89 ideas
6779 | Instrumentalists say distinctions between observation and theory vanish with ostensive definition [Bird] |
18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
18182 | The extension of concepts is not important to me [Maddy] |
18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
6780 | Anti-realism is more plausible about laws than about entities and theories [Bird] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
579 | Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle] |
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] |
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] |
578 | Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle] |
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] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
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] |
6771 | Natural kinds may overlap, or be sub-kinds of one another [Bird] |
6770 | Membership of a purely random collection cannot be used as an explanation [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] |
6746 | There may be many laws, each with only a few instances [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] |
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] |