138 ideas
| 2136 | Philosophers become as divine and orderly as possible, by studying divinity and order [Plato] |
| Full Idea: Because a philosopher's links are with a realm which is divine and orderly, he becomes as divine and orderly as is humanly possible. | |
| From: Plato (The Republic [c.374 BCE], 500d) | |
| A reaction: Can you be too orderly? Without order nothing of any interest (to gods or men) could ever happen. |
| 23767 | The winds of the discussion should decide its destination [Plato] |
| Full Idea: We must let our destination be decided by the winds of the discussion. | |
| From: Plato (The Republic [c.374 BCE], 394d) | |
| A reaction: Always loved that one. Had it on the wall of my teaching room. I take it that the aim is to follow reason, rather than the powerful rhetoric of some member of the group. The spirit of philosophy is to avoid prejudgement of your enquiry. |
| 23682 | It would be absurd to be precise about the small things, but only vague about the big things [Plato] |
| Full Idea: It would be absurd to devote all our energies to securing the greatest possible precision and clarity in matters of little consequence, and not to demand the highest precision in the most important things of all. | |
| From: Plato (The Republic [c.374 BCE], 504e) | |
| A reaction: I offer this to modern analytic philosophers, who often strike me as having this priority the wrong way round. Their defence, of course, is that the important things depend on the things of little consequence - but they can lose the plot with big things. |
| 2151 | Dialectic is the only method of inquiry which uproots the things which it takes for granted [Plato] |
| Full Idea: Dialectic is the only field of inquiry whose quest for certainty causes it to uproot the things it takes for granted in the course of its journey. | |
| From: Plato (The Republic [c.374 BCE], 533c) |
| 2154 | The ability to take an overview is the distinguishing mark of a dialectician [Plato] |
| Full Idea: The ability to take an overview is the distinguishing mark of a dialectician. | |
| From: Plato (The Republic [c.374 BCE], 537c) |
| 4011 | For Plato, rationality is a vision of and love of a cosmic rational order [Plato, by Taylor,C] |
| Full Idea: In Plato's theory, to be rational is to have a vision of rational order, and to love this order. | |
| From: report of Plato (The Republic [c.374 BCE], 537d) by Charles Taylor - Sources of the Self §4.1 | |
| A reaction: There may be a worrying elitism in this, but it helps to pinpoint the sense in which 'all philosophers are Platonists'. |
| 2093 | You must never go against what you actually believe [Plato] |
| Full Idea: You must never go against what you actually believe. | |
| From: Plato (The Republic [c.374 BCE], 350e) |
| 2130 | People often merely practice eristic instead of dialectic, because they don't analyse the subject-matter [Plato] |
| Full Idea: People often think they are practising dialectic when they are practising eristic; this is because of their inability to conduct the enquiry by dividing the subject-matter into its various aspects. | |
| From: Plato (The Republic [c.374 BCE], 454a) |
| 8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
| Full Idea: An 'impredicative' definition is one that uses the terms being defined in order to give the definition; in some way the definition is then circular. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], Glossary) | |
| A reaction: There has been a big controversy in the philosophy of mathematics over these. Shapiro gives the definition of 'village idiot' (which probably mentions 'village') as an example. |
| 8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
| Full Idea: In classical logic definitions are thought of as revealing our attempts to refer to objects, ...but for intuitionist or constructivist logics, if our definitions do not uniquely characterize an object, we are not entitled to discuss the object. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.4) | |
| A reaction: In defining a chess piece we are obviously creating. In defining a 'tree' we are trying to respond to fact, but the borderlines are vague. Philosophical life would be easier if we were allowed a mixture of creation and fact - so let's have that. |
| 3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
| Full Idea: Reductio ad absurdum arguments are ones that start by denying what one wants to prove. We then prove a contradiction from this 'denied' idea and more reasonable ideas in one's theory, showing that we were wrong in denying what we wanted to prove. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This is a mathematical definition, which rests on logical contradiction, but in ordinary life (and philosophy) it would be enough to show that denial led to absurdity, rather than actual contradiction. |
| 8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
| Full Idea: For the anti-realist, truth belongs to us, it is our servant, and as such, it must be 'epistemically constrained'. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.1) | |
| A reaction: Put as clearly as this, it strikes me as being utterly and spectacularly wrong, a complete failure to grasp the elementary meaning of a concept etc. etc. If we aren't the servants of truth then we jolly we ought to be. Truth is above us. |
| 2145 | In mathematics certain things have to be accepted without further explanation [Plato] |
| Full Idea: The practitioners of maths take certain things as basic, and feel no further need to explain them. | |
| From: Plato (The Republic [c.374 BCE], 510c) |
| 8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
| Full Idea: In the classical or realist view of logic the meaning of abstract symbols for logical connectives is given by the truth-tables for the symbol. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007]) | |
| A reaction: Presumably this is realist because it connects them to 'truth', but only if that involves a fairly 'realist' view of truth. You could, of course, translate 'true' and 'false' in the table to empty (formalist) symbols such a 0 and 1. Logic is electronics. |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| Full Idea: In intuitionist logic, if we do not know that we do not know A, it does not follow that we know A, so the inference (and, in general, double negation elimination) is not intuitionistically valid. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2) | |
| A reaction: That inference had better not be valid in any logic! I am unaware of not knowing the birthday of someone I have never heard of. Propositional attitudes such as 'know' are notoriously difficult to explain in formal logic. |
| 8694 | Free logic was developed for fictional or non-existent objects [Friend] |
| Full Idea: Free logic is especially designed to help regiment our reasoning about fictional objects, or nonexistent objects of some sort. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 3.7) | |
| A reaction: This makes it sound marginal, but I wonder whether existential commitment shouldn't be eliminated from all logic. Why do fictional objects need a different logic? What logic should we use for Robin Hood, if we aren't sure whether or not he is real? |
| 15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
| Full Idea: The common feature of every designating term is that designation may change from state to state - thus it can be formalized by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3) | |
| A reaction: Specifying the objects sounds OK, but specifying states sounds rather tough. |
| 15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
| Full Idea: To first order modal logic (with quantification over objects) we can add a second kind of quantification, over intensions. An intensional object, or individual concept, will be modelled by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.3) |
| 15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
| Full Idea: Awareness logic enriched Hintikka's epistemic models with an awareness function, mapping each state to the set of formulas we are aware of at that state. This reflects some bound on the resources we can bring to bear. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) | |
| A reaction: [He cites Fagin and Halpern 1988 for this] |
| 15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
| Full Idea: In justification logics, the logics of knowledge are extended by making reasons explicit. A logic of proof terms was created, with a semantics. In this, mathematical truths are known for explicit reasons, and these provide a measure of complexity. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) |
| 8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
| Full Idea: A 'subset' of A is a set containing only members of A, and a 'proper subset' is one that does not contain all the members of A. Note that the empty set is a subset of every set, but it is not a member of every set. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Is it the same empty set in each case? 'No pens' is a subset of 'pens', but is it a subset of 'paper'? Idea 8219 should be borne in mind when discussing such things, though I am not saying I agree with it. |
| 8672 | A 'powerset' is all the subsets of a set [Friend] |
| Full Idea: The 'powerset' of a set is a set made up of all the subsets of a set. For example, the powerset of {3,7,9} is {null, {3}, {7}, {9}, {3,7}, {3,9}, {7,9}, {3,7,9}}. Taking the powerset of an infinite set gets us from one infinite cardinality to the next. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Note that the null (empty) set occurs once, but not in the combinations. I begin to have queasy sympathies with the constructivist view of mathematics at this point, since no one has the time, space or energy to 'take' an infinite powerset. |
| 8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
| Full Idea: As a realist choice of what is basic in mathematics, set theory is rather clever, because it only makes a very simple ontological claim: that, independent of us, there exists the empty set. The whole hierarchy of finite and infinite sets then follows. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: Even so, for non-logicians the existence of the empty set is rather counterintuitive. "There was nobody on the road, so I overtook him". See Ideas 7035 and 8322. You might work back to the empty set, but how do you start from it? |
| 8666 | Infinite sets correspond one-to-one with a subset [Friend] |
| Full Idea: Two sets are the same size if they can be placed in one-to-one correspondence. But even numbers have one-to-one correspondence with the natural numbers. So a set is infinite if it has one-one correspondence with a proper subset. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Dedekind's definition. We can match 1 with 2, 2 with 4, 3 with 6, 4 with 8, etc. Logicians seem happy to give as a definition anything which fixes the target uniquely, even if it doesn't give the essence. See Frege on 0 and 1, Ideas 8653/4. |
| 8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
| Full Idea: Zermelo-Fraenkel and Gödel-Bernays set theory differ over the notions of ordinal construction and over the notion of class, among other things. Then there are optional axioms which can be attached, such as the axiom of choice and the axiom of infinity. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.6) | |
| A reaction: This summarises the reasons why we cannot just talk about 'set theory' as if it was a single concept. The philosophical interest I would take to be found in disentangling the ontological commitments of each version. |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics. | |
| From: Melvin Fitting (Intensional Logic [2007], §1) |
| 8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
| Full Idea: The law of excluded middle is purely syntactic: it says for any well-formed formula A, either A or not-A. It is not a semantic law; it does not say that either A is true or A is false. The semantic version (true or false) is the law of bivalence. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2) | |
| A reaction: No wonder these two are confusing, sufficiently so for a lot of professional philosophers to blur the distinction. Presumably the 'or' is exclusive. So A-and-not-A is a contradiction; but how do you explain a contradiction without mentioning truth? |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □. | |
| From: Melvin Fitting (Intensional Logic [2007], §3.3) | |
| A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic. |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| Full Idea: In the intuitionist version of quantification, the universal quantifier (normally read as "all") is understood as "we have a procedure for checking every" or "we have checked every". | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.5) | |
| A reaction: It seems better to describe this as 'verificationist' (or, as Dummett prefers, 'justificationist'). Intuition suggests an ability to 'see' beyond the evidence. It strikes me as bizarre to say that you can't discuss things you can't check. |
| 8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
| Full Idea: The realist meets the Burali-Forti paradox by saying that all the ordinals are a 'class', not a set. A proper class is what we discuss when we say "all" the so-and-sos when they cannot be reached by normal set-construction. Grammar is their only limit. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This strategy would be useful for Class Nominalism, which tries to define properties in terms of classes, but gets tangled in paradoxes. But why bother with strict sets if easy-going classes will do just as well? Descartes's Dream: everything is rational. |
| 8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
| Full Idea: The Burali-Forti paradox says that if ordinals are defined by 'gathering' all their predecessors with the empty set, then is the set of all ordinals an ordinal? It is created the same way, so it should be a further member of this 'complete' set! | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This is an example (along with Russell's more famous paradox) of the problems that began to appear in set theory in the early twentieth century. See Idea 8675 for a modern solution. |
| 8726 | Geometry can lead the mind upwards to truth and philosophy [Plato] |
| Full Idea: Geometry can attract the mind towards truth. It can produce philosophical thought, in the sense that it can reverse the midguided downwards tendencies we currently have. | |
| From: Plato (The Republic [c.374 BCE], 527b) | |
| A reaction: Hence the Academy gate bore the inscription "Let no one enter here who is ignorant of geometry". He's not necessarily wrong. Something in early education must straighten out some of the kinks in the messy human mind. |
| 8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
| Full Idea: The set of 'integers' is all of the negative natural numbers, and zero, together with the positive natural numbers. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Zero always looks like a misfit at this party. Credit and debit explain positive and negative nicely, but what is the difference between having no money, and money being irrelevant? I can be 'broke', but can the North Pole be broke? |
| 8668 | The 'rational' numbers are those representable as fractions [Friend] |
| Full Idea: The 'rational' numbers are all those that can be represented in the form m/n (i.e. as fractions), where m and n are natural numbers different from zero. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Pythagoreans needed numbers to stop there, in order to represent the whole of reality numerically. See irrational numbers for the ensuing disaster. How can a universe with a finite number of particles contain numbers that are not 'rational'? |
| 8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
| Full Idea: A number is 'irrational' just in case it cannot be represented as a fraction. An irrational number has an infinite non-repeating decimal expansion. Famous examples are pi and e. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: There must be an infinite number of irrational numbers. You could, for example, take the expansion of pi, and change just one digit to produce a new irrational number, and pi has an infinity of digits to tinker with. |
| 8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
| Full Idea: The natural numbers are quite primitive, and are what we first learn about. The order of objects (the 'ordinals') is one level of abstraction up from the natural numbers: we impose an order on objects. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.4) | |
| A reaction: Note the talk of 'levels of abstraction'. So is there a first level of abstraction? Dedekind disagrees with Friend (Idea 7524). I would say that natural numbers are abstracted from something, but I'm not sure what. See Structuralism in maths. |
| 8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
| Full Idea: The 'cardinal' numbers answer the question 'How many?'; the order of presentation of the objects being counted as immaterial. Def: the cardinality of a set is the number of members of the set. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: If one asks whether cardinals or ordinals are logically prior (see Ideas 7524 and 8661), I am inclined to answer 'neither'. Presenting them as answers to the questions 'how many?' and 'which comes first?' is illuminating. |
| 8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
| Full Idea: The set of 'real' numbers, which consists of the rational numbers and the irrational numbers together, represents "the continuum", since it is like a smooth line which has no gaps (unlike the rational numbers, which have the irrationals missing). | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: The Continuum is the perfect abstract object, because a series of abstractions has arrived at a vast limit in its nature. It still has dizzying infinities contained within it, and at either end of the line. It makes you feel humble. |
| 8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
| Full Idea: After the multiples of omega, we can successively raise omega to powers of omega, and after that is done an infinite number of times we arrive at a new limit ordinal, which is called 'epsilon'. We have an infinite number of infinite ordinals. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.4) | |
| A reaction: When most people are dumbstruck by the idea of a single infinity, Cantor unleashes an infinity of infinities, which must be the highest into the stratosphere of abstract thought that any human being has ever gone. |
| 8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
| Full Idea: The first 'limit ordinal' is called 'omega', which is ordinal because it is greater than other numbers, but it has no immediate predecessor. But it has successors, and after all of those we come to twice-omega, which is the next limit ordinal. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.4) | |
| A reaction: This is the gateway to Cantor's paradise of infinities, which Hilbert loved and defended. Who could resist the pleasure of being totally boggled (like Aristotle) by a concept such as infinity, only to have someone draw a map of it? See 8663 for sequel. |
| 8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
| Full Idea: Since between any two rational numbers there is an infinite number of rational numbers, we could consider that we have infinity in three dimensions: positive numbers, negative numbers, and the 'depth' of infinite numbers between any rational numbers. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: This is before we even reach Cantor's staggering infinities (Ideas 8662 and 8663), which presumably reside at the outer reaches of all three of these dimensions of infinity. The 'deep' infinities come from fractions with huge denominators. |
| 8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
| Full Idea: Successful competing founding disciplines in mathematics include: the various set theories, type theory, category theory, model theory and topology. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: Or none of the above? Set theories are very popular. Type theory is, apparently, discredited. Shapiro has a version of structuralism based on model theory (which sound promising). Topology is the one that intrigues me... |
| 8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
| Full Idea: Most of mathematics can be faithfully redescribed by classical (realist) set theory. More precisely, we can translate other mathematical theories - such as group theory, analysis, calculus, arithmetic, geometry and so on - into the language of set theory. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This is why most mathematicians seem to regard set theory as foundational. We could also translate football matches into the language of atomic physics. |
| 8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
| Full Idea: There is no interest for the mathematician in studying the number 8 in isolation from the other numbers. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: This is a crucial and simple point (arising during a discussion of Shapiro's structuralism). Most things are interesting in themselves, as well as for their relationships, but mathematical 'objects' just are relationships. |
| 8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
| Full Idea: Structuralists give a historical account of why the 'same' number occupies different structures. Numbers are equivalent rather than identical. 8 is the immediate predecessor of 9 in the whole numbers, but in the rationals 9 has no predecessor. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: I don't become a different person if I move from a detached house to a terraced house. This suggests that 8 can't be entirely defined by its relations, and yet it is hard to see what its intrinsic nature could be, apart from the units which compose it. |
| 8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
| Full Idea: Structuralists disagree over whether objects in structures are 'ante rem' (before reality, existing independently of whether the objects exist) or 'in re' (in reality, grounded in the real world, usually in our theories of physics). | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: Shapiro holds the first view, Hellman and Resnik the second. The first view sounds too platonist and ontologically extravagant; the second sounds too contingent and limited. The correct account is somewhere in abstractions from the real. |
| 8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
| Full Idea: According to the structuralist, mathematicians study the concepts (objects of study) such as variable, greater, real, add, similar, infinite set, which are one level of abstraction up from prima facie base objects such as numbers, shapes and lines. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.1) | |
| A reaction: This still seems to imply an ontology in which numbers, shapes and lines exist. I would have thought you could eliminate the 'base objects', and just say that the concepts are one level of abstraction up from the physical world. |
| 8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
| Full Idea: Structuralism says we study whole structures: objects together with their predicates, relations that bear between them, and functions that take us from one domain of objects to a range of other objects. The objects can even be eliminated. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.1) | |
| A reaction: The unity of object and predicate is a Quinean idea. The idea that objects are inessential is the dramatic move. To me the proposal has very strong intuitive appeal. 'Eight' is meaningless out of context. Ordinality precedes cardinality? Ideas 7524/8661. |
| 8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
| Full Idea: In the 'in re' version of mathematical structuralism, pattern-spotting is the process of abstraction. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: This might work for non-mathematical abstraction as well, if we are allowed to spot patterns within sensual experience, and patterns within abstractions. Properties are causal patterns in the world? No - properties cause patterns. |
| 9863 | We aim for elevated discussion of pure numbers, not attaching them to physical objects [Plato] |
| Full Idea: Our discussion of numbers leads the soul forcibly upward and compels it to discuss the numbers themselves, never permitting anyone to propose for discussion numbers attached to visible or tangible bodies. | |
| From: Plato (The Republic [c.374 BCE], 525d) | |
| A reaction: This strikes me as very important, because it shows that the platonist view of numbers places little or no importance on counting, inviting the question of whether they could be understood in complete ignorance of the process of counting. |
| 9864 | In pure numbers, all ones are equal, with no internal parts [Plato] |
| Full Idea: With those numbers that can be grasped only in thought, ..each one is equal to every other, without the least difference and containing no internal parts. | |
| From: Plato (The Republic [c.374 BCE], 526a) | |
| A reaction: [Two voices in the conversation are elided] Intriguing and tantalising. Does 13 have internal parts, in the platonist view? If so, is it more than the sum of its parts? Is Plato committed to numbers being built from indistinguishable abstract units/ |
| 8727 | Geometry is not an activity, but the study of unchanging knowledge [Plato] |
| Full Idea: Geometers talk as if they were actually doing something, and the point of their theorems is to have some effect (like 'squaring'). ...But the sole purpose is knowledge, of things which exist forever, not coming into existence and passing away. | |
| From: Plato (The Republic [c.374 BCE], 527a) | |
| A reaction: Modern Constructivism defends the view which Plato is attacking. The existence of real infinities can be doubted simply because we have not got enough time to construct them. |
| 8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
| Full Idea: The main philosophical problem with the position of platonism or realism is the epistemic problem: of explaining what perception or intuition consists in; how it is possible that we should accurately detect whatever it is we are realists about. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.5) | |
| A reaction: The best bet, I suppose, is that the mind directly perceives concepts just as eyes perceive the physical (see Idea 8679), but it strikes me as implausible. If we have to come up with a special mental faculty for an area of knowledge, we are in trouble. |
| 8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
| Full Idea: Central to naturalism about mathematics are 'indispensability arguments', to the effect that some part of mathematics is indispensable to our best physical theory, and therefore we ought to take that part of mathematics to be true. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 6.1) | |
| A reaction: Quine and Putnam hold this view; Field challenges it. It has the odd consequence that the dispensable parts (if they can be identified!) do not need to be treated as true (even though they might follow logically from the dispensable parts!). Wrong! |
| 9861 | The same thing is both one and an unlimited number at the same time [Plato] |
| Full Idea: We see the same thing to be both one and an unlimited number at the same time. | |
| From: Plato (The Republic [c.374 BCE], 525a) | |
| A reaction: Frege makes the same point, that a pair of boots is both two and one. The point is at its strongest in opposition to empirical accounts of arithmetic. However, Mill observes that pebbles can be both 5 and 3+2, without contradiction. |
| 8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
| Full Idea: There are not enough constraints in the Formalist view of mathematics, so there is no way to select a direction for trying to develop mathematics. There is no part of mathematics that is more important than another. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 6.6) | |
| A reaction: One might reply that an area of maths could be 'important' if lots of other areas depended on it, and big developments would ripple big changes through the interior of the subject. Formalism does, though, seem to reduce maths to a game. |
| 8706 | Constructivism rejects too much mathematics [Friend] |
| Full Idea: Too much of mathematics is rejected by the constructivist. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.1) | |
| A reaction: This was Hilbert's view. This seems to be generally true of verificationism. My favourite example is that legitimate speculations can be labelled as meaningless. |
| 8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
| Full Idea: An intuitionist typically retains bivalence, but rejects the law of excluded middle. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2) | |
| A reaction: The idea would be to say that only T and F are available as truth-values, but failing to be T does not ensure being F, but merely not-T. 'Unproven' is not-T, but may not be F. |
| 9862 | To become rational, philosophers must rise from becoming into being [Plato] |
| Full Idea: Philosophers must rise up out of becoming and grasp being, if they are ever to become rational. | |
| From: Plato (The Republic [c.374 BCE], 525b) | |
| A reaction: I am never quite sure what 'being' means in such contexts, and it seems suffused with mysticism. In Plato's case, it is obviously related to what is unchanging, but why would something lack 'being', just because it underwent change? |
| 21818 | Being depends on the Good, which is not itself being, but superior to being [Plato] |
| Full Idea: Not only do the objects of knowledge owe their being known to the good, but their being is also due to it, although the good is not being, but superior to it in rank and power. | |
| From: Plato (The Republic [c.374 BCE], 509b) | |
| A reaction: I was surprised to find that in Plotinus the One is not being, because it is the source of being, and thus superior to being. Then a footnote sent me here, and I realise that Plato thought that the Form of the Good is superior to Being. |
| 2061 | The best things (gods, healthy bodies, good souls) are least liable to change [Plato] |
| Full Idea: The best things (such as a god, a healthy body, or a good soul) are least liable to alteration or change. | |
| From: Plato (The Republic [c.374 BCE], 380e) |
| 6562 | Plato's reality has unchanging Parmenidean forms, and Heraclitean flux [Plato, by Fogelin] |
| Full Idea: For Plato, the intelligible world - the world of eternal and unchanging forms - is Parmenidean; the world of appearances - the world of flux we inhabit - is Heraclitean. | |
| From: report of Plato (The Republic [c.374 BCE]) by Robert Fogelin - Walking the Tightrope of Reason Ch.1 | |
| A reaction: Parmenides said reality is 'One'; Heraclitus said reality is 'flux'. This is a nice summary of Plato's view, and encapsulates two key influences on Plato, though the mathematical reality of Pythagoras should also be mentioned on the 'forms' side. |
| 2142 | The plurality of beautiful things must belong to a single class, because they have a single particular character [Plato] |
| Full Idea: All the things we refer to as pluralities (e.g. beautiful things) we also count as belonging to a single class by virtue of the fact that they have a single particular character. | |
| From: Plato (The Republic [c.374 BCE], 507b) |
| 5094 | Plato's Forms are said to have no location in space [Plato, by Aristotle] |
| Full Idea: Plato claims that the Forms are not beyond the heavens, because they are not anywhere. | |
| From: report of Plato (The Republic [c.374 BCE]) by Aristotle - Physics 203a09 | |
| A reaction: This is an important corrective to caricature accounts of Plato's Forms (encouraged, I'm afraid, by 'Phaedrus'), when critics talk about 'Platonic Heaven'. Forms are not part of space-time. I like the view that they are hypothetical truths. |
| 12043 | Forms are not universals, as they don't cover every general term [Plato, by Annas] |
| Full Idea: Despite a widely misinterpreted passage in the Republic, Plato does not think that there is a Form for every general term; Forms are not what came to be called universals. | |
| From: report of Plato (The Republic [c.374 BCE]) by Julia Annas - Ancient Philosophy: very short introduction Ch.5 | |
| A reaction: Hm. This is a bit of a blow to someone who has catalogued Platonic Forms under 'Universals'. See also Idea 12042, for what Annas thinks Plato may really have had in mind. |
| 2159 | Craftsmen making furniture refer to the form, but no one manufactures the form of furniture [Plato] |
| Full Idea: The manufacture of beds and tables involves the craftsman looking to the form and then making the furniture. The form itself is not manufactured by anyone. | |
| From: Plato (The Republic [c.374 BCE], 596b) |
| 17 | A Form applies to a set of particular things with the same name [Plato] |
| Full Idea: We always postulate a single form for each set of particular things, to which we apply the same name. | |
| From: Plato (The Republic [c.374 BCE], 596a) | |
| A reaction: This implies that the Forms have a great deal in common with the things, but also hints at the possibility of the Form being quite different from the particular things. |
| 12122 | Plato mistakenly thought forms were totally abstracted away from matter [Bacon on Plato] |
| Full Idea: Plato lost the real fruit of his opinion, by considering forms as absolutely abstracted from matter, and not confined and determined by matter. | |
| From: comment on Plato (The Republic [c.374 BCE]) by Francis Bacon - The Advancement of Learning II.VII.5 | |
| A reaction: This thought is roughly what got me interested in abstraction, on which you will find many ideas in this database. Research into Bacon's thought is hampered by that fact that the logicians have hijacked abstraction in recent philosophy. |
| 5574 | Plato's Forms not only do not come from the senses, but they are beyond possibility of sensing [Plato, by Kant] |
| Full Idea: In Plato's use of the expression 'idea' we can see that he understood by it something that not only could never be borrowed from the senses, but even goes beyond the concepts of the understanding, since nothing in experience could be congruent to it. | |
| From: report of Plato (The Republic [c.374 BCE]) by Immanuel Kant - Critique of Pure Reason B370 | |
| A reaction: This is why Kant is not a Platonist - because he thinks the limits of our world are the limits of our capacity for possible experience, and Platonic Forms exceed that limit. Personally I am with Plato. I'll never experience a quark either. |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| Full Idea: What the mathematician labels an 'object' in her discipline, is called 'a place in a structure' by the structuralist. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.5) | |
| A reaction: This is a strategy for dispersing the idea of an object in the world of thought, parallel to attempts to eliminate them from physical ontology (e.g. Idea 614). |
| 15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
| Full Idea: Definite descriptions pick out different objects in different possible worlds quite naturally. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.4) | |
| A reaction: A definite description can pick out the same object in another possible world, or a very similar one, or an object which has almost nothing in common with the others. |
| 2133 | Knowledge must be of the permanent unchanging nature of things [Plato] |
| Full Idea: Those who can see each thing in itself, in its permanent and unvarying nature, we'll say they have knowledge and are not merely entertaining beliefs. | |
| From: Plato (The Republic [c.374 BCE], 479e) |
| 2162 | If theory and practice conflict, the best part of the mind accepts theory, so the other part is of lower grade [Plato] |
| Full Idea: When appearance and measure conflict…it is the best part of the mind which accepts measurements and calculations, and the part which opposes them, therefore, must be a low-grade part of the mind. | |
| From: Plato (The Republic [c.374 BCE], 603a) |
| 2140 | True belief without knowledge is like blind people on the right road [Plato] |
| Full Idea: Don't people who have a correct belief but no knowledge strike you as exactly like blind people who happen to be taking the right road? | |
| From: Plato (The Republic [c.374 BCE], 506c) | |
| A reaction: Good. I love the style of this. Most philosophical points can be made in one concise sentence, and it is only the industry of journals and academe that forces points to be extended so much. |
| 2096 | Is the function of the mind management, authority and planning - or is it one's whole way of life? [Plato] |
| Full Idea: Does the mind have a function - say, management, authority and planning? And isn't one's way of life a function of the mind? | |
| From: Plato (The Republic [c.374 BCE], 353d) | |
| A reaction: Note that this is Plato, not some Darwinian materialist. This strikes me as the correct starting point - what does a mind appear to be for (with or without the help of Darwin)? Plato's proposals seem good (though we could cut 'authority'). |
| 6009 | Psychic conflict is clear if appetite is close to the body and reason fairly separate [Plato, by Modrak] |
| Full Idea: Plato makes psychic conflict intelligible by appeal to a conception of the soul such that the soul is closely connected to the body at the level of appetite and relatively separate from the body at the level of reason. | |
| From: report of Plato (The Republic [c.374 BCE], 339b) by Deborah K.W. Modrak - Classical theories of Mind | |
| A reaction: I'm not sure about this at the level of biology or ontology, but at the phenomenal level this is obviously right. Hunger makes consciousness feel like a physical event, but doing arithmetic doesn't seem remotely physical. |
| 6041 | There is a third element to the mind - spirit - lying between reason and appetite [Plato] |
| Full Idea: Is the third element of the mind a form of reason, so that there are only two elements to it, reason and appetite? There must be a third element, if spirit ('thumos') can be shown to be distinct - and you can see it in children when they are born. | |
| From: Plato (The Republic [c.374 BCE], 441a) | |
| A reaction: This is Plato's famous tripartite doctrine of the soul, though in other dialogues he says that there is only reason and appetite. The suspicion is that he fixed the soul having three parts, to match the three parts of his republic's social structure. |
| 2127 | The mind has parts, because we have inner conflicts [Plato] |
| Full Idea: If someone is thirsty but something is making the mind resist the pull of its thirst, isn't this bound to be a different part of the mind from the thirsty part? | |
| From: Plato (The Republic [c.374 BCE], 439b) | |
| A reaction: For Descartes there is one mind pulled by appetite and the 'natural light'. For Hume they don't seem to be 'parts' of anything. For Fodor there is an integrated team of modules. I like Fodor, and good integration is virtue. |
| 1737 | The soul seems to have an infinity of parts [Aristotle on Plato] |
| Full Idea: There seem in a way to be an infinity of parts of the soul, and not only those that some have given, distinguishing the reasoning, spirited and desiderative parts, or with others the rational and irrational. | |
| From: comment on Plato (The Republic [c.374 BCE], 439b) by Aristotle - De Anima 432a25 | |
| A reaction: This seems a nice response to Plato's proposal that the psuché has two or three parts. He could have said that the soul was a unity, and has no parts, but the proposal of infinite parts seems much closer to the modern neurological view of the mind. |
| 8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
| Full Idea: In the hierarchy of reduction, when we investigate questions in biology, we have to assume the laws of chemistry but not of economics. We could never find a law of biology that contradicted something in physics or in chemistry. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 3.1) | |
| A reaction: This spells out the idea that there is a direction of dependence between aspects of the world, though we should be cautious of talking about 'levels' (see Idea 7003). We cannot choose the direction in which reduction must go. |
| 8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
| Full Idea: The extensional presentation of a concept is just a list of the objects falling under the concept. In contrast, an intensional presentation of a concept gives a characterization of the concept, which allows us to pick out which objects fall under it. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 3.4) | |
| A reaction: Logicians seem to favour the extensional view, because (in the standard view) sets are defined simply by their members, so concepts can be explained using sets. I take this to be a mistake. The intensional view seems obviously prior. |
| 5945 | The 'Republic' is a great work of rhetorical theory [Lawson-Tancred on Plato] |
| Full Idea: The 'Republic' is the greatest single achievement of ancient rhetorical theory. | |
| From: comment on Plato (The Republic [c.374 BCE]) by Hugh Lawson-Tancred - Plato's Republic and Greek Enlightenment Ch.9 | |
| A reaction: A lovely inversion of our normal reading of Plato! Is the real aim of philosophy the making of good speeches? Is the great aim to display the true beauty of the human mind, as the Olympics display the beauty of the body? |
| 23316 | For Plato and Aristotle there is no will; there is only rational desire for what is seen as good [Plato, by Frede,M] |
| Full Idea: Neither Plato nor Aristotle has a notion of the will. …Willing is a form of desire which is specific to reason. If reason perceives something as good, it wills or desires it. | |
| From: report of Plato (The Republic [c.374 BCE], 577e) by Michael Frede - A Free Will 1 | |
| A reaction: [Frede cites 577e, Aris. 413c8, 1113a15-, 1136b6] How do they explain the apparent decisions of non-rational animals? No modern neuroscientist thinks there is a physical object called a person's 'will'. |
| 16 | We avoid evil either through a natural aversion, or because we have acquired knowledge [Plato] |
| Full Idea: Unless a man is born with a heaven-sent aversion to wrong-doing, or acquires the knowledge to refrain from it, he will never do right of his own free will. | |
| From: Plato (The Republic [c.374 BCE], 366c) | |
| A reaction: This is the territory explored so carefully by Aristotle (after he had read Republic!). It is hard to see what the knowledge could be, other than awareness of consequences. |
| 16565 | Without the surface decoration, poetry shows only appearances and nothing of what is real [Plato] |
| Full Idea: If you strip a poet's works of their musical colorings and take them by themselves, I think you know what they look like. …We say that a maker of an image - an imitator - knows nothing about that which is but only about its appearance. | |
| From: Plato (The Republic [c.374 BCE], 601a) | |
| A reaction: Knowing the appearances well is more than most people can manage, and aspirations to know the true reality may be an idle dream. Poets are, I presume, welcome in the Cave. |
| 2160 | Representation is two steps removed from the truth [Plato] |
| Full Idea: The province of representation is indeed two steps removed from the truth. | |
| From: Plato (The Republic [c.374 BCE], 602c) |
| 2163 | Artists should be excluded from a law-abiding community, because they destroy the rational mind [Plato] |
| Full Idea: We are right to refuse admission to artists in any community which is going to respect convention, because he destroys the rational mind and feeds the irrational - it is like destroying good citizens by giving ruffians power. | |
| From: Plato (The Republic [c.374 BCE], 605b) |
| 2135 | Truth is closely related to proportion [Plato] |
| Full Idea: Truth is closely related to proportion. | |
| From: Plato (The Republic [c.374 BCE], 486d) |
| 2141 | I suggest that we forget about trying to define goodness itself for the time being [Plato] |
| Full Idea: I suggest that we forget about trying to define goodness itself for the time being. | |
| From: Plato (The Republic [c.374 BCE], 506e) | |
| A reaction: This was a source of some humour in the ancient world (in the theatre). Goodness is like some distant glow, which can never be approached in order to learn of its source. |
| 1869 | The good cannot be expressed in words, but imprints itself upon the soul [Plato, by Celsus] |
| Full Idea: Plato points to the truth about the highest good when he says that it cannot be expressed in words, but rather comes from familiarity - like a flash from the blue, imprinting itself upon the soul. | |
| From: report of Plato (The Republic [c.374 BCE]) by Celsus - On the True Doctrine (Against Christians) VII | |
| A reaction: It is reasonable to be drawn to something inexpressible, such as an appealing piece of music, but not good philosophy to build a system around something so obscure. |
| 4115 | Plato found that he could only enforce rational moral justification by creating an authoritarian society [Williams,B on Plato] |
| Full Idea: For Plato, the problem of making the ethical into a force was the problem of making society embody rational justification, and that problem could only have an authoritarian solution. | |
| From: comment on Plato (The Republic [c.374 BCE]) by Bernard Williams - Ethics and the Limits of Philosophy Ch. 2 | |
| A reaction: Plato's citizens were largely illiterate. We can be more carrot and less stick. |
| 4547 | Plato measured the degree of reality by the degree of value [Nietzsche on Plato] |
| Full Idea: Plato measured the degree of reality by the degree of value. | |
| From: comment on Plato (The Republic [c.374 BCE], 518d) by Friedrich Nietzsche - The Will to Power (notebooks) §572 | |
| A reaction: A most interesting comment. It epitomises the Nietzschean reading of Plato, in which the will to power leads the sense of value, which in turn creates the metaphysics. |
| 2094 | A thing's function is what it alone can do, or what it does better than other things [Plato] |
| Full Idea: The function of anything is what it alone can do, or what it can do better than anything else. | |
| From: Plato (The Republic [c.374 BCE], 353a) | |
| A reaction: I take this concept to be the lynchpin of Aristotle's virtue ethics. Note that it arises earlier, in Plato. Perhaps he should say what it is 'meant to do'. |
| 2095 | If something has a function then it has a state of being good [Plato] |
| Full Idea: Anything which has been endowed with a function also has a state of being good. | |
| From: Plato (The Republic [c.374 BCE], 353b) | |
| A reaction: 'ought' from 'is'? |
| 2129 | Goodness is mental health, badness is mental sickness [Plato] |
| Full Idea: Goodness is a state of mental health, bloom and vitality; badness is a state of mental sickness, deformity and infirmity. | |
| From: Plato (The Republic [c.374 BCE], 444e) | |
| A reaction: A nice statement of the closeness of goodness to health for the Greeks. The key point is that health is a deeply natural concept, which bridges the fact-value divide. |
| 12 | If we were invisible, would the just man become like the unjust? [Plato] |
| Full Idea: Glaucon: with a ring of invisibility 'the just man would differ in no way from the unjust'. | |
| From: Plato (The Republic [c.374 BCE], 360c) | |
| A reaction: I think a highly altruistic person would behave well with the ring, but I'm sure Glaucon would claim that these habits would wear off after a while. But I doubt that. |
| 2168 | Clever criminals do well at first, but not in the long run [Plato] |
| Full Idea: Clever criminals are exactly like those runners who do well on the way up the track, and then flag on the way back. | |
| From: Plato (The Republic [c.374 BCE], 613b) | |
| A reaction: Presumably there is some concept of natural justice lurking behind this comparison. Apart from the money, though, it is hard to imagine any professional criminal leading a flourishing life. |
| 2137 | The main aim is to understand goodness, which gives everything its value and advantage [Plato] |
| Full Idea: The most important thing to try to understand is the character of goodness, because this is where anything which is moral (or whatever) gets its value and advantages from. | |
| From: Plato (The Republic [c.374 BCE], 505a) | |
| A reaction: I think I'm with Aristotle on this. I understand a good lunch or a good person, but pure goodness just seems to be an empty placeholder. A vote in favour. |
| 2139 | Every person, and every activity, aims at the good [Plato] |
| Full Idea: The Good is something which everyone is after, and is the goal of all their activities. | |
| From: Plato (The Republic [c.374 BCE], 505d) | |
| A reaction: An obvious danger of tautology. If a blood crazed army is 'after' a massacre of some sort, that seems to qualify. What proportion is needed for 'everyone'? |
| 2143 | Good has the same role in the world of knowledge as the sun has in the physical world [Plato] |
| Full Idea: As goodness stands in the intelligible realm to intelligence and the things we know, so in the visible realm the sun stands to sight and the things we see. | |
| From: Plato (The Republic [c.374 BCE], 508c) | |
| A reaction: The claim seems to be that only goodness makes the world intelligible, but that strikes as closer to mysticism than to objective observation. |
| 2147 | The sight of goodness leads to all that is fine and true and right [Plato] |
| Full Idea: The sight of goodness shows that it is responsible for everything that is right and fine,…and it is the source and provider of truth and knowledge. It is necessary for intelligent conduct of private and public affairs. | |
| From: Plato (The Republic [c.374 BCE], 517c) | |
| A reaction: As so often with Plato, I am baffled by such a claim. I sometimes see things in the world which strike me as right or fine, but I cannot conceive of a separate 'sight of goodness'. |
| 4007 | For Plato we abandon honour and pleasure once we see the Good [Plato, by Taylor,C] |
| Full Idea: For Plato, once we see the Good, we cease to be fascinated by and absorbed in the search for honour and pleasure as we were before. | |
| From: report of Plato (The Republic [c.374 BCE], 505d) by Charles Taylor - Sources of the Self §3.2 | |
| A reaction: This is the quasi-religious aspect of the Good - that it is more like a vision than a reason |
| 2144 | Goodness makes truth and knowledge possible [Plato] |
| Full Idea: It is goodness which gives the things we know their truth and makes it possible for people to have knowledge. | |
| From: Plato (The Republic [c.374 BCE], 508e) | |
| A reaction: If we take truth to be the hallmark of successful thinking, then I have no idea what this means. I can't see how truth would disappear in an amoral cosmos. |
| 2164 | Bad is always destructive, where good preserves and benefits [Plato] |
| Full Idea: Badness always manifests in destruction and corruption, while goodness always manifests in preservation and benefit. | |
| From: Plato (The Republic [c.374 BCE], 608e) | |
| A reaction: Suspicions of tautology in this one. Can we have any concepts of good or bad which are not linked to desirable or undesirable outcomes? |
| 2138 | Pleasure is commonly thought to be the good, though the more ingenious prefer knowledge [Plato] |
| Full Idea: The usual view of goodness is that it is pleasure, while there's also a more ingenious view that it is knowledge. | |
| From: Plato (The Republic [c.374 BCE], 505b) | |
| A reaction: Pleasure clearly has an attraction for everyone (even puritans), and is thus a plausible natural candidate. Is this pure or instrumental knowledge? Hard to justify the former. |
| 2070 | Even people who think pleasure is the good admit that there are bad pleasures [Plato] |
| Full Idea: Those who define good as pleasure are clearly confused, and are compelled to admit that there are bad pleasures, so that the same thing is both good and bad. | |
| From: Plato (The Republic [c.374 BCE], 505c) | |
| A reaction: The issue is whether the pleasure can be disentangled from the action. 'It was a hideous murder, but at least the murderer enjoyed it'. Sounds wrong to me. |
| 2157 | Nice smells are intensive, have no preceding pain, and no bad after-effect [Plato] |
| Full Idea: Nice smells have no preceding feeling of pain, they are very intense, and they leave no distress when they are over. | |
| From: Plato (The Republic [c.374 BCE], 584b) | |
| A reaction: A nice example for extreme puritans to contemplate. Objections to enjoying nice smells seem almost inconceivable. Puritans will, I suppose, say 'slippery slope'. |
| 2134 | Philosophers are concerned with totally non-physical pleasures [Plato] |
| Full Idea: A person concerned with learning is concerned with purely mental pleasure, having nothing to do with pleasures reaching the mind through the body - assuming the person is a genuine philosopher. | |
| From: Plato (The Republic [c.374 BCE], 485d) | |
| A reaction: It is hard to find any argument which can demonstrate that mental pleasures are superior to physical ones. Mill notably failed to do it. |
| 2156 | There are three types of pleasure, for reason, for spirit and for appetite [Plato] |
| Full Idea: Each of the three mental categories (reason, spirit, appetite) has its own particular pleasure, so that there are three kinds of pleasure. | |
| From: Plato (The Republic [c.374 BCE], 580d) | |
| A reaction: I'm not sure why the types of pleasure are distinguished by mental faculties, rather than by the variety of sources of the pleasure. |
| 2158 | Pleasure-seekers desperately seek illusory satisfaction, like filling a leaky vessel [Plato] |
| Full Idea: Pleasure-seekers desperately and violently seek satisfaction in unreal things for a part of themselves which is also unreal - a leaky vessel they're trying to fill. | |
| From: Plato (The Republic [c.374 BCE], 586b) | |
| A reaction: Plato dreams of some enduring 'satisfaction' which never fades. He should have attended more to Heraclitus, and less to Parmenides. |
| 2123 | Excessive pleasure deranges people, making the other virtues impossible [Plato] |
| Full Idea: Self-discipline and excessive pleasure cannot go together, because pleasure deranges people just as much as distress. Excessive pleasure cannot partner any of the other virtues. | |
| From: Plato (The Republic [c.374 BCE], 402e) | |
| A reaction: This invites an examination of the word 'excessive', which seems too subjective. Aristotle says any good is improved by the addition of pleasure. Pleasure can certainly derange people. |
| 2166 | We should behave well even if invisible, for the health of the mind [Plato] |
| Full Idea: There's nothing better for the mind than morality, and a person ought to behave morally whether or not he owns Gyges' ring. | |
| From: Plato (The Republic [c.374 BCE], 612b) |
| 2097 | Isn't it better to have a reputation for goodness than to actually be good? [Plato] |
| Full Idea: Unless I gain a reputation for morality, my actually being moral will do me no good, but an immoral person who has managed to get a reputation for morality is said to have a wonderful life. | |
| From: Plato (The Republic [c.374 BCE], 365b) |
| 19946 | Morality is a compromise, showing restraint, to avoid suffering wrong without compensation [Plato] |
| Full Idea: The origin and nature of morality is a compromise between the ideal of doing wrong without paying for it, and the worst situation, which is having wrong done to one while lacking the means of exacting compensation. | |
| From: Plato (The Republic [c.374 BCE], 359a) | |
| A reaction: This idea is from Glaucon, and is not endorsed by Socrates. Hobbes thought it was right, though he emphasised safety. Game theory makes this approach to moraliy much more plausible. |
| 5 | Justice is merely the interests of the stronger party [Plato] |
| Full Idea: Thrasymachus: Justice or right is simply what is in the interest of the stronger party. | |
| From: Plato (The Republic [c.374 BCE], 338c) | |
| A reaction: Not sure whether this is cynicism about the brutal realities of life, or cynicism about the very concept of justice. |
| 7 | Surely you don't return a borrowed weapon to a mad friend? [Plato] |
| Full Idea: If one borrowed a weapon from a friend who subsequently went out of his mind and then asked for it back, surely one ought not to return it? | |
| From: Plato (The Republic [c.374 BCE], 331c) | |
| A reaction: Only a Kantian would think of disagreeing with this obvious truth. There is no promise here, but an implicit moral commitment. Such things should always have an all-things-being-equal clause. |
| 8 | Is right just the interests of the powerful? [Plato] |
| Full Idea: Thrasymachus: right is the interest of the established government. | |
| From: Plato (The Republic [c.374 BCE], 339a) | |
| A reaction: To believe this you would have to believe the powerful control not what is judged to be right, but also the ordinary language which expresses such judgements. Marxism explains that. |
| 15 | Sin first, then sacrifice to the gods from the proceeds [Plato] |
| Full Idea: The thing to do is to sin first and sacrifice afterwards from the proceeds. | |
| From: Plato (The Republic [c.374 BCE], 365e) | |
| A reaction: A bit like Graham Greene's Catholicism. One Greek view of the gods seems to be that they are quite myopic and naïve. |
| 5944 | For Plato, virtue is its own reward [Lawson-Tancred on Plato] |
| Full Idea: The 'Republic' is the first sustained philosophical defence of the idea that virtue is its own reward. | |
| From: comment on Plato (The Republic [c.374 BCE], Ch.9) by Hugh Lawson-Tancred - Plato's Republic and Greek Enlightenment | |
| A reaction: Sceptics might say that at the heart of his claim is the idea that the virtuous life is the best means of achieving long-term pleasure (as opposed to short-sighted hedonism). What is it about people which could make virtue attractive to them? |
| 2155 | True goodness requires mental unity and harmony [Plato] |
| Full Idea: True goodness requires mental unity and harmony. | |
| From: Plato (The Republic [c.374 BCE], 554e) |
| 2126 | A good community necessarily has wisdom, courage, self-discipline and morality [Plato] |
| Full Idea: A good community has everything which is good, so it necessarily has wisdom, courage, self-discipline and morality. | |
| From: Plato (The Republic [c.374 BCE], 427e) |
| 23562 | If the parts of our soul do their correct work, we will be just people, and will act justly [Plato] |
| Full Idea: Each one of us in whom each part is doing its own work will himself be just and do his own. …So it is appropriate for the rational part to rule …and for the spirited part to obey. | |
| From: Plato (The Republic [c.374 BCE], 441d) | |
| A reaction: 'Do his own' must mean play his own part in society correctly, because his internal faculties are also correctly focused on their role. So balancing the three parts in persons and society is not just an analogy, but one leads to the other. See 443e. |
| 2092 | Simonides said morality is helping one's friends and harming one's enemies [Plato] |
| Full Idea: Simonides claims that morality is doing good to one's friends and harm to one's enemies. | |
| From: Plato (The Republic [c.374 BCE], 332d) |
| 19889 | People need society because the individual has too many needs [Plato] |
| Full Idea: Society originates because the individual is not self-sufficient, but has many needs which he cannot supply himself. | |
| From: Plato (The Republic [c.374 BCE], 369b) | |
| A reaction: Notice that Plato has the liberal individualist approach to problem, of starting with isolated individuals, and asking why they need to gang together. This is despite the dependency of children, and the proximity of extended families. |
| 19890 | All exchanges in a community are for mutual benefit [Plato] |
| Full Idea: In the community all mutual exchanges are made on the assumption that the parties to them stand to gain. | |
| From: Plato (The Republic [c.374 BCE], 369c) | |
| A reaction: The sole purpose of his society appears to be trading, either of goods or of services. The assumption is that if each individual were self-sufficient there would be no society, which strikes me as unlikely. Aristotle offers a better picture. |
| 10 | After a taste of mutual harm, men make a legal contract to avoid it [Plato] |
| Full Idea: Once people experience committing wrong and suffering it, they see the disadvantages are unavoidable and the benefits unobtainable, ...so they enter into a contract, guaranteeing no permitting or receiving wrong, ...and they then make laws and decrees. | |
| From: Plato (The Republic [c.374 BCE], 359a) | |
| A reaction: This seems to be the earliest statement of the social contract idea. Here it both sets up the state and creates morality. This is Glaucon speaking, and is NOT endorsed by Socrates. |
| 23561 | People doing their jobs properly is the fourth cardinal virtue for a city [Plato] |
| Full Idea: The power that consists in everyone's doing his own work rivals wisdom, moderation, and courage in its contribution to the virtue of the city. | |
| From: Plato (The Republic [c.374 BCE], 433d) | |
| A reaction: Making conscientious the fourth cardinal virtue. Well said! My maxim for the modern world is that nearly all human misery consists of either bad health or other people not doing their jobs properly. You know I'm right. |
| 2149 | Reluctant rulers make a better and more unified administration [Plato] |
| Full Idea: The less keen the would-be rulers of a community are to rule, the better and less divided the administration of that community are bound to be. | |
| From: Plato (The Republic [c.374 BCE], 520d) |
| 2132 | Only rule by philosophers of integrity can keep a community healthy [Plato] |
| Full Idea: Unless communities have philosophers as kings, or the people who are currently called kings and rulers practise philosophy with enough integrity, there can be no end to political troubles. | |
| From: Plato (The Republic [c.374 BCE], 473d) |
| 2131 | Is there anything better for a community than to produce excellent people? [Plato] |
| Full Idea: Is anything better for a community than for it to engender women and men who are exceptionally good? | |
| From: Plato (The Republic [c.374 BCE], 456e) |
| 2148 | To gain knowledge, turn away from the world of change, and focus on true goodness [Plato] |
| Full Idea: To gain knowledge we must turn the mind away from the world of becoming, until it becomes capable of bearing the sight of real being and reality at its most bright, which we are saying is goodness. | |
| From: Plato (The Republic [c.374 BCE], 518c) |
| 2152 | Dialectic is the highest and most important part of the curriculum [Plato] |
| Full Idea: Dialectic occupies the highest position and forms, as it were, the copestone of the curriculum. | |
| From: Plato (The Republic [c.374 BCE], 534e) |
| 2153 | Compulsory intellectual work never remains in the mind [Plato] |
| Full Idea: Compulsory intellectual work never remains in the mind. | |
| From: Plato (The Republic [c.374 BCE], 536e) |
| 2630 | If Plato's God is immaterial, he will lack consciousness, wisdom, pleasure and movement, which are essential to him [Cicero on Plato] |
| Full Idea: Plato holds God to be without a body, immaterial; but this is an incomprehensible idea. Such a god would inevitably lack any consciousness, any wisdom and any pleasure (…or motion), all of which are bound up in our idea of God. | |
| From: comment on Plato (The Republic [c.374 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.30 |
| 14 | If the gods are non-existent or indifferent, why bother to deceive them? [Plato] |
| Full Idea: If there are no gods or if they care nothing for human affairs, why should we bother to deceive them? | |
| From: Plato (The Republic [c.374 BCE], 365d) | |
| A reaction: There is incipient deism here, as well as atheism. |
| 2165 | Something is unlikely to be immortal if it is imperfectly made from diverse parts [Plato] |
| Full Idea: Something is unlikely to be immortal if it's a compound, formed imperfectly from diverse parts. | |
| From: Plato (The Republic [c.374 BCE], 611b) |
| 13 | Is the supreme reward for virtue to be drunk for eternity? [Plato] |
| Full Idea: (the poets think) 'the supreme reward of virtue was to be drunk for eternity'. | |
| From: Plato (The Republic [c.374 BCE], 363d) | |
| A reaction: A perceptive thought. Most people consider the best life to contain endless fun and physical pleasure, so a boozy bawdy holiday in the sunshine ticks all the boxes. |
| 2120 | God is responsible for the good things, but we must look elsewhere for the cause of the bad things [Plato] |
| Full Idea: God and God alone must be held responsible for the good things, but responsibility for bad things must be looked for elsewhere, and not attributed to God. | |
| From: Plato (The Republic [c.374 BCE], 379c) |