82 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) |
| 9955 | Contextual definitions replace a complete sentence containing the expression [George/Velleman] |
| Full Idea: A contextual definition shows how to analyse an expression in situ, by replacing a complete sentence (of a particular form) in which the expression occurs by another in which it does not. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: This is a controversial procedure, which (according to Dummett) Frege originally accepted, and later rejected. It might not be the perfect definition that replacing just the expression would give you, but it is a promising step. |
| 10031 | Impredicative definitions quantify over the thing being defined [George/Velleman] |
| Full Idea: When a definition contains a quantifier whose range includes the very entity being defined, the definition is said to be 'impredicative'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: Presumably they are 'impredicative' because they do not predicate a new quality in the definiens, but make use of the qualities already known. |
| 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) |
| 10098 | The 'power set' of A is all the subsets of A [George/Velleman] |
| Full Idea: The 'power set' of A is all the subsets of A. P(A) = {B : B ⊆ A}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10099 | The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}} [George/Velleman] |
| Full Idea: The 'ordered pair' <a, b>, for two sets a and b, is the set {{a, b},{a}}. The existence of this set is guaranteed by three applications of the Axiom of Pairing. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: See Idea 10100 for the Axiom of Pairing. |
| 10101 |
Cartesian Product A x B: the set of all ordered pairs |
| Full Idea: The 'Cartesian Product' of any two sets A and B is the set of all ordered pairs <a, b> in which a ∈ A and b ∈ B, and it is denoted as A x B. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10103 | Grouping by property is common in mathematics, usually using equivalence [George/Velleman] |
| Full Idea: The idea of grouping together objects that share some property is a common one in mathematics, ...and the technique most often involves the use of equivalence relations. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10104 | 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman] |
| Full Idea: A relation is an equivalence relation if it is reflexive, symmetric and transitive. The 'same first letter' is an equivalence relation on the set of English words. Any relation that puts a partition into clusters will be equivalence - and vice versa. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This is a key concept in the Fregean strategy for defining numbers. |
| 10096 | Even the elements of sets in ZFC are sets, resting on the pure empty set [George/Velleman] |
| Full Idea: ZFC is a theory concerned only with sets. Even the elements of all of the sets studied in ZFC are also sets (whose elements are also sets, and so on). This rests on one clearly pure set, the empty set Φ. ..Mathematics only needs pure sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This makes ZFC a much more metaphysically comfortable way to think about sets, because it can be viewed entirely formally. It is rather hard to disentangle a chair from the singleton set of that chair. |
| 10097 | Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y [George/Velleman] |
| Full Idea: The Axiom of Extensionality says that for all sets x and y, if x and y have the same elements then x = y. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This seems fine in pure set theory, but hits the problem of renates and cordates in the real world. The elements coincide, but the axiom can't tell you why they coincide. |
| 10100 | Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman] |
| Full Idea: The Axiom of Pairing says that for all sets x and y, there is a set z containing x and y, and nothing else. In symbols: ∀x∀y∃z∀w(w ∈ z ↔ (w = x ∨ w = y)). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: See Idea 10099 for an application of this axiom. |
| 17900 | The Axiom of Reducibility made impredicative definitions possible [George/Velleman] |
| Full Idea: The Axiom of Reducibility ...had the effect of making impredicative definitions possible. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10109 | ZFC can prove that there is no set corresponding to the concept 'set' [George/Velleman] |
| Full Idea: Sets, unlike extensions, fail to correspond to all concepts. We can prove in ZFC that there is no set corresponding to the concept 'set' - that is, there is no set of all sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: This is rather an important point for Frege. However, all concepts have extensions, but they may be proper classes, rather than precisely defined sets. |
| 10108 | As a reduction of arithmetic, set theory is not fully general, and so not logical [George/Velleman] |
| Full Idea: The problem with reducing arithmetic to ZFC is not that this theory is inconsistent (as far as we know it is not), but rather that is not completely general, and for this reason not logical. For example, it asserts the existence of sets. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: Note that ZFC has not been proved consistent. |
| 10111 | Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman] |
| Full Idea: A hallmark of our realist stance towards the natural world is that we are prepared to assert the Law of Excluded Middle for all statements about it. For all statements S, either S is true, or not-S is true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: Personally I firmly subscribe to realism, so I suppose I must subscribe to Excluded Middle. ...Provided the statement is properly formulated. Or does liking excluded middle lead me to realism? |
| 10129 | A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman] |
| Full Idea: A 'model' of a theory is an assignment of meanings to the symbols of its language which makes all of its axioms come out true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: If the axioms are all true, and the theory is sound, then all of the theorems will also come out true. |
| 10105 | Differences between isomorphic structures seem unimportant [George/Velleman] |
| Full Idea: Mathematicians tend to regard the differences between isomorphic mathematical structures as unimportant. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This seems to be a pointer towards Structuralism as the underlying story in mathematics. The intrinsic character of so-called 'objects' seems unimportant. How theories map onto one another (and onto the world?) is all that matters? |
| 10119 | Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman] |
| Full Idea: Consistency is a purely syntactic property, unlike the semantic property of soundness. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10126 | A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman] |
| Full Idea: If there is a sentence such that both the sentence and its negation are theorems of a theory, then the theory is 'inconsistent'. Otherwise it is 'consistent'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
| 10120 | Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman] |
| Full Idea: Soundness is a semantic property, unlike the purely syntactic property of consistency. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10127 | A 'complete' theory contains either any sentence or its negation [George/Velleman] |
| Full Idea: If there is a sentence such that neither the sentence nor its negation are theorems of a theory, then the theory is 'incomplete'. Otherwise it is 'complete'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: Interesting questions are raised about undecidable sentences, irrelevant sentences, unknown sentences.... |
| 10106 | Rational numbers give answers to division problems with integers [George/Velleman] |
| Full Idea: We can think of rational numbers as providing answers to division problems involving integers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Cf. Idea 10102. |
| 10102 | The integers are answers to subtraction problems involving natural numbers [George/Velleman] |
| Full Idea: In defining the integers in set theory, our definition will be motivated by thinking of the integers as answers to subtraction problems involving natural numbers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Typical of how all of the families of numbers came into existence; they are 'invented' so that we can have answers to problems, even if we can't interpret the answers. It it is money, we may say the minus-number is a 'debt', but is it? Cf Idea 10106. |
| 10107 | Real numbers provide answers to square root problems [George/Velleman] |
| Full Idea: One reason for introducing the real numbers is to provide answers to square root problems. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Presumably the other main reasons is to deal with problems of exact measurement. It is interesting that there seem to be two quite distinct reasons for introducing the reals. Cf. Ideas 10102 and 10106. |
| 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) |
| 9946 | Logicists say mathematics is applicable because it is totally general [George/Velleman] |
| Full Idea: The logicist idea is that if mathematics is logic, and logic is the most general of disciplines, one that applies to all rational thought regardless of its content, then it is not surprising that mathematics is widely applicable. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2) | |
| A reaction: Frege was keen to emphasise this. You are left wondering why pure logic is applicable to the physical world. The only account I can give is big-time Platonism, or Pythagoreanism. Logic reveals the engine-room of nature, where the design is done. |
| 10125 | The classical mathematician believes the real numbers form an actual set [George/Velleman] |
| Full Idea: Unlike the intuitionist, the classical mathematician believes in an actual set that contains all the real numbers. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 17899 | Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman] |
| Full Idea: The first-order version of the induction axiom is weaker than the second-order, because the latter applies to all concepts, but the first-order applies only to concepts definable by a formula in the first-order language of number theory. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7 n7) |
| 10128 | The Incompleteness proofs use arithmetic to talk about formal arithmetic [George/Velleman] |
| Full Idea: The idea behind the proofs of the Incompleteness Theorems is to use the language of Peano Arithmetic to talk about the formal system of Peano Arithmetic itself. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: The mechanism used is to assign a Gödel Number to every possible formula, so that all reasonings become instances of arithmetic. |
| 17902 | A successor is the union of a set with its singleton [George/Velleman] |
| Full Idea: For any set x, we define the 'successor' of x to be the set S(x) = x U {x}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This is the Fregean approach to successor, where the Dedekind approach takes 'successor' to be a primitive. Frege 1884:§76. |
| 10133 | Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman] |
| Full Idea: The derivability of Peano's Postulates from Hume's Principle in second-order logic has been dubbed 'Frege's Theorem', (though Frege would not have been interested, because he didn't think Hume's Principle gave an adequate definition of numebrs). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8 n1) | |
| A reaction: Frege said the numbers were the sets which were the extensions of the sets created by Hume's Principle. |
| 10130 | Set theory can prove the Peano Postulates [George/Velleman] |
| Full Idea: The Peano Postulates can be proven in ZFC. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
| 10089 | Talk of 'abstract entities' is more a label for the problem than a solution to it [George/Velleman] |
| Full Idea: One might well wonder whether talk of abstract entities is less a solution to the empiricist's problem of how a priori knowledge is possible than it is a label for the problem. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Intro) | |
| A reaction: This pinpoints my view nicely. What the platonist postulates is remote, bewildering, implausible and useless! |
| 10131 | If mathematics is not about particulars, observing particulars must be irrelevant [George/Velleman] |
| Full Idea: As, in the logicist view, mathematics is about nothing particular, it is little wonder that nothing in particular needs to be observed in order to acquire mathematical knowledge. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002]) | |
| A reaction: At the very least we can say that no one would have even dreamt of the general system of arithmetic is they hadn't had experience of the particulars. Frege thought generality ensured applicability, but extreme generality might entail irrelevance. |
| 10092 | In the unramified theory of types, the types are objects, then sets of objects, sets of sets etc. [George/Velleman] |
| Full Idea: In the unramified theory of types, all objects are classified into a hierarchy of types. The lowest level has individual objects that are not sets. Next come sets whose elements are individuals, then sets of sets, etc. Variables are confined to types. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: The objects are Type 0, the basic sets Type 1, etc. |
| 10094 | The theory of types seems to rule out harmless sets as well as paradoxical ones. [George/Velleman] |
| Full Idea: The theory of types seems to rule out harmless sets as well as paradoxical ones. If a is an individual and b is a set of individuals, then in type theory we cannot talk about the set {a,b}. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Since we cheerfully talk about 'Cicero and other Romans', this sounds like a rather disasterous weakness. |
| 10095 | Type theory has only finitely many items at each level, which is a problem for mathematics [George/Velleman] |
| Full Idea: A problem with type theory is that there are only finitely many individuals, and finitely many sets of individuals, and so on. The hierarchy may be infinite, but each level is finite. Mathematics required an axiom asserting infinitely many individuals. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: Most accounts of mathematics founder when it comes to infinities. Perhaps we should just reject them? |
| 17901 | Type theory prohibits (oddly) a set containing an individual and a set of individuals [George/Velleman] |
| Full Idea: If a is an individual and b is a set of individuals, then in the theory of types we cannot talk about the set {a,b}, since it is not an individual or a set of individuals, ...but it is hard to see what harm can come from it. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) |
| 10114 | Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman] |
| Full Idea: In the first instance all bounded quantifications are finitary, for they can be viewed as abbreviations for conjunctions and disjunctions. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) | |
| A reaction: This strikes me as quite good support for finitism. The origin of a concept gives a good guide to what it really means (not a popular view, I admit). When Aristotle started quantifying, I suspect of he thought of lists, not totalities. |
| 10134 | Much infinite mathematics can still be justified finitely [George/Velleman] |
| Full Idea: It is possible to use finitary reasoning to justify a significant part of infinitary mathematics. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8) | |
| A reaction: This might save Hilbert's project, by gradually accepting into the fold all the parts which have been giving a finitist justification. |
| 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) |
| 10123 | The intuitionists are the idealists of mathematics [George/Velleman] |
| Full Idea: The intuitionists are the idealists of mathematics. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10124 | Gödel's First Theorem suggests there are truths which are independent of proof [George/Velleman] |
| Full Idea: For intuitionists, truth is not independent of proof, but this independence is precisely what seems to be suggested by Gödel's First Incompleteness Theorem. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8) | |
| A reaction: Thus Gödel was worse news for the Intuitionists than he was for Hilbert's Programme. Gödel himself responded by becoming a platonist about his unprovable truths. |
| 5311 | If observation goes up a level, we expect the laws of the lower level to remain in force [Wilson,EO] |
| Full Idea: When the observer shifts his attention from one level of organisation to the next, as from physics to chemistry, he expects to find obedience to all the laws of the levels below. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.1) | |
| A reaction: This seems to state a necessary condition of reduction, but not a sufficient one. Wilson points out that new phenomena emerge at higher levels. This principle is similar to Hume's argument against miracles. You don't easily overthrow basic laws. |
| 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) |
| 5312 | A child first sees objects as distinct, and later as members of groups [Wilson,EO] |
| Full Idea: From a single-minded effort to move objects a child's activity grows into a detached reflection on the movements themselves. The objects are first perceived as distinct entities, and then as members of groups to be classified. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.3) | |
| A reaction: This does not, of course, prove anything about the philosophical problems of universals, but it does seem to pinpoint the stage in human development when 'universals' are perceived. The basis seems to be groups or sets, but how do we spot those? |
| 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. |
| 5309 | Beliefs are really enabling mechanisms for survival [Wilson,EO] |
| Full Idea: Beliefs are really enabling mechanisms for survival. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.1) | |
| A reaction: How does he know this proposition which he asserts so confidently? Obvious counterexamples seem to be utterly trivial beliefs, and self-destructive beliefs. What is the evolutionary value of low self-esteem? Still, you see his point. |
| 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. |
| 10110 | Corresponding to every concept there is a class (some of them sets) [George/Velleman] |
| Full Idea: Corresponding to every concept there is a class (some classes will be sets, the others proper classes). | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) |
| 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. |
| 5310 | Philosophers study the consequences of ethics instead of its origins [Wilson,EO] |
| Full Idea: Philosophers examine the precepts of ethical systems with reference to their consequences and not their origins. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.1) | |
| A reaction: He is interested in biological origins, but it strikes me that every moral theory has some account of the origins of morality, be it pure reason, or the love of pleasure, or human nature, or eternal ideas, or the will of God, or selfish desires. |
| 5313 | The rules of human decision-making converge and overlap in a 'human nature' [Wilson,EO] |
| Full Idea: The rules followed in human decision-making are tight enough to produce a broad overlap in the decisions taken by all individuals, and hence a convergence powerful enough to be labelled 'human nature'. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.3) | |
| A reaction: This is a nice empirical criterion for asserting the existence of human nature, and it seems right to examine decisions, rather than more thoughtless or conformist behaviour. Existentialists dream of new possibilities, but the old ways always seem best… |
| 5316 | We undermine altruism by rewarding it, but we reward it to encourage it [Wilson,EO] |
| Full Idea: By sanctifying altruism in order to reward it we make it less true, but by that means we promote its recurrence in others. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.7) | |
| A reaction: So is my preference for not rewarding (or even noticing) altruism an anti-social tendency. The very conspicuous charity of sponsorship seems somehow inferior to the truly anonymous gift. Or super-altruism is very public, to encourage it in others? |
| 5318 | Pure hard-core altruism based on kin selection is the enemy of civilisation [Wilson,EO] |
| Full Idea: Pure hard-core altruism based on kin selection is the enemy of civilisation. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.7) | |
| A reaction: By 'hard-core' he means suicidally self-sacrificing, rather than extensive. This seems a good thesis. It strikes me that the development of civil society is often impeded by family loyalty, such as in the case of the Mafia. |
| 5317 | The actor is most convincing who believes that his performance is real [Wilson,EO] |
| Full Idea: The actor is most convincing who believes that his performance is real. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.7) | |
| A reaction: This is a key element of social contract theory. It shows why natural selection of truly altruistic traits might be beneficial to individuals, provided they are surrounded by possible recipricators. We trust those who are genuine and sincere. |
| 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) |
| 5308 | The only human purpose is that created by our genetic history [Wilson,EO] |
| Full Idea: No species, ours included, possesses a purpose beyond the imperatives created by its genetic history. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.1) | |
| A reaction: This invites the question of what that purpose is perceived to be. Some people feel an imperative to play the piano all day, so presumably genetic history has created that feeling. Presumably we can also choose a purpose, even extinction. |
| 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. |
| 5314 | Cultural evolution is Lamarckian and fast, biological evolution is Darwinian and slow [Wilson,EO] |
| Full Idea: Cultural evolution is Lamarckian and very fast, whereas biological evolution is Darwinian and usually very slow. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.4) | |
| A reaction: An intriguing point, given how discredited Lamarckian evolution is. It links with the Dawkins idea of 'memes' - cultural ideas which spread very fast. Is biological evolution suddenly about to become Lamarckian, as culture influences biology? |
| 5315 | Over 99 percent of human evolution has been in the hunter-gatherer phase [Wilson,EO] |
| Full Idea: Selection pressures of hunter-gatherer existence have persisted for over 99 percent of human genetic evolution. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.4) | |
| A reaction: This seems a key point to bear in mind when assessing human nature. Hunter-gathering isn't just one tendency in our genetics; it more or less constitutes everything we are. |
| 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) |
| 5320 | It is estimated that mankind has produced 100,000 religions [Wilson,EO] |
| Full Idea: Since the first recorded religion (in Iraq 60,000 years ago) it is estimated that mankind has produced in the order of one hundred thousand religions. | |
| From: Edmund O. Wilson (On Human Nature [1978], Ch.8) | |
| A reaction: If asked to guess the number, I would probably have said '200'! This staggering figure seems to argue both ways - it suggest a certain arbitrariness in the details of religions, but an extremely intense drive to have some sort of religious belief. |