72 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| Full Idea: We are all post-Kantians, ...because Kant set an agenda for philosophy that we are still working through. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Hart says that the main agenda is set by Kant's desire to defend the principle of sufficient reason against Hume's attack on causation. I would take it more generally to be the assessment of metaphysics, and of a priori knowledge. |
| 326 | For relaxation one can consider the world of change, instead of eternal things [Plato] |
| Full Idea: If, for relaxation, one gives up discussing eternal things, it is pleasant to consider likely accounts of the world of change. | |
| From: Plato (Timaeus [c.349 BCE], 59c) | |
| A reaction: To understand this, examine Plato's example of the Line at 'Republic' 509d. |
| 315 | Philosophy is the supreme gift of the gods to mortals [Plato] |
| Full Idea: Philosophy is the greatest gift the gods have ever given or ever will give to mortals. | |
| From: Plato (Timaeus [c.349 BCE], 47b) | |
| A reaction: I wonder why they gave it to us? |
| 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? |
| 306 | Nothing can come to be without a cause [Plato] |
| Full Idea: Nothing can come to be without a cause. | |
| From: Plato (Timaeus [c.349 BCE], 28a) |
| 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. |
| 13190 | I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz] |
| Full Idea: Notwithstanding my infinitesimal calculus, I do not admit any real infinite numbers, even though I confess that the multitude of things surpasses any finite number, or rather any number. ..I consider infinitesimal quantities to be useful fictions. | |
| From: Gottfried Leibniz (Letters to Samuel Masson [1716], 1716) | |
| A reaction: With the phrase 'useful fictions' we seem to have jumped straight into Harty Field. I'm with Leibniz on this one. The history of mathematics is a series of ingenious inventions, whenever they seem to make further exciting proofs possible. |
| 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) |
| 324 | Before the existence of the world there must have been being, space and becoming [Plato] |
| Full Idea: There were, before the world came into existence, being, space, and becoming, three distinct realities. | |
| From: Plato (Timaeus [c.349 BCE], 52d) |
| 20364 | The apprehensions of reason remain unchanging, but reasonless sensation shows mere becoming [Plato] |
| Full Idea: That which is apprehended by intelligence and reason is always in the same state, but that which is conceived by opinion with the help of sensation and without reason is always in a process of becoming and perishing, and never really is. | |
| From: Plato (Timaeus [c.349 BCE], 28a) | |
| A reaction: Lots of problems with this, of which I take the main one to be the idea that sensation is 'without reason', as if there were a sharp dichotomy in our ways of evaluating reality. Laws of nature seem to be laws of change, not of stasis. |
| 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. |
| 12042 | Plato's Forms were seen as part of physics, rather than of metaphysics [Plato, by Annas] |
| Full Idea: In the ancient world Plato's Theory of Forms was mostly seen as one aspect of Plato's 'physics' or theory of the world (rather than as 'metaphysics'). | |
| From: report of Plato (Timaeus [c.349 BCE]) by Julia Annas - Ancient Philosophy: very short introduction Ch.5 | |
| A reaction: This is how I also see the theory, but then I am inclined to see religion as a rather startling branch of speculative physics. Annas cites 'Timaeus' as the key text for this. |
| 307 | Something will always be well-made if the maker keeps in mind the eternal underlying pattern [Plato] |
| Full Idea: Whenever the maker of anything keeps his eye on the eternally unchanging and uses it as his pattern for the form and function of his product the result must be good. | |
| From: Plato (Timaeus [c.349 BCE], 28b) |
| 318 | In addition to the underlying unchanging model and a changing copy of it, there must also be a foundation of all change [Plato] |
| Full Idea: In addition to an eternal unchanging model and a visible and changing copy of reality, there must be a third part, the receptacle and nurse of all becoming and change. | |
| From: Plato (Timaeus [c.349 BCE], 49b) | |
| A reaction: cf Aristotle's criticism in Metaphysics |
| 321 | For knowledge and true opinion to be different there must be Forms; otherwise we are just stuck with sensations [Plato] |
| Full Idea: If intelligence and true opinion are different, then the forms must exist, but if they are the same, then what our senses perceive must be the most certain reality. | |
| From: Plato (Timaeus [c.349 BCE], 51d) |
| 317 | The universe is basically an intelligible and unchanging model, and a visible and changing copy of it [Plato] |
| Full Idea: Our basic description of the universe contained an intelligible and unchanging model, and a visible and changing copy of it. | |
| From: Plato (Timaeus [c.349 BCE], 48e) |
| 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. |
| 334 | Only bird-brained people think astronomy is entirely a matter of evidence [Plato] |
| Full Idea: Birds are empty-headed men who grew feathers instead of hair, because they were interested in astronomy but thought it was entirely a matter of physical evidence. | |
| From: Plato (Timaeus [c.349 BCE], 91d) |
| 5962 | Plato says the soul is ordered by number [Plato, by Plutarch] |
| Full Idea: Plato regards the substance of soul not as number but as being ordered by number. | |
| From: report of Plato (Timaeus [c.349 BCE]) by Plutarch - 68: Generation of the soul in 'Timaeus' 1023 | |
| A reaction: This remark points towards Plato's esoteric doctrines, which are some sort of mathematical metaphysics. The idea that order and numbers are in some way connected is one of the most powerful in western civilization, with undeniable appeal. |
| 330 | No one wants to be bad, but bad men result from physical and educational failures, which they do not want or choose [Plato] |
| Full Idea: No one wishes to be bad, but a bad man is bad because of some flaw in his physical makeup and failure in his education, neither of which he likes or chooses. | |
| From: Plato (Timaeus [c.349 BCE], 86e) |
| 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. |
| 316 | Music has harmony like the soul, and serves to reorder disharmony within us [Plato] |
| Full Idea: Music has harmonic motions like the orbits of the soul, and is not for irrational pleasure, but to reduce to order any disharmony in the revolutions within us. | |
| From: Plato (Timaeus [c.349 BCE], 47d) |
| 332 | One should exercise both the mind and the body, to avoid imbalance [Plato] |
| Full Idea: One should preserve a balance and avoid exercising the mind or body without the other; mathematicians should exercise physically, and athletes mentally. | |
| From: Plato (Timaeus [c.349 BCE], 88c) | |
| A reaction: Excellent, and very modern. Use it or lose it. It suggests that Plato had a fairly holistic view of a human being, and saw mind and body as closely integrated. |
| 328 | Everything that takes place naturally is pleasant [Plato] |
| Full Idea: Everything that takes place naturally is pleasant. | |
| From: Plato (Timaeus [c.349 BCE], 81e) | |
| A reaction: Not many people would agree with this. I recently watched a sparrowhawk eat a pigeon in my garden. This is the source of the stoic formula of living according to nature. |
| 322 | Intelligence is the result of rational teaching; true opinion can result from irrational persuasion [Plato] |
| Full Idea: Intelligence is produced by teaching, involves truth and reason, and cannot be moved; true opinion involves persuasion, is irrational and can be moved. | |
| From: Plato (Timaeus [c.349 BCE], 51e) |
| 331 | Bad governments prevent discussion, and discourage the study of virtue [Plato] |
| Full Idea: Under a bad government discussion, both public and private, is bad, and no courses of study are available to cure faults of character. | |
| From: Plato (Timaeus [c.349 BCE], 87b) |
| 311 | The cosmos must be unique, because it resembles the creator, who is unique [Plato] |
| Full Idea: So that our universe can resemble the perfect living creature in being unique, the universe was, is and will continue to be its maker's only creation. | |
| From: Plato (Timaeus [c.349 BCE], 31c) |
| 310 | The creator of the cosmos had no envy, and so wanted things to be as like himself as possible [Plato] |
| Full Idea: This changing cosmos was made because its maker is good, and therefore lacks envy; he therefore wished all things to be as like himself as possible. | |
| From: Plato (Timaeus [c.349 BCE], 29e) |
| 325 | We must consider the four basic shapes as too small to see, only becoming visible in large numbers [Plato] |
| Full Idea: We must think of the individual units of all four basic shapes as being far too small to be visible, and only becoming visible when massed together in large numbers. | |
| From: Plato (Timaeus [c.349 BCE], 56c) |
| 327 | There are two types of cause, the necessary and the divine [Plato] |
| Full Idea: We must distinguish two types of cause, the necessary and the divine. | |
| From: Plato (Timaeus [c.349 BCE], 68e) |
| 314 | Heavenly movements gave us the idea of time, and caused us to inquire about the heavens [Plato] |
| Full Idea: Days, months, years and solstices have caused the invention of number, given us the notion of time, and caused us to inquire into the nature of the universe. | |
| From: Plato (Timaeus [c.349 BCE], 47a) |
| 312 | Time came into existence with the heavens, so that there will be a time when they can be dissolved [Plato] |
| Full Idea: Time came into being with the heavens, so that they should be dissolved together if ever they are dissolved. | |
| From: Plato (Timaeus [c.349 BCE], 38c) |
| 309 | Clearly the world is good, so its maker must have been concerned with the eternal, not with change [Plato] |
| Full Idea: If the world is beautiful and its maker good, he had an eye on the eternal; if not, on that which is subject to change; clearly the world is the fairest of things, and he the best of causes, so it is eternal. | |
| From: Plato (Timaeus [c.349 BCE], 29a) |
| 308 | If the cosmos is an object of perception then it must be continually changing [Plato] |
| Full Idea: The cosmos is visible, tangible and corporeal, and therefore perceptible by the senses; therefore it is an object of opinion and sensation, and therefore change and coming into being. | |
| From: Plato (Timaeus [c.349 BCE], 28d) |