92 ideas
| 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. |
| 1695 | Without extensive examination firm statements are hard, but studying the difficulties is profitable [Aristotle] |
| Full Idea: It is hard to make firm statements on these questions without having examined them many times, but to have gone through the various difficulties is not unprofitable. | |
| From: Aristotle (Categories [c.331 BCE], 08b23) | |
| A reaction: Suggesting that philosophy is more like drawing the map than completing the journey. |
| 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? |
| 1697 | The contrary of good is bad, but the contrary of bad is either good or another evil [Aristotle] |
| Full Idea: What is contrary to a good thing is necessarily bad, as we see with health and sickness. But the contrary of bad is sometimes good, sometimes not, as we see with excess, opposed by both deficiency and moderation. | |
| From: Aristotle (Categories [c.331 BCE], 13b36) |
| 1698 | Both sides of contraries need not exist (as health without sickness, white without black) [Aristotle] |
| Full Idea: With contraries it is not necessary if one exists for the other to exist too, for if everyone were well health would exist but not sickness, and if everything were white whiteness would exist but not black. | |
| From: Aristotle (Categories [c.331 BCE], 14a06) |
| 11034 | The differentiae of genera which are different are themselves different in kind [Aristotle] |
| Full Idea: The differentiae of genera which are different and not subordinate one to the other are themselves different in kind. | |
| From: Aristotle (Categories [c.331 BCE], 01b16) | |
| A reaction: This seems to be indicating a category mistake, as he warns us not to attribute the wrong kind of differentiae to something we are picking out. |
| 18367 | A true existence statement has its truth caused by the existence of the thing [Aristotle] |
| Full Idea: Whereas the true statement [that there is a man] is in no way the cause of the actual thing's existence, the actual thing does seem in some way the cause of the statement's being true. | |
| From: Aristotle (Categories [c.331 BCE], 14b18) | |
| A reaction: Armstrong offers this as the earliest statement of the truthmaker principle. Notice the cautious qualification 'seem in some way'. The truthmaker dependence seems even clearer in falsemaking, where the death of the man falsifies the statement. |
| 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. |
| 11033 | Predications of predicates are predications of their subjects [Aristotle] |
| Full Idea: Whenever one thing is predicated of another as of a subject, all things said of what is predicated will be said of the subject also. | |
| From: Aristotle (Categories [c.331 BCE], 01b10) |
| 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? |
| 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'. |
| 11044 | One is prior to two, because its existence is implied by two [Aristotle] |
| Full Idea: One is prior to two because if there are two it follows at once that there is one, whereas if there is one there is not necessarily two. | |
| From: Aristotle (Categories [c.331 BCE], 14a29) | |
| A reaction: The axiomatic introduction of a 'successor' to a number does not seem to introduce this notion of priority, based on inclusiveness. Introducing order by '>' also does not seem to indicate any logical priority. |
| 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) |
| 11042 | Parts of a line join at a point, so it is continuous [Aristotle] |
| Full Idea: A line is a continuous quantity. For it is possible to find a common boundary at which its parts join together, a point. | |
| From: Aristotle (Categories [c.331 BCE], 04b33) | |
| A reaction: This appears to be the essential concept of a Dedekind cut. It seems to be an open question whether a cut defines a unique number, but a boundary seems to be intrinsically unique. Aristotle wins again. |
| 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) |
| 11041 | Some quantities are discrete, like number, and others continuous, like lines, time and space [Aristotle] |
| Full Idea: Of quantities, some are discrete, others continuous. ...Discrete are number and language; continuous are lines, surfaces, bodies, and also, besides these, time and place. | |
| From: Aristotle (Categories [c.331 BCE], 04b20) | |
| A reaction: This distinction seems to me to be extremely illuminating, when comparing natural numbers with real numbers, and it is the foundation of the Greek view of mathematics. |
| 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) |
| 11286 | Primary being must be more than mere indeterminate ultimate subject of predication [Politis on Aristotle] |
| Full Idea: He criticises his 'Categories' view, because if primary being is simply the ultimate subject of predication the primary being is, in virtue of itself, something indeterminate; it would be a necessary but not a sufficient condition for primary being. | |
| From: comment on Aristotle (Categories [c.331 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 7.5 | |
| A reaction: Thus, Politis argues, primary being is essence in the later work. The words 'substance' and 'ousia' cause confusion here, and must be watched closely. Wedin argues that Aristotle merely develops his 'Categories' view, but most disagree. |
| 1700 | There are six kinds of change: generation, destruction, increase, diminution, alteration, change of place [Aristotle] |
| Full Idea: There are six kinds of change: generation, destruction, increase, diminution, alteration, change of place. A change in our affections would be an example of alteration. | |
| From: Aristotle (Categories [c.331 BCE], 15a13) | |
| A reaction: You've got to love someone who is willing to attempt assertions of this kind. These all strike me as correct, and I can't think of any others. |
| 1699 | A thing is prior to another if it implies its existence [Aristotle] |
| Full Idea: That from which the implication of existence does not hold reciprocally is thought to be prior. | |
| From: Aristotle (Categories [c.331 BCE], 14a32) | |
| A reaction: shadows and objects |
| 18366 | Of interdependent things, the prior one causes the other's existence [Aristotle] |
| Full Idea: For of things which reciprocate as to implication of existence, that which is in some way the cause of the other's existence might reasonably by called prior by nature. | |
| From: Aristotle (Categories [c.331 BCE], 14b12) | |
| A reaction: Not so clear when you seek examples. The bus is prior to its redness, but you can't have a colourless bus, so being coloured is prior to being a bus. Aristotle's example is a man being prior to the truths about him. |
| 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. |
| 13121 | Substance,Quantity,Quality,Relation,Place,Time,Being-in-a-position,Having,Doing,Being affected [Aristotle, by Westerhoff] |
| Full Idea: Aristotle's list of ten categories proved to be the most influential scheme found in his works: Substance, Quantity, Quality, Relation, Place, Time, Being-in-a-position, Having, Doing, Being affected. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Jan Westerhoff - Ontological Categories §01 |
| 11035 | There are ten basic categories for thinking about things [Aristotle] |
| Full Idea: Of things said without any combination, each signifies either substance or quantity or qualification or a relative or where or when or being-in-a-position or having or doing or being-affected. | |
| From: Aristotle (Categories [c.331 BCE], 01b25) | |
| A reaction: This sums up the earlier of Aristotle's two metaphysical view, and each of this categories is discussed in the present text. |
| 3311 | The categories (substance, quality, quantity, relation, action, passion, place, time) peter out inconsequentially [Benardete,JA on Aristotle] |
| Full Idea: The Aristotelian schedule of categories - substance, quality, quantity, relation, action, passion, place, time, and so forth - appears to peter out inconsequentially. | |
| From: comment on Aristotle (Categories [c.331 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.7 | |
| A reaction: Compare Idea 5544 for Kant's attempt to classify categories. Personally I like the way Aristotle's 'peter out'. That seems to me a more plausible character for good metaphysics. |
| 16116 | Aristotle derived categories as answers to basic questions about nature, size, quality, location etc. [Aristotle, by Gill,ML] |
| Full Idea: Aristotle seems to have worked out his list of categories by considering various questions that one might ask about a particular object, such as What is it? How big is it? How is it qualified? And Where is it? | |
| From: report of Aristotle (Categories [c.331 BCE]) by Mary Louise Gill - Aristotle on Substance | |
| A reaction: Of course, to think of his questions, Aristotle already had categories in his mind. How would he approach a proposal to recategorise reality more efficiently? |
| 21345 | Aristotle said relations are not substances, so (if they exist) they must be accidents [Aristotle, by Heil] |
| Full Idea: Aristotle categorised relations as accidents - Socrates's whiteness, the sphericity of this ball - entities dependent on substances. Relations are not substances, so they must be, if anything at all, accidents. | |
| From: report of Aristotle (Categories [c.331 BCE], §7) by John Heil - Relations 'Historical' | |
| A reaction: Heil says this thought encouraged anti-realist views of relations, which became the norm until Russell. |
| 16155 | Aristotle promoted the importance of properties and objects (rather than general and particular) [Aristotle, by Frede,M] |
| Full Idea: In 'Categories' Aristotle is taking a first step in making the distinction between objects and properties central to ontology. This plays virtually no role in Plato, and was overshadowed by the distinction between general and particular. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Michael Frede - Individuals in Aristotle I | |
| A reaction: Frede says he gets in a tangle because he mixes the earlier and the new views. Because we are nowadays in a total muddle about properties, I'm thinking we should go back to the earlier view! Modern commentators make him a trope theorist. |
| 11032 | Some things said 'of' a subject are not 'in' the subject [Aristotle] |
| Full Idea: Of things there are, some are said of a subject, but are not in any subject. For example, man is said of a subject, the individual man, but is not in any subject. | |
| From: Aristotle (Categories [c.331 BCE], 01a20) | |
| A reaction: See? 'Being a man' is not a property of a man! Only the properties which are 'in' the man are properties of the man. The rest are things which are said 'of' men, usually as classifications. A classification is not a property. |
| 11038 | We call them secondary 'substances' because they reveal the primary substances [Aristotle] |
| Full Idea: It is reasonable that, after the primary substances, their species and genera should be the only other things called (secondary) substances. For only they, of things predicated, reveal the primary substance. | |
| From: Aristotle (Categories [c.331 BCE], 02b29) | |
| A reaction: This is the key passage in all of Aristotle for sortal essentialists like Wiggins, especially the word 'only'. I take it that this observation is superseded by the Metaphysics. Definition is the route to substance (which involves general terms). |
| 16739 | Four species of quality: states, capacities, affects, and forms [Aristotle, by Pasnau] |
| Full Idea: In Categories 8 there are four species of qualities: States and conditions, Natural capacities and incapacities, Affective qualities or affections, and Shape and external form. | |
| From: report of Aristotle (Categories [c.331 BCE], Ch.8) by Robert Pasnau - Metaphysical Themes 1274-1671 23.5 |
| 11037 | Colour must be in an individual body, or it is not embodied [Aristotle] |
| Full Idea: Colour is in body and therefore also in an individual body; for were it not in some individual body it would not be in body at all. | |
| From: Aristotle (Categories [c.331 BCE], 02b02) | |
| A reaction: This may be just a truism, or it may be the Aristotelian commitment to universals only existing if they are instantiated. |
| 16154 | Aristotle gave up his earlier notion of individuals, because it relied on universals [Aristotle, by Frede,M] |
| Full Idea: In 'Metaphysics' Aristotle abandons the notion of an individual which he had relied on in the 'Categories', since it presupposes that there are general things, that there are universals. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Michael Frede - Individuals in Aristotle Intro | |
| A reaction: Ah, very illuminating. So all the way through we have a concept of individuals, first relying on universals, and then relying on hylomorphism? I suppose a bundle theory of individuals would need universals. |
| 12351 | Genus and species are substances, because only they reveal the primary substance [Aristotle, by Wedin] |
| Full Idea: The reason Aristotle gives for calling species and genera substances is that of what is predicated only they reveal what the primary substance is. | |
| From: report of Aristotle (Categories [c.331 BCE], 02b29-37) by Michael V. Wedin - Aristotle's Theory of Substance III.6 | |
| A reaction: Thus we should not be misled into thinking that the genus and species ARE the essence. We edge our way towards the essence of an individual by subdividing its categories. |
| 1694 | Substances have no opposites, and don't come in degrees (including if the substance is a man) [Aristotle] |
| Full Idea: There is nothing contrary to substances,…. and a substance does not admit of a more and a less. If this substance is a man, it will not be more a man or less a man either than itself or than another man. | |
| From: Aristotle (Categories [c.331 BCE], 03b33) |
| 16091 | Is primary substance just an ultimate subject, or some aspect of a complex body? [Aristotle, by Gill,ML] |
| Full Idea: 'Categories' treats something's being an ultimate subject as a test for being a primary substance, but it does not treat its primary objects as complex bodies consisting of matter and form. In that case, is the composite or a feature the ultimate subject? | |
| From: report of Aristotle (Categories [c.331 BCE]) by Mary Louise Gill - Aristotle on Substance Ch.1 | |
| A reaction: Gill is trying to throw light on the difference between 'Categories' and 'Metaphysics'. Once you have hylomorphism (form-plus-matter) you have a new difficulty in explaining unity. The answer is revealed once we understand 'form'. |
| 11280 | Primary being is 'that which lies under', or 'particular substance' [Aristotle, by Politis] |
| Full Idea: In 'Categories' Aristotle argues the primary being (proté ousia) is the ultimate subject of predication (to hupokeimenon, meaning 'that which lies under'), nowadays referred to as the 'particular substance' view. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 4.4 | |
| A reaction: Politis says that Aristotle shifts to the quite different view in 'Metaphysics', that primary being is essence, rather than mere subject of predication. |
| 11040 | A single substance can receive contrary properties [Aristotle] |
| Full Idea: It seems distinctive of substance that what is numerically one and the same is able to receive contraries. ...For example, an individual man - one and the same - becomes pale at one time and dark at another. | |
| From: Aristotle (Categories [c.331 BCE], 04a10/20) |
| 16140 | Secondary substances do have subjects, so they are not ultimate in the ontology [Aristotle, by Frede,M] |
| Full Idea: The concept of substance applies to secondary substances only with some deletions; ..it is not true that they have no subjects, and hence they are not ultimate subjects for all other elements of the ontology. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Michael Frede - Title, Unity, Authenticity of the 'Categories' V | |
| A reaction: It increasingly strikes that to treat secondary substance (roughly, species) as essence is a shocking misreading of Aristotle. Frede says they are substances, because they do indeed 'underlie'. |
| 10965 | In earlier Aristotle the substances were particulars, not kinds [Aristotle, by Lawson-Tancred] |
| Full Idea: In 'Metaphysics' Aristotle changed his view, as in 'Categories' the substances, the basic realities, were particular items, notably individual men, horses, cabbages etc. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Hugh Lawson-Tancred - Introductions to 'Metaphysics' p.178 | |
| A reaction: The charge is that having successfully rebelled against Plato, Aristotle gradually succumbed to his teacher's influence, and ended up with a more platonist view. For anti-platonists like myself, the 'Categories' seems to be the key text. |
| 11036 | A 'primary' substance is in each subject, with species or genera as 'secondary' substances [Aristotle] |
| Full Idea: A substance, in its most primary sense, is that which is neither said of a subject nor in a subject, e.g. the individual man or horse. The species in which things primarily called substances are, are called secondary substances, as are the genera. | |
| From: Aristotle (Categories [c.331 BCE], 02a11) | |
| A reaction: This distinction between 'primary' and 'secondary' substances is characteristic of Aristotle's earlier metaphysical view, with the later view (more unified and Platonic) in the 'Metaphysics'. |
| 8287 | Earlier Aristotle had objects as primary substances, but later he switched to substantial form [Aristotle, by Lowe] |
| Full Idea: In 'Categories' primary substances are individual concrete objects, such as a particular horse, whereas in 'Metaphysics' such things are combinations of matter and substantial form, with the latter being the primary substances. | |
| From: report of Aristotle (Categories [c.331 BCE]) by E.J. Lowe - The Possibility of Metaphysics 9.1 | |
| A reaction: Lowe claims there is no real difference. Aristotle came to think that matter was not part of primary substance, so the shift seems to be that substance was concrete, but then he decided it was abstract. Physicists will prefer 'Metaphysics'. |
| 12350 | Things are called 'substances' because they are subjects for everything else [Aristotle] |
| Full Idea: It is because the primary substances are subjects for everything else that they are called substances [ousiai] most strictly. | |
| From: Aristotle (Categories [c.331 BCE], 03a04) | |
| A reaction: This points to a rather minimal account of substance, as possibly the 'bare particular' which has no other role than to have properties. This expands in 'Metaphysics' to be matter which has form, making properties possible. |
| 11039 | A primary substance reveals a 'this', which is an individual unit [Aristotle] |
| Full Idea: Every substance seems to signify a certain 'this'. As regards the primary substances, it is indisputably true that each of them signifies a certain 'this'; for the thing revealed is individual and numerically one. | |
| From: Aristotle (Categories [c.331 BCE], 03b10) | |
| A reaction: The notion of 'primary' substance is confined to this earlier metaphysics of Aristotle. |
| 12361 | Primary substances are ontological in 'Categories', and explanatory in 'Metaphysics' [Aristotle, by Wedin] |
| Full Idea: The primacy of 'Categories' primary substances is a kind of ontological primacy, whereas the primacy of form is a kind of structural or explanatory primacy. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Michael V. Wedin - Aristotle's Theory of Substance X.9 | |
| A reaction: 'Structural' and 'explanatory' sound very different, since the former sounds ontological and the latter epistemological (and more subjective). |
| 3315 | Aristotle denigrates the category of relation, but for modern absolutists self-relation is basic [Benardete,JA on Aristotle] |
| Full Idea: Aristotle denigrates the whole category of relations, but modern logical absolutists single out self-relation (in the mode of identity) as metaphysically privileged. | |
| From: comment on Aristotle (Categories [c.331 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.8 | |
| A reaction: I think this refers to Plantinga and Merrihew Adams, who make identity-with-itself the basic component of individual existences. |
| 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. |
| 411 | If we succeed in speaking the truth, we cannot know we have done it [Xenophanes] |
| Full Idea: No man has seen certain truth, and no man will ever know about the gods and other things I mentioned; for if he succeeds in saying what is fully true, he himself is unaware of it; opinion is fixed by fate on all things. | |
| From: Xenophanes (fragments/reports [c.530 BCE], B34), quoted by Sextus Empiricus - Against the Professors (six books) 7.49.4 |
| 412 | If God had not created honey, men would say figs are sweeter [Xenophanes] |
| Full Idea: If God had not created yellow honey, men would say that figs were sweeter. | |
| From: Xenophanes (fragments/reports [c.530 BCE], B38), quoted by Herodian - On Peculiar Speech 41.5 |
| 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. |
| 12349 | Only what can be said of many things is a predicable [Aristotle, by Wedin] |
| Full Idea: Aristotle reminds us that nothing is to count as predicable that cannot be said-of many things. | |
| From: report of Aristotle (Categories [c.331 BCE]) by Michael V. Wedin - Aristotle's Theory of Substance III.1 | |
| A reaction: Thus there wouldn't be any predicates if there were not universals. Could we have proper names for individual qualities (tropes), in the way that we have them for individual objects? |
| 11837 | Some predicates signify qualification of a substance, others the substance itself [Aristotle] |
| Full Idea: 'White' signifies nothing but a qualification, whereas the species ('man') and the genus ('animal') mark off the qualification of substance - they signify substance of a certain qualification. | |
| From: Aristotle (Categories [c.331 BCE], 03b18) | |
| A reaction: This is making a fundamental distinction between two different types of predication. I would describe them as one attributing a real property, and the other attributing a category (as a result of the properties). I don't think 'substance' helps here. |
| 1640 | The basic Eleatic belief was that all things are one [Xenophanes, by Plato] |
| Full Idea: The Eleatic tribe, which had its beginnings from Xenophanes and still earlier, proceed on the grounds that all things so-called are one. | |
| From: report of Xenophanes (fragments/reports [c.530 BCE]) by Plato - The Sophist 242d |
| 11043 | It is not possible for fire to be cold or snow black [Aristotle] |
| Full Idea: It is not possible for fire to be cold or snow black. | |
| From: Aristotle (Categories [c.331 BCE], 12b01) |
| 1696 | Change goes from possession to loss (as in baldness), but not the other way round [Aristotle] |
| Full Idea: Change occurs from possession to privation, but from privation to possession is impossible; one who has gone blind does not recover sight nor does a bald man regain his hair nor does a toothless man grow new ones. | |
| From: Aristotle (Categories [c.331 BCE], 13a35) | |
| A reaction: Although this seems like an insight into entropy, it isn't an accurate observation, since trees lose their leaves, and then regain them in spring. Maybe somewhere men regrow their hair each spring. |
| 3055 | Xenophanes said the essence of God was spherical and utterly inhuman [Xenophanes, by Diog. Laertius] |
| Full Idea: Xenophanes taught that the essence of God was of a spherical form, in no respect resembling man. | |
| From: report of Xenophanes (fragments/reports [c.530 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.2.3 |
| 407 | Mortals believe gods are born, and have voices and clothes just like mortals [Xenophanes] |
| Full Idea: Mortals believe the gods to be created by birth, and to have raiment, voice and body like mortals'. | |
| From: Xenophanes (fragments/reports [c.530 BCE], B14), quoted by Clement - Miscellanies 5.109.2 |
| 408 | Ethiopian gods have black hair, and Thracian gods have red hair [Xenophanes] |
| Full Idea: Ethiopians have gods with snub noses and black hair, Thracians have gods with grey eyes and red hair. | |
| From: Xenophanes (fragments/reports [c.530 BCE], B16), quoted by Clement - Miscellanies 7.22.1 |