9218 | Maybe what distinguishes philosophy from science is its pursuit of necessary truths |

14721 | Metaphysical enquiry can survive if its conclusions are tentative |

15010 | Your metaphysics is 'cheating' if your ontology won't support the beliefs you accept |

14977 | Metaphysics is not about what exists or is true or essential; it is about the structure of reality |

14994 | Extreme doubts about metaphysics also threaten to undermine the science of unobservables |

15003 | It seems unlikely that the way we speak will give insights into the universe |

14986 | Conceptual analysts trust particular intuitions much more than general ones |

14981 | Philosophical concepts are rarely defined, and are not understood by means of definitions |

15015 | It seems possible for a correct definition to be factually incorrect, as in defining 'contact' |

14992 | We don't care about plain truth, but truth in joint-carving terms |

15012 | Orthodox truthmaker theories make entities fundamental, but that is poor for explanation |

13689 | 'Theorems' are formulas provable from no premises at all |

13705 | Truth tables assume truth functionality, and are just pictures of truth functions |

13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial |

13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary |

13711 | System B introduces iterated modalities |

13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid |

13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) |

13714 | We can treat modal worlds as different times |

13723 | System B is needed to prove the Barcan Formula |

13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic |

13720 | Converse Barcan Formula: □∀αφ→∀α□φ |

15023 | The Barcan schema implies if X might have fathered something, there is something X might have fathered |

13715 | You can employ intuitionist logic without intuitionism about mathematics |

15004 | 'Gunk' is an object in which proper parts all endlessly have further proper parts |

14984 | Which should be primitive in mereology - part, or overlap? |

14980 | There is a real issue over what is the 'correct' logic |

15000 | 'It is raining' and 'it is not raining' can't be legislated, so we can't legislate 'p or ¬p' |

15020 | Classical logic is good for mathematics and science, but less good for natural language |

13678 | The most popular account of logical consequence is the semantic or model-theoretic one |

13679 | Maybe logical consequence is more a matter of provability than of truth-preservation |

13680 | Maybe logical consequence is a primitive notion |

13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false |

15029 | Modal accounts of logical consequence are simple necessity, or essential use of logical words |

13722 | A 'theorem' is an axiom, or the last line of a legitimate proof |

15019 | Define logical constants by role in proofs, or as fixed in meaning, or as topic-neutral |

13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity |

13700 | A 'total' function must always produce an output for a given domain |

13703 | λ can treat 'is cold and hungry' as a single predicate |

13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio |

13688 | Good axioms should be indisputable logical truths |

13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' |

13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms |

13685 | Natural deduction helpfully allows reasoning with assumptions |

15001 | 'Tonk' is supposed to follow the elimination and introduction rules, but it can't be so interpreted |

13686 | We can build proofs just from conclusions, rather than from plain formulae |

13697 | Valuations in PC assign truth values to formulas relative to variable assignments |

13684 | The semantical notion of a logical truth is validity, being true in all interpretations |

13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators |

13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation |

13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences |

13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite |

13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically |

14760 | Four-dimensionalism sees things and processes as belonging in the same category |

15017 | Supervenience is a modal connection |

15008 | Is fundamentality in whole propositions (and holistic), or in concepts (and atomic)? |

15013 | Tables and chairs have fundamental existence, but not fundamental natures |

15014 | Unlike things, stuff obeys unrestricted composition and mereological essentialism |

15009 | We must distinguish 'concrete' from 'abstract' and necessary states of affairs. |

13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator |

13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings |

13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation |

13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification |

14983 | Accept the ontology of your best theory - and also that it carves nature at the joints |

13683 | A relation is a feature of multiple objects taken together |

14978 | A property is intrinsic if an object alone in the world can instantiate it |

14194 | Proper ontology should only use categorical (actual) properties, not hypothetical ones |

14995 | Predicates can be 'sparse' if there is a universal, or if there is a natural property or relation |

14745 | If sortal terms fix the kind and the persistence conditions, we need to know what kinds there are |

14740 | If Tib is all of Tibbles bar her tail, when Tibbles loses her tail, two different things become one |

14752 | Artists 'create' statues because they are essentially statues, and so lack identity with the lump of clay |

14743 | The stage view of objects is best for dealing with coincident entities |

14747 | 'Composition as identity' says that an object just is the objects which compose it |

14757 | Mereological essentialism says an object's parts are necessary for its existence |

15026 | Essence (even if nonmodal) is not fundamental in metaphysics |

14727 | Three-dimensionalists assert 'enduring', being wholly present at each moment, and deny 'temporal parts' |

14738 | Some might say that its inconsistency with time travel is a reason to favour three-dimensionalism |

14726 | Four-dimensionalists assert 'temporal parts', 'perduring', and being spread out over time |

14729 | 4D says each spatiotemporal object must have a temporal part at every moment at which it exists |

14728 | 4D says intrinsic change is difference between successive parts |

14731 | Temporal parts are instantaneous |

14758 | How can an instantaneous stage believe anything, if beliefs take time? |

14730 | Temporal parts exist, but are not prior building blocks for objects |

14762 | Four-dimensionalism says temporal parts are caused (through laws of motion) by previous temporal parts |

14741 | The ship undergoes 'asymmetric' fission, where one candidate is seen as stronger |

13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property |

14754 | If you say Leibniz's Law doesn't apply to 'timebound' properties, you are no longer discussing identity |

13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist |

13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible |

13709 | Logical truths must be necessary if anything is |

13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true |

15030 | Humeans say that we decide what is necessary |

15031 | Modal terms in English are entirely contextual, with no modality outside the language |

15028 | Conventionalism doesn't seem to apply to examples of the necessary a posteriori |

15027 | If truths are necessary 'by convention', that seems to make them contingent |

15033 | Humeans says mathematics and logic are necessary because that is how our concept of necessity works |

15025 | The world does not contain necessity and possibility - merely how things are |

13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual |

14763 | Counterparts rest on similarity, so there are many such relations in different contexts |

13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost |

14988 | A theory which doesn't fit nature is unexplanatory, even if it is true |

14982 | If I used ramsey sentences to eliminate fundamentality from my theory, that would be a real loss |

14989 | Problem predicates in induction don't reflect the structure of nature |

14997 | Two applications of 'grue' do not guarantee a similarity between two things |

14990 | Bayes produces weird results if the prior probabilities are bizarre |

15005 | Explanations must cite generalisations |

15011 | If the ultimate explanation is a list of entities, no laws, patterns or mechanisms can be cited |

15018 | Intentionality is too superficial to appear in the catalogue of ultimate physics |

14999 | Prior to conventions, not all green things were green? |

14739 | 'Water' is two-dimensionally inconstant, with different intensions in different worlds |

14998 | Conventions are contingent and analytic truths are necessary, so that isn't their explanation |

15016 | Analyticity has lost its traditional role, which relied on truth by convention |

14991 | Space has real betweenness and congruence structure (though it is not the Euclidean concepts) |

15021 | The central question in the philosophy of time is: How alike are time and space? |

14723 | Talk using tenses can be eliminated, by reducing it to indexical connections for an utterance |

14734 | The B-series involves eternalism, and the reduction of tense |

14736 | The B-theory is adequate, except that it omits to say which time is present |

14724 | Presentists must deny truths about multiple times |

14756 | For Presentists there must always be a temporal vantage point for any description |

15024 | The spotlight theorists accepts eternal time, but with a spotlight of the present moving across it |

14722 | Between presentism and eternalism is the 'growing block' view - the past is real, the future is not |

14735 | Space is 3D and lacks a direction; time seems connected to causation |

14985 | The notion of law doesn't seem to enhance physical theories |

14987 | Many of the key theories of modern physics do not appear to be 'laws' |

14725 | Maybe motion is a dynamical quantity intrinsic to a thing at a particular time |