89 ideas
| 23350 | A wise philosophers uses reason to cautiously judge each aspect of living [Epictetus] |
| Full Idea: The sinews of a philosopher are desire that never fails in its achievement; aversion that never meets with what it would avoid; appropriate impulse; carefully considered purpose; and assent that is never precipitate. | |
| From: Epictetus (The Discourses [c.56], 2.08.29) | |
| A reaction: This is a very individual view of wisdom and the philosopher, whereas wisdom is often thought to have a social role. Is it not important for a philosopher to at least offer advice? |
| 23355 | The task of philosophy is to establish standards, as occurs with weights and measures [Epictetus] |
| Full Idea: Things are judged and weighed, when we have the standards ready. This is the task of philosophy: to examine and establish the standards. | |
| From: Epictetus (The Discourses [c.56], 2.11.24) | |
| A reaction: It is interesting that this gives philosophers a very specific social role, and also that it seems to identify epistemology as First Philosophy. Other disciplines, of course, establish their own standards without reference to philosophy. |
| 21394 | Philosophy is knowing each logos, how they fit together, and what follows from them [Epictetus] |
| Full Idea: [Philosophical speculation] consists in knowing the elements of 'logos', what each of them is like, how they fit together, and what follows from them. | |
| From: Epictetus (The Discourses [c.56], 4.08.14), quoted by A.A. Long - Hellenistic Philosophy 4.1 | |
| A reaction: [Said to echo Zeno] If you substitute understanding for 'logos' (plausibly), I think this is exactly the view of philosophy I would subscribe to. We want to understand each aspect of life, and we want those understandings to cohere with one another. |
| 20876 | Philosophy investigates the causes of disagreements, and seeks a standard for settling them [Epictetus] |
| Full Idea: The start of philosophy is perception of the mutual conflict among people, and a search for its cause, plus the rejection and distrust of mere opinion, an investigation to see if opinion is right, and the discovery of some canon, like scales for weighing. | |
| From: Epictetus (The Discourses [c.56], 2.11.13) | |
| A reaction: So the number one aim of philosophy is epistemological, to find the criterion for true opinion. But it starts in real life, and would cease to trade if people would just agree. I think we should set the bar higher than that. |
| 23344 | Reason itself must be compounded from some of our impressions [Epictetus] |
| Full Idea: What is reason itself? Something compounded from impressions of a certain kind. | |
| From: Epictetus (The Discourses [c.56], 1.20.05) | |
| A reaction: This seems to be the only escape from the dead end attempts to rationally justify reason. Making reason a primitive absolute is crazy metaphysics. |
| 23343 | Because reason performs all analysis, we should analyse reason - but how? [Epictetus] |
| Full Idea: Since it is reason that analyses and completes all other things, reason itself should not be left unanalysed. But by what shall it be analysed? ..That is why philosophers put logic first, just as when measuring grain we first examine the measure. | |
| From: Epictetus (The Discourses [c.56], 1.17.01) | |
| A reaction: The problem of the definitive metre rule in Paris. I say we have to test reason against the physical world, and the measure of reason is truth. Something has to be primitive, but reason is too vague for that role. Idea 23344 agrees with me! |
| 10073 | There cannot be a set theory which is complete [Smith,P] |
| Full Idea: By Gödel's First Incompleteness Theorem, there cannot be a negation-complete set theory. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.3) | |
| A reaction: This means that we can never prove all the truths of a system of set theory. |
| 10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
| Full Idea: Going second-order in arithmetic enables us to prove new first-order arithmetical sentences that we couldn't prove before. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 23.4) | |
| A reaction: The wages of Satan, perhaps. We can prove things about objects by proving things about their properties and sets and functions. Smith says this fact goes all the way up the hierarchy. |
| 16489 | Is it possible to state every possible truth about the whole course of nature without using 'not'? [Russell] |
| Full Idea: Imagine a person who knew everything that can be stated without using the word 'not' or some equivalent; would such a person know the whole course of nature, or would he not? | |
| From: Bertrand Russell (Human Knowledge: its scope and limits [1948], 9) | |
| A reaction: Nowadays we might express Russell's thought as 'Does God need the word 'not'?'. Russell's thesis is that such words concern psychology, and not physics. God would need 'not' to describe how human minds work. |
| 10075 | A 'partial function' maps only some elements to another set [Smith,P] |
| Full Idea: A 'partial function' is one which maps only some elements of a domain to elements in another set. For example, the reciprocal function 1/x is not defined for x=0. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1 n1) |
| 10074 | A 'total function' maps every element to one element in another set [Smith,P] |
| Full Idea: A 'total function' is one which maps every element of a domain to exactly one corresponding value in another set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) |
| 10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
| Full Idea: If a function f maps the argument a back to a itself, so that f(a) = a, then a is said to be a 'fixed point' for f. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 20.5) |
| 10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
| Full Idea: The 'range' of a function is the set of elements in the output set that are values of the function for elements in the original set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) | |
| A reaction: In other words, the range is the set of values that were created by the function. |
| 10605 | Two functions are the same if they have the same extension [Smith,P] |
| Full Idea: We count two functions as being the same if they have the same extension, i.e. if they pair up arguments with values in the same way. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 11.3) | |
| A reaction: So there's only one way to skin a cat in mathematical logic. |
| 10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
| Full Idea: The so-called Comprehension Schema ∃X∀x(Xx ↔ φ(x)) says that there is a property which is had by just those things which satisfy the condition φ. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 22.3) |
| 10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
| Full Idea: 'Theorem': given a derivation of the sentence φ from the axioms of the theory T using the background logical proof system, we will say that φ is a 'theorem' of the theory. Standard abbreviation is T |- φ. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
| Full Idea: A 'natural deduction system' will have no logical axioms but may rules of inference. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 09.1) | |
| A reaction: He contrasts this with 'Hilbert-style systems', which have many axioms but few rules. Natural deduction uses many assumptions which are then discharged, and so tree-systems are good for representing it. |
| 10613 | No nice theory can define truth for its own language [Smith,P] |
| Full Idea: No nice theory can define truth for its own language. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 21.5) | |
| A reaction: This leads on to Tarski's account of truth. |
| 10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
| Full Idea: An 'injective' function is 'one-to-one' - each element of the output set results from a different element of the original set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) | |
| A reaction: That is, two different original elements cannot lead to the same output element. |
| 10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
| Full Idea: A 'surjective' function is 'onto' - the whole of the output set results from the function being applied to elements of the original set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) |
| 10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
| Full Idea: A 'bijective' function has 'one-to-one correspondence' - it is both surjective and injective, so that every element in each of the original and the output sets has a matching element in the other. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) | |
| A reaction: Note that 'injective' is also one-to-one, but only in the one direction. |
| 10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
| Full Idea: If everything that a theory proves must be true, then it is a 'sound' theory. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.1) |
| 10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
| Full Idea: Soundness is normally a matter of having true axioms and a truth-preserving proof system. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) | |
| A reaction: The only exception I can think of is if a theory consisted of nothing but the axioms. |
| 10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
| Full Idea: A theory is 'sound' iff every theorem of it is true (i.e. true on the interpretation built into its language). Soundness is normally a matter of having true axioms and a truth-preserving proof system. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
| Full Idea: A theory is 'negation complete' if it decides every sentence of its language (either the sentence, or its negation). | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
| Full Idea: There is an annoying double-use of 'complete': a logic may be semantically complete, but there may be an incomplete theory expressed in it. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
| Full Idea: Logicians say that a theory T is '(negation) complete' if, for every sentence φ in the language of the theory, either φ or ¬φ is deducible in T's proof system. If this were the case, then truth could be equated with provability. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.1) | |
| A reaction: The word 'negation' seems to be a recent addition to the concept. Presumable it might be the case that φ can always be proved, but not ¬φ. |
| 10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
| Full Idea: There are two routes to Incompleteness results. One goes via the semantic assumption that we are dealing with sound theories, using a result about what they can express. The other uses the syntactic notion of consistency, with stronger notions of proof. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 18.1) |
| 10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
| Full Idea: An 'effectively decidable' (or 'computable') algorithm will be step-by-small-step, with no need for intuition, or for independent sources, with no random methods, possible for a dumb computer, and terminates in finite steps. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.2) | |
| A reaction: [a compressed paragraph] |
| 10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
| Full Idea: A theory is 'decidable' iff there is a mechanical procedure for determining whether any sentence of its language can be proved. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) | |
| A reaction: Note that it doesn't actually have to be proved. The theorems of the theory are all effectively decidable. |
| 10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
| Full Idea: Any consistent, axiomatized, negation-complete formal theory is decidable. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.6) |
| 10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
| Full Idea: A set is 'enumerable' iff either the set is empty, or there is a surjective function to the set from the set of natural numbers, so that the set is in the range of that function. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.3) |
| 10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
| Full Idea: A set is 'effectively enumerable' if an (idealised) computer could be programmed to generate a list of its members such that any member will eventually be mentioned (even if the list is empty, or without end, or contains repetitions). | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.4) |
| 10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
| Full Idea: A finite set of finitely specifiable objects is always effectively enumerable (for example, the prime numbers). | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.4) |
| 10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
| Full Idea: The set of ordered pairs of natural numbers (i,j) is effectively enumerable, as proven by listing them in an array (across: <0,0>, <0,1>, <0,2> ..., and down: <0,0>, <1,0>, <2,0>...), and then zig-zagging. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.5) |
| 10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
| Full Idea: The theorems of any properly axiomatized theory can be effectively enumerated. However, the truths of any sufficiently expressive arithmetic can't be effectively enumerated. Hence the theorems and truths of arithmetic cannot be the same. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 05 Intro) |
| 10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
| Full Idea: Whether a property is 'expressible' in a given theory depends on the richness of the theory's language. Whether the property can be 'captured' (or 'represented') by the theory depends on the richness of the axioms and proof system. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 04.7) |
| 10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
| Full Idea: For prime numbers we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))). That is, the only way to multiply two numbers and a get a prime is if one of them is 1. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 04.5) |
| 10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
| Full Idea: It has been proved (by Tarski) that the real numbers R is a complete theory. But this means that while the real numbers contain the natural numbers, the pure theory of real numbers doesn't contain the theory of natural numbers. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 18.2) |
| 10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
| Full Idea: The truths of arithmetic are just the true equations involving particular numbers, and universally quantified versions of such equations. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 27.7) | |
| A reaction: Must each equation be universally quantified? Why can't we just universally quantify over the whole system? |
| 10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
| Full Idea: All numbers are related to zero by the ancestral of the successor relation. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 23.5) | |
| A reaction: The successor relation only ties a number to the previous one, not to the whole series. Ancestrals are a higher level of abstraction. |
| 10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
| Full Idea: The number of Fs is the 'successor' of the number of Gs if there is an object which is an F, and the remaining things that are F but not identical to the object are equinumerous with the Gs. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 14.1) |
| 10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
| Full Idea: Baby Arithmetic 'knows' the addition of particular numbers and multiplication, but can't express general facts about numbers, because it lacks quantification. It has a constant '0', a function 'S', and functions '+' and 'x', and identity and negation. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.1) |
| 10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
| Full Idea: Baby Arithmetic is negation complete, so it can prove every claim (or its negation) that it can express, but it is expressively extremely impoverished. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.3) |
| 10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
| Full Idea: We can beef up Baby Arithmetic into Robinson Arithmetic (referred to as 'Q'), by restoring quantifiers and variables. It has seven generalised axioms, plus standard first-order logic. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.3) |
| 10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
| Full Idea: Robinson Arithmetic (Q) is not negation complete | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.4) |
| 10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
| Full Idea: The sequence of natural numbers starts from zero, and each number has just one immediate successor; the sequence continues without end, never circling back on itself, and there are no 'stray' numbers, lurking outside the sequence. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.1) | |
| A reaction: These are the characteristics of the natural numbers which have to be pinned down by any axiom system, such as Peano's, or any more modern axiomatic structures. We are in the territory of Gödel's theorems. |
| 10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
| Full Idea: If the logic of arithmetic doesn't have second-order quantifiers to range over properties of numbers, how can it handle induction? | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 10.1) |
| 10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
| Full Idea: Multiplication in itself isn't is intractable. In 1929 Skolem showed a complete theory for a first-order language with multiplication but lacking addition (or successor). Multiplication together with addition and successor produces incompleteness. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 10.7 n8) |
| 10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
| Full Idea: Putting multiplication together with addition and successor in the language of arithmetic produces incompleteness. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 10.7) | |
| A reaction: His 'Baby Arithmetic' has all three and is complete, but lacks quantification (p.51) |
| 10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
| Full Idea: The 'ancestral' of a relation is that relation which holds when there is an indefinitely long chain of things having the initial relation. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 23.5) | |
| A reaction: The standard example is spotting the relation 'ancestor' from the receding relation 'parent'. This is a sort of abstraction derived from a relation which is not equivalent (parenthood being transitive but not reflexive). The idea originated with Frege. |
| 16490 | Some facts about experience feel like logical necessities [Russell] |
| Full Idea: The impossibility of seeing two colours simultaneously in a given direction feels like a logical impossibility. | |
| From: Bertrand Russell (Human Knowledge: its scope and limits [1948], 9) | |
| A reaction: I presume all necessities feel equally necessary. If we distinguish necessities by what gives rise to them (a view I favour) then how strong they 'feel' will be irrelevant. We can see why Russell is puzzled by the phenomenon, though. |
| 23359 | We can't believe apparent falsehoods, or deny apparent truths [Epictetus] |
| Full Idea: It is impossible to assent to an apparent falsehood, or to deny an apparent truth. | |
| From: Epictetus (The Discourses [c.56], 3.07.15) | |
| A reaction: The way some philosophers write you would think that most beliefs just result from private whims or social fashion. That happens, of course, but most beliefs result from direct contact with reality. |
| 23356 | Self-evidence is most obvious when people who deny a proposition still have to use it [Epictetus] |
| Full Idea: It is about the strongest proof one could offer of a proposition being evident, that even he who contradicts it finds himself having to make use of it. | |
| From: Epictetus (The Discourses [c.56], 2.20.01) | |
| A reaction: Philosophers sometimes make fools of themselves by trying, by the use of elaborate sophistry, to demolish propositions which are self-evidently true. Don't be one of these philosophers! |
| 16488 | It is hard to explain how a sentence like 'it is not raining' can be found true by observation [Russell] |
| Full Idea: If 'it is not raining' means 'the sentence "it is raining" is false', that makes it almost impossible to understand how a sentence containing the word 'not' can be found true by observation. | |
| From: Bertrand Russell (Human Knowledge: its scope and limits [1948], 9) | |
| A reaction: Russell goes on to explore the general difficulty of deciding negative truths by observation. The same problem arises for truthmaker theory. Obviously I can observe that it isn't raining, but it seems parasitic on observing when it is raining. |
| 23329 | We make progress when we improve and naturalise our choices, asserting their freedom [Epictetus] |
| Full Idea: Progress is when any of you turns to his own faculty of choice, working at it and perfecting it, so as to bring it fully into harmony with nature; elevated, free, unrestrained, unhindered, faithful, self-respecting. | |
| From: Epictetus (The Discourses [c.56], 1.04.18) | |
| A reaction: [See also Disc.3.5.7] Rationality is the stoic concept of being in 'harmony with nature'. It appears (from reading Frede) that this may be the FIRST EVER reference to free will. Note the very rhetorical way in which it is presented. |
| 23342 | Freedom is acting by choice, with no constraint possible [Epictetus] |
| Full Idea: He is free for whom all things happen in accordance with his choice, and whom no one can constrain. | |
| From: Epictetus (The Discourses [c.56], 1.12.09) | |
| A reaction: Presumable this means that constraint is absolutely impossible, even by Zeus, and not just contingent possibility, when no one sees me raid the fridge. |
| 23330 | Freedom is making all things happen by choice, without constraint [Epictetus] |
| Full Idea: He is free for whom all things happen in accordance with his choice, and whom no one can constrain. | |
| From: Epictetus (The Discourses [c.56], 1.12.09) | |
| A reaction: The idea of 'free' will seems to have resulted from a wide extension of the idea of constraint, with global determinism lurking in the background. |
| 23332 | Zeus gave me a nature which is free (like himself) from all compulsion [Epictetus] |
| Full Idea: Zeus placed my good nature in my own power, and gave it to me as he has it himself, free from all hindrance, compulsion and restraint. | |
| From: Epictetus (The Discourses [c.56], 3.03.10) | |
| A reaction: Although Frede traces the origin of free will to the centrality of choice in moral life (and hence to the elevation of its importance), this remark shows that there is a religious aspect to it. Zeus is supreme, and obviously has free will. |
| 23331 | Not even Zeus can control what I choose [Epictetus] |
| Full Idea: You can fetter my leg, but not even Zeus himself can get the better of my choice. | |
| From: Epictetus (The Discourses [c.56], 1.01.23) | |
| A reaction: This is the beginnings of the idea of free will. It is based on the accurate observation that the intrinsic privacy of a mind means that no external force can be assured of controlling its actions. Epictetus failed to think of internal forces. |
| 23338 | You can fetter my leg, but not even Zeus can control my power of choice [Epictetus] |
| Full Idea: What are you saying, man? Fetter me? You will fetter my leg; but not even Zeus himself can get the better of my choice. | |
| From: Epictetus (The Discourses [c.56], 1.01.23) | |
| A reaction: This seems to be the beginning of the idea of 'absolute' freedom, which is conjured up to preserve perfect inegrity and complete responsibility. Obviously you can be prevented from doing what you choose, so this is not compatibilism. |
| 20875 | If we could foresee the future, we should collaborate with disease and death [Epictetus] |
| Full Idea: The philosophers are right to say that if the honorable and good person knew what was going to happen, he would even collaborate with disease, death and lameness. | |
| From: Epictetus (The Discourses [c.56], 2.10.05) | |
| A reaction: The 'philosophers' must be the earlier stoics, founders of his school. |
| 23347 | If I know I am fated to be ill, I should want to be ill [Epictetus] |
| Full Idea: If I really knew that it was ordained for me to be ill at this moment, I would aspire to be so. | |
| From: Epictetus (The Discourses [c.56], 2.06.10) | |
| A reaction: The rub, of course, is that it is presumably impossible to know what is fated. Book 2.7 is on divination. I don't see any good in a mortally ill person desiring, for that reason alone, to die. Rage against the dying of the light, I say. |
| 16491 | If we define 'this is not blue' as disbelief in 'this is blue', we eliminate 'not' as an ingredient of facts [Russell] |
| Full Idea: We can reintroduce 'not' by a definition: the words 'this is not blue' are defined as expressing disbelief in what is expressed by the words 'this is blue'. In this way the need of 'not' as an indefinable constituent of facts is avoided. | |
| From: Bertrand Russell (Human Knowledge: its scope and limits [1948], 9) | |
| A reaction: This is part of Russell's programme of giving a psychological account of logical connectives. See other ideas from his 1940 and 1948 works. He observes that disbelief is a state just as positive as belief. I love it. |
| 23325 | Epictetus developed a notion of will as the source of our responsibility [Epictetus, by Frede,M] |
| Full Idea: The notion of will in Epictetus is clearly developed to pinpoint the source of our responsibility for our actions and to identify precisely what it is that makes them our own doings. | |
| From: report of Epictetus (The Discourses [c.56]) by Michael Frede - A Free Will 3 | |
| A reaction: So the key move is that responsibility needs a 'source', rather than being a generalisation about how our actions arise. The next step is demand an 'ultimate' source, and this leads to the idea that this new will is 'free'. This will can be good or bad. |
| 20873 | Tragedies are versified sufferings of people impressed by externals [Epictetus] |
| Full Idea: Tragedies are nothing but the sufferings of people who are impressed by externals, performed in the right sort of meter. | |
| From: Epictetus (The Discourses [c.56], 1.04.26) | |
| A reaction: The externals are things like honour, position and wealth. Wonderfully dismissive! |
| 23364 | Homer wrote to show that the most blessed men can be ruined by poor judgement [Epictetus] |
| Full Idea: Did not Homer write to show us that the noblest, the strongest, the richest, the handsomest of men may nevertheless be the most unfortunate and wretched, if they do not hold the judgements that they ought to hold? | |
| From: Epictetus (The Discourses [c.56], 4.10.36) | |
| A reaction: This seems to be right. He clearly wrote about the greatest and most memorable events of recent times, but not just to record triumphs, because almost every hero (in the Iliad, at least) ends in disaster. |
| 23340 | We consist of animal bodies and god-like reason [Epictetus] |
| Full Idea: We have these two elements mingled within us, a body in common with the animals, and reason and intelligence in common with the gods. | |
| From: Epictetus (The Discourses [c.56], 1.03.03) | |
| A reaction: This is what I call Human Exceptionalism, but note that it doesn't invoke a Christian soul or spiritual aspect. This separation of reason goes back at least to Plato. High time we stopped thinking this way. Animals behave very sensibly. |
| 23358 | Every species produces exceptional beings, and we must just accept their nature [Epictetus] |
| Full Idea: In every species nature produces some exceptional being, in oxen, in dogs, in bees, in horses. We do not say to them 'Who are you?' It will tell you 'I am like the purple in the robe. Do not expect me to be like the rest, or find fault with my nature'. | |
| From: Epictetus (The Discourses [c.56], 3.01.23) | |
| A reaction: This idea began with Aristotle's 'great soul', and presumably culminates in Nietzsche, who fills in more detail. In the modern world such people are mostly nothing but trouble. |
| 23339 | I will die as becomes a person returning what he does not own [Epictetus] |
| Full Idea: When the time comes, then I will die - as becomes a person who gives back what is not his own. | |
| From: Epictetus (The Discourses [c.56], 1.01.32) | |
| A reaction: There is a tension between his demand that he have full control of his choices, and this humility that says his actual life is not his own. The things which can't be controlled, though, are 'indifferents' so life and death are indifferent. |
| 23345 | Don't be frightened of pain or death; only be frightened of fearing them [Epictetus] |
| Full Idea: It is not pain or death that is to be feared, but the fear of pain or death. | |
| From: Epictetus (The Discourses [c.56], 2.01.13) | |
| A reaction: These two cases are quite different, I would say. I'm much more frightened of pain than I am of the fear of pain, and the opposite view seems absurd. About death, though, I think this is right. Mostly I'm with Spinoza: think about life, not death. |
| 23357 | Knowledge of what is good leads to love; only the wise, who distinguish good from evil, can love [Epictetus] |
| Full Idea: Whoever has knowledge of good things would know how to love them; and how could he who cannot distinguish good things from evil still have to power to love? It follows that the wise man alone has the power to love. | |
| From: Epictetus (The Discourses [c.56], 2.22.03) | |
| A reaction: A rather heartwarming remark, but hard to assess for its truth. Evil people are unable to love? Not even love a cat, or their favourite car? We would never call someone wise if they lacked love. |
| 23363 | The evil for everything is what is contrary to its nature [Epictetus] |
| Full Idea: Where is the paradox if we say that what is evil for everything is what is contrary to its nature? | |
| From: Epictetus (The Discourses [c.56], 4.01.125) | |
| A reaction: A very Greek view. For humans, it must rely on the belief that human nature is essentially good. If I am sometimes grumpy and annoying, why is that not part of my nature? |
| 23328 | The essences of good and evil are in dispositions to choose [Epictetus] |
| Full Idea: The essence of the good is a certain disposition of our choice, and essence of evil likewise. | |
| From: Epictetus (The Discourses [c.56], 1.29.01) | |
| A reaction: This is the origin of Kant's famous view, that the only true good is a good will. This is the alternative to good character or good states of affairs as the good. It points towards the modern more legalistic view of morality, as concerning actions. |
| 23362 | All human ills result from failure to apply preconceptions to particular cases [Epictetus] |
| Full Idea: The cause of all human ills is that people are incapable of applying their general preconceptions to particular cases. | |
| From: Epictetus (The Discourses [c.56], 4.01.42) | |
| A reaction: I'm not sure whether 'preconceptions' is meant pejoratively (as unthinking, and opposed to true principles). This sounds like modern particularism (e.g. Jonathan Dancy) to the letter. |
| 23353 | We have a natural sense of honour [Epictetus] |
| Full Idea: What faculty do you mean? - Have we not a natural sense of honour? - We have. | |
| From: Epictetus (The Discourses [c.56], 2.10.22) | |
| A reaction: This seems unlikely, given the lower status that honour now has with us, compared to two hundred years ago. But there may be a natural sense of status, and of humiliation and shame. |
| 23354 | If someone harms themselves in harming me, then I harm myself by returning the harm [Epictetus] |
| Full Idea: Since he has harmed himself by wronging me, shall not I harm myself by harming him? | |
| From: Epictetus (The Discourses [c.56], 2.10.26) | |
| A reaction: I am very keen on this idea. See Hamlet's remarks to Polonius about 'honour and dignity'. The best strategy for achieving moral excellence is to focus on our own characters, rather than how to act, and to respond to others. |
| 23324 | In the Discourses choice [prohairesis] defines our character and behaviour [Epictetus, by Frede,M] |
| Full Idea: In Epictetus's 'Discourses' the notion of choice [prohairesis] plays perhaps the central role. It is our prohairesis which defines us a person, as the sort of person we are; it is our prohairesis which determines how we behave. | |
| From: report of Epictetus (The Discourses [c.56]) by Michael Frede - A Free Will 3 | |
| A reaction: Frede is charting the gradual move in Greek philosophy from action by desire, reason and habit to action by the will (which then turns out to be 'free'). Character started as dispositions and ended as choices. |
| 23361 | Health is only a good when it is used well [Epictetus] |
| Full Idea: Is health a good and sickness an evil? No. Health is good when used well, and bad when used ill. | |
| From: Epictetus (The Discourses [c.56], 3.20.04) | |
| A reaction: Although I like the idea that health is a natural value, which bridges the gap from facts to values (as a successful function), there is no denying that the health of very evil people is not something the rest of us hope for. |
| 23346 | A person is as naturally a part of a city as a foot is part of the body [Epictetus] |
| Full Idea: Just as the foot in detachment is no longer a foot, so you in detachment are not longer a man. For what is a man? A part of a city, first. | |
| From: Epictetus (The Discourses [c.56], 2.05.26) | |
| A reaction: It is, of course, not true that a detached foot ceases to be a foot (and an isolated human is still a human). This an extreme version of the Aristotelian idea that we are essentially social. It is, though, the sort of view favoured by totalitarianism. |
| 23351 | We are citizens of the universe, and principal parts of it [Epictetus] |
| Full Idea: You are a citizen of the universe, and a part of it; and no subservient, but a principal part of it. | |
| From: Epictetus (The Discourses [c.56], 2.10.03) | |
| A reaction: He got this view from Diogenes of Sinope, one of his heroes. What community you are a part of seems to be a choice as much as a fact. Am I British or a European? |
| 20874 | A citizen is committed to ignore private advantage, and seek communal good [Epictetus] |
| Full Idea: The commitment of the citizen is to have no private advantage, not to deliberate about anything as though one were a separate part. | |
| From: Epictetus (The Discourses [c.56], 2.10.04) | |
| A reaction: This is the modern problem of whether democratic voters are choosing for themselves or for the community. I think we should make an active effort at every election to persuade voters to aim for the communal good. Cf Rawls. |
| 23352 | A citizen should only consider what is good for the whole society [Epictetus] |
| Full Idea: The calling of a citizen is to consider nothing in terms of personal advantage, never to deliberate on anything as though detached from the whole, but be like our hand or foot. | |
| From: Epictetus (The Discourses [c.56], 2.10.04) | |
| A reaction: Fat chance of that in an aggressively capitalist society. I've always voted for what I thought was the common good, and was shocked to gradually realise that many people only vote for what promotes their own interests. Heigh ho. |
| 22604 | Punishing a criminal for moral ignorance is the same as punishing someone for being blind [Epictetus] |
| Full Idea: You should ask 'Ought not this man to be put to death, who is deceived in things of the greatest importance, and is blinded in distinguishing good from evil?' …You then see how inhuman it is, and the same as 'Ought not this blind man to be put to death?' | |
| From: Epictetus (The Discourses [c.56], 1.18.6-7) | |
| A reaction: This is the doctrine of Socrates, that evil is ignorance (and weakness of will [akrasia] is impossible). Epictetus wants us to reason with the man, but what should be do if reasoning fails and he persists in his crimes? |
| 23349 | Asses are born to carry human burdens, not as ends in themselves [Epictetus] |
| Full Idea: An ass is surely not born as an end in itself? No, but because we had need of a back that is able to carry burdens. | |
| From: Epictetus (The Discourses [c.56], 2.08.07) | |
| A reaction: This is the absurd human exceptionalism which plagues our thinking. It would be somewhat true of animals which are specifically bred for human work, such as large cart horses. |
| 4786 | Russell's 'at-at' theory says motion is to be at the intervening points at the intervening instants [Russell, by Psillos] |
| Full Idea: To reply to Zeno's Arrow Paradox, Russell developed his 'at-at' theory of motion, which says that to move from A to B is to be at the intervening points at the intervening instants. | |
| From: report of Bertrand Russell (Human Knowledge: its scope and limits [1948]) by Stathis Psillos - Causation and Explanation §4.2 | |
| A reaction: I wonder whether Russell's target was actually Zeno, or was it a simplified ontology of points and instants? The ontology will also need identity, to ensure it is the same thing which arrives at each point. |
| 23341 | God created humans as spectators and interpreters of God's works [Epictetus] |
| Full Idea: God has introduced man into the world as a spectator of himself and of his works: and not only as a spectator of them, but an interpreter of them as well. | |
| From: Epictetus (The Discourses [c.56], 1.06.19) | |
| A reaction: This idea (which strikes me as bizarre) was picked up directly by the Christians. I can't imagine every Johnson wanting to creating their own Boswell. If you think we are divinely created, you have to propose some motive for it, I suppose. |
| 23348 | Both god and the good bring benefits, so their true nature seems to be the same [Epictetus] |
| Full Idea: God brings benefits; but the good also brings benefit. It would seem, then, that where the true nature of god is, there too is the true nature of good. | |
| From: Epictetus (The Discourses [c.56], 2.08.01) | |
| A reaction: An enthymeme, missing the premise that there can only be one source of benefit (which sounds unlikely). Does god bring anything other than benefits? And does the good? I think this is an idea from later platonism. |
| 23360 | Each of the four elements in you is entirely scattered after death [Epictetus] |
| Full Idea: Whatever was in you of fire, departs into fire; what was of earth, into earth; what of air, into air; what of water, into water. There is no Hades, nor Acheron. | |
| From: Epictetus (The Discourses [c.56], 3.13.15) | |
| A reaction: This sort of remark may explain why so few of the great Stoic texts (such as those of Chrysippus) survived the Christian era. |