43 ideas
| 1502 | Parmenides was much more cautious about accepting ideas than his predecessors [Simplicius on Parmenides] |
| Full Idea: Parmenides would not agree with anything unless it seemed necessary, whereas his predecessors used to come up with unsubstantiated assertions. | |
| From: comment on Parmenides (fragments/reports [c.474 BCE], A28) by Simplicius - On Aristotle's 'Physics' 9.116.2- | |
| A reaction: from Eudemus |
| 9821 | A definition need not capture the sense of an expression - just get the reference right [Frege, by Dummett] |
| Full Idea: Frege expressly denies that a correct definition need capture the sense of the expression it defines: it need only get the reference right. | |
| From: report of Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.3 | |
| A reaction: This might hit up against the renate/cordate problem, of two co-extensive concepts, where the definition gets the extension right, but the intension wrong. |
| 9585 | Since every definition is an equation, one cannot define equality itself [Frege] |
| Full Idea: Since every definition is an equation, one cannot define equality itself. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.327) | |
| A reaction: This seems a particularly nice instance of the general rule that 'you have to start somewhere'. It is a nice test case for the nature of meaning to ask 'what do you understand when you understand equality?', given that you can't define it. |
| 17446 | Counting rests on one-one correspondence, of numerals to objects [Frege] |
| Full Idea: Counting rests itself on a one-one correlation, namely of numerals 1 to n and the objects. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894]), quoted by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: Parsons observes that counting will establish a one-one correspondence, but that doesn't make it the aim of counting, and so Frege hasn't answered Husserl properly. Which of the two is conceptually prior? How do you decide. |
| 9582 | Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege] |
| Full Idea: When Husserl says that sameness of number can be shown by one-one correlation, he forgets that this counting itself rests on a univocal one-one correlation, namely that between the numerals 1 to n and the objects of the set. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.326) | |
| A reaction: This is the platonist talking. Neo-logicism is attempting to build numbers just from the one-one correlation of objects. |
| 9586 | In a number-statement, something is predicated of a concept [Frege] |
| Full Idea: In a number-statement, something is predicated of a concept. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.328) | |
| A reaction: A succinct statement of Frege's theory of numbers. By my lights that would make numbers at least second-order abstractions. |
| 9580 | Our concepts recognise existing relations, they don't change them [Frege] |
| Full Idea: The bringing of an object under a concept is merely the recognition of a relation which previously already obtained, [but in the abstractionist view] objects are essentially changed by the process, so that objects brought under a concept become similar. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324) | |
| A reaction: Frege's view would have to account for occasional misapplications of concepts, like taking a dolphin to be a fish, or falsely thinking there is someone in the cellar. |
| 9589 | Numbers are not real like the sea, but (crucially) they are still objective [Frege] |
| Full Idea: The sea is something real and a number is not; but this does not prevent it from being something objective; and that is the important thing. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.337) | |
| A reaction: This seems a qualification of Frege's platonism. It is why people start talking about abstract items which 'subsist', instead of 'exist'. It shows Frege's motivation in all this, which is to secure logic and maths from the vagaries of psychology. |
| 9577 | The naïve view of number is that it is like a heap of things, or maybe a property of a heap [Frege] |
| Full Idea: The most naïve opinion of number is that it is something like a heap in which things are contained. The next most naïve view is the conception of number as the property of a heap, cleansing the objects of their particulars. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.323) | |
| A reaction: A hundred toothbrushes and a hundred sponges can be seen to contain the same number (by one-to-one mapping), without actually knowing what that number is. There is something numerical in the heap, even if the number is absent. |
| 448 | No necessity could produce Being either later or earlier, so it must exist absolutely or not at all [Parmenides] |
| Full Idea: What necessity impelled Being, if it did spring from nothing, to be produced later or earlier? Thus it must be absolutely, or not at all. | |
| From: Parmenides (fragments/reports [c.474 BCE], B08 ll.?), quoted by Simplicius - On Aristotle's 'Physics' 9.145.1- | |
| A reaction: If there is a moment when Being is created, it is reasonable to ask why then, and not some other time? Obviously a conscious God can fill that gap,but that only defers the problem. |
| 449 | Being is not divisible, since it is all alike [Parmenides] |
| Full Idea: Being is not divisible, since it is all alike. | |
| From: Parmenides (fragments/reports [c.474 BCE], B08 ll.?), quoted by Simplicius - On Aristotle's 'Physics' 9.145.1- | |
| A reaction: A baffling proposal when it appears to be extremely diverse. A microscope would have forced him to rethink somewhat. |
| 447 | Being must be eternal and uncreated, and hence it is timeless [Parmenides] |
| Full Idea: Being has no coming-to-be and no destruction, for it is whole of limb, without motion, and without end. And it never was, nor will be, because it is now, a whole all together, one, continuous; for what creation of it will you look for? | |
| From: Parmenides (fragments/reports [c.474 BCE], B08 ll.?), quoted by Simplicius - On Aristotle's 'Physics' 9.145.1- | |
| A reaction: That being is eternal is a reasonable speculation, since its creation seems inconceivable. But why think it is without motion, when we see motion everywhere? That was Aristotle's reaction, too. |
| 445 | The realm of necessary non-existence cannot be explored, because it is unknowable [Parmenides] |
| Full Idea: The other way of enquiry, that IT IS NOT, and IT is bound NOT TO BE, cannot be explored, for you could neither recognise nor express that which IS NOT. | |
| From: Parmenides (fragments/reports [c.474 BCE], B02), quoted by Simplicius - On Aristotle's 'Physics' 9.116.28- | |
| A reaction: There is not much to say about that which is not, but quite a lot, I would have thought, about what is 'bound not to be'. What prevents it from being? |
| 1503 | There is no such thing as nothing [Parmenides] |
| Full Idea: There is no such thing as nothing. | |
| From: Parmenides (fragments/reports [c.474 BCE], B06), quoted by Simplicius - On Aristotle's 'Physics' 9.86.27- | |
| A reaction: See Meinong on this. It is not an empty concept, because things can be predicated of nothing, such as weighing less than an apple. CF. the role of zero in arithmetic. |
| 21820 | Parmenides at least saw Being as the same as Nous, and separate from the sensed realm [Parmenides, by Plotinus] |
| Full Idea: Parmenides made some approach to the doctrine of Plato in identifying Being with Intellectual-Principle [Nous] while separating Real Being from the realm of sense. | |
| From: report of Parmenides (fragments/reports [c.474 BCE]) by Plotinus - The Enneads 5.1.08 | |
| A reaction: The point is that for Parmenides the One is the essence of Being, but for platonists there is something prior to and higher than Being. For Plato it is the Good; for Plotinus it is a revised (non-Being) concept of the One. |
| 452 | All our concepts of change and permanence are just names, not the truth [Parmenides] |
| Full Idea: All things that mortals have established, believing in their truth, are just a name: Becoming and Perishing, Being and Not-Being, and change of position, and alteration of bright colour. | |
| From: Parmenides (fragments/reports [c.474 BCE], B08 ll.?), quoted by Simplicius - On Aristotle's 'Physics' 9.145.1- | |
| A reaction: He has to say this, once he has decided that Being is homogeneous eternal unity, but if normal human beliefs are just names, presumably that applies to his views too. Is 'Being' just a name? |
| 9578 | If objects are just presentation, we get increasing abstraction by ignoring their properties [Frege] |
| Full Idea: If an object is just presentation, we can pay less attention to a property and it disappears. By letting one characteristic after another disappear, we obtain concepts that are increasingly more abstract. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324) | |
| A reaction: Frege despises this view. Note there is scope in the despised view for degrees or levels of abstraction, defined in terms of number of properties ignored. Part of Frege's criticism is realist. He retains the object, while Husserl imagines it different. |
| 1504 | Something must be unchanging to make recognition and knowledge possible [Aristotle on Parmenides] |
| Full Idea: Parmenides and Melissus were the first to appreciate that there must be unchanging entities, if recognition and knowledge are to exist. | |
| From: comment on Parmenides (fragments/reports [c.474 BCE], A25) by Aristotle - On the Heavens 298b14 |
| 444 | The first way of enquiry involves necessary existence [Parmenides] |
| Full Idea: The first way of enquiry is the one that IT IS, and it is not possible for IT NOT TO BE, which is the way of credibility, for it follows truth. | |
| From: Parmenides (fragments/reports [c.474 BCE], B02), quoted by Simplicius - On Aristotle's 'Physics' 9.116.28- | |
| A reaction: also Proclus 'Timeus' |
| 450 | Necessity sets limits on being, in order to give it identity [Parmenides] |
| Full Idea: Powerful necessity holds Being in the bonds of a limit, which constrains it round about, because divine law decrees that Being shall not be without boundary. For it is not lacking, but if it were spatially infinite, it would lack everything. | |
| From: Parmenides (fragments/reports [c.474 BCE], B08 ll.?), quoted by Simplicius - On Aristotle's 'Physics' 9.145.1- |
| 451 | Thinking implies existence, because thinking depends on it [Parmenides] |
| Full Idea: To think is the same as the thought that IT IS, for you will not find thinking without Being, on which it depends for its expression. | |
| From: Parmenides (fragments/reports [c.474 BCE], B08 ll.?), quoted by Simplicius - On Aristotle's 'Physics' 9.145.1- |
| 1506 | Parmenides treats perception and intellectual activity as the same [Theophrastus on Parmenides] |
| Full Idea: Parmenides treats perception and intellectual activity as the same. | |
| From: comment on Parmenides (fragments/reports [c.474 BCE], A46) by Theophrastus - On the Senses 3.1 | |
| A reaction: cf Theaetetus pt 1 |
| 3058 | Only reason can prove the truth of facts [Parmenides] |
| Full Idea: Reason alone will prove the truth of facts. | |
| From: Parmenides (fragments/reports [c.474 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 09.3.3 |
| 9581 | Many people have the same thought, which is the component, not the private presentation [Frege] |
| Full Idea: The same thought can be grasped by many people. The components of a thought, and even more so the things themselves, must be distinguished from the presentations which in the soul accompany the grasping of a thought. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.325) | |
| A reaction: This is the basic realisation, also found in Russell, of how so much confusion has crept into philosophy, in Berkeley, for example. Frege starts down the road which leads to the externalist view of content. |
| 9579 | Disregarding properties of two cats still leaves different objects, but what is now the difference? [Frege] |
| Full Idea: If from a black cat and a white cat we disregard colour, then posture, then location, ..we finally derive something which is completely without restrictions on content; but what is derived from the objects does differ, although it is not easy to say how. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324) | |
| A reaction: This is a key objection to abstractionism for Frege - we are counting two cats, not two substrata of essential catness, or whatever. But what makes a cat countable? (Key question!) It isn't its colour, or posture or location. |
| 9587 | How do you find the right level of inattention; you eliminate too many or too few characteristics [Frege] |
| Full Idea: Inattention is a very strong lye which must not be too concentrated, or it dissolves everything (such as the connection between the objects), but must not be too weak, to produce sufficient change. Personally I cannot find the proper dilution. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.330) | |
| A reaction: We may sympathise with the lack of precision here (frustrating for a logician), but it is not difficult to say of a baseball defence 'just concentrate on the relations, and ignore the individuals who implement it'. You retain basic baseball skills. |
| 9588 | Number-abstraction somehow makes things identical without changing them! [Frege] |
| Full Idea: Number-abstraction simply has the wonderful and very fruitful property of making things absolutely the same as one another without altering them. Something like this is possible only in the psychological wash-tub. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.332) | |
| A reaction: Frege can be awfully sarcastic. I don't really see his difficulty. For mathematics we only need to know what is countable about an object - we don't need to know how many hairs there are on the cat, only that it has identity. |
| 9583 | Psychological logicians are concerned with sense of words, but mathematicians study the reference [Frege] |
| Full Idea: The psychological logicians are concerned with the sense of the words and with the presentations, which they do not distinguish from the sense; but the mathematicians are concerned with the matter itself, with the reference of the words. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.326) | |
| A reaction: This is helpful for showing the point of his sense/reference distinction; it is part of his campaign against psychologism, by showing that there is a non-psychological component to language - the reference, where it meets the public world. |
| 9584 | Identity baffles psychologists, since A and B must be presented differently to identify them [Frege] |
| Full Idea: The relation of sameness remains puzzling to a psychological logician. They cannot say 'A is the same as B', because that requires distinguishing A from B, so that these would have to be different presentations. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.327) | |
| A reaction: This is why Frege needed the concept of reference, so that identity could be outside the mind (as in Hesperus = Phosophorus). Think about an electron; now think about a different electron. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 226 | The one is without any kind of motion [Parmenides] |
| Full Idea: The one is without any kind of motion. | |
| From: Parmenides (fragments/reports [c.474 BCE]), quoted by Plato - Parmenides 139a |
| 5081 | There could be movement within one thing, as there is within water [Aristotle on Parmenides] |
| Full Idea: Why does it follow from there being only one thing that it is unmoving, since, for example, water moves internally while remaining one? | |
| From: comment on Parmenides (fragments/reports [c.474 BCE]) by Aristotle - Physics 186a16 | |
| A reaction: One suspects that Parmenides wasn't used to critical questions like this, and would have sharpened up his theory if it had been subjected to criticism. How big was the One? Maybe Aristotle is the real father of philosophy. |
| 1509 | The one can't be divisible, because if it was it could be infinitely divided down to nothing [Parmenides, by Simplicius] |
| Full Idea: Since the one is everywhere alike, then if it is divisible, it will be equally divisible everywhere….so let it be divided everywhere. It is obvious that nothing will remain and the whole will vanish, and so (if it is compound) it is composed of nothing. | |
| From: report of Parmenides (fragments/reports [c.474 BCE]) by Simplicius - On Aristotle's 'Physics' 9.139.5- | |
| A reaction: he is quoting Porphyry |
| 20900 | Defenders of the One say motion needs the void - but that is not part of Being [Parmenides, by Aristotle] |
| Full Idea: Defenders of the One say that there could not be motion without a void, and that void is what does not exist, and that nothing that is not belongs to being. | |
| From: report of Parmenides (fragments/reports [c.474 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 325a26 | |
| A reaction: This is why motion is an illusion, a view also supported by the paradoxes of Zeno of Elea. Aristotle goes on to give Democritus's response to this idea. Parmenides was contemplating 'void', before Democritus got to it. |
| 1505 | Reason sees reality as one, the senses see it as many [Aristotle on Parmenides] |
| Full Idea: Since he is forced to be guided by appearances, he assumes that the one exists from the viewpoint of reason, but that a plurality exists from the viewpoint of the sense, and so he posits two principles and causes - hot and cold. | |
| From: comment on Parmenides (fragments/reports [c.474 BCE], A24) by Aristotle - Metaphysics 986b27- | |
| A reaction: A profound thought. Empiricists emphasies experience, and end up with fragmented reality. Reason explains experience, and in the process sees the world as unities (like objects), though a single unity is going too far. |
| 453 | Reality is symmetrical and balanced, like a sphere, with no reason to be greater one way rather than another [Parmenides] |
| Full Idea: Since there is a spatial limit, it is complete on every side, like the mass of a well-rounded sphere, equally balanced from its centre in every direction; for it is not bound to be at all either greater or less in this direction or that. | |
| From: Parmenides (fragments/reports [c.474 BCE], B08 ll.?), quoted by Simplicius - On Aristotle's 'Physics' 9.145.1- |
| 555 | People who say that the cosmos is one forget that they must explain movement [Aristotle on Parmenides] |
| Full Idea: Those who assert that the universe is one and a single nature, when they try to give the causes of generation and destruction, miss out the cause of movement. | |
| From: comment on Parmenides (fragments/reports [c.474 BCE]) by Aristotle - Metaphysics 988b |
| 1792 | He taught that there are two elements, fire the maker, and earth the matter [Parmenides, by Diog. Laertius] |
| Full Idea: He taught that there were two elements, fire and earth; and that one of them occupies the place of the maker, the other that of the matter. | |
| From: report of Parmenides (fragments/reports [c.474 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Pa.2 |
| 5115 | It is feeble-minded to look for explanations of everything being at rest [Aristotle on Parmenides] |
| Full Idea: For people to ignore the evidence of their senses and look for an explanation for everything being at rest is feeble-minded. | |
| From: comment on Parmenides (fragments/reports [c.474 BCE]) by Aristotle - Physics 253a32 | |
| A reaction: Not exactly an argument, but an interestingly robust assertion of commonsense against dodgy arguments. Aristotle is not exactly an empiricist, but he is on that side of the fence. |
| 13217 | The void can't exist, and without the void there can't be movement or separation [Parmenides, by Aristotle] |
| Full Idea: Some philosophers thought what is must be one and immovable. The void, they say, is not: but unless there is a void what is cannot be moved, nor can it be many, since there is nothing to keep things apart. | |
| From: report of Parmenides (fragments/reports [c.474 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 325a06 | |
| A reaction: Somehow this doesn't seem very persuasive any more! I suppose we would distinguish various degrees of void, and assert the existence of sufficient void to allow movement and separation. We must surely agree that total nothingness doesn't exist. |
| 22918 | What could have triggered the beginning [of time and being]? [Parmenides] |
| Full Idea: What need would have aroused it later or sooner, starting from nothing to come into being? | |
| From: Parmenides (fragments/reports [c.474 BCE]), quoted by Robin Le Poidevin - Travels in Four Dimensions 02 'Everything' | |
| A reaction: [Barnes 1982:178] This remains an excellent question. The last I heard was a 'quantum fluctuation', but that seems to be an event, which therefore needs time. |
| 1791 | He was the first person to say the earth is spherical [Parmenides, by Diog. Laertius] |
| Full Idea: He was the first person who asserted that the earth was of a spherical form. | |
| From: report of Parmenides (fragments/reports [c.474 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Pa.2 |
| 1794 | He was the first to discover the identity of the Morning and Evening Stars [Parmenides, by Diog. Laertius] |
| Full Idea: He appears to have been the first to discover that Hesperus and Lucifer were the same star. | |
| From: report of Parmenides (fragments/reports [c.474 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Pa.3 | |
| A reaction: This is the famous example used by Frege to discuss reference and meaning. |