relations [Nietzsche] |
| 23185 | In chemistry every substance pushes, and thus creates new substances [Nietzsche] |