83 ideas
| 14027 | If we are to use words in enquiry, we need their main, unambiguous and uncontested meanings [Epicurus] |
| 14001 | People who use science to make philosophical points don't realise how philosophical science is [Markosian] |
| 14040 | Observation and applied thought are always true [Epicurus] |
| 13991 | Presentism has the problem that if Socrates ceases to exist, so do propositions about him [Markosian] |
| 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] |
| 14028 | Nothing comes to be from what doesn't exist [Epicurus] |
| 14029 | If disappearing things went to nothingness, nothing could return, and it would all be gone by now [Epicurus] |
| 14030 | The totality is complete, so there is no room for it to change, and nothing extraneous to change it [Epicurus] |
| 14048 | Astronomical movements are blessed, but they don't need the help of the gods [Epicurus] |
| 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] |
| 14044 | The perceived accidental properties of bodies cannot be conceived of as independent natures [Epicurus] |
| 14045 | Accidental properties give a body its nature, but are not themselves bodies or parts of bodies [Epicurus] |
| 14046 | A 'body' is a conception of an aggregate, with properties defined by application conditions [Epicurus] |
| 14047 | Bodies have impermanent properties, and permanent ones which define its conceived nature [Epicurus] |
| 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] |
| 14039 | Above and below us will never appear to be the same, because it is inconceivable [Epicurus] |
| 14002 | Possible worlds must be abstract, because two qualitatively identical worlds are just one world [Markosian] |
| 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] |
| 14050 | We aim to dissolve our fears, by understanding their causes [Epicurus] |
| 14037 | Atoms only have shape, weight and size, and the properties which accompany shape [Epicurus] |
| 6010 | Illusions are not false perceptions, as we accurately perceive the pattern of atoms [Epicurus, by Modrak] |
| 14041 | The soul is fine parts distributed through the body, resembling hot breath [Epicurus] |
| 14042 | The soul cannot be incorporeal, because then it could neither act nor be acted upon [Epicurus] |
| 14000 | 'Grabby' truth conditions first select their object, unlike 'searchy' truth conditions [Markosian] |
| 14032 | Totality has no edge; an edge implies a contrast beyond the edge, and there can't be one [Epicurus] |
| 14033 | Bodies are unlimited as well as void, since the two necessarily go together [Epicurus] |
| 14034 | There exists an infinity of each shape of atom, but the number of shapes is beyond our knowledge [Epicurus] |
| 14035 | Atoms just have shape, size and weight; colour results from their arrangement [Epicurus] |
| 14038 | There cannot be unlimited division, because it would reduce things to non-existence [Epicurus] |
| 14049 | We aim to know the natures which are observed in natural phenomena [Epicurus] |
| 14043 | The void cannot interact, but just gives the possibility of motion [Epicurus] |
| 14031 | Space must exist, since movement is obvious, and there must be somewhere to move in [Epicurus] |
| 13990 | Presentism is the view that only present objects exist [Markosian] |
| 13992 | Presentism says if objects don't exist now, we can't have attitudes to them or relations with them [Markosian] |
| 13994 | Presentism seems to entail that we cannot talk about other times [Markosian] |
| 13995 | Serious Presentism says things must exist to have relations and properties; Unrestricted version denies this [Markosian] |
| 13996 | Maybe Presentists can refer to the haecceity of a thing, after the thing itself disappears [Markosian] |
| 13997 | Maybe Presentists can paraphrase singular propositions about the past [Markosian] |
| 13993 | Special Relativity denies the absolute present which Presentism needs [Markosian] |
| 13998 | Objects in the past, like Socrates, are more like imaginary objects than like remote spatial objects [Markosian] |
| 13999 | People are mistaken when they think 'Socrates was a philosopher' says something [Markosian] |
| 14036 | There are endless cosmoi, some like and some unlike this one [Epicurus] |