48 ideas
| 3879 | Philosophy aims to provide a theory of everything [Scruton] |
| Full Idea: Philosophy studies everything: it tries to provide a theory of the whole of things. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 1.2) | |
| A reaction: Good, but you can't avoid value-judgements about which things are important; philosophers place more value on moral theories than on theories about glacier movement. There is a tension in philosophy between human and eternal concerns. |
| 3891 | If p entails q, then p is sufficient for q, and q is necessary for p [Scruton] |
| Full Idea: If p entails q, then p is sufficient for q, and q is necessary for p. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 15.7) |
| 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. |
| 3894 | We may define 'good' correctly, but then ask whether the application of the definition is good [Scruton] |
| Full Idea: The 'open question' argument is clearly invalid. A question remains open just so long as our ignorance permits. …It may be an open question whether promoting happiness is good, even though this is what 'good' means. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 20.1) | |
| A reaction: A nice objection. Like small children, we can keep asking questions forever. Whether there is a question to be asked about a thing is not a property of that thing, but of us who ask it. |
| 3883 | A true proposition is consistent with every other true proposition [Scruton] |
| Full Idea: A true proposition is consistent with every other true proposition: no truth is contradicted by another. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 9.1) | |
| A reaction: Interesting. It resembles the rule that if you always tell the truth you don't need to remember what you said. Close to the heart of the concept of truth. Coherence and correspondence. |
| 3884 | The pragmatist does not really have a theory of truth [Scruton] |
| Full Idea: The pragmatist does not really have a theory of truth. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 9.4) |
| 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. |
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| Full Idea: One of Hilbert's aims in 'The Foundations of Geometry' was to eliminate number [as measure of lengths and angles] from geometry. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: Presumably this would particularly have to include the elimination of ratios (rather than actual specific lengths). |
| 3907 | Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton] |
| Full Idea: Could someone have a perfect intellectual acquaintance with numbers, but be incapable of counting a flock of sheep? | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 26.6) |
| 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. |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| Full Idea: Hilbert's geometrical axioms were existential in character, asserting the existence of certain geometrical objects (points and lines). Euclid's postulates do not assert the existence of anything; they assert the possibility of certain constructions. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Charles Chihara - A Structural Account of Mathematics 01.1 | |
| A reaction: Chihara says geometry was originally understood modally, but came to be understood existentially. It seems extraordinary to me that philosophers of mathematics can have become more platonist over the centuries. |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| Full Idea: In his formal investigation of Euclidean geometry, Hilbert uncovered congruence axioms that implicitly played a role in Euclid's proofs but were not explicitly recognised. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 2 | |
| A reaction: The writers are offering this as a good example of the benefits of a precise and formal approach to foundational questions. It's hard to disagree, but dispiriting if you need a PhD in maths before you can start doing philosophy. |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| Full Idea: Hilbert's formulation of the Euclidean theory is of special interest because (besides being rigorously axiomatised) it does not employ the real numbers in the axioms. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3 | |
| A reaction: Notice that this job was done by Hilbert, and not by the fictionalist Hartry Field. |
| 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. |
| 3908 | If maths contains unprovable truths, then maths cannot be reduced to a set of proofs [Scruton] |
| Full Idea: If there can be unprovable truths of mathematics, then mathematics cannot be reduced to the proofs whereby we construct it. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 26.7) |
| 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. |
| 3906 | If possible worlds are needed to define properties, maybe we should abandon properties [Scruton] |
| Full Idea: If the only way of defining properties involves quantifying over possible worlds, this could be taken as another reason for abandoning properties altogether. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 26.4) |
| 3888 | Hume assumes that necessity can only be de dicto, not de re [Scruton] |
| Full Idea: It was one of the assumptions of Hume's empiricism that all necessities are de dicto: i.e. they are artefacts of language. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 13.5) |
| 3903 | The conceivable can't be a test of the possible, if there are things which are possible but inconceivable [Scruton] |
| Full Idea: If there are things which are possible but inconceivable, we must abandon the view, which has had a considerable following since Descartes, that the conceivable is a test of the possible. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 25) |
| 3897 | Epistemology is about the justification of belief, not the definition of knowledge [Scruton] |
| Full Idea: In my view the concept of knowledge is of no very great interest in epistemology, which actually concerns the justification of belief. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 22) | |
| A reaction: I think this is an excellent thought. I see knowledge as slippery, and partially contextual, and I don't care whether someone precisely 'knows' something. I just want to know why they believe it. |
| 3881 | In the Cogito argument consciousness develops into self-consciousness [Scruton] |
| Full Idea: In the course of the argument the first person has acquired a character; he is not merely conscious, but self-conscious. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 4) |
| 3887 | Maybe our knowledge of truth and causation is synthetic a priori [Scruton] |
| Full Idea: 'Every event has a cause' and 'truth is correspondence to facts' are candidates for being synthetic a priori knowledge. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 13.2) |
| 3901 | Touch only seems to reveal primary qualities [Scruton] |
| Full Idea: Touch seems to deliver a purely primary-quality account of the world. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 24) | |
| A reaction: Interesting, though a little over-confident. It seems occasionally possible for touch to be an illusion. |
| 3885 | We only conceive of primary qualities as attached to secondary qualities [Scruton] |
| Full Idea: Bradley argued that we cannot conceive of primary qualities except as attached to secondary qualities. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 10.1) |
| 3910 | If primary and secondary qualities are distinct, what has the secondary qualities? [Scruton] |
| Full Idea: If primary and secondary qualities are distinct, what do secondary qualities inhere in? | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], Ch.10 n) | |
| A reaction: What is the problem? A pin causes me pain, but I know the pain isn't in the pin. It is the same with colour. It is a mental property, if you like, triggered by a wavelength of radiation. |
| 3899 | The representational theory says perceptual states are intentional states [Scruton] |
| Full Idea: The representational theory is the unsurprising view that perceptual states are intentional, like beliefs, emotions and desires. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 23.3) |
| 3898 | My belief that it will rain tomorrow can't be caused by its raining tomorrow [Scruton] |
| Full Idea: It is impossible that my present belief that it will rain tomorrow is caused by its raining tomorrow. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 22.4) | |
| A reaction: This doesn't demolish a causal account of belief. It would be very surprising if I were to believe it was going to rain tomorrow for no cause whatsoever. That would be irrational. |
| 3880 | Logical positivism avoids scepticism, by closing the gap between evidence and conclusion [Scruton] |
| Full Idea: If the evidence for p is q, and that is the only evidence there is or can be, then 'p' means q. Hence there is no gap between evidence and conclusion, and the sceptical problem does not arise. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 3.2) |
| 3878 | Why should you believe someone who says there are no truths? [Scruton] |
| Full Idea: A writer who says that there are no truths, or that all truth is 'merely relative', is asking you not to believe him. So don't. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 1.1) |
| 3892 | Every event having a cause, and every event being determined by its cause, are not the same [Scruton] |
| Full Idea: To say that every event has a cause is one thing; to say that every event is determined by its cause is quite another thing. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 17.1) |
| 3911 | The very concept of a substance denies the possibility of mutual interaction and dependence [Scruton] |
| Full Idea: It is often held to be a consequence of the rationalist conception of substance, that separate substances cannot interact (since causal interaction is a form of mutual dependence). | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], Ch.16 n) | |
| A reaction: Yes, substances seem incapable of interaction, just as Leibniz argues that perfections could never interact. They are too pure. |
| 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. |
| 3882 | Wittgenstein makes it impossible to build foundations from something that is totally private [Scruton] |
| Full Idea: Wittgenstein's point is that if I search for foundations in what can only be known to me, then the belief that I have discovered those foundations will also fall victim to Descartes' demon. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 5.3) | |
| A reaction: Why should foundations based in wider society or a language community fare any better? Getting a lot of people to agree won't trouble the demon too much. Flat earthers. |
| 3896 | Any social theory of morality has the problem of the 'free rider', who only pretends to join in [Scruton] |
| Full Idea: Any attempt to provide a social justification of morality runs the risk of the 'free rider' - one who pretends to play the game in order to enjoy the fruits of it. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 20.6) |
| 3886 | Membership is the greatest source of obligation [Scruton] |
| Full Idea: Membership is the greatest source of obligation. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 11.2) | |
| A reaction: An interesting and rather Aristotelian idea. The alternative is individual debt or obligation. |
| 3895 | The categorical imperative is not just individual, but can be used for negotiations between strangers [Scruton] |
| Full Idea: The categorical imperative is also an instrument of negotiation and compromise between strangers, through which they can rise out of enmity and confront each other as equals. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 20.6) |
| 3890 | 'Cause' used to just mean any valid explanation [Scruton] |
| Full Idea: Traditionally (before Leibniz and Spinoza) the world 'cause' signified any valid explanation. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 14) |
| 3904 | Measuring space requires no movement while I do it [Scruton] |
| Full Idea: I can measure the length of something only if I know that it has not moved between the moment when I locate one end of it and the moment when I locate the other. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 25.3) | |
| A reaction: A nice example of how even simple propositions have many presuppositions. |
| 3905 | 'Existence' is not a predicate of 'man', but of the concept of man, saying it has at least one instance [Scruton] |
| Full Idea: When I say that a man exists, Frege argues, I do not predicate existence of a man, but rather of the concept man: I say the concept has at least one instance (and existence is a predicate of predicates). | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 26.2) |