78 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. |
| 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 |
| 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? |
| 18486 | We might define truth as arising from the truth-maker relation [MacBride] |
| Full Idea: We might define truth using the truth-maker relation, albeit in a roundabout way, according to the pattern of saying 'S is true' is equivalent to 'there is something which makes S true'. | |
| From: Fraser MacBride (Truthmakers [2013], 3.3) | |
| A reaction: [MacBride gives it more algebraically, but I prefer English!] You would need to explain 'truth-making' without reference to truth. Horwich objects, reasonably, that ordinary people grasp 'truth' much more clearly than 'truth-making'. Bad idea, I think. |
| 18484 | Phenomenalists, behaviourists and presentists can't supply credible truth-makers [MacBride] |
| Full Idea: For Martin the fatal error of phenomenalists was their inability to supply credible truth-makers for truths about unobserved objects; the same error afflicted Ryle's behaviourism, ...and Prior's Presentism (for past-tensed and future-tensed truths). | |
| From: Fraser MacBride (Truthmakers [2013], 3.1) | |
| A reaction: This seems to be the original motivation for the modern rise of the truthmaker idea. Personally I find 'Napoleon won at Austerlitz' is a perfectly good past-tensed truthmaker which is compatible with presentism. Truth-making is an excellent challenge. |
| 18466 | If truthmaking is classical entailment, then anything whatsoever makes a necessary truth [MacBride] |
| Full Idea: If a truthmaker entails its truth, this threatens to over-generate truth-makers for necessary truths - at least if the entailment is classical. It's a feature of this notion that anything whatsoever entails a given necessary truth. | |
| From: Fraser MacBride (Truthmakers [2013], 1.1) | |
| A reaction: This is a good reason to think that the truth-making relation does not consist of logical entailment. |
| 18473 | 'Maximalism' says every truth has an actual truthmaker [MacBride] |
| Full Idea: The principle of 'maximalism' is that for every truth, then there must be something in the world that makes it true. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1) | |
| A reaction: That seems to mean that no truths can be uttered about anything which is not in the world. If I say 'pigs might have flown', that isn't about the modal profile of actual pigs, it is about what might have resulted from that profile. |
| 18481 | Maximalism follows Russell, and optimalism (no negative or universal truthmakers) follows Wittgenstein [MacBride] |
| Full Idea: If maximalism is intellectual heir to Russell's logical atomism, then 'optimalism' (the denial that universal and negative statements need truth-makers) is heir to Wittgenstein's version, where only atomic propositions represent states of affairs. | |
| From: Fraser MacBride (Truthmakers [2013], 2.2) | |
| A reaction: Wittgenstein's idea is that you can use the logical connectives to construct all the other universal and negative facts. 'Optimalism' restricts truthmaking to atomic statements. |
| 18483 | The main idea of truth-making is that what a proposition is about is what matters [MacBride] |
| Full Idea: According the Lewis, the kernel of truth in truth-making is the idea that propositions have a subject matter. They are about things, so whether they are true or false depends on how those things stand. | |
| From: Fraser MacBride (Truthmakers [2013], 2.4.1) | |
| A reaction: [Lewis 'Things Qua Truth-makers' 2003] That sounds like the first step in the story, rather than the 'kernel' of the truth-making approach. |
| 18479 | There are different types of truthmakers for different types of negative truth [MacBride] |
| Full Idea: We recognise that what makes it true that there is no oil in this engine is different from what makes it true that there are no dodos left. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.4.1) | |
| A reaction: This looks like a local particular negation up against a universal negation. I'm not sure there is a big difference between 'my dodo's gone missing' (like my oil), and 'all the dodos have gone permanently missing'. |
| 18477 | There aren't enough positive states out there to support all the negative truths [MacBride] |
| Full Idea: It's not obvious that there are enough positive states out there to underwrite all the negative truths. Even though it may be true that this liquid is odourless this needn't be because there's something further about it that excludes its being odourless. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.4.1) | |
| A reaction: What is the ontological status of all these hypothetical truths? What is the truthmaker for 'a trillion trillion negative truths exist'? What is the status of 'this is not not-red'? |
| 18482 | Optimalists say that negative and universal are true 'by default' from the positive truths [MacBride] |
| Full Idea: Optimalists say that negative truths are 'true by default' (having the opposite truth value of p), and universal truths are too. Universal truths are equivalent to negative existential truths, which are true by default. | |
| From: Fraser MacBride (Truthmakers [2013], 2.2) | |
| A reaction: The background idea is Wittgenstein's, that if p is false, then not-p is true by default, without anyone having to assert the negation. This strikes me as a very promising approach to truthmaking. See Simons 2008. |
| 18474 | Does 'this sentence has no truth-maker' have a truth-maker? Reductio suggests it can't have [MacBride] |
| Full Idea: If the sentence 'This sentence has no truth-maker' has a truth-maker, then it must be true. But then what it says must be the case, so it has no truth-maker. Hence by reductio the sentence has no truth-maker. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.1) | |
| A reaction: [Argument proposed by Peter Milne 2005] Rodriguez-Pereyra replies that the sentence is meaningless, so that it can't possibly be true. The Liar sentence is also said to be meaningless. The argument opposes Maximalism. |
| 18485 | Even idealists could accept truthmakers, as mind-dependent [MacBride] |
| Full Idea: Even an idealist could accept that there are truth-makers whilst thinking of them as mind-dependent entities. | |
| From: Fraser MacBride (Truthmakers [2013], 3.1) | |
| A reaction: This undercuts anyone (me, perhaps?) who was hoping to prop up their robust realism with an angry demand to be shown the truthmakers. |
| 18490 | Maybe 'makes true' is not an active verb, but just a formal connective like 'because'? [MacBride] |
| Full Idea: Maybe the truth-maker panegyrists have misconstrued the logical form of 'makes true'. They have taken it to be a verb like 'x hits y', when really it is akin to the connective '→' or 'because'. | |
| From: Fraser MacBride (Truthmakers [2013], 3.7) | |
| A reaction: [He cites Melia 2005] This isn't any sort of refutation of truth-making, but an offer of how to think of the phenomenon if you reject the big principle. I like truth-making, but resist the 'makes' that brings unthought propositions into existence. |
| 18493 | Truthmaker talk of 'something' making sentences true, which presupposes objectual quantification [MacBride] |
| Full Idea: When supporters of truth-making talk of 'something' which makes a sentence true, they make the assumption that it is an objectual quantifier in name position. | |
| From: Fraser MacBride (Truthmakers [2013], 3.8) | |
| A reaction: We might say, more concisely, that they are 'reifying' the something. This makes it sound as if Armstrong and Bigelow have made a mistake, but that are simply asserting that this particular quantification is indeed objectual. |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| Full Idea: Second-order set theory is just like first-order set-theory, except that we use the version of Replacement with a universal second-order quantifier over functions from set to sets. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VII.4) |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| Full Idea: A member m of M is an 'upper bound' of a subset N of M if m is not less than any member of N. A member m of M is a 'least upper bound' of N if m is an upper bound of N such that if l is any other upper bound of N, then m is less than l. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: [if you don't follow that, you'll have to keep rereading it till you do] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| Full Idea: Since combinatorial collections are enumerated, some multiplicities may be too large to be gathered into combinatorial collections. But the size of a multiplicity seems quite irrelevant to whether it forms a logical connection. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| Full Idea: Many of those who are skeptical about the existence of infinite combinatorial collections would want to doubt or deny the Axiom of Choice. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.2) |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| Full Idea: The Power Set is just he codification of the fact that the collection of functions from a mathematical collection to a mathematical collection is itself a mathematical collection that can serve as a domain of mathematical study. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| Full Idea: The Axiom of Replacement (of Skolem and Fraenkel) was remarkable for its universal acceptance, though it seemed to have no consequences except for the properties of the higher reaches of the Cantorian infinite. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| Full Idea: The Axiom of Foundation (Zermelo 1930) says 'Every (descending) chain in which each element is a member of the previous one is of finite length'. ..This forbids circles of membership, or ungrounded sets. ..The iterative conception gives this centre stage. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.4) |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| Full Idea: Combinatorial collections (defined just by the members) obviously obey the Axiom of Choice, while it is at best dubious whether logical connections (defined by a rule) do. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| Full Idea: The controversy was not about Choice per se, but about the correct notion of function - between advocates of taking mathematics to be about arbitrary functions and advocates of taking it to be about functions given by rules. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| Full Idea: The Peano-Russell notion of class is the 'logical' notion, where each collection is associated with some kind of definition or rule that characterises the members of the collection. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.1) |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| Full Idea: The iterative conception of set was not so much as suggested, let alone advocated by anyone, until 1947. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], I) |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| Full Idea: The iterative conception of sets does not tell us how far to iterate, and so we must start with an Axiom of Infinity. It also presupposes the notion of 'transfinite iteration'. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| Full Idea: The iterative conception does not provide a conception that unifies the axioms of set theory, ...and it has had very little impact on what theorems can be proved. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) | |
| A reaction: He says he would like to reject the iterative conception, but it may turn out that Foundation enables new proofs in mathematics (though it hasn't so far). |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| Full Idea: Limitation of Size has it that if a collection is the same size as a set, then it is a set. The Axiom of Replacement is characteristic of limitation of size. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.5) |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| Full Idea: A collection M is 'well-ordered' by a relation < if < linearly orders M with a least element, and every subset of M that has an upper bound not in it has an immediate successor. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) |
| 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. |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| Full Idea: The distinctive feature of second-order logic is that it presupposes that, given a domain, there is a fact of the matter about what the relations on it are, so that the range of the second-order quantifiers is fixed as soon as the domain is fixed. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3) | |
| A reaction: This sounds like a rather large assumption, which is open to challenge. I am not sure whether it was the basis of Quine's challenge to second-order logic. He seems to have disliked its vagueness, because it didn't stick with 'objects'. |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| Full Idea: The Law of Excluded Middle is (part of) the foundation of the mathematical practice of employing proofs by contradiction. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) | |
| A reaction: This applies in a lot of logic, as well as in mathematics. Come to think of it, it applies in Sudoku. |
| 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. |
| 18489 | Connectives link sentences without linking their meanings [MacBride] |
| Full Idea: The 'connectives' are expressions that link sentences but without expressing a relation that holds between the states of affairs, facts or tropes that these sentences denote. | |
| From: Fraser MacBride (Truthmakers [2013], 3.7) | |
| A reaction: MacBride notes that these contrast with ordinary verbs, which do express meaningful relations. |
| 18476 | 'A is F' may not be positive ('is dead'), and 'A is not-F' may not be negative ('is not blind') [MacBride] |
| Full Idea: Statements of the form 'a is F' aren't invariably positive ('a is dead'), and nor are statements of the form 'a isn't F' ('a isn't blind') always negative. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.4) | |
| A reaction: The point is that the negation may be implicit in the predicate. There are many ways to affirm or deny something, other than by use of the standard syntax. |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| Full Idea: Mathematics is today thought of as the study of abstract structure, not the study of quantity. That point of view arose directly out of the development of the set-theoretic notion of abstract structure. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.2) | |
| A reaction: It sounds as if Structuralism, which is a controversial view in philosophy, is a fait accompli among mathematicians. |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| Full Idea: One reason to introduce the rational numbers is that it simplifes the theory of division, since every rational number is divisible by every nonzero rational number, while the analogous statement is false for the natural numbers. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.3) | |
| A reaction: That is, with rations every division operation has an answer. |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| Full Idea: The chief importance of the Continuum Hypothesis for Cantor (I believe) was that it would show that the real numbers form a set, and hence that they were encompassed by his theory. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], IV.2) |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| Full Idea: The Cauchy convergence criterion for a sequence: the sequence S0,S1,... has a limit if |S(n+r) - S(n)| is less than any given quantity for every value of r and sufficiently large values of n. He proved this necessary, but not sufficient. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], 2.5) |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| Full Idea: Roughly speaking, the upper and lower parts of the Dedekind cut correspond to the commensurable ratios greater than and less than a given incommensurable ratio. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], II.6) | |
| A reaction: Thus there is the problem of whether the contents of the gap are one unique thing, or many. |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| Full Idea: Counting a set produces a well-ordering of it. Conversely, if one has a well-ordering of a set, one can count it by following the well-ordering. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: Cantor didn't mean that you could literally count the set, only in principle. |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| Full Idea: The indiscernibility of indefinitely large sizes will be a critical part of the theory of indefinitely large sizes. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VIII.2) |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| Full Idea: My proposal is that the concept of the infinite began with an extrapolation from the experience of indefinitely large size. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VIII.2) | |
| A reaction: I think it might be better to talk of an 'abstraction' than an 'extrapolition', since the latter is just more of the same, which doesn't get you to concept. Lavine spends 100 pages working out his proposal. |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| Full Idea: The intuitionist endorse the actual finite, but only the potential infinite. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.2) |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| Full Idea: The symbol 'aleph-nought' denotes the cardinal number of the set of natural numbers. The symbol 'aleph-one' denotes the next larger cardinal number. 'Aleph-omega' denotes the omega-th cardinal number. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.3) |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| Full Idea: The ordinals are basic because the transfinite sets are those that can be counted, or (equivalently for Cantor), those that can be numbered by an ordinal or are well-ordered. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.4) | |
| A reaction: Lavine observes (p.55) that for Cantor 'countable' meant 'countable by God'! |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| Full Idea: The paradox of the largest ordinal (the 'Burali-Forti') is that the class of all ordinal numbers is apparently well-ordered, and so it has an ordinal number as order type, which must be the largest ordinal - but all ordinals can be increased by one. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.5) |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| Full Idea: The paradox of the largest cardinal ('Cantor's Paradox') says the diagonal argument shows there is no largest cardinal, but the class of all individuals (including the classes) must be the largest cardinal number. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], III.5) |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| Full Idea: Every theorem of mathematics has a counterpart with set theory - ...but that theory cannot serve as a basis for the notion of proof. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3) |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| Full Idea: In modern mathematics virtually all work is only up to isomorphism and no one cares what the numbers or points and lines 'really are'. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) | |
| A reaction: At least that leaves the field open for philosophers, because we do care what things really are. So should everybody else, but there is no persuading some people. |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| Full Idea: Intuitionism in philosophy of mathematics rejects set-theoretic foundations. | |
| From: Shaughan Lavine (Understanding the Infinite [1994], V.3 n33) |
| 18480 | Maybe it only exists if it is a truthmaker (rather than the value of a variable)? [MacBride] |
| Full Idea: 'To be is to be a truth-maker' has been proposed as a replacement the standard conception of ontological commitment, that to be is to be the value of a variable. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.4.2) | |
| A reaction: [He cites Ross Cameron 2008] Unconvincing. What does it mean to say that some remote unexperienced bit of the universe 'makes truths'? How many truths? Where do these truths reside when they aren't doing anything useful? |
| 18471 | Different types of 'grounding' seem to have no more than a family resemblance relation [MacBride] |
| Full Idea: The concept of 'grounding' appears to cry out for treatment as a family resemblance concept, a concept whose instances have no more in common than different games do. | |
| From: Fraser MacBride (Truthmakers [2013], 1.6) | |
| A reaction: I like the word 'determinations', though MacBride's point my also apply to that. I take causation to be one species of determination, and truth-making to be another. They form a real family, with no adoptees. |
| 18472 | Which has priority - 'grounding' or 'truth-making'? [MacBride] |
| Full Idea: Some philosophers define 'grounding' in terms of 'truth-making', rather than the other way around. | |
| From: Fraser MacBride (Truthmakers [2013], 1.6) | |
| A reaction: [Cameron exemplifies the first, and Schaffer the second] I would have thought that grounding was in the world, but truth-making required the introduction of propositions about the world by minds, so grounding is prior. Schaffer is right. |
| 18475 | Russell allows some complex facts, but Wittgenstein only allows atomic facts [MacBride] |
| Full Idea: The logical atomism of Russell admitted some logically complex facts but not others - in contrast to Wittgenstein's version which admitted only atomic facts. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.3) | |
| A reaction: For truthmakers, it looks as if the Wittgenstein version might do a better job (e.g. with negative truths). I quite like the Russell approach, where complex facts underwrite the logical connectives. Disjunctive, negative, conjunctive, hypothetical facts. |
| 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. |
| 18478 | Wittgenstein's plan to show there is only logical necessity failed, because of colours [MacBride] |
| Full Idea: It is almost universally acknowledged that Wittgenstein's plan to show all necessity is logical necessity ended in failure - indeed foundered upon the very problem of explaining colour incompatibilities. | |
| From: Fraser MacBride (Truthmakers [2013], 2.1.4.1) | |
| A reaction: I'm not sure whether you can 'show' that colour incompatibility is some sort of necessity, though intuitively it seems so. I'm thinking that 'necessity' is a unitary concept, with a wide variety of sources generating it. |
| 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. |
| 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 Michèle 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). |