83 ideas
16841 | Good inference has mechanism, precision, scope, simplicity, fertility and background fit [Lipton] |
16854 | Contrary pairs entail contradictions; one member entails negation of the other [Lipton] |
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] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
16814 | Understanding is not mysterious - it is just more knowledge, of causes [Lipton] |
16825 | How do we distinguish negative from irrelevant evidence, if both match the hypothesis? [Lipton] |
16851 | The inference to observables and unobservables is almost the same, so why distinguish them? [Lipton] |
16798 | We infer from evidence by working out what would explain that evidence [Lipton] |
16799 | Inductive inference is not proof, but weighing evidence and probability [Lipton] |
16856 | It is more impressive that relativity predicted Mercury's orbit than if it had accommodated it [Lipton] |
16857 | Predictions are best for finding explanations, because mere accommodations can be fudged [Lipton] |
16827 | If we make a hypothesis about data, then a deduction, where does the hypothesis come from? [Lipton] |
16804 | Induction is repetition, instances, deduction, probability or causation [Lipton] |
16823 | Standard induction does not allow for vertical inferences, to some unobservable lower level [Lipton] |
16858 | We can argue to support our beliefs, so induction will support induction, for believers in induction [Lipton] |
16800 | An inductive inference is underdetermined, by definition [Lipton] |
16832 | If something in ravens makes them black, it may be essential (definitive of ravens) [Lipton] |
16836 | My shoes are not white because they lack some black essence of ravens [Lipton] |
16831 | A theory may explain the blackness of a raven, but say nothing about the whiteness of shoes [Lipton] |
16833 | We can't turn non-black non-ravens into ravens, to test the theory [Lipton] |
16834 | To pick a suitable contrast to ravens, we need a hypothesis about their genes [Lipton] |
16801 | A hypothesis is confirmed if an unlikely prediction comes true [Lipton] |
16802 | Bayes seems to rule out prior evidence, since that has a probability of one [Lipton] |
16803 | Bayes is too liberal, since any logical consequence of a hypothesis confirms it [Lipton] |
16837 | Bayes involves 'prior' probabilities, 'likelihood', 'posterior' probability, and 'conditionalising' [Lipton] |
16839 | Explanation may be an important part of implementing Bayes's Theorem [Lipton] |
16850 | Explanation may describe induction, but may not show how it justifies, or leads to truth [Lipton] |
16807 | An explanation gives the reason the phenomenon occurred [Lipton] |
16808 | An explanation is what makes the unfamiliar familiar to us [Lipton] |
16806 | An explanation is what is added to knowledge to yield understanding [Lipton] |
16822 | Seaching for explanations is a good way to discover the structure of the world [Lipton] |
16816 | In 'contrastive' explanation there is a fact and a foil - why that fact, rather than this foil? [Lipton] |
16826 | With too many causes, find a suitable 'foil' for contrast, and the field narrows right down [Lipton] |
16811 | An explanation unifies a phenomenon with our account of other phenomena [Lipton] |
16810 | Deduction explanation is too easy; any law at all will imply the facts - together with the facts! [Lipton] |
16829 | We reject deductive explanations if they don't explain, not if the deduction is bad [Lipton] |
16809 | Good explanations may involve no laws and no deductions [Lipton] |
16812 | An explanation shows why it was necessary that the effect occurred [Lipton] |
16813 | To explain is to give either the causal history, or the causal mechanism [Lipton] |
16815 | Mathematical and philosophical explanations are not causal [Lipton] |
16846 | A cause may not be an explanation [Lipton] |
16849 | Explanations may be easier to find than causes [Lipton] |
16848 | Causal inferences are clearest when we can manipulate things [Lipton] |
16842 | We want to know not just the cause, but how the cause operated [Lipton] |
16840 | To maximise probability, don't go beyond your data [Lipton] |
16824 | Is Inference to the Best Explanation nothing more than inferring the likeliest cause? [Lipton] |
16817 | Best Explanation as a guide to inference is preferable to best standard explanations [Lipton] |
16818 | The 'likeliest' explanation is the best supported; the 'loveliest' gives the most understanding [Lipton] |
16820 | Finding the 'loveliest' potential explanation links truth to understanding [Lipton] |
16819 | IBE is inferring that the best potential explanation is the actual explanation [Lipton] |
16828 | IBE is not passive treatment of data, but involves feedback between theory and data search [Lipton] |
16844 | A contrasting difference is the cause if it offers the best explanation [Lipton] |
16853 | We select possible explanations for explanatory reasons, as well as choosing among them [Lipton] |
16821 | Must we only have one explanation, and must all the data be made relevant? [Lipton] |
16838 | Bayesians say best explanations build up an incoherent overall position [Lipton] |
16855 | The best theory is boring: compare 'all planets move elliptically' with 'most of them do' [Lipton] |
16852 | Best explanation can't be a guide to truth, because the truth must precede explanation [Lipton] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
15998 | Perfect love is not in spite of imperfections; the imperfections must be loved as well [Kierkegaard] |
16847 | Counterfactual causation makes causes necessary but not sufficient [Lipton] |