76 ideas
| 23890 | For Plato true wisdom is supernatural [Plato, by Weil] |
| Full Idea: It is evident that Plato regards true wisdom as something supernatural. | |
| From: report of Plato (works [c.375 BCE]) by Simone Weil - God in Plato p.61 | |
| A reaction: Taken literally, I assume this is wrong, but we can empathise with the thought. Wisdom has the feeling of rising above the level of mere knowledge, to achieve the overview I associate with philosophy. |
| 3060 | Plato never mentions Democritus, and wished to burn his books [Plato, by Diog. Laertius] |
| Full Idea: Plato, who mentions nearly all the ancient philosophers, nowhere speaks of Democritus; he wished to burn all of his books, but was persuaded that it was futile. | |
| From: report of Plato (works [c.375 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.7.8 |
| 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? |
| 23891 | Two contradictories force us to find a relation which will correlate them [Plato, by Weil] |
| Full Idea: Where contradictions appear there is a correlation of contraries, which is relation. If a contradiction is imposed on the intelligence, it is forced to think of a relation to transform the contradiction into a correlation, which draws the soul higher. | |
| From: report of Plato (works [c.375 BCE]) by Simone Weil - God in Plato p.70 | |
| A reaction: A much better account of the dialectic than anything I have yet seen in Hegel. For the first time I see some sense in it. A contradiction is not a falsehood, and it must be addressed rather than side-stepped. A kink in the system, that needs ironing. |
| 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. |
| 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. |
| 14502 | Plato's idea of 'structure' tends to be mathematically expressed [Plato, by Koslicki] |
| Full Idea: 'Structure' tends to be characterized by Plato as something that is mathematically expressed. | |
| From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects V.3 iv | |
| A reaction: [Koslicki is drawing on Verity Harte here] |
| 3039 | When Diogenes said he could only see objects but not their forms, Plato said it was because he had eyes but no intellect [Plato, by Diog. Laertius] |
| Full Idea: When Diogenes told Plato he saw tables and cups, but not 'tableness' and 'cupness', Plato replied that this was because Diogenes had eyes but no intellect. | |
| From: report of Plato (works [c.375 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.2.6 |
| 20906 | Platonists argue for the indivisible triangle-in-itself [Plato, by Aristotle] |
| Full Idea: The Platonists, on the basis of purely logical arguments, posit the existence of an indivisible 'triangle in itself'. | |
| From: report of Plato (works [c.375 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 316a15 | |
| A reaction: A helpful confirmation that geometrical figures really are among the Forms (bearing in mind that numbers are not, because they contain one another). What shape is the Form of the triangle? |
| 17948 | Plato's Forms meant that the sophists only taught the appearance of wisdom and virtue [Plato, by Nehamas] |
| Full Idea: Plato's theory of Forms allowed him to claim that the sophists and other opponents were trapped in the world of appearance. What they therefore taught was only apparent wisdom and virtue. | |
| From: report of Plato (works [c.375 BCE]) by Alexander Nehamas - Eristic,Antilogic,Sophistic,Dialectic p.118 |
| 556 | If there is one Form for both the Form and its participants, they must have something in common [Aristotle on Plato] |
| Full Idea: If there is the same Form for the Forms and for their participants, then they must have something in common. | |
| From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 991a |
| 563 | If gods are like men, they are just eternal men; similarly, Forms must differ from particulars [Aristotle on Plato] |
| Full Idea: We say there is the form of man, horse and health, but nothing else, making the same mistake as those who say that there are gods but that they are in the form of men. They just posit eternal men, and here we are not positing forms but eternal sensibles. | |
| From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 997b |
| 565 | The Forms cannot be changeless if they are in changing things [Aristotle on Plato] |
| Full Idea: The Forms could not be changeless if they were in changing things. | |
| From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 998a |
| 557 | A Form is a cause of things only in the way that white mixed with white is a cause [Aristotle on Plato] |
| Full Idea: A Form is a cause of things only in the way that white mixed with white is a cause. | |
| From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 991a |
| 9607 | The greatest discovery in human thought is Plato's discovery of abstract objects [Brown,JR on Plato] |
| Full Idea: The greatest discovery in the history of human thought is Plato's discovery of abstract objects. | |
| From: comment on Plato (works [c.375 BCE]) by James Robert Brown - Philosophy of Mathematics Ch. 2 | |
| A reaction: Compare Idea 2860! Given the diametrically opposed views, it is clearly likely that Plato's central view is the most important idea in the history of human thought, even if it is wrong. |
| 13263 | We can grasp whole things in science, because they have a mathematics and a teleology [Plato, by Koslicki] |
| Full Idea: Due to the mathematical nature of structure and the teleological cause underlying the creation of Platonic wholes, these wholes are intelligible, and are in fact the proper objects of science. | |
| From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.3 | |
| A reaction: I like this idea, because it pays attention to the connection between how we conceive objects to be, and how we are able to think about objects. Only examining these two together enables us to grasp metaphysics. |
| 13261 | Plato sees an object's structure as expressible in mathematics [Plato, by Koslicki] |
| Full Idea: The 'structure' of an object tends to be characterised by Plato as something that is mathematically expressible. | |
| From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.3 | |
| A reaction: This seems to be pure Pythagoreanism (see Idea 644). Plato is pursuing Pythagoras's research programme, of trying to find mathematics buried in every aspect of reality. |
| 13265 | Plato was less concerned than Aristotle with the source of unity in a complex object [Plato, by Koslicki] |
| Full Idea: Plato was less concerned than Aristotle with the project of how to account, in completely general terms, for the source of unity within a mereologically complex object. | |
| From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.5 | |
| A reaction: Plato seems to have simply asserted that some sort of harmony held things together. Aristotles puts the forms [eidos] within objects, rather than external, so he has to give a fuller account of what is going on in an object. He never managed it! |
| 593 | Plato's holds that there are three substances: Forms, mathematical entities, and perceptible bodies [Plato, by Aristotle] |
| Full Idea: Plato's doctrine was that the Forms and mathematicals are two substances and that the third substance is that of perceptible bodies. | |
| From: report of Plato (works [c.375 BCE]) by Aristotle - Metaphysics 1028b |
| 13260 | Plato says wholes are either containers, or they're atomic, or they don't exist [Plato, by Koslicki] |
| Full Idea: Plato considers a 'container' model for wholes (which are disjoint from their parts) [Parm 144e3-], and a 'nihilist' model, in which only wholes are mereological atoms, and a 'bare pluralities' view, in which wholes are not really one at all. | |
| From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.2 | |
| A reaction: [She cites Verity Harte for this analysis of Plato] The fourth, and best, seems to be that wholes are parts which fall under some unifying force or structure or principle. |
| 11237 | Only universals have essence [Plato, by Politis] |
| Full Idea: Plato argues that only universals have essence. | |
| From: report of Plato (works [c.375 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.4 |
| 11238 | Plato and Aristotle take essence to make a thing what it is [Plato, by Politis] |
| Full Idea: Plato and Aristotle have a shared general conception of essence: the essence of a thing is what that thing is simply in virtue of itself and in virtue of being the very thing it is. It answers the question 'What is this very thing?' | |
| From: report of Plato (works [c.375 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.4 |
| 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. |
| 17085 | A good explanation totally rules out the opposite explanation (so Forms are required) [Plato, by Ruben] |
| Full Idea: For Plato, an acceptable explanation is one such that there is no possibility of there being the opposite explanation at all, and he thought that only explanations in terms of the Forms, but never physical explanations, could meet this requirement. | |
| From: report of Plato (works [c.375 BCE]) by David-Hillel Ruben - Explaining Explanation Ch 2 | |
| A reaction: [Republic 436c is cited] |
| 1651 | Plato wanted to somehow control and purify the passions [Vlastos on Plato] |
| Full Idea: Plato put high on his agenda a project which did not figure in Socrates' programme at all: the hygienic conditioning of the passions. This cannot be an intellectual process, as argument cannot touch them. | |
| From: comment on Plato (works [c.375 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.88 | |
| A reaction: This is the standard traditional view of any thinker who exaggerates the importance and potential of reason in our lives. |
| 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. |
| 3324 | Plato's whole philosophy may be based on being duped by reification - a figure of speech [Benardete,JA on Plato] |
| Full Idea: Plato is liable to the charge of having been duped by a figure of speech, albeit the most profound of all, the trope of reification. | |
| From: comment on Plato (works [c.375 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.12 | |
| A reaction: That might be a plausible account if his view was ridiculous, but given how many powerful friends Plato has, especially in the philosophy of mathematics, we should assume he was cleverer than that. |
| 7503 | Plato never refers to examining the conscience [Plato, by Foucault] |
| Full Idea: Plato never speaks of the examination of conscience - never! | |
| From: report of Plato (works [c.375 BCE]) by Michel Foucault - On the Genealogy of Ethics p.276 | |
| A reaction: Plato does imply some sort of self-evident direct knowledge about that nature of a healthy soul. Presumably the full-blown concept of conscience is something given from outside, from God. In 'Euthyphro', Plato asserts the primacy of morality (Idea 337). |
| 2173 | As religion and convention collapsed, Plato sought morals not just in knowledge, but in the soul [Williams,B on Plato] |
| Full Idea: Once gods and fate and social expectation were no longer there, Plato felt it necessary to discover ethics inside human nature, not just as ethical knowledge (Socrates' view), but in the structure of the soul. | |
| From: comment on Plato (works [c.375 BCE]) by Bernard Williams - Shame and Necessity II - p.43 | |
| A reaction: anti Charles Taylor |
| 9274 | Plato's legacy to European thought was the Good, the Beautiful and the True [Plato, by Gray] |
| Full Idea: Plato's legacy to European thought was a trio of capital letters - the Good, the Beautiful and the True. | |
| From: report of Plato (works [c.375 BCE]) by John Gray - Straw Dogs 2.8 | |
| A reaction: It seems to have been Baumgarten who turned this into a slogan (Idea 8117). Gray says these ideals are lethal, but I identify with them very strongly, and am quite happy to see the good life as an attempt to find the right balance between them. |
| 94 | Pleasure is better with the addition of intelligence, so pleasure is not the good [Plato, by Aristotle] |
| Full Idea: Plato says the life of pleasure is more desirable with the addition of intelligence, and if the combination is better, pleasure is not the good. | |
| From: report of Plato (works [c.375 BCE]) by Aristotle - Nicomachean Ethics 1172b27 | |
| A reaction: It is obvious why we like pleasure, but not why intelligence makes it 'better'. Maybe it is just because we enjoy intelligence? |
| 17947 | Plato decided that the virtuous and happy life was the philosophical life [Plato, by Nehamas] |
| Full Idea: Plato came to the conclusion that virtue and happiness consist in the life of philosophy itself. | |
| From: report of Plato (works [c.375 BCE]) by Alexander Nehamas - Eristic,Antilogic,Sophistic,Dialectic p.117 | |
| A reaction: This view is obviously ridiculous, because it largely excludes almost the entire human race, which sees philosophy as a cul-de-sac, even if it is good. But virtue and happiness need some serious thought. |
| 6015 | Plato, unusually, said that theoretical and practical wisdom are inseparable [Plato, by Kraut] |
| Full Idea: Two virtues that are ordinarily kept distinct - theoretical and practical wisdom - are joined by Plato; he thinks that neither one can be fully possessed unless it is combined with the other. | |
| From: report of Plato (works [c.375 BCE]) by Richard Kraut - Plato | |
| A reaction: I get the impression that this doctrine comes from Socrates, whose position is widely reported as 'intellectualist'. Aristotle certainly held the opposite view. |
| 2912 | Plato is boring [Nietzsche on Plato] |
| Full Idea: Plato is boring. | |
| From: comment on Plato (works [c.375 BCE]) by Friedrich Nietzsche - Twilight of the Idols 9.2 |
| 22232 | Authenticity is taking responsibility for a situation, with all its risks and emotions [Sartre] |
| Full Idea: Authenticity consists in having a true and lucid consciousness of the situation, in assuming the responsibilities and risks that it involves, in accepting it in pride of humiliation, sometimes in horror and hate. | |
| From: Jean-Paul Sartre (Anti-Semite and Jew [1946], p.90), quoted by Christine Daigle - Jean-Paul Sartre 2.4 | |
| A reaction: [Not sure what 'pride of humiliation' is, so it may be a typo for 'or'] |
| 1526 | Almost everyone except Plato thinks that time could not have been generated [Plato, by Aristotle] |
| Full Idea: With a single exception (Plato) everyone agrees about time - that it is not generated. Democritus says time is an obvious example of something not generated. | |
| From: report of Plato (works [c.375 BCE]) by Aristotle - Physics 251b14 |