31 ideas
10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection. | |
From: Leon Horsten (Philosophy of Mathematics [2007], §2.4) |
16477 | Asserting not-p is saying p is false [Russell] |
Full Idea: When you do what a logician would call 'asserting not-p', you are saying 'p is false'. | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5) | |
A reaction: This is presumably classical logic. If we could label p as 'undetermined' (a third truth value), then 'not-p' might equally mean 'undetermined'. |
16484 | There are four experiences that lead us to talk of 'some' things [Russell] |
Full Idea: Propositions about 'some' arise, in practice, in four ways: as generalisations of disjunctions; when an instance suggests compatibility of terms we thought incompatible; as steps to a generalisation; and in cases of imperfect memory. | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5) | |
A reaction: Modern logicians seem to have no interest in the question Russell is investigating here, but I love his attempt, however vague the result, to connect logic to real experience and thought. |
16486 | The physical world doesn't need logic, but the mental world does [Russell] |
Full Idea: The non-mental world can be completely described without the use of any logical word, but when it comes to the mental world, there are facts which cannot be mentioned without the use of logical words. | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5) | |
A reaction: He adds that logical words are not needed for physics, but are needed for psychology. I love Russell's interest in the psychology of logic (in defiance of the anti-psychologism of Frege). See also the ideas of Robert Hanna. |
2947 | Questions wouldn't lead anywhere without the law of excluded middle [Russell] |
Full Idea: Without the law of excluded middle, we could not ask the questions that give rise to discoveries. | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], c.p.88) |
16480 | A disjunction expresses indecision [Russell] |
Full Idea: A disjunction is the verbal expression of indecision, or, if a question, of the desire to reach a decision. | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5) | |
A reaction: Russell is fishing here for Grice's conversational implicature. If you want to assert a simple proposition, you don't introduce it into an irrelevant disjunction, because that would have a particular expressive purpose. |
16479 | 'Or' expresses hesitation, in a dog at a crossroads, or birds risking grabbing crumbs [Russell] |
Full Idea: Psychologically, 'or' corresponds to a state of hesitation. A dog waits at a fork in the road, to see which way you are going. For crumbs on a windowsill, birds behave in a manner we would express by 'shall I be brave, or go hungry?'. | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5) | |
A reaction: I love two facts here - first, that Russell wants to link the connective to the psychology of experience, and second, that a great logician wants to connect his logic to the minds of animals. |
16481 | 'Or' expresses a mental state, not something about the world [Russell] |
Full Idea: When we assert 'p or q' we are in a state which is derivative from two previous states, and we express this state, not something about the world. | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5) | |
A reaction: His example: at a junction this road or that road goes to Oxford, but the world only contains the roads, not some state of 'this or that road'. He doesn't deny that in one sense 'p or q' tells you something about the world. |
16487 | Maybe the 'or' used to describe mental states is not the 'or' of logic [Russell] |
Full Idea: It might be contended that, in describing what happens when a man believes 'p or q', the 'or' that we must use is not the same as the 'or' of logic. | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5) | |
A reaction: This seems to be the general verdict on Russell's enquiries in this chapter, but I love any attempt, however lacking in rigour etc., to connect formal logic to how we think, and thence to the world. |
16483 | Disjunction may also arise in practice if there is imperfect memory. [Russell] |
Full Idea: Another situation in which a disjunction may arise is practice is imperfect memory. 'Either Brown or Jones told me that'. | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5) |
10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'. | |
From: Leon Horsten (Philosophy of Mathematics [2007], §5.2) |
16475 | A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no! [Russell] |
Full Idea: A predicate is 'heterological' when it cannot be predicated of itself; thus 'long' is heterological because it is not a long word, but 'short' is homological. So is 'heterological' heterological? Either answer leads to a contradiction. | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5) | |
A reaction: [Grelling's Paradox] Yes: 'heterological' is heterological because it isn't heterological; No: it isn't, because it is. Russell says we therefore need a hierarchy of languages (types), and the word 'word' is outside the system. |
10885 | Computer proofs don't provide explanations [Horsten] |
Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds. | |
From: Leon Horsten (Philosophy of Mathematics [2007], §5.3) |
10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept. | |
From: Leon Horsten (Philosophy of Mathematics [2007], §2.3) |
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. |
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? |
16482 | All our knowledge (if verbal) is general, because all sentences contain general words [Russell] |
Full Idea: All our knowledge about the world, in so far as it is expressed in words, is more or less general, because every sentence contains at least one word that is not a proper name, and all such words are general. | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5) | |
A reaction: I really like this, especially because it addresses the excessive reliance of some essentialists on sortals, categories and natural kinds, instead of focusing on the actual physical essences of individual objects. |
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. |
4758 | Naļve realism leads to physics, but physics then shows that naļve realism is false [Russell] |
Full Idea: Naļve realism leads to physics, and physics, if true, shows that naļve realism is false. Therefore naļve realism, if true, is false, therefore it is false. | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], p.13) | |
A reaction: I'm inclined to agree with this, though once you have gone off and explored representation and sense data you may be driven back to naļve realism again. |
16476 | For simple words, a single experience can show that they are true [Russell] |
Full Idea: So long as a man avoids words which are condensed inductions (such as 'dog'), and confines himself to words that can describe a single experience, it is possible for a single experience to show that his words are true. | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5) | |
A reaction: One might question whether a line can be drawn between the inductive and the non-inductive in this way. I'm inclined just to say that the simpler the proposition the less room there is for error in confirming it. |
16485 | Perception can't prove universal generalisations, so abandon them, or abandon empiricism? [Russell] |
Full Idea: Propositions about 'some' may be proved empirically, but propositions about 'all' are difficult to know, and can't be proved unless such propositions are in the premisses. These aren't in perception, so forgo general propositions, or abandon empiricism? | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5) | |
A reaction: This is obviously related to the difficulty empiricists have with induction. You could hardly persuade logicians to give up the universal quantifier, because it is needed in mathematics. Do we actually know any universal empirical truths? |
16478 | A mother cat is paralysed if equidistant between two needy kittens [Russell] |
Full Idea: I once, to test the story of Buridan's Ass, put a cat exactly half-way between her two kittens, both too young to move: for a time she found the disjunction paralysing. | |
From: Bertrand Russell (An Inquiry into Meaning and Truth [1940], 5) | |
A reaction: Buridan's Ass is said to have starved between two equal piles of hay. Reason can't be the tie-breaker; reason obviously says 'choose one!', but intellectualism demands a reason for the one you choose. |
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. |
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. |
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. |
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. |