31 ideas
| 22659 | It is wisdom to believe what you desire, because belief is needed to achieve it [James] |
| Full Idea: Clearly it is often the part of wisdom to believe what one desires; for the belief is one of indispensable preliminary conditions of the realisation of its object. | |
| From: William James (The Sentiment of Rationality [1882], p.43) | |
| A reaction: Roughly, action is impossible without optimism about possible success. This may count as instinct, rather than 'wisdom'. |
| 22657 | All good philosophers start from a dumb conviction about which truths can be revealed [James] |
| Full Idea: Every philosopher whose initiative counts for anything in the evolution of thought has taken his stand on a sort of dumb conviction that the truth must lie in one direction rather than another, and a preliminary assurance that this can be made to work. | |
| From: William James (The Sentiment of Rationality [1882], p.40) | |
| A reaction: I would refer to this as 'intuition', which I think of as reasons (probably good reasons) which cannot yet be articulated. Hence I like this idea very much, except for the word 'dumb'. It is more like a rational vision, yet to be filled in. |
| 22647 | A complete system is just a classification of the whole world's ingredients [James] |
| Full Idea: A completed theoretic philosophy can never be anything more than a completed classification of the world's ingredients. | |
| From: William James (The Sentiment of Rationality [1882], p.23) | |
| A reaction: I assume this is not just the physical ingredients, but must also include our conceptual scheme - but then we must first decide which is the best conceptual scheme to classify, and that's where the real action is. [He scorns such classifation later]. |
| 22648 | A single explanation must have a single point of view [James] |
| Full Idea: A single explanation of a fact only explains it from a single point of view. | |
| From: William James (The Sentiment of Rationality [1882], p.23) | |
| A reaction: I take this to imply that multiple viewpoints lead us towards objectivity. The single viewpoint of an expert is of much greater value than that of a novice, on the whole. |
| 22644 | Our greatest pleasure is the economy of reducing chaotic facts to one single fact [James] |
| Full Idea: Our pleasure at finding that a chaos of facts is the expression of single underlying fact is like a musician's relief at discovering harmony. …The passion for economy of means in thought is the philosophic passion par excellence. | |
| From: William James (The Sentiment of Rationality [1882], p.21) | |
| A reaction: We do, though, possess an inner klaxon warning against stupid simplistic reductions. Reducing all the miseries of life to the workings of the Devil is not satisfactory, even it it is economical. Simplicities are dangerously tempting. |
| 17453 | The meaning of a number isn't just the numerals leading up to it [Heck] |
| Full Idea: My knowing what the number '33' denotes cannot consist in my knowing that it denotes the number of decimal numbers between '1' and '33', because I would know that even if it were in hexadecimal (which I don't know well). | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: Obviously you wouldn't understand '33' if you didn't understand what '33 things' meant. |
| 17457 | A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck] |
| Full Idea: An appreciation of the connection between sameness of number and equinumerosity that it reports is essential to even the most primitive grasp of the concept of cardinal number. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) |
| 17448 | In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck] |
| Full Idea: One need not conceive of the numerals as objects in their own right in order to count. The numerals are not mentioned in counting (as objects to be correlated with baseball players), but are used. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3) | |
| A reaction: He observes that when you name the team, you aren't correlating a list of names with the players. I could correlate any old tags with some objects, and you could tell me the cardinality denoted by the last tag. I do ordinals, you do cardinals. |
| 17455 | Is counting basically mindless, and independent of the cardinality involved? [Heck] |
| Full Idea: I am not denying that counting can be done mindlessly, without making judgments of cardinality along the way. ...But the question is whether counting is, as it were, fundamentally a mindless exercise. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: He says no. It seems to me like going on a journey, where you can forget where you are going and where you have got to so far, but those underlying facts are always there. If you just tag things with unknown foreign numbers, you aren't really counting. |
| 17456 | Counting is the assignment of successively larger cardinal numbers to collections [Heck] |
| Full Idea: Counting is not mere tagging: it is the successive assignment of cardinal numbers to increasingly large collections of objects. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: That the cardinals are 'successive' seems to mean that they are ordinals as well. If you don't know that 'seven' means a cardinality, as well as 'successor of six', you haven't understood it. Days of the week have successors. Does PA capture cardinality? |
| 17450 | Understanding 'just as many' needn't involve grasping one-one correspondence [Heck] |
| Full Idea: It is far from obvious that knowing what 'just as many' means requires knowing what a one-one correspondence is. The notion of a one-one correspondence is very sophisticated, and it is far from clear that five-year-olds have any grasp of it. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4) | |
| A reaction: The point is that children decide 'just as many' by counting each group and arriving at the same numeral, not by matching up. He cites psychological research by Gelman and Galistel. |
| 17451 | We can know 'just as many' without the concepts of equinumerosity or numbers [Heck] |
| Full Idea: 'Just as many' is independent of the ability to count, and we shouldn't characterise equinumerosity through counting. It is also independent of the concept of number. Enough cookies to go round doesn't need how many cookies. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4) | |
| A reaction: [compressed] He talks of children having an 'operational' ability which is independent of these more sophisticated concepts. Interesting. You see how early man could relate 'how many' prior to the development of numbers. |
| 17459 | Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck] |
| Full Idea: The interest of Frege's Theorem is that it offers us an explanation of the fact that the numbers satisfy the Dedekind-Peano axioms. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) | |
| A reaction: He says 'explaining' does not make it more fundamental, since all proofs explain why their conclusions hold. |
| 17454 | Children can use numbers, without a concept of them as countable objects [Heck] |
| Full Idea: For a long time my daughter had no understanding of the question of how many numerals or numbers there are between 'one' and 'five'. I think she lacked the concept of numerals as objects which can themselves be counted. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: I can't make any sense of numbers actually being objects, though clearly treating all sorts of things as objects helps thinking (as in 'the victory is all that matters'). |
| 17458 | Equinumerosity is not the same concept as one-one correspondence [Heck] |
| Full Idea: Equinumerosity is not the same concept as being in one-one correspondence with. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) | |
| A reaction: He says this is the case, even if they are coextensive, like renate and cordate. You can see that five loaves are equinumerous with five fishes, without doing a one-one matchup. |
| 17449 | We can understand cardinality without the idea of one-one correspondence [Heck] |
| Full Idea: One can have a perfectly serviceable concept of cardinality without so much as having the concept of one-one correspondence. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3) | |
| A reaction: This is the culmination of a lengthy discussion. It includes citations about the psychology of children's counting. Cardinality needs one group of things, and 1-1 needs two groups. |
| 22649 | Classification can only ever be for a particular purpose [James] |
| Full Idea: Every way of classifying a thing is but a way of handling it for some particular purpose. Conceptions, 'kinds', are teleological instruments. | |
| From: William James (The Sentiment of Rationality [1882], p.24) | |
| A reaction: Could there not be ways of classifying which suit all of our purposes? If there were a naturally correct way to classifying things, then any pragmatist would probably welcome that. (I don't say there is such a way). |
| 22655 | Scientific genius extracts more than other people from the same evidence [James] |
| Full Idea: What is the use of being a genius, unless with the same scientific evidence as other men, one can reach more truth than they? | |
| From: William James (The Sentiment of Rationality [1882], p.40) | |
| A reaction: This is aimed at Clifford's famous principle. He isn't actually contraverting the principle, but it is a nice point about evidence. Simple empiricists think detectives only have to stare at the evidence and the solution creates itself. |
| 22658 | Experimenters assume the theory is true, and stick to it as long as result don't disappoint [James] |
| Full Idea: Each tester of the truth of a theory …acts as if it were true, and expects the result to disappoint him if his assumption is false. The longer disappointment is delayed, the stronger grows his faith in his theory. | |
| From: William James (The Sentiment of Rationality [1882], p.42) | |
| A reaction: This is almost exactly Popper's falsificationist proposal for science, which interestingly shows the close relationship of his view to pragmatism. Believe it as long as it is still working. |
| 22654 | We can't know if the laws of nature are stable, but we must postulate it or assume it [James] |
| Full Idea: That nature will follow tomorrow the same laws that she follows today is a truth which no man can know; but in the interests of cognition as well as of action we must postulate or assume it. | |
| From: William James (The Sentiment of Rationality [1882], p.39) | |
| A reaction: The stability of nature is something to be assessed, not something taken for granted. If you arrive in a new city and it all seems quiet, you keep your fingers crossed and treat it as stable. But revolution or coup could be just round the corner. |
| 22656 | Trying to assess probabilities by mere calculation is absurd and impossible [James] |
| Full Idea: The absurd abstraction of an intellect verbally formulating all its evidence and carefully estimating the probability thereof solely by the size of a vulgar fraction, is as ideally inept as it is practically impossible. | |
| From: William James (The Sentiment of Rationality [1882], p.40) | |
| A reaction: James probably didn't know about Bayes, but this is directed at the Bayesian approach. My view is that full rational assessment of coherence is a much better bet than a Bayesian calculation. Factors must be weighted. |
| 22646 | We have a passion for knowing the parts of something, rather than the whole [James] |
| Full Idea: Alongside the passion for simplification …is the passion for distinguishing; it is the passion to be acquainted with the parts rather than to comprehend the whole. | |
| From: William James (The Sentiment of Rationality [1882], p.22) | |
| A reaction: As I child I dismantled almost every toy I was given. This seems to be the motivation for a lot of analytic philosophy, but Aristotle also tended to think that way. |
| 22652 | The mind has evolved entirely for practical interests, seen in our reflex actions [James] |
| Full Idea: It is far too little recognised how entirely the intellect is built up of practical interests. The theory of evolution is beginning to do very good service by its reduction of all mentality to the type of reflex action. | |
| From: William James (The Sentiment of Rationality [1882], p.34) | |
| A reaction: Hands evolved for manipulating tools end up playing the piano. Minds evolved for action can be afflicted with boredom. He's not wrong, but he is risking the etymological fallacy (origin = purpose). I take navigation to be the original purpose of mind. |
| 22651 | Dogs' curiosity only concerns what will happen next [James] |
| Full Idea: A dog's curiosity about the movements of his master or a strange object only extends as far as the point of what is going to happen next. | |
| From: William James (The Sentiment of Rationality [1882], p.31) | |
| A reaction: Good. A nice corrective to people like myself who are tempted to inflate animal rationality, in order to emphasise human evolutionary continuity with them. It is hard to disagree with his observation. But dogs do make judgements! True/false! |
| 22650 | How can the ground of rationality be itself rational? [James] |
| Full Idea: Can that which is the ground of rationality in all else be itself properly called rational? | |
| From: William James (The Sentiment of Rationality [1882], p.25) | |
| A reaction: This is the perennial problem in deciding grounds, and in deciding what to treat as primitive. The stoics see the whole of nature as rational. Cf how can the ground of what is physical be itself physical? |
| 22643 | It seems that we feel rational when we detect no irrationality [James] |
| Full Idea: I think there are very good grounds for upholding the view that the feeling of rationality is constituted merely by the absence of any feelings of irrationality. | |
| From: William James (The Sentiment of Rationality [1882], p.20) | |
| A reaction: A very interesting proposal. Nothing is more basic to logic (well, plausible versions of logic) than the principle of non-contradiction - perhaps because it is the foundation of our natural intellectual equipment. |
| 22660 | Evolution suggests prevailing or survival as a new criterion of right and wrong [James] |
| Full Idea: The philosophy of evolution offers us today a new criterion, which is objective and fixed, as an ethical test between right and wrong: That is to be called good which is destined to prevail or survive. | |
| From: William James (The Sentiment of Rationality [1882], p.44) | |
| A reaction: Perceptive for its time. Herbert Spencer may have suggested the idea. James dismisses it, because it implies a sort of fatalism, whereas genuine moral choices are involved in what survives. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 22645 | Understanding by means of causes is useless if they are not reduced to a minimum number [James] |
| Full Idea: The knowledge of things by their causes, which is often given as a definition of rational knowledge, is useless unless the causes converge to a minimum number, while still producing the maximum number of effects. | |
| From: William James (The Sentiment of Rationality [1882], p.21) | |
| A reaction: This is certainly the psychological motivation for trying to identify 'the' cause of something, but James always tries to sell such things as subjective. 'Useless' to one person is a subjective criterion; useless to anyone is much more objective. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |
| 22653 | Early Christianity says God recognises the neglected weak and tender impulses [James] |
| Full Idea: In what did the emancipating message of primitive Christianity consist but in the announcement that God recognizes those weak and tender impulses which paganism had so rudely overlooked. | |
| From: William James (The Sentiment of Rationality [1882], p.36) | |
| A reaction: Nietzsche says these are the virtues of a good slave. Previous virtues were dominated by military needs, but the new virtues are those of large cities, where communal living with strangers is the challenge. |