105 ideas
| 16606 | Original philosophers invariably seek inspiration from past thinkers [Pasnau] |
| Full Idea: Philosophers almost never strike out on wholly new ground, without the historical inspiration of some figure or other. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 05.1) |
| 16604 | Philosophy consists of choosing between Plato, Aristotle and Democritus [Pasnau] |
| Full Idea: The history of philosophy consists in a series of choices between three primordial rivals: Plato, Aristotle and Democritus. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 05.1) | |
| A reaction: Pasnau's point is that the importance of Democritus is not usually appreciated. As far as I can see, Democritus may have been the greatest of all philosophers, but most of his works are lost. His fragments are the best fragments. |
| 16586 | The commentaries of Averroes were the leading guide to Aristotle [Pasnau] |
| Full Idea: The commentaries of Averroes on virtually the whole Aristotelian corpus became by far the most important scholastic guide to the interpretation of Aristotle. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 03.1) |
| 16568 | Modernity begins in the late 12th century, with Averroes's commentaries on Aristotle [Pasnau] |
| Full Idea: I tend to think of modernity as coming in the late twelfth century, with Averroes's magisterial commentaries on Aristotle. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 1.1) | |
| A reaction: A rather quirky use of 'modernity', but this seems to be a huge landmark. Note that it comes from the Islamic Arab world, not from Europe. |
| 16653 | Once accidents were seen as real, 'Categories' became the major text for ontology [Pasnau] |
| Full Idea: Originally you count substances for ontology. Once there is the doctrine of real accidents (in the 14th cent) the list of ten categories begins to look like an inventory of the kinds of things there are, and 'Categories' looks like the fundamental text. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 12.1) | |
| A reaction: Prior to this development, 'Categories' was treated as a mere beginner's text, once the major corpus of Aristotle had been rediscovered in the 13th century. The result of this development is sortal essentialism, which I don't like. |
| 16704 | In 1347, the Church effectively stopped philosophy for the next 300 years [Pasnau] |
| Full Idea: The year 1347 is a great milestone in the history of philosophy, because then the route to modern philosophy was blocked by Church authorities, and effectively put on hold for almost 300 years. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 19.3) | |
| A reaction: It is interesting that it was 100 years after the Reformation before philosophy got going again, and then only thanks to one man. Islam stopped philosophy earlier. |
| 16605 | After c.1450 all of Plato was available. Before that, only the first half of 'Timaeus' was known [Pasnau] |
| Full Idea: From the mid-fifteenth century forward, for the first time, the whole Platonic corpus was available in Ficino's Latin translation. Before then, only the first half of the 'Timaeus' had widely circulated in Latin. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 05.1) |
| 16607 | Renaissance Platonism is peripheral [Pasnau] |
| Full Idea: The fabled phenomenon of Renaissance Platonism is peripheral. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 05.3) | |
| A reaction: The point is that only a few Italians pursued the Platonic line. Pasnau suggests Cartesian dualism as a possible influence from Plato. |
| 16715 | Plato only made an impact locally in 15th century Italy [Pasnau] |
| Full Idea: In certain limited circles in Italy, Plato made an impact in the fifteenth century, but his influence never came close to challenging Aristotle's. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 20.2) |
| 16781 | The 17th century is a metaphysical train wreck [Pasnau] |
| Full Idea: The seventeenth century is a metaphysical train wreck. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 26.6) | |
| A reaction: This is, roughly, because the corpuscularian philosophy lacked the resources to answer all the problems dealt with by substantial forms. |
| 16610 | Philosophy could easily have died in 17th century, if it weren't for Descartes [Pasnau] |
| Full Idea: As scholasticism collapsed in the 17th century, it might easily have happened is that philosophy simply died. That this did not happen is due in large part to René Descartes. …It is remarkable that this brilliant man insisted on still doing philosophy. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 05.5) | |
| A reaction: The alternative view is, of course, that you just can't stop people from thinking philosophically (except by totalitarian education). Are there philosophers in North Korea, or among the Taliban? |
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| Full Idea: We are all post-Kantians, ...because Kant set an agenda for philosophy that we are still working through. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Hart says that the main agenda is set by Kant's desire to defend the principle of sufficient reason against Hume's attack on causation. I would take it more generally to be the assessment of metaphysics, and of a priori knowledge. |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| Full Idea: The real monuments of philosophy are its problems. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Presumably he means '....rather than its solutions'. No other subject would be very happy with that sort of claim. Compare Idea 8243. A complaint against analytic philosophy is that it has achieved no consensus at all. |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| Full Idea: By now, no education in abstract pursuits is adequate without some familiarity with sets. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: A heart-sinking observation for those who aspire to study metaphysics and modality. The question is, what will count as 'some' familiarity? Are only professional logicians now allowed to be proper philosophers? |
| 16677 | Anti-Razor: if you can't account for a truth, keep positing things until you can [Pasnau] |
| Full Idea: The Anti-Razor says 'whenever an affirmative proposition is truly stated, if one thing does not suffice to account for its truth, then one must posit things, and if two do not suffice then three, and so on to infinity'. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 14.3) | |
| A reaction: This is quoted from an anonymous logic text of 1325. Apparently Ockham himself articulated the idea more than once. |
| 11178 | The essence or definition of an essence involves either a class of properties or a class of propositions [Fine,K] |
| Full Idea: If each object has a unique essence or definition, this may be identified with either the class of properties that it essentially has, or with the class of propositions that are true in virtue of what it is. | |
| From: Kit Fine (Senses of Essence [1995], §8) | |
| A reaction: Elsewhere Fine says that it is easier to work with the propositions view, but that the properties (or predicates) view is probably more fundamental. He goes on here to raise the question of whether either view makes the essence unique. |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| Full Idea: It is an ancient and honourable view that truth is correspondence to fact; Tarski showed us how to do without facts here. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This is a very interesting spin on Tarski, who certainly seems to endorse the correspondence theory, even while apparently inventing a new 'semantic' theory of truth. It is controversial how far Tarski's theory really is a 'correspondence' theory. |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| Full Idea: We explain truth for sentences in terms of satisfaction of formulae. The crux here is that for a sentence, either all sequences satisfy it or none do (with no middle ground). For formulae, some sequences may satisfy it and others not. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This is the hardest part of Tarski's theory of truth to grasp. |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| Full Idea: In any first-order language, there are infinitely many T-sentences. Since definitions should be finite, the agglomeration of all the T-sentences is not a definition of truth. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This may be a warning shot aimed at Davidson's extensive use of Tarski's formal account in his own views on meaning in natural language. |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| Full Idea: A 'conditional proof' licenses inferences to a conditional from a deduction of its consequent from its antecedent. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: That is, a proof can be enshrined in an arrow. |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| Full Idea: When a quantifier is attached to a variable, as in '∃(y)....', then it should be read as 'There exists an individual, call it y, such that....'. One should not read it as 'There exists a y such that...', which would attach predicate to quantifier. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: The point is to make clear that in classical logic the predicates attach to the objects, and not to some formal component like a quantifier. |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| Full Idea: It is set theory, and more specifically the theory of relations, that articulates order. | |
| From: William D. Hart (The Evolution of Logic [2010]) | |
| A reaction: It would seem that we mainly need set theory in order to talk accurately about order, and about infinity. The two come together in the study of the ordinal numbers. |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| Full Idea: The theory of types is a thing of the past. There is now nothing to choose between ZFC and NBG (Neumann-Bernays-Gödel). NF (Quine's) is a more specialized taste, but is a place to look if you want the universe. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| Full Idea: ∈ relates across layers (Plato is a member of his unit set and the set of people), while ⊆ relates within layers (the singleton of Plato is a subset of the set of people). This distinction only became clear in the 19th century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: Getting these two clear may be the most important distinction needed to understand how set theory works. |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| Full Idea: Without the empty set, disjoint sets would have no intersection, and we could not form a∩b without checking that a and b meet. This is an example of the utility of the empty set. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: A novice might plausibly ask why there should be an intersection for every pair of sets, if they have nothing in common except for containing this little puff of nothingness. But then what do novices know? |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| Full Idea: In the second half of the twentieth century there emerged the opinion that foundation is the heart of the way to do set theory. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: It is foundation which is the central axiom of the iterative conception of sets, where each level of sets is built on previous levels, and they are all 'well-founded'. |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| Full Idea: The usual statement of Foundation is that any nonempty set has a member disjoint from it. This phrasing is ordinal-free and closer to the primitives of ZFC. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| Full Idea: When a set is finite, we can prove it has a choice function (∀x x∈A → f(x)∈A), but we need an axiom when A is infinite and the members opaque. From infinite shoes we can pick a left one, but from socks we need the axiom of choice. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The socks example in from Russell 1919:126. |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| Full Idea: It follows from the Axiom of Choice that every set can be well-ordered. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: For 'well-ordered' see Idea 13460. Every set can be ordered with a least member. |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| Full Idea: It has been said (by Burt Dreben) that the only reason set theorists do not generally buy the view that V = L is that it would put them out of business by settling their open questions. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: Hart says V=L breaks with the interative conception of sets at level ω+1, which is countable is the constructible view, but has continuum many in the cumulative (iterative) hierarch. The constructible V=L view is anti-platonist. |
| 13441 | Naďve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| Full Idea: 'Comprehension' is the assumption that every predicate has an extension. Naďve set theory is the theory whose axioms are extensionality and comprehension, and comprehension is thought to be its naivety. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: This doesn't, of course, mean that there couldn't be a more modest version of comprehension. The notorious difficulty come with the discovery of self-referring predicates which can't possibly have extensions. |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| Full Idea: That the iterative sets suffice for most of ZFC does not show they are necessary, nor is it evident that the set of operations has no fixed points (as 0 is a fixed point for square-of), and no infinitely descending chains (like negative integers). | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: People don't seem to worry that they aren't 'necessary', and further measures are possible to block infinitely descending chains. |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| Full Idea: We say that a binary relation R 'partially orders' a field A just in case R is irreflexive (so that nothing bears R to itself) and transitive. When the set is {a,b}, its subsets {a} and {b} are incomparable in a partial ordering. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| Full Idea: A partial ordering is a 'total ordering' just in case any two members of its field are comparable, that is, either a is R to b, or b is R to a, or a is b. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: See Idea 13457 for 'partial ordering'. The three conditions are known as the 'trichotomy' condition. |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| Full Idea: One of the glories of Von Neumann's theory of numbers is to define α < β to mean that α ∈ β. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| Full Idea: A total order 'well-orders' its field just in case any nonempty subset B of its field has an R-least member, that is, there is a b in B such that for any a in B different from b, b bears R to a. So less-than well-orders natural numbers, but not integers. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The natural numbers have a starting point, but the integers are infinite in both directions. In plain English, an order is 'well-ordered' if there is a starting point. |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| Full Idea: Some have claimed that sets should be rethought in terms of still more basic things, categories. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: [He cites F.William Lawvere 1966] It appears to the the context of foundations for mathematics that he has in mind. |
| 11175 | Logical concepts rest on certain inferences, not on facts about implications [Fine,K] |
| Full Idea: The nature of the logical concepts is given, not by certain logical truths, but by certain logical inferences. What properly belongs to disjunction is the inference from p to (p or q), rather than the fact that p implies (p or q). | |
| From: Kit Fine (Senses of Essence [1995], §3) | |
| A reaction: Does this mean that Fine is wickedly starting with the psychology, rather than with the pure truth of the connection? Frege is shuddering. This view seems to imply that the truth table for 'or' is secondary. |
| 11176 | The property of Property Abstraction says any suitable condition must imply a property [Fine,K] |
| Full Idea: According to the principle of Property Abstraction, there is, for any suitable condition, a property that is possessed by an object just in case it conforms to the condition. This is usually taken to be a second-order logical truth. | |
| From: Kit Fine (Senses of Essence [1995], §4) | |
| A reaction: Fine objects that it is implied that if Socrates is essentially a man, then he essentially has the property of being a man. Like Fine, I think this conclusion is distasteful. A classification is not a property, at least the way most people use 'property'. |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| Full Idea: All the main set theories deny that there is a set of which everything is a member. No interpretation has a domain with everything in it. So the universal quantifier never gets to mean everything all at once; 'all' does not mean all. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: Could you have an 'uncompleted' universal set, in the spirit of uncompleted infinities? In ordinary English we can talk about 'absolutely everything' - we just can't define a set of everything. Must we 'define' our domain? |
| 11174 | A logical truth is true in virtue of the nature of the logical concepts [Fine,K] |
| Full Idea: One wants to define a logical truth as one that is true in virtue of the nature of the logical concepts. | |
| From: Kit Fine (Senses of Essence [1995], §3) | |
| A reaction: This is part of Fine's project to give a revised account of essence, which includes the essence of concepts as well as the essence of objects. Everyone should pay close attention to this project. |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| Full Idea: Models are ways the world might be from a first-order point of view. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| Full Idea: Modern model theory investigates which set theoretic structures are models for which collections of sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: So first you must choose your set theory (see Idea 13497). Then you presumably look at how to formalise sentences, and then look at the really tricky ones, many of which will involve various degrees of infinity. |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| Full Idea: There is no developed methematics of models for second-order theories, so for the most part, model theory is about models for first-order theories. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| Full Idea: The beginning of modern model theory was when Morley proved Los's Conjecture in 1962 - that a complete theory in a countable language categorical in one uncountable cardinal is categorical in all. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| Full Idea: First-order logic is 'compact', which means that any logical consequence of a set (finite or infinite) of first-order sentences is a logical consequence of a finite subset of those sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| Full Idea: Berry's Paradox: by the least number principle 'the least number denoted by no description of fewer than 79 letters' exists, but we just referred to it using a description of 77 letters. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: I struggle with this. If I refer to 'an object to which no human being could possibly refer', have I just referred to something? Graham Priest likes this sort of idea. |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| Full Idea: The Burali-Forti Paradox was a crisis for Cantor's theory of ordinal numbers. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| Full Idea: In effect, the machinery introduced to solve the liar can always be rejigged to yield another version the liar. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: [He cites Hans Herzberger 1980-81] The machinery is Tarski's device of only talking about sentences of a language by using a 'metalanguage'. |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| Full Idea: We can show (using the axiom of choice) that the less-than relation, <, well-orders the ordinals, ...and that it partially orders the ordinals, ...and that it totally orders the ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| Full Idea: Since we can map the transfinite ordinals one-one into the infinite cardinals, there are at least as many infinite cardinals as transfinite ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| Full Idea: The axiom of infinity with separation yields a least limit ordinal, which is called ω. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| Full Idea: It is easier to generalize von Neumann's finite ordinals into the transfinite. All Zermelo's nonzero finite ordinals are singletons, but if ω were a singleton it is hard to see how if could fail to be the successor of its member and so not a limit. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| Full Idea: The real numbers were not isolated from geometry until the arithmetization of analysis during the nineteenth century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| Full Idea: Mathematical induction is a way to establish truths about the infinity of natural numbers by a finite proof. | |
| From: William D. Hart (The Evolution of Logic [2010], 5) | |
| A reaction: If there are truths about infinities, it is very tempting to infer that the infinities must therefore 'exist'. A nice, and large, question in philosophy is whether there can be truths without corresponding implications of existence. |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| Full Idea: There is a familiar comparison between Euclid (unique parallel) and 'spherical' geometry (no parallel) and 'saddle' geometry (several parallels). | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| Full Idea: The thesis that no existence proposition is analytic is one of the few constants in philosophical consciences, but there are many existence claims in mathematics, such as the infinity of primes, five regular solids, and certain undecidable propositions. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 16598 | Priority was a major topic of dispute for scholastics [Pasnau] |
| Full Idea: For a scholastic author, hardly anything was so likely to precipitate a lengthy disputatio as talk of priority, in its various kinds. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 04.3) |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| Full Idea: Jespersen calls a noun a mass word when it has no plural, does not take numerical adjectives, and does not take 'fewer'. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: Jespersen was a great linguistics expert. |
| 16727 | In mixtures, the four elements ceased to exist, replaced by a mixed body with a form [Pasnau] |
| Full Idea: The standard view was that in a mixture there is only the mixed body and its substantial form (gold). There are no further substantial forms of the elements, because the elements do not actually exist within the body. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 22.3) | |
| A reaction: This seems to me to be the key idea that was overthrown in the seventeenth century, so that corpuscular matter kept aspects of its ingredients, which science could then investigate. With the substantial form, investigation seemed impossible. |
| 16732 | 17th C qualities are either microphysical, or phenomenal, or powers [Pasnau] |
| Full Idea: The seventeenth century is often said to have bequeathed us three ways of thinking about sensible qualities: either in reductive microphysical terms, or as internal phenomenal states, or else as powers or dispositions. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 23.1) | |
| A reaction: Pasnau goes on to claim that no one in the 17th century believed the third one. I take it to be a very new, and totally wonderful and correct, view. |
| 16733 | 17th century authors only recognised categorical properties, never dispositions [Pasnau] |
| Full Idea: In the seventeenth century, my claim is that authors during the period recognise only categorical properties, and never dispositional properties. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 23.1) |
| 16662 | The biggest question for scholastics is whether properties are real, or modes of substances [Pasnau] |
| Full Idea: Among scholastics the primary agreement is that what primarily exist are substances. The primary disagreement concerns the nature of their changeable properties. Are they real accidents, or mere modes of substance? | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 13.1) |
| 16767 | There is no centralised power, but we still need essence for a metaphysical understanding [Pasnau] |
| Full Idea: One could empirically reject a centralised power within a substance - and still think a genuine substance requires a form of some more abstract kind, not for a physical explanation, but for a full metaphysical understanding of how things are. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 25.2) | |
| A reaction: This divorce of the 'metaphysical' from the physical is a running theme in Pasnau, and he cites support from Leibniz. I'm not sure I understand 'metaphysical' understanding, if it is actually contrary to physics. I take it to be 'psychological'. |
| 16788 | Instead of adding Aristotelian forms to physical stuff, one could add dispositions [Pasnau] |
| Full Idea: Someone who wants to enrich a strict corpuscularian account with other metaphysical entities has alternatives other than Aristotelian hylomorphism. One can, for instance, introduce dispositions. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 28.2) | |
| A reaction: This slightly throws me, because I have been flirting with a dispositional account of hylomorphism. The implication is that the form is abstract and structural, where the disposition is real and physical. But dispositions can do the job of forms. |
| 16738 | Scholastics reject dispositions, because they are not actual, as forms require [Pasnau] |
| Full Idea: Scholastics reject anything like bare dispositions, on Aristotelian principles. Powers are forms, and forms actualise their subject, and are causally efficacious. Therefore no powers can be bare dispositions. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 23.5) | |
| A reaction: The point seems to be that a mere disposition is not actual, as a form is required to be. I would have thought that a power does not have to be operational to be actual. A live electric wire is a real phenomenon. It isn't waiting to be live. |
| 16649 | Scholastics say there is a genuine thing if it is 'separable' [Pasnau] |
| Full Idea: Among the scholastics (after Duns Scotus) it would be come to be taken for granted that the crucial test for being a genuine thing - a 'res' - is separability. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 11.2) | |
| A reaction: The idea of separability is implicit in Aristotle. In borderline cases, it seems that they are tempted to claim that things like accidental properties are separable, simply because they want them to be genuine things. A criterion for separability? |
| 16785 | If you reject essences, questions of individuation become extremely difficult [Pasnau] |
| Full Idea: Given the accepted linkage between a thing's essence and its identity, the rejection of essences makes a complete mess out of questions of individuation. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 27.6) | |
| A reaction: I note that he talks of a thing having 'identity', contra the view of identity as a two-place relation. I agree with this, but there is a chicken-egg problem. Do I perceive an identity and surmise an essence, or surmise an essence and deduce identity? |
| 16680 | Scholastics thought Quantity could be the principle of individuation [Pasnau] |
| Full Idea: Quantity was a leading scholastic contender for the principle of individuation. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 14.4) |
| 16628 | Corpuscularianism promised a decent account of substance [Pasnau] |
| Full Idea: One of the great attractions of corpuscularianism is that it promises to put our acquaintance with substances on a solid foundation. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 07.3) | |
| A reaction: This is why the seventeenth century did not abandon 'substance', even though they banished 'substantial form'. |
| 16617 | Corpuscularian critics of scholasticism say only substances exist [Pasnau] |
| Full Idea: Corpuscularian critics of scholasticism tend to think that only substances exist. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 06.2) | |
| A reaction: Pasnau treats this as an extreme 17th C reaction which was hopelessly inadequate as metaphysics. We have been struggling with the nature of 'properties' ever since, while losing our grip on the concept of a unified 'substance'. |
| 16741 | Scholastics wanted to treat Aristotelianism as physics, rather than as metaphysics [Pasnau] |
| Full Idea: There is a broad scholastic tendency to understand Aristotelianism not in abstract, metaphysical terms, but as a concrete, physical theory of the world. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 23.5) | |
| A reaction: This seems to give a good explanation of why Aristotelianism plummeted to oblivion in the 17th C. Pasnau obviously wants to revive it, by drawing a sharp line between metaphysics and science. I doubt the line. |
| 16777 | If crowds are things at all, they seem to be Substances, since they bear properties [Pasnau] |
| Full Idea: Crowds seem to be the bearers of properties, and if they are things at all, then there is no place for them other than in the category of Substance. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 26.1) | |
| A reaction: It is tempting to say, based on Aristotle, that a substance is whatever 1) bears properties, and 2) endures in spite of change, but a crowd is a nice problem case, because it looks too disunited to be a 'substance'. |
| 16615 | Scholastics use 'substantia' for thick concrete entities, and for thin metaphysical ones [Pasnau] |
| Full Idea: Scholastic texts are rife with different senses of 'substantia', using the term to refer, among other things, both to thick concrete entities and to thin metaphysical ones. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 06.1) | |
| A reaction: Pasnau introduces 'thin' and 'thick' substance for this reason. I may adopt this. Without distinctions between thin and thick concepts of things we can get very muddled. I like the word to label something which is an 'entity'. |
| 16775 | For corpuscularians, a substance is just its integral parts [Pasnau] |
| Full Idea: According to strict corpuscularianism the only real constituents of a substance are its integral parts. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 26.1) | |
| A reaction: An understandable reaction to the emptiness of Aristotelian substantial forms in science. It seems to leave out the structural principles that distinguish one arrangement of parts from another. See Koslicki on this. |
| 16769 | If clay survives destruction of the statue, the statue wasn't a substance, but a mere accident [Pasnau] |
| Full Idea: The unitarian view of substance says it cannot be divided. If the clay can survive the destruction of the statue, then that shows that the statue was not a substance at all, and that its shape (or whatever made it a statue) was merely a passing accident. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 25.3) | |
| A reaction: This seems to give the orthodox Aristotelian/Thomist reading, assuming that a substance only has one form, which unifies it. Since clay must have shape, and statues must have matter, I have never understood how there were two objects here. |
| 16602 | Corpuscularianism rejected not only form, but also the dependence of matter on form [Pasnau] |
| Full Idea: What marks the rise of the corpuscularian movement is not just the rejection of form, but the rejection of matter as dependent on form. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 04.5) | |
| A reaction: The point was that matter required form to have any kind of actual existence, but now matter can stand on its own. |
| 16612 | Hylomorphism may not be a rival to science, but an abstract account of unity and endurance [Pasnau] |
| Full Idea: Hylomorphism admits of an alternative formulation, as an explanatory schema at a different level of analysis, not competing with corpuscular-mechanistic theory, but accounting for abstract features of the world - notably unity and endurance of substances. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 06.1) | |
| A reaction: Pasnau is clearly sympathetic. As a view of why normal objects have unity and persist over time it is almost the only decent theory around. Hawley, for example, struggles to explain how 'stages' of a thing are linked. Classical mereology is silly. |
| 16613 | Hylomorphism declined because scholastics made it into a testable physical theory [Pasnau] |
| Full Idea: Scholastics lost their grip on hylomorphism as a metaphysical theory, conceiving of it as a concrete, physical hypothesis about causal forces. Once form and matter were made subject to empirical research, their days were inevitably numbered. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 06.1) | |
| A reaction: Pasnau seems to make a sharp distinction between science, and a separate realm he labels 'metaphysical'. You can't keep causation out of Aristotelian hylomorphism. The defence is that it is at a higher level of generality than science. |
| 16747 | Scholastics made forms substantial, in a way unintended by Aristotle [Pasnau] |
| Full Idea: The conception of form as somehow substantial took on new life among scholastic Aristotelians, and was developed in ways that Aristotle himself never suggested. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 24.1) | |
| A reaction: This is music to we modern neo-Aristotelians, because scholasticism was rightly dumped in the 17th C, but we can go back and start again from what The Philosopher actually said. |
| 16759 | Scholastics began to see substantial form more as Aristotle's 'efficient' cause [Pasnau] |
| Full Idea: The whole scholastic conception of substantial form came to have more and more in common with an Aristotelian efficient cause. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 24.2) | |
| A reaction: Aristotle, of course, identified the form with the 'formal cause [aitia]', which is the shape of the statue, rather than the efficient cause, which is the sculptor. |
| 16748 | Aquinas says a substance has one form; Scotists say it has many forms [Pasnau] |
| Full Idea: Aquinas subscribes to the unitarian doctrine that a single substance has just a single substantial form, but authors like Scotus subscribe to a plurality of substantial forms. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 24.1) | |
| A reaction: The Scotists seem to think that qualities themselve can have forms. I take it that Aristotle would have agreed with Aquinas. |
| 16671 | Scholastic Quantity either gives a body parts, or spreads them out in a unified way [Pasnau] |
| Full Idea: On one version of Quantity realism it is what makes a body have parts; on another version, it is what makes the body's parts be spread out in a continuous and unified way. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 14.1) |
| 16596 | A substratum can't be 'bare', because it has a job to do [Pasnau] |
| Full Idea: A completely bare substratum seems not just incoherent but also unable to carry out the function for which it is intended - to be a substratum. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 03.3) |
| 16579 | There may be different types of substrate, or temporary substrates [Pasnau] |
| Full Idea: The substratum thesis says …perhaps there is a different subject for different kinds of changes, and perhaps what endures through one kind of change will be corrupted by another. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 02.5) |
| 16584 | If a substrate gives causal support for change, quite a lot of the ingredients must endure [Pasnau] |
| Full Idea: When the substratum thesis is grounded on the idea that the ingredients must endure through the change, if they are to play a causal role, then it is natural to suppose that quite a lot of the ingredients must endure. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 02.5) | |
| A reaction: Aristotle sharply distinguishes alteration from substantial change, but as the substrate gets thinner, the boundary between those two would blur. |
| 16580 | A substrate may be 'prime matter', which endures through every change [Pasnau] |
| Full Idea: The 'conservation thesis' about substrates says that there is a single, most basic substrate that endures through every material change, something we call 'prime matter'. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 02.5) |
| 11177 | Can the essence of an object circularly involve itself, or involve another object? [Fine,K] |
| Full Idea: Can the essence of an object (ineliminably) involve that object itself (perhaps through self-identity, giving a direct circularity), or have an indirect circularity involving two or more objects (such as admiration between Watson and Holmes). | |
| From: Kit Fine (Senses of Essence [1995], §7) | |
| A reaction: [compressed] This looks like one of the basic questions which any theory of essentialism must address. |
| 11173 | Being a man is a consequence of his essence, not constitutive of it [Fine,K] |
| Full Idea: If we distinguish 'constitutive' from 'consequential' essence, ..then the essence of Socrates will, in part, be constituted by his being a man. But being a man (or a mountain) will merely be consequential upon, and not constitutive of, his essence. | |
| From: Kit Fine (Senses of Essence [1995], §3) | |
| A reaction: Yes yes yes. I think it is absurd to say that the class to which something belongs is part of its essential nature, given that it presumably can only belong to the class if it already has a certain essential nature. What did Frankenstein construct? |
| 11179 | If there are alternative definitions, then we have three possibilities for essence [Fine,K] |
| Full Idea: If there are alternative definitions for an essence, we must distinguish three notions. There is the essence as the manifold (the combined definitions), or as the range of alternative definitions (with component essences), or there is the common essence. | |
| From: Kit Fine (Senses of Essence [1995], §8) | |
| A reaction: Fine opts for the third alternative (what the definitions all have in common) as the best account. He says (p.68) 'definitive' properties come from one definition, and 'essential' properties from every possible definition. |
| 16749 | Aristotelians deny that all necessary properties are essential [Pasnau] |
| Full Idea: For an Aristotelian not all necessary properties are essential; the essential properties are those that define a thing as what it is. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 24.1) | |
| A reaction: I take it as basic that whatever is essential is in some way important, whereas necessities can be trivial. |
| 16694 | Typical successive things are time and motion [Pasnau] |
| Full Idea: The standard scholastic examples of 'entia successiva' are time and motion. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 18.1) | |
| A reaction: Aristotle's examples of a day and the Games seem clearer, as time and motion do not count so clearly as 'things'. |
| 16583 | Weak ex nihilo says it all comes from something; strong version says the old must partly endure [Pasnau] |
| Full Idea: The weak ex nihilo principle says that everything comes from something, and the strong ex nihilo principle says that in everything new, something of the old must endure | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 02.5) |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| Full Idea: The conception of Frege is that self-evidence is an intrinsic property of the basic truths, rules, and thoughts expressed by definitions. | |
| From: William D. Hart (The Evolution of Logic [2010], p.350) | |
| A reaction: The problem is always that what appears to be self-evident may turn out to be wrong. Presumably the effort of arriving at a definition ought to clarify and support the self-evident ingredient. |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| Full Idea: In the case of the parallels postulate, Euclid's fifth axiom (the whole is greater than the part), and comprehension, saying was believing for a while, but what was said was false. This should make a shrewd philosopher sceptical about a priori knowledge. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Euclid's fifth is challenged by infinite numbers, and comprehension is challenged by Russell's paradox. I can't see a defender of the a priori being greatly worried about these cases. No one ever said we would be right - in doing arithmetic, for example. |
| 16783 | Essences must explain, so we can infer them causally from the accidents [Pasnau] |
| Full Idea: Without the explanatory role of essence, the underlying epistemic picture would be jeopardised, because there would no longer be any causal route by which we might get from accidents to essence. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 27.5) | |
| A reaction: There is a slight whiff of circularity here. It could be that we are psychologically desperate for essences, and so we invent bogus causal routes from the accidents to get at them. Can we know there are essences awaiting us, on independent grounds? |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| Full Idea: A Fregean concept is a function that assigns to each object a truth value. So instead of the colour green, the concept GREEN assigns truth to each green thing, but falsity to anything else. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This would seem to immediately hit the renate/cordate problem, if there was a world in which all and only the green things happened to be square. How could Frege then distinguish the green from the square? Compare Idea 8245. |
| 16609 | Atomists say causation is mechanical collisions, and all true qualities are microscopic [Pasnau] |
| Full Idea: The atomist view is that causation is limited to collisions among corpuscles (which is 'mechanism'), and the only bodily qualities are those found at the microcorpuscular level; sensible qualities are in fact sensations. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 05.4) | |
| A reaction: [Part of a full summary of atomism by Pasnau] |
| 16603 | In the 17th C matter became body, and was then studied by science [Pasnau] |
| Full Idea: In the seventeenth century, matter becomes body, and body becomes the object of natural science. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 04.5) |
| 16592 | Atomism is the commonest version of corpuscularianism, but isn't required by it [Pasnau] |
| Full Idea: Atomism is the most common version of corpuscular prime matter, but it is not the only option. Indeed, atomism neither entails nor is entailed by the combination of corpuscularianism and the substratum thesis. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 03.2) | |
| A reaction: The point is that the corpuscles may be endlessly divisible (which Lewis called 'gunk'). |
| 16750 | If there are just arrangements of corpuscles, where are the boundaries between substances? [Pasnau] |
| Full Idea: If all there are corpuscles of various shapes and sizes, variously arranged, it is not easy to see how we might draw the boundary lines, at any given moment, between one substance and another. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 24.2) | |
| A reaction: We still have precisely that problem, and it leads to the nihilism about ordinary objects found in Unger, Van Inwagen and Merricks. I have so far found modern defences of ordinary objects unpersuasive. |
| 16722 | Scholastic causation is by changes in the primary qualities of hot, cold, wet, dry [Pasnau] |
| Full Idea: There is a scholastic theory of causation. Of Aristotle's Four Causes, the main one is the 'formal' cause, and that consists of changes in the primary, elemental qualities, which are hot, cold, wet and dry. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 21.2) | |
| A reaction: [my summary] It is probably right to call this 'scholastic' rather than 'Aristotelian', as I take Aristotelian essence to run deeper than this, and involve principles as well as qualities. |
| 16760 | Substantial forms were a step towards scientific essentialism [Pasnau] |
| Full Idea: Substantial forms might well be viewed as an early step in the development of scientific essentialism. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 24.4) | |
| A reaction: This is the scholastic view of substantial forms, which is much more physical and causal, rather than Aristotle's more abstract view. The rejection of substantial forms led to the 'Humean' view of laws of nature. |
| 16581 | Scholastic authors agree that matter was created by God, out of nothing [Pasnau] |
| Full Idea: Authors from 1274 to 1671 unanimously endorse the Christian doctrine that matter was created by God, before which time there was no material world at all. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 02.5) |
| 16642 | Transubstantion says accidents of bread and wine don't inhere in the substance [Pasnau] |
| Full Idea: Transubstantiation maintains that the accidents of the bread and wine endure after consecration without inhering in the substance. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 10.3) | |
| A reaction: It's a big puzzle to outsiders why softness and nice taste should have theological significance. If it is the body and blood of Christ, presumably a miracle has occurred, so normal theories don't apply. It is the key difficulty for scholastic metaphysics. |