79 ideas
| 14179 | The finest branch of wisdom is justice and moderation in ordering states and families [Plato] |
| Full Idea: By far the greatest and fairest branch of wisdom is that which is concerned with the due ordering of states and families, whose name is moderation and justice. | |
| From: Plato (The Symposium [c.384 BCE], 209a) | |
| A reaction: ['Justice' is probably 'dikaiosune'] It is hard to disagree with this, and it relegates ivory tower philosophical contemplation to second place, unlike the late books of Aristotle's Ethics. |
| 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. |
| 6947 | Metaphysics does not rest on facts, but on what we are inclined to believe [Peirce] |
| Full Idea: Metaphysical systems have not usually rested upon any observed facts, or not in any great degree. They are chiefly adopted because their fundamental propositions seem 'agreeable to reason', which means that which we find ourselves inclined to believe. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.15) | |
| A reaction: This leads to Peirce's key claim - that we should allow our beliefs to be formed by something outside of ourselves. I don't share Peirce's contempt for metaphysics, which I take to be about the most abstract presuppositions of our ordinary beliefs. |
| 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? |
| 6937 | Reason aims to discover the unknown by thinking about the known [Peirce] |
| Full Idea: The object of reasoning is to find out, from the consideration of what we already know, something else which we do not know. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p. 7) | |
| A reaction: I defy anyone to come up with a better definition of reasoning than that. The emphasis is on knowledge rather than truth, which you would expect from a pragmatist. …Actually the definition doesn't cover conditional reasoning terribly well. |
| 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. |
| 21492 | Realism is basic to the scientific method [Peirce] |
| Full Idea: The fundamental hypothesis of the method of science is this: There are real things, whose characters are entirely independent of our opinion of them. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877]), quoted by Albert Atkin - Peirce 3 'method' | |
| A reaction: He admits later that this is only a commitment and not a fact. It seems to me that when you combine this idea with the huge success of science, the denial of realism is crazy. Philosophy has a lot to answer for. |
| 6949 | If someone doubted reality, they would not actually feel dissatisfaction [Peirce] |
| Full Idea: Nobody can really doubt that there are Reals, for, if he did, doubt would not be a source of dissatisfaction. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.19) | |
| A reaction: This rests on Peirce's view that all that really matters is a sense of genuine dissatisfaction, rather than a theoretical idea. So even at the end of Meditation One, Descartes isn't actually worried about whether his furniture exists. |
| 1607 | Diotima said the Forms are the objects of desire in philosophical discourse [Plato, by Roochnik] |
| Full Idea: According to Diotima, the Forms are the objects of desire operative in philosophical discourse. | |
| From: report of Plato (The Symposium [c.384 BCE], 210a4-) by David Roochnik - The Tragedy of Reason p.199 |
| 6940 | The feeling of belief shows a habit which will determine our actions [Peirce] |
| Full Idea: The feeling of believing is a more or less sure indication of there being established in our nature some habit which will determine our actions. Doubt never has such an effect. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.10) | |
| A reaction: It is one thing to assert this fairly accurate observation, and another to assert that this is the essence or definition of a belief. Perhaps it is the purpose of belief, without being the phenomenological essence of it. We act in states of uncertainty. |
| 6941 | We are entirely satisfied with a firm belief, even if it is false [Peirce] |
| Full Idea: As soon as a firm belief is reached we are entirely satisfied, whether the belief be true or false. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.10) | |
| A reaction: This does not deny that the truth or falsehood of a belief is independent of whether we are satisfied with it. It is making a fair point, though, about why we believe things, and it can't be because of truth, because we don't know how to ensure that. |
| 6942 | We want true beliefs, but obviously we think our beliefs are true [Peirce] |
| Full Idea: We seek for a belief that we shall think to be true; but we think each one of our beliefs to be true, and, indeed, it is mere tautology to say so. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.11) | |
| A reaction: If, as I do, you like to define belief as 'commitment to truth', Peirce makes a rather startling observation. You are rendered unable to ask whether your beliefs are true, because you have defined them as true. Nice point… |
| 6943 | A mere question does not stimulate a struggle for belief; there must be a real doubt [Peirce] |
| Full Idea: The mere putting of a proposition into the interrogative form does not stimulate the mind to any struggle after belief; there must be a real and living doubt. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.11) | |
| A reaction: This the attractive aspect of Peirce's pragmatism, that he is always focusing on real life rather than abstract theory or pure logic. |
| 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. |
| 174 | True opinion without reason is midway between wisdom and ignorance [Plato] |
| Full Idea: There is a state of mind half-way between wisdom and ignorance - having true opinions without being able to give reasons for them. | |
| From: Plato (The Symposium [c.384 BCE], 202a) | |
| A reaction: Compare Idea 2140, where Plato scorns this state of mind. What he describes could be split into two - purely lucky true beliefs, and 'externalist knowledge', with non-conscious justification. |
| 6598 | We need our beliefs to be determined by some external inhuman permanency [Peirce] |
| Full Idea: It is necessary that a method should be found by which our beliefs be determined by nothing human, but by some external permanency - by something upon which our thinking has no effect. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877]), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.5 | |
| A reaction: This very sensible and interesting remark hovers somewhere between empiricism and pragmatism. Fogelin very persuasively builds his account of knowledge on it. The key point is that we hardly ever choose what to believe. See Idea 2454. |
| 6944 | Demonstration does not rest on first principles of reason or sensation, but on freedom from actual doubt [Peirce] |
| Full Idea: It is a common idea that demonstration must rest on indubitable propositions, either first principles of a general nature, or first sensations; but actual demonstration is completely satisfactory if it starts from propositions free from all actual doubt. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.11) | |
| A reaction: Another nice example of Peirce focusing on the practical business of thinking, rather than abstract theory. I agree with this approach, that explanation and proof do not aim at perfection and indubitability, but at what satisfies a critical mind. |
| 6948 | Doubts should be satisfied by some external permanency upon which thinking has no effect [Peirce] |
| Full Idea: To satisfy our doubts it is necessary that a method should be found by which our beliefs may be determined by nothing human, but by some external permanency - by something upon which our thinking has no effect. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.18) | |
| A reaction: This may be the single most important idea in pragmatism and in the philosophy of science. See Fodor on experiments (Idea 2455). Put the question to nature. The essential aim is to be passive in our beliefs - just let reality form them. |
| 6945 | Once doubt ceases, there is no point in continuing to argue [Peirce] |
| Full Idea: Some people seem to love to argue a point after all the world is fully convinced of it. But no further advance can be made. When doubt ceases, mental action on the subject comes to an end; and, if it did go on, it would be without purpose. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.11) | |
| A reaction: This is the way Peirce's pragmatism, which deals with how real thinking actually works (rather than abstract logic), deals with scepticism. However, there is a borderline where almost everyone is satisfied, but the very wise person remains sceptical. |
| 180 | We call a person the same throughout life, but all their attributes change [Plato] |
| Full Idea: During the period from boyhood to old age, man does not retain the same attributes, though he is called the same person. | |
| From: Plato (The Symposium [c.384 BCE], 207d) | |
| A reaction: This precisely identifies the basic problem of personal identity over time. If this is the problem, DNA looks more and more significant for the answer, though it would be an awful mistake to think a pattern of DNA was a person. |
| 181 | Only the gods stay unchanged; we replace our losses with similar acquisitions [Plato] |
| Full Idea: We retain identity not by staying the same (the preserve of gods) but by replacing losses with new similar acquisitions. | |
| From: Plato (The Symposium [c.384 BCE], 208b) | |
| A reaction: Any modern student of personal identity should be intrigued by this remark! It appears to take a rather physical view of the matter, and to be aware of human biology as a process. Are my continuing desires token-identical, or just 'similar'? |
| 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. |
| 4026 | Beauty is harmony with what is divine, and ugliness is lack of such harmony [Plato] |
| Full Idea: Ugliness is out of harmony with everything that is godly; beauty, however, is in harmony with the divine. | |
| From: Plato (The Symposium [c.384 BCE], 206d) | |
| A reaction: This remark shows how the concept of 'harmony' is at the centre of Greek thought (and is a potential bridge of the is/ought gap). |
| 172 | Love of ugliness is impossible [Plato] |
| Full Idea: There cannot be such a thing as love of ugliness. | |
| From: Plato (The Symposium [c.384 BCE], 201a) |
| 173 | Beauty and goodness are the same [Plato] |
| Full Idea: What is good is the same as what is beautiful. | |
| From: Plato (The Symposium [c.384 BCE], 201c) |
| 183 | Stage two is the realisation that beauty of soul is of more value than beauty of body [Plato] |
| Full Idea: The second stage of progress is to realise that beauty of soul is more valuable than beauty of body. | |
| From: Plato (The Symposium [c.384 BCE], 210b) |
| 184 | Progress goes from physical beauty, to moral beauty, to the beauty of knowledge, and reaches absolute beauty [Plato] |
| Full Idea: One should step up from physical beauty, to moral beauty, to the beauty of knowledge, until at last one knows what absolute beauty is. | |
| From: Plato (The Symposium [c.384 BCE], 211c) | |
| A reaction: Presumably this is why Socrates refused sexual favours to Alcibiades. The idea is inspiring, and yet it is a rejection of humanity. |
| 171 | Music is a knowledge of love in the realm of harmony and rhythm [Plato] |
| Full Idea: Music may be called a knowledge of the principles of love in the realm of harmony and rhythm. | |
| From: Plato (The Symposium [c.384 BCE], 187c) |
| 176 | Love follows beauty, wisdom is exceptionally beautiful, so love follows wisdom [Plato] |
| Full Idea: Wisdom is one of the most beautiful of things, and Love is love of beauty, so it follows that Love must be a love of wisdom. | |
| From: Plato (The Symposium [c.384 BCE], 204b) | |
| A reaction: Good, but wisdom isn't the only exceptionally beautiful thing. Music is beautiful partly because it is devoid of ideas. |
| 14177 | Love assists men in achieving merit and happiness [Plato] |
| Full Idea: Phaedrus: Love is not only the oldest and most honourable of the gods, but also the most powerful to assist men in the acquisition of merit and happiness, both here and hereafter. | |
| From: Plato (The Symposium [c.384 BCE], 180b) | |
| A reaction: Maybe we should talk less of love as a feeling, and more as a motivation, not just in human relationships, but in activities like gardening and database compilation. |
| 179 | Love is desire for perpetual possession of the good [Plato] |
| Full Idea: Love is desire for perpetual possession of the good. | |
| From: Plato (The Symposium [c.384 BCE], 206a) | |
| A reaction: Even the worst human beings often have lovers. 'Perpetual' is a nice observation. |
| 177 | If a person is good they will automatically become happy [Plato] |
| Full Idea: 'What will be gained by a man who is good?' 'That is easy - he will be happy'. | |
| From: Plato (The Symposium [c.384 BCE], 205a) | |
| A reaction: Suppose you tried to assassinate Hitler in 1944 (a good deed), but failed. Happiness presumably results from success, rather than mere good intentions. |
| 14178 | Happiness is secure enjoyment of what is good and beautiful [Plato] |
| Full Idea: By happy you mean in secure enjoyment of what is good and beautiful? - Certainly. | |
| From: Plato (The Symposium [c.384 BCE], 202c) | |
| A reaction: We seem to have lost track of the idea that beauty might be an essential ingredient of happiness. |
| 170 | The only slavery which is not dishonourable is slavery to excellence [Plato] |
| Full Idea: The only form of servitude which has no dishonour has for its object the acquisition of excellence. | |
| From: Plato (The Symposium [c.384 BCE], 184c) |
| 182 | The first step on the right path is the contemplation of physical beauty when young [Plato] |
| Full Idea: The man who would pursue the right way to his goal must begin, when he is young, by contemplating physical beauty. | |
| From: Plato (The Symposium [c.384 BCE], 210a) |
| 6939 | What is true of one piece of copper is true of another (unlike brass) [Peirce] |
| Full Idea: The guiding principle is that what is true of one piece of copper is true of another; such a guiding principle with regard to copper would be much safer than with regard to many other substances - brass, for example. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p. 8) | |
| A reaction: Peirce is so beautifully simple and sensible. This gives the essential notion of a natural kind, and is a key notion in our whole understanding of physical reality. |
| 6938 | Natural selection might well fill an animal's mind with pleasing thoughts rather than true ones [Peirce] |
| Full Idea: It is probably of more advantage to an animal to have his mind filled with pleasing and encouraging visions, independently of their truth; and thus, upon unpractical subjects, natural selection might occasion a fallacious tendency of thought. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p. 8) | |
| A reaction: Note that this is a pragmatist saying that a set of beliefs might work fine but be untrue. So Peirce does not have the highly relativistic notion of truth of some later pragmatists. Good for him. Note the early date to be thinking about Darwin. |
| 175 | Gods are not lovers of wisdom, because they are already wise [Plato] |
| Full Idea: No god is a lover of wisdom or desires to be wise, for he is wise already. | |
| From: Plato (The Symposium [c.384 BCE], 204a) |
| 6946 | If death is annihilation, belief in heaven is a cheap pleasure with no disappointment [Peirce] |
| Full Idea: If death is annihilation, then the man who believes that he will certainly go straight to heaven when he dies, provided he have fulfilled certain simple observances in this life, has a cheap pleasure which will not be followed by the least disappointment. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.12) | |
| A reaction: This is a nicely wicked summary of one side of Pascal's options. All the problems of the argument are built into Peirce's word "cheap". Peirce goes on to talk about ostriches burying their heads. |