107 ideas
6779 | Instrumentalists say distinctions between observation and theory vanish with ostensive definition [Bird] |
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] |
13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [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] |
13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
13680 | Maybe logical consequence is a primitive notion [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] |
13688 | Good axioms should be indisputable logical truths [Sider] |
13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [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] |
6780 | Anti-realism is more plausible about laws than about entities and theories [Bird] |
13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [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] |
6796 | Subjective probability measures personal beliefs; objective probability measures the chance of an event happening [Bird] |
6797 | Objective probability of tails measures the bias of the coin, not our beliefs about it [Bird] |
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] |
6800 | Many philosophers rate justification as a more important concept than knowledge [Bird] |
6786 | As science investigates more phenomena, the theories it needs decreases [Bird] |
6792 | If theories need observation, and observations need theories, how do we start? [Bird] |
6757 | Explanation predicts after the event; prediction explains before the event [Bird] |
6805 | Relativity ousted Newtonian mechanics despite a loss of simplicity [Bird] |
6777 | Realists say their theories involve truth and the existence of their phenomena [Bird] |
6804 | There is no agreement on scientific method - because there is no such thing [Bird] |
6778 | Instrumentalists regard theories as tools for prediction, with truth being irrelevant [Bird] |
6775 | Induction is inference to the best explanation, where the explanation is a law [Bird] |
6791 | If Hume is right about induction, there is no scientific knowledge [Bird] |
6790 | Anything justifying inferences from observed to unobserved must itself do that [Bird] |
6738 | Any conclusion can be drawn from an induction, if we use grue-like predicates [Bird] |
6739 | Several months of observing beech trees supports the deciduous and evergreen hypotheses [Bird] |
6799 | We normally learn natural kinds from laws, but Goodman shows laws require prior natural kinds [Bird] |
6798 | Bayesianism claims to find rationality and truth in induction, and show how science works [Bird] |
6752 | The objective component of explanations is the things that must exist for the explanation [Bird] |
6754 | We talk both of 'people' explaining things, and of 'facts' explaining things [Bird] |
6750 | Explanations are causal, nomic, psychological, psychoanalytic, Darwinian or functional [Bird] |
6761 | Contrastive explanations say why one thing happened but not another [Bird] |
6758 | 'Covering law' explanations only work if no other explanations are to be found [Bird] |
6759 | Livers always accompany hearts, but they don't explain hearts [Bird] |
6756 | Probabilistic-statistical explanations don't entail the explanandum, but makes it more likely [Bird] |
6760 | An operation might reduce the probability of death, yet explain a death [Bird] |
6785 | Inference to the Best Explanation is done with facts, so it has to be realist [Bird] |
6788 | Maybe bad explanations are the true ones, in this messy world [Bird] |
6787 | Which explanation is 'best' is bound to be subjective, and no guide to truth [Bird] |
6751 | Maybe explanation is so subjective that it cannot be a part of science [Bird] |
6776 | Natural kinds are those that we use in induction [Bird] |
6767 | Rubies and sapphires are both corundum, with traces of metals varying their colours [Bird] |
6768 | Tin is not one natural kind, but appears to be 21, depending on isotope [Bird] |
6770 | Membership of a purely random collection cannot be used as an explanation [Bird] |
6771 | Natural kinds may overlap, or be sub-kinds of one another [Bird] |
6773 | If F is a universal appearing in a natural law, then Fs form a natural kind [Bird] |
6769 | In the Kripke-Putnam view only nuclear physicists can know natural kinds [Bird] |
6774 | Darwinism suggests that we should have a native ability to detect natural kinds [Bird] |
6764 | Nominal essence of a natural kind is the features that make it fit its name [Bird] |
6766 | Jadeite and nephrite are superficially identical, but have different composition [Bird] |
6808 | Reference to scientific terms is by explanatory role, not by descriptions [Bird] |
6753 | Laws are more fundamental in science than causes, and laws will explain causes [Bird] |
6762 | Newton's laws cannot be confirmed individually, but only in combinations [Bird] |
6763 | Parapsychology is mere speculation, because it offers no mechanisms for its working [Bird] |
6772 | Existence requires laws, as inertia or gravity are needed for mass or matter [Bird] |
6740 | 'All uranium lumps are small' is a law, but 'all gold lumps are small' is not [Bird] |
6741 | There can be remarkable uniformities in nature that are purely coincidental [Bird] |
6742 | A law might have no instances, if it was about things that only exist momentarily [Bird] |
6743 | If laws are just instances, the law should either have gaps, or join the instances arbitrarily [Bird] |
6744 | Where is the regularity in a law predicting nuclear decay? [Bird] |
6747 | Laws cannot explain instances if they are regularities, as something can't explain itself [Bird] |
6746 | There may be many laws, each with only a few instances [Bird] |
6748 | Similar appearance of siblings is a regularity, but shared parents is what links them [Bird] |
6749 | We can only infer a true regularity if something binds the instances together [Bird] |
6803 | If we only infer laws from regularities among observations, we can't infer unobservable entities. [Bird] |
6801 | Accidental regularities are not laws, and an apparent regularity may not be actual [Bird] |
6745 | A regularity is only a law if it is part of a complete system which is simple and strong [Bird] |
6802 | With strange enough predicates, anything could be made out to be a regularity [Bird] |
6789 | If flame colour is characteristic of a metal, that is an empirical claim needing justification [Bird] |
6807 | In Newton mass is conserved, but in Einstein it can convert into energy [Bird] |
1558 | Clearly the gods ignore human affairs, or they would have given us justice [Thrasymachus] |