108 ideas
| 16604 | Philosophy consists of choosing between Plato, Aristotle and Democritus [Pasnau] |
| 16606 | Original philosophers invariably seek inspiration from past thinkers [Pasnau] |
| 16586 | The commentaries of Averroes were the leading guide to Aristotle [Pasnau] |
| 16568 | Modernity begins in the late 12th century, with Averroes's commentaries on Aristotle [Pasnau] |
| 16653 | Once accidents were seen as real, 'Categories' became the major text for ontology [Pasnau] |
| 16704 | In 1347, the Church effectively stopped philosophy for the next 300 years [Pasnau] |
| 16605 | After c.1450 all of Plato was available. Before that, only the first half of 'Timaeus' was known [Pasnau] |
| 16607 | Renaissance Platonism is peripheral [Pasnau] |
| 16715 | Plato only made an impact locally in 15th century Italy [Pasnau] |
| 16610 | Philosophy could easily have died in 17th century, if it weren't for Descartes [Pasnau] |
| 16781 | The 17th century is a metaphysical train wreck [Pasnau] |
| 8251 | The logical space of reasons is a natural phenomenon, and it is the realm of freedom [McDowell] |
| 16677 | Anti-Razor: if you can't account for a truth, keep positing things until you can [Pasnau] |
| 13634 | Satisfaction is 'truth in a model', which is a model of 'truth' [Shapiro] |
| 13643 | Aristotelian logic is complete [Shapiro] |
| 13651 | A set is 'transitive' if contains every member of each of its members [Shapiro] |
| 13647 | Choice is essential for proving downward Löwenheim-Skolem [Shapiro] |
| 13631 | Are sets part of logic, or part of mathematics? [Shapiro] |
| 13654 | It is central to the iterative conception that membership is well-founded, with no infinite descending chains [Shapiro] |
| 13640 | Russell's paradox shows that there are classes which are not iterative sets [Shapiro] |
| 13666 | Iterative sets are not Boolean; the complement of an iterative set is not an iterative sets [Shapiro] |
| 13653 | 'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element [Shapiro] |
| 13627 | There is no 'correct' logic for natural languages [Shapiro] |
| 13642 | Logic is the ideal for learning new propositions on the basis of others [Shapiro] |
| 13668 | Bernays (1918) formulated and proved the completeness of propositional logic [Shapiro] |
| 13669 | Can one develop set theory first, then derive numbers, or are numbers more basic? [Shapiro] |
| 13667 | Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order [Shapiro] |
| 13662 | First-order logic was an afterthought in the development of modern logic [Shapiro] |
| 13624 | The 'triumph' of first-order logic may be related to logicism and the Hilbert programme, which failed [Shapiro] |
| 13660 | Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable [Shapiro] |
| 13673 | The notion of finitude is actually built into first-order languages [Shapiro] |
| 15944 | Second-order logic is better than set theory, since it only adds relations and operations, and nothing else [Shapiro, by Lavine] |
| 13629 | Broad standard semantics, or Henkin semantics with a subclass, or many-sorted first-order semantics? [Shapiro] |
| 13650 | Henkin semantics has separate variables ranging over the relations and over the functions [Shapiro] |
| 13645 | In standard semantics for second-order logic, a single domain fixes the ranges for the variables [Shapiro] |
| 13649 | Completeness, Compactness and Löwenheim-Skolem fail in second-order standard semantics [Shapiro] |
| 13626 | Semantic consequence is ineffective in second-order logic [Shapiro] |
| 13637 | If a logic is incomplete, its semantic consequence relation is not effective [Shapiro] |
| 13632 | Finding the logical form of a sentence is difficult, and there are no criteria of correctness [Shapiro] |
| 13674 | We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models [Shapiro] |
| 13633 | 'Satisfaction' is a function from models, assignments, and formulas to {true,false} [Shapiro] |
| 13644 | Semantics for models uses set-theory [Shapiro] |
| 13636 | An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation [Shapiro] |
| 13670 | Categoricity can't be reached in a first-order language [Shapiro] |
| 13658 | Downward Löwenheim-Skolem: each satisfiable countable set always has countable models [Shapiro] |
| 13659 | Upward Löwenheim-Skolem: each infinite model has infinite models of all sizes [Shapiro] |
| 13648 | The Löwenheim-Skolem theorems show an explosion of infinite models, so 1st-order is useless for infinity [Shapiro] |
| 13675 | Substitutional semantics only has countably many terms, so Upward Löwenheim-Skolem trivially fails [Shapiro] |
| 13635 | 'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence [Shapiro] |
| 13628 | We can live well without completeness in logic [Shapiro] |
| 13630 | Non-compactness is a strength of second-order logic, enabling characterisation of infinite structures [Shapiro] |
| 13646 | Compactness is derived from soundness and completeness [Shapiro] |
| 13661 | A language is 'semantically effective' if its logical truths are recursively enumerable [Shapiro] |
| 13641 | Complex numbers can be defined as reals, which are defined as rationals, then integers, then naturals [Shapiro] |
| 13676 | Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro] |
| 13677 | Natural numbers are the finite ordinals, and integers are equivalence classes of pairs of finite ordinals [Shapiro] |
| 13652 | The 'continuum' is the cardinality of the powerset of a denumerably infinite set [Shapiro] |
| 13657 | First-order arithmetic can't even represent basic number theory [Shapiro] |
| 13656 | Some sets of natural numbers are definable in set-theory but not in arithmetic [Shapiro] |
| 13664 | Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro] |
| 13625 | Mathematics and logic have no border, and logic must involve mathematics and its ontology [Shapiro] |
| 13663 | Some reject formal properties if they are not defined, or defined impredicatively [Shapiro] |
| 16598 | Priority was a major topic of dispute for scholastics [Pasnau] |
| 16727 | In mixtures, the four elements ceased to exist, replaced by a mixed body with a form [Pasnau] |
| 16732 | 17th C qualities are either microphysical, or phenomenal, or powers [Pasnau] |
| 16733 | 17th century authors only recognised categorical properties, never dispositions [Pasnau] |
| 16662 | The biggest question for scholastics is whether properties are real, or modes of substances [Pasnau] |
| 13638 | Properties are often seen as intensional; equiangular and equilateral are different, despite identity of objects [Shapiro] |
| 16767 | There is no centralised power, but we still need essence for a metaphysical understanding [Pasnau] |
| 16788 | Instead of adding Aristotelian forms to physical stuff, one could add dispositions [Pasnau] |
| 16738 | Scholastics reject dispositions, because they are not actual, as forms require [Pasnau] |
| 16649 | Scholastics say there is a genuine thing if it is 'separable' [Pasnau] |
| 16785 | If you reject essences, questions of individuation become extremely difficult [Pasnau] |
| 16680 | Scholastics thought Quantity could be the principle of individuation [Pasnau] |
| 16628 | Corpuscularianism promised a decent account of substance [Pasnau] |
| 16617 | Corpuscularian critics of scholasticism say only substances exist [Pasnau] |
| 16741 | Scholastics wanted to treat Aristotelianism as physics, rather than as metaphysics [Pasnau] |
| 16777 | If crowds are things at all, they seem to be Substances, since they bear properties [Pasnau] |
| 16615 | Scholastics use 'substantia' for thick concrete entities, and for thin metaphysical ones [Pasnau] |
| 16775 | For corpuscularians, a substance is just its integral parts [Pasnau] |
| 16769 | If clay survives destruction of the statue, the statue wasn't a substance, but a mere accident [Pasnau] |
| 16602 | Corpuscularianism rejected not only form, but also the dependence of matter on form [Pasnau] |
| 16612 | Hylomorphism may not be a rival to science, but an abstract account of unity and endurance [Pasnau] |
| 16613 | Hylomorphism declined because scholastics made it into a testable physical theory [Pasnau] |
| 16747 | Scholastics made forms substantial, in a way unintended by Aristotle [Pasnau] |
| 16759 | Scholastics began to see substantial form more as Aristotle's 'efficient' cause [Pasnau] |
| 16748 | Aquinas says a substance has one form; Scotists say it has many forms [Pasnau] |
| 16671 | Scholastic Quantity either gives a body parts, or spreads them out in a unified way [Pasnau] |
| 16579 | There may be different types of substrate, or temporary substrates [Pasnau] |
| 16596 | A substratum can't be 'bare', because it has a job to do [Pasnau] |
| 16584 | If a substrate gives causal support for change, quite a lot of the ingredients must endure [Pasnau] |
| 16580 | A substrate may be 'prime matter', which endures through every change [Pasnau] |
| 16749 | Aristotelians deny that all necessary properties are essential [Pasnau] |
| 16694 | Typical successive things are time and motion [Pasnau] |
| 16583 | Weak ex nihilo says it all comes from something; strong version says the old must partly endure [Pasnau] |
| 8128 | Representation must be propositional if it can give reasons and be epistemological [McDowell, by Burge] |
| 19092 | There is no pure Given, but it is cultured, rather than entirely relative [McDowell, by Macbeth] |
| 8253 | Sense impressions already have conceptual content [McDowell] |
| 16783 | Essences must explain, so we can infer them causally from the accidents [Pasnau] |
| 8254 | Forming concepts by abstraction from the Given is private definition, which the Private Lang. Arg. attacks [McDowell] |
| 16609 | Atomists say causation is mechanical collisions, and all true qualities are microscopic [Pasnau] |
| 16603 | In the 17th C matter became body, and was then studied by science [Pasnau] |
| 16592 | Atomism is the commonest version of corpuscularianism, but isn't required by it [Pasnau] |
| 16750 | If there are just arrangements of corpuscles, where are the boundaries between substances? [Pasnau] |
| 16722 | Scholastic causation is by changes in the primary qualities of hot, cold, wet, dry [Pasnau] |
| 16760 | Substantial forms were a step towards scientific essentialism [Pasnau] |
| 16581 | Scholastic authors agree that matter was created by God, out of nothing [Pasnau] |
| 16642 | Transubstantion says accidents of bread and wine don't inhere in the substance [Pasnau] |