81 ideas
| 19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
| Full Idea: Aristotle takes wisdom to come in two forms, the practical and the theoretical, the former of which is good judgement about how to act, and the latter of which is deep knowledge or understanding. | |
| From: report of Aristotle (works [c.330 BCE]) by Dennis Whitcomb - Wisdom Intro | |
| A reaction: The interesting question is then whether the two are connected. One might be thoroughly 'sensible' about action, without counting as 'wise', which seems to require a broader view of what is being done. Whitcomb endorses Aristotle on this idea. |
| 13734 | Modern Quinean metaphysics is about what exists, but Aristotelian metaphysics asks about grounding [Schaffer,J] |
| Full Idea: On the now dominant Quinean view, metaphysics is about what there is (such as properties, meanings and numbers). I will argue for the revival of a more traditional Aristotelian view, on which metaphysics is about what grounds what. | |
| From: Jonathan Schaffer (On What Grounds What [2009], Intro) | |
| A reaction: I find that an enormously helpful distinction, and support the Aristotelian view. Schaffer's general line is that what exists is fairly uncontroversial and dull, but the interesting truths about the world emerge when we grasp its structure. |
| 13751 | If you tore the metaphysics out of philosophy, the whole enterprise would collapse [Schaffer,J] |
| Full Idea: Traditional metaphysics is so tightly woven into the fabric of philosophy that it cannot be torn out without the whole tapestry unravelling. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.3) | |
| A reaction: I often wonder why the opponents of metaphysics still continue to do philosophy. I don't see how you address questions of ethics, or philosophy of mathematics (etc) without coming up against highly general and abstract over-questions. |
| 1575 | For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle] |
| Full Idea: For Aristotle logos is the ability to speak rationally about, with the hope of attaining knowledge, questions of value. | |
| From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.26 |
| 1589 | Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle] |
| Full Idea: Aristotle is the great theoretician who articulates a vision of a world in which natural and stable structures can be rationally discovered. His is the most optimistic and richest view of the possibilities of logos | |
| From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.95 |
| 13743 | We should not multiply basic entities, but we can have as many derivative entities as we like [Schaffer,J] |
| Full Idea: Occam's Razor should only be understood to concern substances: do not multiply basic entities without necessity. There is no problem with the multiplication of derivative entities - they are an 'ontological free lunch'. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
| A reaction: The phrase 'ontological free lunch' comes from Armstrong. This is probably what Occam meant. A few extra specks of dust, or even a few more numbers (thank you, Cantor!) don't seem to challenge the principle. |
| 8200 | Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine] |
| Full Idea: A real definition, according to the Aristotelian tradition, gives the essence of the kind of thing defined. Man is defined as a rational animal, and thus rationality and animality are of the essence of each of us. | |
| From: report of Aristotle (works [c.330 BCE]) by Willard Quine - Vagaries of Definition p.51 | |
| A reaction: Compare Idea 4385. Personally I prefer the Aristotelian approach, but we may have to say 'We cannot identify the essence of x, and so x cannot be defined'. Compare 'his mood was hard to define' with 'his mood was hostile'. |
| 4385 | Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson] |
| Full Idea: For Aristotle, to give a definition one must first state the genus and then the differentia of the kind of thing to be defined. | |
| From: report of Aristotle (works [c.330 BCE]) by J.O. Urmson - Aristotle's Doctrine of the Mean p.157 | |
| A reaction: Presumably a modern definition would just be a list of properties, but Aristotle seeks the substance. How does he define a genus? - by placing it in a further genus? |
| 10073 | There cannot be a set theory which is complete [Smith,P] |
| Full Idea: By Gödel's First Incompleteness Theorem, there cannot be a negation-complete set theory. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.3) | |
| A reaction: This means that we can never prove all the truths of a system of set theory. |
| 13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
| Full Idea: Aristotle proposes to relativise unity and plurality, so that a single object can be both one (indivisible) and many (divisible) simultaneously, without contradiction, relative to different measures. Wholeness has degrees, with the strength of the unity. | |
| From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.12 | |
| A reaction: [see Koslicki's account of Aristotle for details] As always, the Aristotelian approach looks by far the most promising. Simplistic mechanical accounts of how parts make wholes aren't going to work. We must include the conventional and conceptual bit. |
| 10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
| Full Idea: Going second-order in arithmetic enables us to prove new first-order arithmetical sentences that we couldn't prove before. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 23.4) | |
| A reaction: The wages of Satan, perhaps. We can prove things about objects by proving things about their properties and sets and functions. Smith says this fact goes all the way up the hierarchy. |
| 4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
| Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality. | |
| From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4 | |
| A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional. |
| 10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
| Full Idea: The 'range' of a function is the set of elements in the output set that are values of the function for elements in the original set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) | |
| A reaction: In other words, the range is the set of values that were created by the function. |
| 10605 | Two functions are the same if they have the same extension [Smith,P] |
| Full Idea: We count two functions as being the same if they have the same extension, i.e. if they pair up arguments with values in the same way. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 11.3) | |
| A reaction: So there's only one way to skin a cat in mathematical logic. |
| 10075 | A 'partial function' maps only some elements to another set [Smith,P] |
| Full Idea: A 'partial function' is one which maps only some elements of a domain to elements in another set. For example, the reciprocal function 1/x is not defined for x=0. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1 n1) |
| 10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
| Full Idea: If a function f maps the argument a back to a itself, so that f(a) = a, then a is said to be a 'fixed point' for f. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 20.5) |
| 10074 | A 'total function' maps every element to one element in another set [Smith,P] |
| Full Idea: A 'total function' is one which maps every element of a domain to exactly one corresponding value in another set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) |
| 10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
| Full Idea: The so-called Comprehension Schema ∃X∀x(Xx ↔ φ(x)) says that there is a property which is had by just those things which satisfy the condition φ. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 22.3) |
| 10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
| Full Idea: 'Theorem': given a derivation of the sentence φ from the axioms of the theory T using the background logical proof system, we will say that φ is a 'theorem' of the theory. Standard abbreviation is T |- φ. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
| Full Idea: A 'natural deduction system' will have no logical axioms but may rules of inference. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 09.1) | |
| A reaction: He contrasts this with 'Hilbert-style systems', which have many axioms but few rules. Natural deduction uses many assumptions which are then discharged, and so tree-systems are good for representing it. |
| 10613 | No nice theory can define truth for its own language [Smith,P] |
| Full Idea: No nice theory can define truth for its own language. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 21.5) | |
| A reaction: This leads on to Tarski's account of truth. |
| 10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
| Full Idea: A 'surjective' function is 'onto' - the whole of the output set results from the function being applied to elements of the original set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) |
| 10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
| Full Idea: An 'injective' function is 'one-to-one' - each element of the output set results from a different element of the original set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) | |
| A reaction: That is, two different original elements cannot lead to the same output element. |
| 10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
| Full Idea: A 'bijective' function has 'one-to-one correspondence' - it is both surjective and injective, so that every element in each of the original and the output sets has a matching element in the other. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) | |
| A reaction: Note that 'injective' is also one-to-one, but only in the one direction. |
| 10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
| Full Idea: If everything that a theory proves must be true, then it is a 'sound' theory. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.1) |
| 10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
| Full Idea: Soundness is normally a matter of having true axioms and a truth-preserving proof system. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) | |
| A reaction: The only exception I can think of is if a theory consisted of nothing but the axioms. |
| 10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
| Full Idea: A theory is 'sound' iff every theorem of it is true (i.e. true on the interpretation built into its language). Soundness is normally a matter of having true axioms and a truth-preserving proof system. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
| Full Idea: Logicians say that a theory T is '(negation) complete' if, for every sentence φ in the language of the theory, either φ or ¬φ is deducible in T's proof system. If this were the case, then truth could be equated with provability. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.1) | |
| A reaction: The word 'negation' seems to be a recent addition to the concept. Presumable it might be the case that φ can always be proved, but not ¬φ. |
| 10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
| Full Idea: A theory is 'negation complete' if it decides every sentence of its language (either the sentence, or its negation). | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
| Full Idea: There is an annoying double-use of 'complete': a logic may be semantically complete, but there may be an incomplete theory expressed in it. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
| Full Idea: There are two routes to Incompleteness results. One goes via the semantic assumption that we are dealing with sound theories, using a result about what they can express. The other uses the syntactic notion of consistency, with stronger notions of proof. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 18.1) |
| 10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
| Full Idea: An 'effectively decidable' (or 'computable') algorithm will be step-by-small-step, with no need for intuition, or for independent sources, with no random methods, possible for a dumb computer, and terminates in finite steps. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.2) | |
| A reaction: [a compressed paragraph] |
| 10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
| Full Idea: A theory is 'decidable' iff there is a mechanical procedure for determining whether any sentence of its language can be proved. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) | |
| A reaction: Note that it doesn't actually have to be proved. The theorems of the theory are all effectively decidable. |
| 10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
| Full Idea: Any consistent, axiomatized, negation-complete formal theory is decidable. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.6) |
| 10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
| Full Idea: A set is 'enumerable' iff either the set is empty, or there is a surjective function to the set from the set of natural numbers, so that the set is in the range of that function. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.3) |
| 10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
| Full Idea: A finite set of finitely specifiable objects is always effectively enumerable (for example, the prime numbers). | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.4) |
| 10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
| Full Idea: The set of ordered pairs of natural numbers (i,j) is effectively enumerable, as proven by listing them in an array (across: <0,0>, <0,1>, <0,2> ..., and down: <0,0>, <1,0>, <2,0>...), and then zig-zagging. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.5) |
| 10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
| Full Idea: The theorems of any properly axiomatized theory can be effectively enumerated. However, the truths of any sufficiently expressive arithmetic can't be effectively enumerated. Hence the theorems and truths of arithmetic cannot be the same. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 05 Intro) |
| 10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
| Full Idea: A set is 'effectively enumerable' if an (idealised) computer could be programmed to generate a list of its members such that any member will eventually be mentioned (even if the list is empty, or without end, or contains repetitions). | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.4) |
| 10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
| Full Idea: Whether a property is 'expressible' in a given theory depends on the richness of the theory's language. Whether the property can be 'captured' (or 'represented') by the theory depends on the richness of the axioms and proof system. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 04.7) |
| 10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
| Full Idea: For prime numbers we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))). That is, the only way to multiply two numbers and a get a prime is if one of them is 1. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 04.5) |
| 10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
| Full Idea: It has been proved (by Tarski) that the real numbers R is a complete theory. But this means that while the real numbers contain the natural numbers, the pure theory of real numbers doesn't contain the theory of natural numbers. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 18.2) |
| 10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
| Full Idea: The truths of arithmetic are just the true equations involving particular numbers, and universally quantified versions of such equations. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 27.7) | |
| A reaction: Must each equation be universally quantified? Why can't we just universally quantify over the whole system? |
| 10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
| Full Idea: All numbers are related to zero by the ancestral of the successor relation. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 23.5) | |
| A reaction: The successor relation only ties a number to the previous one, not to the whole series. Ancestrals are a higher level of abstraction. |
| 10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
| Full Idea: The number of Fs is the 'successor' of the number of Gs if there is an object which is an F, and the remaining things that are F but not identical to the object are equinumerous with the Gs. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 14.1) |
| 10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
| Full Idea: Baby Arithmetic 'knows' the addition of particular numbers and multiplication, but can't express general facts about numbers, because it lacks quantification. It has a constant '0', a function 'S', and functions '+' and 'x', and identity and negation. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.1) |
| 10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
| Full Idea: Baby Arithmetic is negation complete, so it can prove every claim (or its negation) that it can express, but it is expressively extremely impoverished. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.3) |
| 10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
| Full Idea: Robinson Arithmetic (Q) is not negation complete | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.4) |
| 10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
| Full Idea: We can beef up Baby Arithmetic into Robinson Arithmetic (referred to as 'Q'), by restoring quantifiers and variables. It has seven generalised axioms, plus standard first-order logic. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.3) |
| 10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
| Full Idea: The sequence of natural numbers starts from zero, and each number has just one immediate successor; the sequence continues without end, never circling back on itself, and there are no 'stray' numbers, lurking outside the sequence. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.1) | |
| A reaction: These are the characteristics of the natural numbers which have to be pinned down by any axiom system, such as Peano's, or any more modern axiomatic structures. We are in the territory of Gödel's theorems. |
| 10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
| Full Idea: If the logic of arithmetic doesn't have second-order quantifiers to range over properties of numbers, how can it handle induction? | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 10.1) |
| 10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
| Full Idea: Putting multiplication together with addition and successor in the language of arithmetic produces incompleteness. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 10.7) | |
| A reaction: His 'Baby Arithmetic' has all three and is complete, but lacks quantification (p.51) |
| 10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
| Full Idea: Multiplication in itself isn't is intractable. In 1929 Skolem showed a complete theory for a first-order language with multiplication but lacking addition (or successor). Multiplication together with addition and successor produces incompleteness. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 10.7 n8) |
| 13741 | If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers' [Schaffer,J] |
| Full Idea: We can automatically infer 'there are roses' from 'there are red roses' (with no shift in the meaning of 'roses'). Likewise one can automatically infer 'there are numbers' from 'there are prime numbers'. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
| A reaction: He similarly observes that the atheist's 'God is a fictional character' implies 'there are fictional characters'. Schaffer is not committing to a strong platonism with his claim - merely that the existence of numbers is hardly worth disputing. |
| 13748 | Grounding is unanalysable and primitive, and is the basic structuring concept in metaphysics [Schaffer,J] |
| Full Idea: Grounding should be taken as primitive, as per the neo-Aristotelian approach. Grounding is an unanalyzable but needed notion - it is the primitive structuring conception of metaphysics. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.2) | |
| A reaction: [he cites K.Fine 1991] I find that this simple claim clarifies the discussions of Kit Fine, where you are not always quite sure what the game is. I agree fully with it. It makes metaphysics interesting, where cataloguing entities is boring. |
| 13747 | Supervenience is just modal correlation [Schaffer,J] |
| Full Idea: Supervenience is mere modal correlation. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.2) |
| 13744 | The cosmos is the only fundamental entity, from which all else exists by abstraction [Schaffer,J] |
| Full Idea: My preferred view is that there is only one fundamental entity - the whole concrete cosmos - from which all else exists by abstraction. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
| A reaction: This looks to me like weak anti-realism - that there are no natural 'joints' in nature - but I don't think Schaffer intends that. I take the joints to be fundamentals, which necessitates that the cosmos has parts. His 'abstraction' is clearly a process. |
| 13739 | Maybe categories are just the different ways that things depend on basic substances [Schaffer,J] |
| Full Idea: Maybe the categories are determined by the different grounding relations, ..so that categories just are the ways things depend on substances. ...Categories are places in the dependence ordering. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 1.3) |
| 10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
| Full Idea: The 'ancestral' of a relation is that relation which holds when there is an indefinitely long chain of things having the initial relation. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 23.5) | |
| A reaction: The standard example is spotting the relation 'ancestor' from the receding relation 'parent'. This is a sort of abstraction derived from a relation which is not equivalent (parenthood being transitive but not reflexive). The idea originated with Frege. |
| 13276 | The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki] |
| Full Idea: Aristotle's discussion of the unmoved mover and of the soul confirms the suspicion that form, when it is not thought of as the object represented in a definition, plays the role of the ultimate mereological atom within his system. | |
| From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 6.6 | |
| A reaction: Aristotle is concerned with which things are 'divisible', and he cites these two examples as indivisible, but they may be too unusual to offer an actual theory of how Aristotle builds up wholes from atoms. He denies atoms in matter. |
| 13277 | The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki] |
| Full Idea: Thus in Aristotle we may think of an object's formal components as a sort of recipe for how to build wholes of that particular kind. | |
| From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.5 | |
| A reaction: In the elusive business of pinning down what Aristotle means by the crucial idea of 'form', this analogy strikes me as being quite illuminating. It would fit DNA in living things, and the design of an artifact. |
| 13742 | There exist heaps with no integral unity, so we should accept arbitrary composites in the same way [Schaffer,J] |
| Full Idea: I am happy to accept universal composition, on the grounds that there are heaps, piles etc with no integral unity, and that arbitrary composites are no less unified than heaps. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1 n11) | |
| A reaction: The metaphysical focus is then placed on what constitutes 'integral unity', which is precisely the question which most interested Aristotle. Clearly if there is nothing more to an entity than its components, scattering them isn't destruction. |
| 13752 | The notion of 'grounding' can explain integrated wholes in a way that mere aggregates can't [Schaffer,J] |
| Full Idea: The notion of grounding my capture a crucial mereological distinction (missing from classical mereology) between an integrated whole with genuine unity, and a mere aggregate. x is an integrated whole if it grounds its proper parts. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 3.1) | |
| A reaction: That gives a nice theoretical notion, but if you remove each of the proper parts, does x remain? Is it a bare particular? I take it that it will have to be an abstract principle, the one Aristotle was aiming at with his notion of 'form'. Schaffer agrees. |
| 13749 | Belief in impossible worlds may require dialetheism [Schaffer,J] |
| Full Idea: One motivation for dialetheism is the view that there are impossible worlds. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.3) |
| 5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
| Full Idea: Aristotle thinks that in general we have knowledge or understanding when we grasp causes, and he distinguishes three fundamental types of knowledge - theoretical, practical and productive. | |
| From: report of Aristotle (works [c.330 BCE]) by Alan D. Code - Aristotle | |
| A reaction: Productive knowledge we tend to label as 'knowing how'. The centrality of causes for knowledge would get Aristotle nowadays labelled as a 'naturalist'. It is hard to disagree with his three types, though they may overlap. |
| 13740 | 'Moorean certainties' are more credible than any sceptical argument [Schaffer,J] |
| Full Idea: A 'Moorean certainty' is when something is more credible than any philosopher's argument to the contrary. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
| A reaction: The reference is to G.E. Moore's famous claim that the existence of his hand is more certain than standard sceptical arguments. It sounds empiricist, but they might be parallel rational truths, of basic logic or arithmetic. |
| 11239 | The notion of a priori truth is absent in Aristotle [Aristotle, by Politis] |
| Full Idea: The notion of a priori truth is conspicuously absent in Aristotle. | |
| From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.5 | |
| A reaction: Cf. Idea 11240. |
| 23312 | Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M] |
| Full Idea: Aristotle is a rationalist …but reason for him is a disposition which we only acquire over time. Its acquisition is made possible primarily by perception and experience. | |
| From: report of Aristotle (works [c.330 BCE]) by Michael Frede - Aristotle's Rationalism p.173 | |
| A reaction: I would describe this process as the gradual acquisition of the skill of objectivity, which needs the right knowledge and concepts to evaluate new experiences. |
| 16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
| Full Idea: Since Aristotle generally prefers a metaphysical theory that accords with common intuitions, he frequently relies on facts about language to guide his metaphysical claims. | |
| From: report of Aristotle (works [c.330 BCE]) by Mary Louise Gill - Aristotle on Substance Ch.5 | |
| A reaction: I approve of his procedure. I take intuition to be largely rational justifications too complex for us to enunciate fully, and language embodies folk intuitions in its concepts (especially if the concepts occur in many languages). |
| 16971 | Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik] |
| Full Idea: Plato's unity of science principle states that all - legitimate - sciences are ultimately about the Forms. Aristotle's principle states that all sciences must be, ultimately, about substances, or aspects of substances. | |
| From: report of Aristotle (works [c.330 BCE], 1) by Julius Moravcsik - Aristotle on Adequate Explanations 1 |
| 11243 | Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis] |
| Full Idea: For Aristotle things which explain (the explanantia) are facts, which should not be associated with the modern view that says explanations are dependent on how we conceive and describe the world (where causes are independent of us). | |
| From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 2.1 | |
| A reaction: There must be some room in modern thought for the Aristotelian view, if some sort of robust scientific realism is being maintained against the highly linguistic view of philosophy found in the twentieth century. |
| 3320 | Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA] |
| Full Idea: The standard Aristotelian doctrine of species and genus in the theory of anything whatever involves specifying what the thing is in terms of something more general. | |
| From: report of Aristotle (works [c.330 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.10 |
| 12000 | Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung] |
| Full Idea: The view that essential properties are those in virtue of which other significant properties of the subjects under investigation can be explained is encountered repeatedly in Aristotle's work. | |
| From: report of Aristotle (works [c.330 BCE]) by Joan Kung - Aristotle on Essence and Explanation IV | |
| A reaction: What does 'significant' mean here? I take it that the significant properties are the ones which explain the role, function and powers of the object. |
| 23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
| Full Idea: Aristotle, and also the Stoics, denied rationality to animals. …The Platonists, the Pythagoreans, and some more independent Aristotelians, did grant reason and intellect to animals. | |
| From: report of Aristotle (works [c.330 BCE]) by Richard Sorabji - Rationality 'Denial' | |
| A reaction: This is not the same as affirming or denying their consciousness. The debate depends on how rationality is conceived. |
| 11240 | The notion of analytic truth is absent in Aristotle [Aristotle, by Politis] |
| Full Idea: The notion of analytic truth is conspicuously absent in Aristotle. | |
| From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.5 | |
| A reaction: Cf. Idea 11239. |
| 6559 | Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin] |
| Full Idea: To the best of my knowledge (and somewhat to my surprise), Aristotle never actually says that man is a rational animal; however, he all but says it. | |
| From: report of Aristotle (works [c.330 BCE]) by Robert Fogelin - Walking the Tightrope of Reason Ch.1 | |
| A reaction: When I read this I thought that this database would prove Fogelin wrong, but it actually supports him, as I can't find it in Aristotle either. Descartes refers to it in Med.Two. In Idea 5133 Aristotle does say that man is a 'social being'. But 22586! |
| 11150 | It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle] |
| Full Idea: It is the mark of an educated mind to be able to entertain an idea without accepting it. | |
| From: Aristotle (works [c.330 BCE]) | |
| A reaction: The epigraph on a David Chalmers website. A wonderful remark, and it should be on the wall of every beginners' philosophy class. However, while it is in the spirit of Aristotle, it appears to be a misattribution with no ancient provenance. |
| 3037 | Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius] |
| Full Idea: Aristotle was asked how much educated men were superior to those uneducated; "As much," he said, "as the living are to the dead." | |
| From: report of Aristotle (works [c.330 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 05.1.11 |
| 8660 | There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend] |
| Full Idea: Aristotle developed his own distinction between potential infinity (never running out) and actual infinity (there being a collection of an actual infinite number of things, such as places, times, objects). He decided that actual infinity was incoherent. | |
| From: report of Aristotle (works [c.330 BCE]) by Michčle Friend - Introducing the Philosophy of Mathematics 1.3 | |
| A reaction: Friend argues, plausibly, that this won't do, since potential infinity doesn't make much sense if there is not an actual infinity of things to supply the demand. It seems to just illustrate how boggling and uncongenial infinity was to Aristotle. |
| 12058 | Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins] |
| Full Idea: Aristotle's conception of matter permits any kind of matter to become any other kind of matter. | |
| From: report of Aristotle (works [c.330 BCE]) by David Wiggins - Substance 4.11.2 | |
| A reaction: This is obviously crucial background information when we read Aristotle on matter. Our 92+ elements, and fixed fundamental particles, gives a quite different picture. Aristotle would discuss form and matter quite differently now. |
| 22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |
| Full Idea: Aristotle said that the conception of gods arose among mankind from two originating causes, namely from events which concern the soul and from celestial phenomena. | |
| From: report of Aristotle (works [c.330 BCE], Frag 10) by Sextus Empiricus - Against the Physicists (two books) I.20 | |
| A reaction: The cosmos suggests order, and possible creation. What do events of the soul suggest? It doesn't seem to be its non-physical nature, because Aristotle is more of a functionalist. Puzzling. (It says later that gods are like the soul). |