81 ideas
| 13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C] |
| Full Idea: We can learn from the work of philosophers of other periods only if we are prepared to run the risk of radical and almost inevitable misrepresentation of his thought. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], Pref) | |
| A reaction: This sounds about right, and a motto for my own approach to Aristotle and Leibniz, but I see the effort as more collaborative than this suggests. Professional specialists in older philosophers are a vital part of the team. Read them! |
| 13883 | The best way to understand a philosophical idea is to defend it [Wright,C] |
| Full Idea: The most productive way in which to attempt an understanding of any philosophical idea is to work on its defence. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.vii) | |
| A reaction: Very nice. The key point is that this brings greater understanding than working on attacking an idea, which presumably has the dangers of caricature, straw men etc. It is the Socratic insight that dialectic is the route to wisdom. |
| 10142 | The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K] |
| Full Idea: Frege gave up on the attempt to introduce natural numbers by contextual definition, but the project has been revived by neo-logicists. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Kit Fine - The Limits of Abstraction II |
| 5728 | The concept of truth was originated by the senses [Lucretius] |
| Full Idea: The concept of truth was originated by the senses. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], IV.479) | |
| A reaction: This is a refreshing challenge to the modern view of truth, which seems entirely entangled with language. Truth seems a useful concept when discussing the workings of an animal mind. As you get closer to an object, you see it more 'truly'. |
| 9868 | An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett] |
| Full Idea: For Wright, an expression refers to an object if it fulfils the 'syntactic role' of a singular term, and if we have fixed the truth-conditions of sentences containing it in such a way that some of them come out true. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Michael Dummett - Frege philosophy of mathematics Ch.15 | |
| A reaction: Much waffle is written about reference, and it is nice to hear of someone actually trying to state the necessary and sufficient conditions for reference to be successful. So is it possible for 'the round square' to ever refer? '...is impossible to draw' |
| 13861 | Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C] |
| Full Idea: In the Fregean view number theory is a science, aimed at those truths furnished by the essential properties of zero and its successors. The two broad question are then the nature of the objects, and the epistemology of those facts. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro) | |
| A reaction: [compressed] I pounce on the word 'essence' here (my thing). My first question is about the extent to which the natural numbers all have one generic essence, and the extent to which they are individuals (bless their little cotton socks). |
| 13892 | One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C] |
| Full Idea: Someone could be clear about number identities, and distinguish numbers from other things, without conceiving them as ordered in a progression at all. The point of them would be to make comparisons between sizes of groups. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 3.xv) | |
| A reaction: Hm. Could you grasp size if you couldn't grasp which of two groups was the bigger? What's the point of noting that I have ten pounds and you only have five, if you don't realise that I have more than you? You could have called them Caesar and Brutus. |
| 13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
| Full Idea: The invitation to number the instances of some non-sortal concept is intelligible only if it is relativised to a sortal. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i) | |
| A reaction: I take this to be an essentially Fregean idea, as when we count the boots when we have decided whether they fall under the concept 'boot' or the concept 'pair'. I also take this to be the traditional question 'what units are you using'? |
| 17441 | Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck] |
| Full Idea: Wright is claiming that HP is a special sort of truth in some way: it is supposed to be the fundamental truth about cardinality; ...in particular, HP is supposed to be more fundamental, in some sense than the Dedekind-Peano axioms. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 1 | |
| A reaction: Heck notes that although PA can be proved from HP, HP can be proven from PA plus definitions, so direction of proof won't show fundamentality. He adds that Wright thinks HP is 'more illuminating'. |
| 13862 | There are five Peano axioms, which can be expressed informally [Wright,C] |
| Full Idea: Informally, Peano's axioms are: 0 is a number, numbers have a successor, different numbers have different successors, 0 isn't a successor, properties of 0 which carry over to successors are properties of all numbers. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro) | |
| A reaction: Each statement of the famous axioms is slightly different from the others, and I have reworded Wright to fit him in. Since the last one (the 'induction axiom') is about properties, it invites formalization in second-order logic. |
| 17853 | Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C] |
| Full Idea: The intuitive proposal is the essential number theoretic truths are precisely the logical consequences of the Peano axioms, ...but the notion of consequence is a semantic one...and it is not obvious that we possess a semantic notion of the requisite kind. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro) | |
| A reaction: (Not sure I understand this, but it is his starting point for rejecting PA as the essence of arithmetic). |
| 17854 | What facts underpin the truths of the Peano axioms? [Wright,C] |
| Full Idea: We incline to think of the Peano axioms as truths of some sort; so there has to be a philosophical question how we ought to conceive of the nature of the facts which make those statements true. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro) | |
| A reaction: [He also asks about how we know the truths] |
| 13894 | Sameness of number is fundamental, not counting, despite children learning that first [Wright,C] |
| Full Idea: We teach our children to count, sometimes with no attempt to explain what the sounds mean. Doubtless it is this habit which makes it so natural to think of the number series as fundamental. Frege's insight is that sameness of number is fundamental. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 3.xv) | |
| A reaction: 'When do children understand number?' rather than when they can recite numerals. I can't make sense of someone being supposed to understand number without a grasp of which numbers are bigger or smaller. To make 13='15' do I add or subtract? |
| 10140 | We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K] |
| Full Idea: Wright says the Fregean arithmetic can be broken down into two steps: first, Hume's Law may be derived from Law V; and then, arithmetic may be derived from Hume's Law without any help from Law V. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Kit Fine - The Limits of Abstraction I.4 | |
| A reaction: This sounds odd if Law V is false, but presumably Hume's Law ends up as free-standing. It seems doubtful whether the resulting theory would count as logic. |
| 8692 | Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend] |
| Full Idea: Wright proposed removing Frege's basic law V (which led to paradox), replacing it with Frege's 'number principle' (identity of numbers is one-to-one correspondence). The new system is formally consistent, and the Peano axioms can be derived from it. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.7 | |
| A reaction: The 'number principle' is also called 'Hume's principle'. This idea of Wright's resurrected the project of logicism. The jury is ought again... Frege himself questioned whether the number principle was a part of logic, which would be bad for 'logicism'. |
| 17440 | Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck] |
| Full Idea: Wright intends the claim that Hume's Principle (HP) embodies an explanation of the concept of number to imply that it is analytic of the concept of cardinal number - so it is an analytic or conceptual truth, much as a definition would be. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 1 | |
| A reaction: Boolos is quoted as disagreeing. Wright is claiming a fundamental truth. Boolos says something can fix the character of something (as yellow fixes bananas), but that doesn't make it 'fundamental'. I want to defend 'fundamental'. |
| 13893 | It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C] |
| Full Idea: What is fundamental to possession of any notion of natural number at all is not the knowledge that the numbers may be arrayed in a progression but the knowledge that they are identified and distinguished by reference to 1-1 correlation among concepts. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 3.xv) | |
| A reaction: My question is 'what is the essence of number?', and my inclination to disagree with Wright on this point suggests that the essence of number is indeed caught in the Dedekind-Peano axioms. But what of infinite numbers? |
| 13888 | If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C] |
| Full Idea: Identifying numbers with extensions will not solve the Caesar problem for numbers unless we have already solved the Caesar problem for extensions. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 3.xiv) |
| 13869 | Number platonism says that natural number is a sortal concept [Wright,C] |
| Full Idea: Number-theoretic platonism is just the thesis that natural number is a sortal concept. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i) | |
| A reaction: See Crispin Wright on sortals to expound this. An odd way to express platonism, but he is presenting the Fregean version of it. |
| 13870 | We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C] |
| Full Idea: We may not be able to settle whether some general form of empiricism is correct independently of natural numbers. It might be precisely our grasp of the abstract sortal, natural number, which shows the hypothesis of empiricism to be wrong. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i) | |
| A reaction: A nice turning of the tables. In the end only coherence decides these things. You may accept numbers and reject empiricism, and then find you have opened the floodgates for abstracta. Excessive floodgates, or blockages of healthy streams? |
| 13873 | Treating numbers adjectivally is treating them as quantifiers [Wright,C] |
| Full Idea: Treating numbers adjectivally is, in effect, treating the numbers as quantifiers. Frege observes that we can always parse out any apparently adjectival use of a number word in terms of substantival use. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.iii) | |
| A reaction: The immediate response to this is that any substantival use can equally be expressed adjectivally. If you say 'the number of moons of Jupiter is four', I can reply 'oh, you mean Jupiter has four moons'. |
| 13899 | The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C] |
| Full Idea: The Peano Axioms are logical consequences of a statement constituting the core of an explanation of the notion of cardinal number. The infinity of cardinal numbers emerges as a consequence of the way cardinal number is explained. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 4.xix) | |
| A reaction: This, along with Idea 13896, nicely summarises the neo-logicist project. I tend to favour a strategy which starts from ordering, rather than identities (1-1), but an attraction is that this approach is closer to counting objects in its basics. |
| 13896 | The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C] |
| Full Idea: We shall endeavour to see whether it is possible to follow through the strategy adumbrated in 'Grundlagen' for establishing the Peano Axioms without at any stage invoking classes. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 4.xvi) | |
| A reaction: The key idea of neo-logicism. If you can avoid classes entirely, then set theory paradoxes become irrelevant, and classes aren't logic. Philosophers now try to derive the Peano Axioms from all sorts of things. Wright admits infinity is a problem. |
| 7804 | Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA] |
| Full Idea: Crispin Wright has reactivated Frege's logistic program, which for decades just about everybody assumed was a lost cause. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by José A. Benardete - Logic and Ontology 3 | |
| A reaction: [This opens Bernadete's section called "Back to Strong Logicism?"] |
| 13863 | Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C] |
| Full Idea: Most would cite Russell's paradox, the non-logical character of the axioms which Russell and Whitehead's reconstruction of Frege's enterprise was constrained to employ, and the incompleteness theorems of Gödel, as decisive for logicism's failure. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro) |
| 13895 | The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C] |
| Full Idea: The general view is that Russell's Paradox put paid to Frege's logicist attempt, and Russell's own attempt is vitiated by the non-logical character of his axioms (esp. Infinity), and by the incompleteness theorems of Gödel. But these are bad reasons. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 4.xvi) | |
| A reaction: Wright's work is the famous modern attempt to reestablish logicism, in the face of these objections. |
| 13884 | The idea that 'exist' has multiple senses is not coherent [Wright,C] |
| Full Idea: I have the gravest doubts whether any coherent account could be given of any multiplicity of senses of 'exist'. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 2.x) | |
| A reaction: I thoroughly agree with this thought. Do water and wind exist in different senses of 'exist'? |
| 13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C] |
| Full Idea: When a class of terms functions as singular terms, and the sentences are true, then those terms genuinely refer. Being singular terms, their reference is to objects. There is no further question whether they really refer, and there are such objects. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.iii) | |
| A reaction: This seems to be a key sentence, because this whole view is standardly called 'platonic', but it certainly isn't platonism as we know it, Jim. Ontology has become an entirely linguistic matter, but do we then have 'sakes' and 'whereaboutses'? |
| 9878 | Contextually defined abstract terms genuinely refer to objects [Wright,C, by Dummett] |
| Full Idea: Wright says we should accord to contextually defined abstract terms a genuine full-blown reference to objects. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Michael Dummett - Frege philosophy of mathematics Ch.18 | |
| A reaction: This is the punch line of Wright's neo-logicist programme. See Idea 9868 for his view of reference. Dummett regards this strong view of contextual definition as 'exorbitant'. Wright's view strikes me as blatantly false. |
| 13868 | Sortal concepts cannot require that things don't survive their loss, because of phase sortals [Wright,C] |
| Full Idea: The claim that no concept counts as sortal if an instance of it can survive its loss, runs foul of so-called phase sortals like 'embryo' and 'chrysalis'. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i) | |
| A reaction: The point being that those items only fall under that sortal for one phase of their career, and of their identity. I've always thought such claims absurd, and this gives a good reason for my view. |
| 5729 | If the senses are deceptive, reason, which rests on them, is even worse [Lucretius] |
| Full Idea: The structure of your reasoning must be rickety and defective, if the senses on which it rests are themselves deceptive. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], IV.518) | |
| A reaction: This strikes me as one of the most basic tenets of empiricism. It denies the existence of 'pure' reason, and instead asserts that it is built out of complex and abstracted sense experience, which makes it ultimately a second-class citizen. |
| 5702 | The senses are much the best way to distinguish true from false [Lucretius] |
| Full Idea: What can be a surer guide to the distinction of true from false than our own senses? | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.700) | |
| A reaction: This doesn't say they are the only guide, which leaves room for guides such as what is consistent or self-evident or inferred. There is enough here, though, to show that the Epicureans were empiricists in a fairly modern way. |
| 5697 | The only possible standard for settling doubts is the foundation of the senses [Lucretius] |
| Full Idea: If a belief resting directly on the foundation of the senses is not valid, there will be no standard to which we can refer any doubt on obscure questions for rational confirmation. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.422) | |
| A reaction: A classic statement of empiricist foundationalism. The Epicureans don't appear to have any time for a priori truths at all. I wonder if they settled mathematical disputes by counting objects and drawing diagrams? |
| 5727 | Most supposed delusions of the senses are really misinterpretations by the mind [Lucretius] |
| Full Idea: Paradoxical experiences (such a dreams and illusions) cannot shake our faith in the senses. Most of the illusion is due to the mental assumptions we ourselves superimpose, so that things not perceived by the senses pass for perceptions. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], IV.462) | |
| A reaction: Some misinterpretations of the senses, such as thinking a square tower round, are the result of foolish lack of judgement, but actual delusions within the senses, such as a ringing in the ears, or a pain in a amputated leg, seem like real sense failures. |
| 5714 | Even simple facts are hard to believe at first hearing [Lucretius] |
| Full Idea: No fact is so simple that it is not harder to believe than to doubt at the first presentation. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.1022) | |
| A reaction: Hence induction is just 'drumming it in' until you come to believe it. There are good evolutionary reasons why we should be like this, because we would otherwise believe all sorts of silly half-perceptions in the gloaming. |
| 5718 | The mind is in the middle of the breast, because there we experience fear and joy [Lucretius] |
| Full Idea: The guiding principle of the whole body is the mind or intellect, which is firmly lodged in the mid-region of the breast. Here is felt fear and alarm, and the caressing pulse of joy. Here, then is the seat of the intellect and mind. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.140) | |
| A reaction: Even by this date thinking people were not clear that the mind is in the brain. They paid insufficient attention to head injuries. The emotions are felt to have a location, but intellect and principles are not. |
| 5717 | The mind is a part of a man, just like a hand or an eye [Lucretius] |
| Full Idea: First, I maintain that the mind, which we often call the intellect, the seat of guidance and control of life, is part of a man, no less than hand or foot or eyes are parts of a whole living creature. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.95) | |
| A reaction: Presumably Lucretius asserts this because some people were denying it. Sounds like common sense to me. The only reason I can see for anyone denying what he says is if they are desperate to survive death. |
| 21387 | The separate elements and capacities of a mind cannot be distinguished [Lucretius] |
| Full Idea: No single element [of the soul] can be separated, nor can their capacities be divided spatially; they are like the multiple powers of a single body | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.262), quoted by A.A. Long - Hellenistic Philosophy 2.7 | |
| A reaction: It is interesting that this comes from someone with a strongly physicalist view of the mind (though not, if I recall, focusing on the brain). He is still totally impressed by the unified phenomenology of mental experience. He is an empiricist. |
| 5709 | The actions of the mind are not determinate and passive, because atoms can swerve [Lucretius] |
| Full Idea: The fact that the mind itself has no internal necessity to determine its every act and compel it to suffer in helpless passivity - this is due to the slight swerve of the atoms at no determinate time or place. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.294) | |
| A reaction: No one likes this proposal much, but it is very intriguing. The Epicureans had seen a problem, one which doesn't bother me much. If, nowadays, you are a reductive physicalist who believes in free will, you have a philosophical nightmare ahead of you. |
| 5695 | Only bodies can touch one another [Lucretius] |
| Full Idea: Nothing can touch or be touched except body. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.303) | |
| A reaction: This is the key objection to interactionism, and the main reason why the atomists have a thoroughly material view of the mind. It is an induction from a very large number of instances, but the argument is not, of course, conclusive. |
| 5711 | The earth is and always has been an insentient being [Lucretius] |
| Full Idea: The earth is and always has been an insentient being. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.658) | |
| A reaction: The fact that Epicurus needs to deny this shows that some idea close to panpsychism must still have been around in his time. He is discussing gods at the time, so maybe pantheism was the view being attacked, but that is a subset of panpsychism. |
| 5712 | Particles may have sensation, but eggs turning into chicks suggests otherwise [Lucretius] |
| Full Idea: There is the possibility that particles have senses like those of an animate being as a whole, …but from the fact that we perceive eggs turning into live fledglings, we may infer that sense can be generated from the insentient. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.914) | |
| A reaction: He gives other arguments for his view. The egg example is not a strong argument, but is precisely our puzzle of how consciousness can emerge from the process of evolution, and natural selection makes dualism look unlikely. |
| 5719 | The mind moves limbs, wakes the body up, changes facial expressions, which involve touch [Lucretius] |
| Full Idea: Mind and spirit are both composed of matter, as we see them propelling limbs, rousing the body from sleep, changing the expression of the face, and guiding the whole man - activities which clearly involves touch, which involves matter. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.164) | |
| A reaction: This is the inverse of Descartes' interaction problem, and strikes me as a straightforward common sense truth. However, if you believe in spiritual gods, this gives you a model for the interaction (however mysterious) of matter and spirit. |
| 5724 | Lions, foxes and deer have distinct characters because their minds share in their bodies [Lucretius] |
| Full Idea: Why are lions ferocious, foxes crafty, and deer timid? It can only be because the mind always shares in the specific growth of the body according to its seed and breed. If it were immortal and reincarnated, living things would have jumbled characters. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.743) | |
| A reaction: A nice argument which I have not encountered in modern times. Of course, even Descartes admits that the mind is intermingled with the body, but it seems that the essential character of a mind is dictated by the body. |
| 5713 | You needn't be made of laughing particles to laugh, so why not sensation from senseless seeds? [Lucretius] |
| Full Idea: One can laugh without being composed of laughing particles, ..so why cannot the things that we see gifted with sensation be compounded of seeds that are wholly senseless? | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.988) | |
| A reaction: Lovely argument! You might feel driven to panpsychism in your desperation to explain the 'weirdness' of consciousness, but it would be mad to attribute laughter to basic matter, so comedy has to 'emerge' at some point. |
| 13866 | A concept is only a sortal if it gives genuine identity [Wright,C] |
| Full Idea: Before we can conclude that φ expresses a sortal concept, we need to ensure that 'is the same φ as' generates statements of genuine identity rather than of some other equivalence relation. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i) |
| 13865 | 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C] |
| Full Idea: A concept is 'sortal' if it exemplifies a kind of object. ..In English predication of a sortal concept needs an indefinite article ('an' elm). ..What really constitutes the distinction is that it involves grasping identity for things which fall under it. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i) | |
| A reaction: This is a key notion, which underlies the claims of 'sortal essentialism' (see David Wiggins). |
| 13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C] |
| Full Idea: 'Tree' is not a sortal concept under which directions fall since we cannot adequately explain the truth-conditions of any identity statement involving a pair of tree-denoting singular terms by appealing to facts to do with parallelism between lines. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 3.xiv) | |
| A reaction: The idea seems to be that these two fall under 'hedgehog', because that is a respect in which they are identical. I like to notion of explanation as a part of this. |
| 13898 | If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C] |
| Full Idea: The fact that it seems possible to establish a sortal notion of direction by reference to lines and parallelism, discloses tacit commitments to directions in statements about parallelism...There is incoherence in the idea that a line might lack direction. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 4.xviii) | |
| A reaction: This seems like a slippery slope into a very extravagant platonism about concepts. Are concepts like direction as much a part of the natural world as rivers are? What other undiscovered concepts await us? |
| 13882 | A milder claim is that understanding requires some evidence of that understanding [Wright,C] |
| Full Idea: A mild version of the verification principle would say that it makes sense to think of someone as understanding an expression only if he is able, by his use of the expression, to give the best possible evidence that he understands it. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.vii) | |
| A reaction: That doesn't seem to tell us what understanding actually consists of, and may just be the truism that to demonstrate anything whatsoever will necessarily involve some evidence. |
| 13885 | If apparent reference can mislead, then so can apparent lack of reference [Wright,C] |
| Full Idea: If the appearance of reference can be misleading, why cannot an apparent lack of reference be misleading? | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 2.xi) | |
| A reaction: A nice simple thought. Analytic philosophy has concerned itself a lot with sentences that seem to refer, but the reference can be analysed away. For me, this takes the question of reference out of the linguistic sphere, which wasn't Wright's plan. |
| 17857 | We can accept Frege's idea of object without assuming that predicates have a reference [Wright,C] |
| Full Idea: The heart of the problem is Frege's assumption that predicates have Bedeutungen at all; and no reason is at present evident why someone who espouses Frege's notion of object is contrained to make that assumption. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.iv) | |
| A reaction: This seems like a penetrating objection to Frege's view of reference, and presumably supports the Kripke approach. |
| 6611 | One man's meat is another man's poison [Lucretius] |
| Full Idea: What is food to one may be literally poison to others. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], IV.638) | |
| A reaction: This seems to be the origin of the well-known saying. This is not relativism of perception, but a relativism of how individuals actually respond to the world. It sums up the position with, say, the operas of Wagner. |
| 5730 | Our bodies weren't created to be used; on the contrary, their creation makes a use possible [Lucretius] |
| Full Idea: Nothing in our bodies was born in order that we might be able to use it, but the thing born creates the use. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], IV.834) | |
| A reaction: This remark (strongly opposed to Aristotle's view of human function and nature) raises the obvious question of why the body is so very useful for staying alive. Most of its uses are not random. Lucretius would abandon this view if he read Darwin. |
| 6000 | The goal is rationality in the selection of things according to nature [Diogenes of Babylon, by Blank] |
| Full Idea: Diogenes of Babylon defined the goal to be rationality in the selection and rejection of the things according to nature. | |
| From: report of Diogenes (Bab) (fragments/reports [c.180 BCE]) by D.L. Blank - Diogenes of Babylon | |
| A reaction: This captures the central Stoic idea quite nicely. 'Live according to nature', but this always meant 'live according to reason', because that is (as Aristotle had taught) the essence of our nature. This only makes sense if reason and nature coincide. |
| 5726 | The dead are no different from those who were never born [Lucretius] |
| Full Idea: One who no longer is cannot suffer, or differ in any way from one who has never been born. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.867) | |
| A reaction: There is a special kind of pain in being poor if you were once rich, which is not suffered by those who experience only poverty. Lucretius is right, but we are concerned with how we feel now, not with how we won't feel once dead. |
| 5999 | The good is what is perfect by nature [Diogenes of Babylon, by Blank] |
| Full Idea: Diogenes of Babylon defined the good as what is perfect by nature. | |
| From: report of Diogenes (Bab) (fragments/reports [c.180 BCE]) by D.L. Blank - Diogenes of Babylon | |
| A reaction: This might come close to G.E. Moore's Ideal Utilitarianism, but its dependence on the rather uneasy of concept of 'perfection' makes it questionable. Personally I find it appealing. I wish we had Diogenes' explanation. |
| 5705 | Nature only wants two things: freedom from pain, and pleasure [Lucretius] |
| Full Idea: Nature only clamours for two things, a body free from pain, a mind released from worry and fear for the enjoyment of pleasurable sensation. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.21) | |
| A reaction: I can't help agreeing with those (like Aristotle) who consider this a very demeaning view of human life. See Idea 99. Bentham agrees with Lucretius (Idea 3777). I think they are largely right, but not entirely. Other motives are possible than sensations. |
| 6001 | Justice is a disposition to distribute according to desert [Diogenes of Babylon, by Blank] |
| Full Idea: Diogenes of Babylon defined justice as the disposition which distributes to everyone what he deserves. | |
| From: report of Diogenes (Bab) (fragments/reports [c.180 BCE]) by D.L. Blank - Diogenes of Babylon | |
| A reaction: The questions that arise would be 'what does a new-born baby deserve?', and 'what do animals deserve?', and 'does the lowest and worst of criminals deserve anything at all?' |
| 5716 | Nature runs the universe by herself without the aid of gods [Lucretius] |
| Full Idea: Nature is free and uncontrolled by proud masters and runs the universe by herself without the aid of gods. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.1094) | |
| A reaction: A nice remark. This apparent personification of nature implies the application of laws to an essentially passive reality. See Idea 5442 and Nature|Laws of Nature|Essentialism for a different view. |
| 5704 | There can be no centre in infinity [Lucretius] |
| Full Idea: There can be no centre in infinity. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.1069) | |
| A reaction: This is highly significant, because if we can establish that the universe is infinite (as Epicurus believes), it follows that the human race cannot be at the centre of it, as the Ptolemaic/medieval view proposed. |
| 5703 | The universe must be limitless, since there could be nothing outside to limit it [Lucretius] |
| Full Idea: The universe is not bounded in any direction. If it were, it would necessarily have a limit somewhere, but a thing cannot have a limit unless there is something outside to limit it. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.959) | |
| A reaction: This is a subtler argument than the mere enquiry about why you would have to stop at the end of the universe. It still seems a nice argument, though Einstein's curvature of space seems to have thwarted it. |
| 5693 | Everything is created and fed by nature from atoms, and they return to atoms in death [Lucretius] |
| Full Idea: The ultimate realities of heaven and the gods are the atoms, from which nature creates all things and increases and feeds them, and into which, when they perish, nature again resolves them. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.46) | |
| A reaction: Sounds right to me. Nothing in modern particle theory and string theory has refuted this claim. But what makes the atoms move, and what makes them combine in an orderly way? Is the orderliness of atoms made of atoms? Essences? |
| 5701 | If an object is infinitely subdivisible, it will be the same as the whole universe [Lucretius] |
| Full Idea: If there are no atoms, the smallest bodies will have infinite parts, since they can be endlessly halved. ..But then there will be no difference between the smallest thing and the whole universe, as they will equally have infinite parts. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.620) | |
| A reaction: Another argument which remains effective even now. There must surely (intuitively) be more divisions possible in a large object than in a small one? Unless of course there were many different sizes of infinity…. See Cantor. |
| 5708 | In downward motion, atoms occasionally swerve slightly for no reason [Lucretius] |
| Full Idea: When atoms are travelling straight down through empty space by their own weight, at quite indeterminate times and places they swerve ever so little from their course. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.217) | |
| A reaction: Never a popular theory because it seems to breach the Principle of Sufficient Reason (Ideas 306 + 3646). This seems to be the beginning of a strong need for the concept of free will, and an underlying explanation. Most thinkers put mind outside nature. |
| 17004 | Nothing can break the binding laws of eternity [Lucretius] |
| Full Idea: Nothing has power to break the binding laws of eternity. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], 5.56) | |
| A reaction: This seems to be virtually the only remark from the ancient world suggesting that there are 'laws' of nature, so I'm guessing it is a transient metaphor, not a theory about nature. 'Even the gods must bow to necessity'. |
| 5696 | If there were no space there could be no movement, or even creation [Lucretius] |
| Full Idea: We see movement everywhere, but if there were no empty space, things would be denied the power of movement - or rather, they could not possibly have come into existence, embedded as they would have been in motionless matter. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.342) | |
| A reaction: This still seems a good argument, if reality is made of particles. People can move in a crowd until it becomes too dense. |
| 5706 | Atoms move themselves [Lucretius] |
| Full Idea: Atoms move themselves. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.133) | |
| A reaction: Something has to move itself, I suppose, but then that could be psuché, giving us free will (see Idea 1424). Why does Epicurus need the 'swerve' if atoms are self-movers? See Idea 5708. |
| 5700 | It is quicker to break things up than to assemble them [Lucretius] |
| Full Idea: Anything can be more speedily disintegrated than put together again. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.558) | |
| A reaction: Clearly the concept of entropy was around long before anyone tried to give a systematic or mathematical account of it. |
| 5698 | We can only sense time by means of movement, or its absence [Lucretius] |
| Full Idea: It must not be claimed that anyone can sense time by itself apart from the movement of things or their restful immobility. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.465) | |
| A reaction: This seems a remarkably Einsteinian remark, though he is only talking of the epistemology of the matter, not the ontology. We are not far from the concept of space-time here. |
| 5715 | This earth is very unlikely to be the only one created [Lucretius] |
| Full Idea: It is in the highest degree unlikely that this earth and sky is the only one to have been created. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.1057) | |
| A reaction: I can only admire the science fiction imagination of this, which roughly agrees with the assessment of modern cosmologists. We think imagination was cramped in the ancient world, and now wanders free - but that is not so. |
| 5694 | Nothing can be created by divine power out of nothing [Lucretius] |
| Full Idea: In studying the workings of nature, our starting-point will be this principle: nothing can ever be created by divine power out of nothing. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.152) | |
| A reaction: This claim seems to cry out for a bit of empiricist caution. What observation has convinced Lucretius that creation out of nothing is impossible? The early Christians switched to the view that divine creation is 'ex nihilo' - out of nothing. |
| 5699 | If matter wasn't everlasting, everything would have disappeared by now [Lucretius] |
| Full Idea: If the matter in things had not been everlasting, everything by now would have gone back to nothing, and the things we see would be the product of rebirth out of nothing. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.544) | |
| A reaction: See Idea 1431, which is Aquinas's Third Way of proving God. Aquinas thinks there must be a necessary being outside of the system, but Lucretius thinks there must be some necessary existence within the system (as Hume had suggested). |
| 5707 | The universe can't have been created by gods, because it is too imperfect [Lucretius] |
| Full Idea: The universe was certainly not created for us by divine power: it is so full of imperfections. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.180) | |
| A reaction: This is certainly a problem if God is 'supremely perfect', as Descartes proposed, because then the universe would also have to be supremely perfect. See Idea 2114 for a possible answer from Leibniz. Hume agrees with Epicurus about design. |
| 5710 | Gods are tranquil and aloof, and have no need of or interest in us [Lucretius] |
| Full Idea: The nature of deity is to enjoy immortal existence in utter tranquillity, aloof and detached from our affairs. It is free from all pain and peril, strong in its own resources, exempt from any need of us, indifferent to our merits and immune from anger. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.652) | |
| A reaction: This seems to be the seed of late seventeenth century deism - the idea of a Creator who is now absent, and ignores our prayers. At that time 'Epicurean' became a synonym for atheist, but Epicureans never quite reached that point. |
| 5731 | Why does Jupiter never hurl lightning from a blue sky? [Lucretius] |
| Full Idea: Why does Jupiter never hurl his thunderbolt upon the earth and let loose his thunder out of a sky that is wholly blue? | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], VI.400) | |
| A reaction: Nice question! It really doesn't take very much to see through superstition, and the fact that most people believed such things shows how staggeringly uncritical they were in their thinking, until philosophers appeared and taught them how to reason. |
| 5722 | For a separated spirit to remain sentient it would need sense organs attached to it [Lucretius] |
| Full Idea: If spirit is immortal and can remain sentient when divorced from our body, we must credit it with possession of five senses; but eyes or nostrils or hand or tongue or ears cannot be attached to a disembodied spirit. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.624) | |
| A reaction: This is a powerful argument against immortality. If you are going to see, you must interact with photons; to hear you must respond to compression waves; to smell you must react to certain molecules. Immortality without those would be a bit dull. |
| 5725 | An immortal mind couldn't work harmoniously with a mortal body [Lucretius] |
| Full Idea: It is crazy to couple a mortal object with an eternal and suppose that they can work in harmony and mutually interact. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.799) | |
| A reaction: An interesting thought, though not a terrible persuasive argument. A god would indeed be a bit restless if it were chained to a human being, but it would presumably knuckle down to the task if firmly instructed to do it by Zeus. |
| 5720 | Spirit is mortal [Lucretius] |
| Full Idea: Spirit is mortal. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.542) | |
| A reaction: This is asserted at an historical moment when immortality is beginning to grip everyone's imagination. |
| 5721 | The mind is very small smooth particles, which evaporate at death [Lucretius] |
| Full Idea: Since the substance of the mind is extraordinarily mobile, it must consist of particles exceptionally small and smooth and round, ..so that, when the spirit has escaped from the body, the outside of the limbs appears intact and there is no loss of weight. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.201) | |
| A reaction: Lucretius is wonderfully attentive to interesting evidence. He goes on to compare it to the evaporation of perfume. The fine-grained connections of the brain are not far off what he is proposing. |
| 5723 | If spirit is immortal and enters us at birth, why don't we remember a previous existence? [Lucretius] |
| Full Idea: If the spirit is by nature immortal and is slipped into the body at birth, why do we retain no memory of an earlier existence, no impress of antecedent events? | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.670) | |
| A reaction: Plato took the view that we do recall previous existence, as seen in our innate ideas. This problem forced the Christian church into the uncomfortable claim that God creates the soul at conception, but that it then goes on to immortality. |