71 ideas
| 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. |
| 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. |
| 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) |
| 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? |
| 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) |
| 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. |
| 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) |
| 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) |
| 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) |
| 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) |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| Full Idea: It seems unavoidable that the facts about logically necessary relations between levels of facts are themselves logically distinct further facts, irreducible to the microphysical facts. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: I'm beginning to think that rejecting every theory of reality that is proposed by carefully exposing some infinite regress hidden in it is a rather lazy way to do philosophy. Almost as bad as rejecting anything if it can't be defined. |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| Full Idea: Logical supervenience, restricted to individuals, seems to imply strong reduction. It is said that where the B-facts logically supervene on the A-facts, the B-facts simply re-describe what the A-facts describe, and the B-facts come along 'for free'. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: This seems to be taking 'logically' to mean 'analytically'. Presumably an entailment is logically supervenient on its premisses, and may therefore be very revealing, even if some people think such things are analytic. |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| Full Idea: The root intuition behind nonreductive materialism is that reality is composed of ontologically distinct layers or levels. …The upper levels depend on the physical without reducing to it. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], B) | |
| A reaction: A nice clear statement of a view which I take to be false. This relationship is the sort of thing that drives people fishing for an account of it to use the word 'supervenience', which just says two things seem to hang out together. Fluffy materialism. |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| Full Idea: Jessica Wilson (1999) says what makes physicalist accounts different from emergentism etc. is that each individual causal power associated with a supervenient property is numerically identical with a causal power associated with its base property. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], n 11) | |
| A reaction: Hence the key thought in so-called (serious, rather than self-evident) 'emergentism' is so-called 'downward causation', which I take to be an idle daydream. |
| 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. |
| 9240 | Love creates a necessity concerning what to care about [Frankfurt] |
| Full Idea: The necessity with which love binds the will puts an end to indecisiveness concerning what to care about. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.13) | |
| A reaction: I put this here as a reminder that there may be more to necessity than the dry concept of metaphysicians and logicians. 'Why did you rescue that man first?' 'Because I love him'. Kit Fine recognises many sorts of necessity. |
| 9264 | Persons are distinguished by a capacity for second-order desires [Frankfurt] |
| Full Idea: The essential difference between persons and other creatures is in the structure of the will, with their peculiar characteristic of being able to form 'second-order desires'. | |
| From: Harry G. Frankfurt (Freedom of the Will and concept of a person [1971], Intro) | |
| A reaction: There are problems with this - notably that all strategies of this kind just shift the problem up to the next order, without solving it - but this still strikes me as a very promising line of thinking when trying to understand ourselves. See Idea 9266. |
| 9266 | A person essentially has second-order volitions, and not just second-order desires [Frankfurt] |
| Full Idea: It is having second-order volitions, and not having second-order desires generally, that I regard as essential to being a person. | |
| From: Harry G. Frankfurt (Freedom of the Will and concept of a person [1971], §II) | |
| A reaction: Watson criticises Frankfurt for just pushing the problem up to the the next level, but Frankfurt is not offering to explain the will. He merely notes that this structure produces the sort of behaviour which is characteristic of persons, and he is right. |
| 9267 | Free will is the capacity to choose what sort of will you have [Frankfurt] |
| Full Idea: The statement that a person enjoys freedom of the will means that he is free to want what he wants to want. More precisely, he is free to will what he wants to will, or to have the will he wants. | |
| From: Harry G. Frankfurt (Freedom of the Will and concept of a person [1971], §III) | |
| A reaction: A good proposal. It covers kleptomaniacs and drug addicts quite well. Thieves have second-order desires (to steal) of which kleptomaniacs are incapable. There is actually no such thing as free will, but this sort of thing will do. |
| 9265 | The will is the effective desire which actually leads to an action [Frankfurt] |
| Full Idea: A person's will is the effective desire which moves (or will or would move) a person all the way to action. The will is not coextensive with what an agent intends to do, since he may do something else instead. | |
| From: Harry G. Frankfurt (Freedom of the Will and concept of a person [1971], §I) | |
| A reaction: Essentially Hobbes's view, but with an arbitrary distinction added. If the desire is only definitely a 'will' if it really does lead to action, then it only becomes the will after the action starts. The error is thinking that will is all-or-nothing. |
| 20015 | Freedom of action needs the agent to identify with their reason for acting [Frankfurt, by Wilson/Schpall] |
| Full Idea: Frankfurt says that basic issues concerning freedom of action presuppose and give weight to a concept of 'acting on a desire with which the agent identifies'. | |
| From: report of Harry G. Frankfurt (Freedom of the Will and concept of a person [1971]) by Wilson,G/Schpall,S - Action 1 | |
| A reaction: [the cite Frankfurt 1988 and 1999] I'm not sure how that works when performing a grim duty, but it sounds quite plausible. |
| 9228 | Ranking order of desires reveals nothing, because none of them may be considered important [Frankfurt] |
| Full Idea: Ranking desires in order of preference is no help, because a person who wants one thing more than another may not regard the former as any more important to him than the latter. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.5) | |
| A reaction: A salutary warning. Someone may pursue something with incredible intensity, but only to stave off a boring and empty existence. The only way I can think of to assess what really matters to people is - to ask them! |
| 9270 | A 'wanton' is not a person, because they lack second-order volitions [Frankfurt] |
| Full Idea: I use the term 'wanton' to refer to agents who have first-order desires but who are not persons because, whether or not they have desires of the second-order, they have no second-order volitions. | |
| From: Harry G. Frankfurt (Freedom of the Will and concept of a person [1971], §II) | |
| A reaction: He seems to be describing someone who behaves like an animal, performing actions without ever stopping to think about them. Presumably some persons occasionally become wantons, if, for example, they have an anger problem. |
| 9269 | A person may be morally responsible without free will [Frankfurt] |
| Full Idea: It is not true that a person is morally responsible for what he has done only if his will was free when he did it. He may be morally responsible for having done it even though his will was not free at all. | |
| From: Harry G. Frankfurt (Freedom of the Will and concept of a person [1971], §IV) | |
| A reaction: Frankfurt seems to be one of the first to assert this break with the traditional view. Good for him. I take moral responsibility to hinge on an action being caused by a person, but not with a mystical view of what a person is. |
| 9238 | Morality isn't based on reason; moral indignation is quite unlike disapproval of irrationality [Frankfurt] |
| Full Idea: The ultimate warrant for moral principles cannot be found in reason. The sort of opprobrium that attaches to moral transgressions is quite unlike the sort of opprobrium that attaches to the requirements of reason. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.5 n6) | |
| A reaction: More like a piece of evidence than a proper argument. We may not feel indignant if someone fails a maths exam, but we might if they mess up the arithmetic of our bank account, even though they meant well. |
| 9232 | It is by caring about things that we infuse the world with importance [Frankfurt] |
| Full Idea: It is by caring about things that we infuse the world with importance. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.10) | |
| A reaction: This book is a lovely attempt at getting to the heart of where values come from. 'Football isn't a matter of life and death; it's more important than that' - Bill Shankly (manager of Liverpool). Frankfurt is right. |
| 9234 | If you don't care about at least one thing, you can't find reasons to care about anything [Frankfurt] |
| Full Idea: It is not possible for a person who does not already care at least about something to discover reasons for caring about anything. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.11) | |
| A reaction: This is the key idea of this lovely book. Without a glimmer of love somewhere, it is not possible to bootstrap a meaningful life. The glimmer of caring about one thing is transferable. See the Ancient Mariner and the watersnake. |
| 9229 | What is worthwhile for its own sake alone may be worth very little [Frankfurt] |
| Full Idea: What is worth having or worth doing for its own sake alone may nonetheless be worth very little. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.5) | |
| A reaction: That is one of my cherished notions sunk without trace! Aristotle's idea that ends are what matter, not means, always struck me as crucial. But Frankfurt is right. Collecting trivia is done for its own sake. Great tasks are performed as a means. |
| 9233 | Our criteria for evaluating how to live offer an answer to the problem [Frankfurt] |
| Full Idea: Identifying the criteria to be employed in evaluating various ways of living is also tantamount to providing an answer to the question of how to live. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.10) | |
| A reaction: Presumably critical reflection is still possible about those criteria, even though he implies that they just arise out of you (in a rather Nietzschean way). The fear is that critical reflection on basic criteria kills in infant in its cradle. |
| 9235 | Rather than loving things because we value them, I think we value things because we love them [Frankfurt] |
| Full Idea: It is often understood that we begin loving things because we are struck by their value. ..However, what I have in mind is rather that what we love necessarily acquires value for us because we love it. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.3) | |
| A reaction: The uneasy thought here is that this makes value much less rational. If you love because you value, you could probably give reasons for the value. If love comes first it must be instinctive. He says he loved his children before they were born. |
| 9236 | Love can be cool, and it may not involve liking its object [Frankfurt] |
| Full Idea: It is not among the defining features of love that it must be hot rather than cool, ..and nor is it essential that a person like what he loves. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.4) | |
| A reaction: An interesting pair of observations. The greatness of love would probably be measured by length, or by sacrifice. Extreme heat makes us a little suspicious. It would be hard to love something that was actually disliked. |
| 9237 | The paradigm case of pure love is not romantic, but that between parents and infants [Frankfurt] |
| Full Idea: Relationships that are primarily romantic or sexual do not provide very authentic or illuminating paradigms of love. ...The love of parents for their small children comes closest to offering recognizably pure instances of love. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.4) | |
| A reaction: Excellent. Though perhaps a relationships which began romantically might settle into something like the more 'pure' love that he has in mind. Such a relationship must, I trust, be possible between adults. |
| 9239 | I value my children for their sake, but I also value my love for them for its own sake [Frankfurt] |
| Full Idea: Beside the fact that my children are important to me for their own sakes, there is the additional fact that loving my children is important to me for its own sake. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.7) | |
| A reaction: This is at the heart of Frankfurt's thesis, that love is the bedrock of our values in life, and we therefore all need to love in order to generate any values in our life, quite apart from what our love is directed at. Nice thought. |
| 9227 | We might not choose a very moral life, if the character or constitution was deficient [Frankfurt] |
| Full Idea: People who are scrupulously moral may nonetheless be destined by deficiencies of character or of constitution to lead lives that no reasonable person would freely choose. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.2) | |
| A reaction: This fairly firmly refutes any Greek dream that all there is to happiness is leading a virtuous life. Frankfurt is with Aristotle more than with the Stoics. It would be tempting to sacrifice virtue to get a sunny character and good health. |
| 9230 | People want to fulfill their desires, but also for their desires to be sustained [Frankfurt] |
| Full Idea: Besides wanting to fulfil his desire, the person who cares about what he desires wants something else as well: he wants the desire to be sustained. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.6) | |
| A reaction: Plato, in 'Gorgias', makes this fact sound like a nightmare, resembling drug addiction, but in Frankfurt's formulation it looks like a good thing. If you want to make your family happy because you love them, you would dread finding your love had died. |
| 9241 | Loving oneself is not a failing, but is essential to a successful life [Frankfurt] |
| Full Idea: Far from demonstrating a flaw in character or being a sign of weakness, coming to love oneself is the deepest and most essential - and by no means the most readily attainable - achievement of a serious and successful life. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.14) | |
| A reaction: Obviously it will be necessary to dilineate the healthy form of self-love, which Frankfurt attempts to do. Ruthless vanity and self-seeking certainly look like the worst possible weaknesses of character. With that proviso, he is right. |
| 9300 | Boredom is serious, not just uncomfortable; it threatens our psychic survival [Frankfurt] |
| Full Idea: Boredom is a serious matter. It is not a condition that we seek to avoid just because we do not find it enjoyable. ..It threatens the very continuation of conscious mental life. ..Avoiding bored is a primitive urge for psychic survival. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.8) | |
| A reaction: Presumably nihilism will flood into the emptiness created by boredom. Frankfurt will see it as a lack of love for anything in your life, and hence an absence of value. Frankfurt is very good. |
| 9231 | Freedom needs autonomy (rather than causal independence) - embracing our own desires and choices [Frankfurt] |
| Full Idea: What counts as far as freedom goes is not causal independence, but autonomy. It is a matter of whether we are active rather than passive in our motives and choices, whether those are what we really want, and not alien to us. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.8) | |
| A reaction: This is why setting your own targets is excellent, but having targets set for you by authorities is pernicious. These kind of principles need to be clear before any plausible theory of liberalism can be developed. |