79 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. |
13560 | A wise man is not subservient to anything [Seneca] |
Full Idea: I do not call any man wise who is subservient to anything. | |
From: Seneca the Younger (On the Happy Life [c.60], §11) | |
A reaction: At the very least, a wise man should be subservient to a wiser man. |
13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
Full Idea: We are all post-Kantians, ...because Kant set an agenda for philosophy that we are still working through. | |
From: William D. Hart (The Evolution of Logic [2010], 2) | |
A reaction: Hart says that the main agenda is set by Kant's desire to defend the principle of sufficient reason against Hume's attack on causation. I would take it more generally to be the assessment of metaphysics, and of a priori knowledge. |
13477 | The problems are the monuments of philosophy [Hart,WD] |
Full Idea: The real monuments of philosophy are its problems. | |
From: William D. Hart (The Evolution of Logic [2010], 2) | |
A reaction: Presumably he means '....rather than its solutions'. No other subject would be very happy with that sort of claim. Compare Idea 8243. A complaint against analytic philosophy is that it has achieved no consensus at all. |
13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
Full Idea: By now, no education in abstract pursuits is adequate without some familiarity with sets. | |
From: William D. Hart (The Evolution of Logic [2010], 10) | |
A reaction: A heart-sinking observation for those who aspire to study metaphysics and modality. The question is, what will count as 'some' familiarity? Are only professional logicians now allowed to be proper philosophers? |
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? |
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 | Naïve 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. Naïve 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. |
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. |
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) |
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. |
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. |
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. |
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? |
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) |
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) |
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) |
13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
Full Idea: First-order logic is 'compact', which means that any logical consequence of a set (finite or infinite) of first-order sentences is a logical consequence of a finite subset of those sentences. | |
From: William D. Hart (The Evolution of Logic [2010], 3) |
13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
Full Idea: Berry's Paradox: by the least number principle 'the least number denoted by no description of fewer than 79 letters' exists, but we just referred to it using a description of 77 letters. | |
From: William D. Hart (The Evolution of Logic [2010], 3) | |
A reaction: I struggle with this. If I refer to 'an object to which no human being could possibly refer', have I just referred to something? Graham Priest likes this sort of idea. |
13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
Full Idea: The Burali-Forti Paradox was a crisis for Cantor's theory of ordinal numbers. | |
From: William D. Hart (The Evolution of Logic [2010], 3) |
13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
Full Idea: In effect, the machinery introduced to solve the liar can always be rejigged to yield another version the liar. | |
From: William D. Hart (The Evolution of Logic [2010], 4) | |
A reaction: [He cites Hans Herzberger 1980-81] The machinery is Tarski's device of only talking about sentences of a language by using a 'metalanguage'. |
13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
Full Idea: We can show (using the axiom of choice) that the less-than relation, <, well-orders the ordinals, ...and that it partially orders the ordinals, ...and that it totally orders the ordinals. | |
From: William D. Hart (The Evolution of Logic [2010], 1) |
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) |
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) |
13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
Full Idea: It is easier to generalize von Neumann's finite ordinals into the transfinite. All Zermelo's nonzero finite ordinals are singletons, but if ω were a singleton it is hard to see how if could fail to be the successor of its member and so not a limit. | |
From: William D. Hart (The Evolution of Logic [2010], 3) |
13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
Full Idea: The real numbers were not isolated from geometry until the arithmetization of analysis during the nineteenth century. | |
From: William D. Hart (The Evolution of Logic [2010], 1) |
13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
Full Idea: Mathematical induction is a way to establish truths about the infinity of natural numbers by a finite proof. | |
From: William D. Hart (The Evolution of Logic [2010], 5) | |
A reaction: If there are truths about infinities, it is very tempting to infer that the infinities must therefore 'exist'. A nice, and large, question in philosophy is whether there can be truths without corresponding implications of existence. |
13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
Full Idea: There is a familiar comparison between Euclid (unique parallel) and 'spherical' geometry (no parallel) and 'saddle' geometry (several parallels). | |
From: William D. Hart (The Evolution of Logic [2010], 2) |
13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
Full Idea: The thesis that no existence proposition is analytic is one of the few constants in philosophical consciences, but there are many existence claims in mathematics, such as the infinity of primes, five regular solids, and certain undecidable propositions. | |
From: William D. Hart (The Evolution of Logic [2010], 2) |
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. |
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. |
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. |
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. |
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. |
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. |
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. |
13558 | The supreme good is harmony of spirit [Seneca] |
Full Idea: The highest good is harmony of spirit. | |
From: Seneca the Younger (On the Happy Life [c.60], §08) | |
A reaction: This idea is straight from Plato's Republic. |
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! |
13559 | I seek virtue, because it is its own reward [Seneca] |
Full Idea: You ask what I seek from virtue? Virtue herself. For she has nothing better, she is herself her own reward. | |
From: Seneca the Younger (On the Happy Life [c.60], §09) | |
A reaction: Presumably this is the source of the popular saying that 'virtue is its own reward'. The trouble is that this doesn't seem a very persuasive thing to say to a sceptic who doubts whether being virtuous is worth the trouble. |
13561 | Virtue is always moderate, so excess need not be feared [Seneca] |
Full Idea: In the case of virtue excess should not be feared, since in virtue resides moderation. | |
From: Seneca the Younger (On the Happy Life [c.60], §13) | |
A reaction: This seems to imply that all of the virtues are unified in the one achievement of the virtuous state. It leaves the notion of 'virtue' a bit thin in content, though. |
13562 | It is shameful to not even recognise your own slaves [Seneca] |
Full Idea: Why, to your shame, are you so careless that you do not know your handful of slaves by sight? | |
From: Seneca the Younger (On the Happy Life [c.60], §17) |
13564 | There is far more scope for virtue if you are wealthy; poverty only allows endurance [Seneca] |
Full Idea: What doubt can there be that the wise man has greater scope for displaying his powers if he is rich than if he is poor, since in the case of poverty only one kind of virtue exists - refusal to be bowed down and crushed. | |
From: Seneca the Younger (On the Happy Life [c.60], §22) | |
A reaction: It is against this view that I see Jesus proposing poverty as central to virtue. But then he has the surprising view (to Seneca) that humility is a virtue. What Nietzsche calls the slaves' inversion of values. |
13563 | Why does your wife wear in her ears the income of a wealthy house? [Seneca] |
Full Idea: Why does your wife wear in her ears the income of a wealthy house? | |
From: Seneca the Younger (On the Happy Life [c.60], §17) |
13565 | If wealth was a good, it would make men good [Seneca] |
Full Idea: Wealth is not a good; for it it was, it would make men good. | |
From: Seneca the Younger (On the Happy Life [c.60], §24) | |
A reaction: An immediately attractive argument, but should we assume that anything which is good will enhance our personal goodness? If goodness is a habit, then continual pursuit of wealth is the test case to examine. Seneca is right! |
13557 | Unfortunately the majority do not tend to favour what is best [Seneca] |
Full Idea: Human concerns are not so happily arranged that the majority favours the better things. | |
From: Seneca the Younger (On the Happy Life [c.60], §02) | |
A reaction: On the whole Seneca is unimpressed by democracy, as people are rushed into decisions by the crowd, and live to regret them. |
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). |