tag:blogger.com,1999:blog-24371659079153504802024-02-20T19:22:51.659+01:00Inquiry and PedagogyMikolkahttp://www.blogger.com/profile/06474496860871759825noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-2437165907915350480.post-34290297813029371542008-07-03T20:44:00.001+02:002008-07-05T16:34:50.279+02:00Qu'est-ce qu'un problème philosophique?Sur le blog <a href="http://zulio.org/journal/">Varia</a>, il y eut une discussion très intéressante sur ce qu'est un <a href="http://zulio.org/journal/post/2006/09/20/qu-est-ce-qu-un-probleme">problème philosophique</a>.<br /><br /><span class="fullpost"></span>Mikolkahttp://www.blogger.com/profile/06474496860871759825noreply@blogger.com0tag:blogger.com,1999:blog-2437165907915350480.post-78915093244284910402008-06-23T16:47:00.002+02:002008-06-23T17:48:53.134+02:00Writing style, Peter Smith<a href="http://www.phil.cam.ac.uk/teaching_staff/Smith/index.html">Peter Smith</a> est professeur de Logique à <span style="font-style: italic;">Cambridge University</span>. Il fut le directeur de la revue britannique <a style="font-style: italic;" href="http://www.nottingham.ac.uk/journals/analysis/">Analysis</a><span style="font-style: italic;">.</span> Il donne des conseils pour améliorer ses qualités d'écriture et d'organisation dans la rédaction d'un essai, d'une dissertation, d'un article. Le texte se trouve originellement <a href="http://www.phil.cam.ac.uk/teaching_staff/Smith/students/writing.html">ici</a>. <span class="fullpost"><br /><br /><br /><span style="font-weight: bold;">Warning</span><br /><br />This is just one person's view, not an Official Faculty Guide. Others will want to stress other virtues and vices in writing. Make what use of these remarks you can!<br /><br /><br /><span style="font-weight: bold;"><br />Introduction</span><br /><br />As you may know, I used to edit one of the philosophy journals. This means that, during the average year, I read getting on for four hundred submissions to the journal -- and yes, I did read them all.<br /><br />Like the other major journals, ANALYSIS can accept less than 10% of submissions. So standards are fierce. Many submissions are ruled out of court for being badly argued or for re-inventing the wheel or for being plain boring. But a fair proportion end up on the rejection pile simply because they are badly written. I saw far too much bad prose (to be sure, some of the prose that gets published is not exactly wonderful: I assure you that a lot that doesn't get published is very much worse).<br /><br />Since ANALYSIS publishes relatively short articles, it attracts papers from philosophers finishing graduate school or starting out on professional careers. And bad writing is perhaps particularly common in the pieces by these younger authors, your almost-contemporaries. Now, we are not necessarily expecting you to be submitting articles for publication in the next year or two. But the faults that make for bad writing in potential articles equally make for bad writing in essays and theses. This is the time to start getting into good habits.<br /><br />So the idea of these notes [written for part of a "Research Training Programme"] is that I try to impart some of what I've learnt about bad writing and the mistakes to avoid. However, it is one thing to be able to recognize bad writing when you see it; it is quite another thing to be able to say, crisply and clearly, what makes it bad. Prose can be dull, stodgy and unreadable; yet it may be very difficult to say exactly what makes it so and suggest how to improve it. And while I think I am a rather good judge of the quality of writing, I claim no special expertise at therapy for bad prose. A lot of what I'll be saying, then, will be pretty banal and obvious (with a little help from Goerge Orwell and Jonathan Bennett, I'll be making points that it doesn't need an editor's eye to spot). Still, even if you just follow the banal and obvious advice, that will be a start.<br /><br /><br /><span style="font-weight: bold;">Writing and reading</span><br /><br />It shouldn't need saying -- but I won't let that stop me saying it: you won't develop a good English prose style if you never read good English prose stylists. The great authors show just how much can be achieved in well-crafted plain prose, written without affectation or self-conscious stylishness. Choose your favourite examples. My first choice as an author for philosophers to emulate is George Orwell. Do look at some of his essays -- there are various collections. Read in particular 'Politics and the English Language', both for Orwell's reminders about how bad writing corrupts thought and for his own rules about how to improve our writing. Among more recent writers, I'd mention ...<br /><br />But hold on! I'm already in danger of getting distracted. We are not here to exchange notes about favourite writers: you will have your own. Do spend some time, though, thinking (and thinking much more carefully and self-consciously than you usually do) about why your favourite stylists write well -- ask what it is about their work that makes it speak directly to you.<br /><br />And now do the same for some contemporary philosophical authors as well. In different ways, Gilbert Ryle and W. V. O. Quine (for example) show how it is possible to be lucid and direct and uncluttered yet be a wonderful stylist. Frank Jackson and David Lewis are still more lucid, and (I'd say) to be emulated even more. But again, let's not pause to debate who has the best style. You will have your own favourite philosophical authors who strike you as particularly clear and direct, authors whose work makes you think "I wish I could write like that". Well, look at some of their work again, and try to work out what makes it particularly approachable and attractive.<br /><br />In sum: read some of the best writers of good plain prose, philosophical and otherwise, and attend to how they achieve their effects. This must be time well spent.<br /><br /><br /><span style="font-weight: bold;">Eye and ear</span><br /><br />If I had to give just one rule to help improve your writing it would be this. Read aloud what you have written. Jonathan Bennett reports that Ryle once said to him "What doesn't read well to the ear doesn't read well to the eye". And I endorse that emphatically.<br /><br />Imagine an audience, and read out your completed paragraphs (yes, aloud, and trying to put some real life into the performance). If you can't do this with conviction, you will know that something is wrong with the writing. If your tongue stumbles over laborious sentences, or if a sentence sounds ugly or flat or tedious when read out, then it needs revision. If the passage from one sentence to the next is jerky or unnatural, if a paragraph lacks shape and rhythm, then (again) revision is needed.<br /><br />I can't stress enough the effectiveness of this "read aloud" test. Even better, if you can bear it, is to get someone else to read your prose aloud to you (and you are not allowed to follow on paper while you listen). If your reader finds it difficult to give shape to the sentences and to the paragraphs, if your reader stumbles when trying to your prose read aloud, then why suppose she will do any better when trying to read the same passage quietly to herself? If your writing sounds ugly or banal or repetitious or unclear when you have to listen to it (and you at least have the benefit of knowing what is supposed to be going on), then it is going to seem at least as bad to everyone else.<br /><br />So Rule One: read your work aloud. Don't inflict on your supervisor or an editor anything that falls down at this hurdle.<br /><br /><span style="font-weight: bold;"><br />The virtue of brevity</span><br /><br />If you follow the "read aloud" rule, you are likely (even without thinking about it) to keep close to three of George Orwell's cardinal rules for decent prose. But let's state them explicitly all the same. Two of them are: Never use a long word where a short one will do (thus, don't write "exhibit" when you could write "show"; don't use "demonstrate" when "prove" will do as well). And Never use the passive when the active will do. So don't use<br /><br />"It is claimed by Jones that realism is refuted by Putnam's argument"<br /><br />when you could write<br /><br />"Jones claims that Putnam's argument refutes realism"<br /><br />And so on.<br /><br />But Orwell's most important rule is If it is possible to cut out a word, always cut it out. And we can generalize this: If it is possible to rephrase a sentence to make it shorter without serious loss of content, do so. Thus, don't write the likes of<br /><br />"He advanced an argument for the proposition that"<br /><br />when you could write<br /><br />"He argued that"<br /><br />And so on. Here is an example of published prose quoted by Jonathan Bennett (in a very useful piece on 'Improving Academic Writing', Teaching Philosophy 1997):<br /><br />"If what has been previously claimed (though not conclusively defended) is true-that the thesis that "ought" implies "can" is untenable even in the moral domain-then it is altogether possible that a man believe that he ought to act in such and such a way and yet, in the relevant circumstances, fail to act not merely through reasons of ignorance, inadvertance, change of heart, or the like but also (a decisive possibility) because of an incapacity to act."<br /><br />Rewritten by Bennett:<br /><br /> "If I have been right in saying (not proving) that "ought" implies "can" is untenable even in the moral domain, then someone can fail to act as he thinks he ought because he cannot act in that way."<br /><br />That's less than half the length, and is a lot clearer (exercise: do even better!).<br /><br />The journal submissions I saw for ANALYSIS are, of course, authors' final drafts. The work has already been lovingly revised and polished a number of times. Yet quite often I used to ask authors to cut their work by ten or fifteen percent. And almost invariably, when I did this, authors comment (when they sent in their shortened revised version) that they thought that their paper is improved by being made leaner and fitter. If final drafts can usefully be trimmed by ten or fifteen percent, then there is likely to be a lot more redundant material in earlier drafts. Be firm: take your prose to the gym, and keep working at it until the bones and sinews show through! That's Rule Two.<br /><br /><br /><span style="font-weight: bold;">Detailed rules of thumb?</span><br /><br />If you follow those two master rules -- test your writing by reading it aloud, and keep your prose very lean and brisk -- then you'll certainly be on the right road. And if you look at (say) Fowler's Modern English Usage you'll find plenty of more detailed suggestions for cultivating good writing habits. We could spend a lot of time on such detailed suggestions: I'll mention just four (fairly arbitrarily selected).<br /><br />-First, <span style="font-style: italic;">avoid repetition</span>. That's banal. Yet over-repetition is a sin that a lot of beginning authors fall into. Clarity is not helped by saying the same thing over and over again in slightly different words. And euphony is not helped by repeatedly using the same word or phrase. (If you are writing about utilitarianism, then-to be sure-that word is perhaps going to appear often. But not every three sentences, please!).<br /><br />-Second, <span style="font-style: italic;">avoid the first person pronoun</span>. Nearly all those uses of "I think", "in my view", "it seems to me", and "in this section, I want to" can and should be axed.<br /><br />-Third, <span style="font-style: italic;">avoid over-emphasis</span>. Keep the use of italics to a minimum. Avoid over-using "very", "extremely", "really", "crucial", "obviously", "it is important to note that", and so forth.<br /><br />-Fourth, <span style="font-style: italic;">favour the Anglo-Saxon</span> -- another rule stressed by Orwell, echoed by Bennett. This makes for brevity again. Thus "hasten" is shorter than "expedite"; "secret" is shorter than "clandestine"; and so on. Again, "It is possible for us to show that " is long-winded compared with "We can show that"; "He has an obligation to show that " is long-winded compared with "He ought to show that".<br /><br /><br /><span style="font-weight: bold;">Overall construction</span><br /><br />But let's pass on from advice about how to write clear sentences and paragraphs to advice about the overall construction of your work. For is quite possible to write elegant sentences and even elegant paragraphs, and yet compose a whole which adds up to much less than the sum of its parts.<br /><br />If it is difficult to discern a clear line of argument in something you have written, perhaps that's because there isn't one. The bad construction may just reflect bad philosophy. But even when there is a good line of argument in the background, you may well not be getting it across. Here are three linked suggestions about how to check that your structure is working:<br /><br />First, divide your essay/chapter/paper into bite-sized chunks. Separate your piece into headed sections (and perhaps divide the sections into subsections), with no part more than about 500 words long. If you can't do this neatly and naturally, that strongly suggests that your line of argument is rambling without sufficient direction.<br /><br />Second, write a brief abstract of each (sub)section. Can you give (at no more than 10% of the length) the headline news for each (sub)section? If you can't do this neatly and naturally, that again strongly suggests that your argument is not under tight control.<br /><br />Third, check whether the abstracts for each (sub)section add up to a coherent overall story. When O. R. Jones and I were writing The Philosophy of Mind there was a chapter which Dr. Jones had drafted which he liked but I thought didn't work well. So I asked "How can we frame an analytical table of contents for this chapter?" -- and when we tried to compress the argument into brisk headlines and failed, we quickly agreed that something was indeed wrong. In this case, the material needed completely reordering. Likewise, if you find that the abstract for your whole piece doesn't flow well, then try reordering your material. Make imaginative use of your word-processor's cut-and-paste tools: rearranging paragraphs or sections may suddenly reveal a much better order of presentation.<br /><br />I think I'd headline this advice about breaking the work into sections and writing abstracts as the basic Rule Three, to be put alongside Rule One about reading your work aloud, and Rule Two about aiming for brevity. Following Rules One and Two will help you get the micro-structure right, sentence by sentence. Following Rule Three will do a lot to get the macro-structure right.<br /><br />In the hey-day of linguistic philosophy, a volume of dissenting essays was published entitled Clarity is Not Enough. And indeed it isn't enough. But complete clarity is certainly a necessary condition of any good philosophy (well, the editor of ANALYSIS would say that, wouldn't he?). Your aim, then, should always and everywhere be to write with transparent clarity. Following the suggested Rules must promote that aim.<br /><br /><br /><span style="font-weight: bold;">All your own work?</span><br /><br />Finally, let me say something about a topic that is partly a question of style, partly a question of content.<br /><br />I turned down quite a few papers for ANALYSIS simply because they are 75% scene-setting. Now, a review of the current state of the debate and/or exposition of the position that you want to criticize are fine in their place. And a supervisor may very well ask you to write something more or less purely expository as an exercise to help you get clear about basics. So I'm certainly not saying "never write anything that is mainly expository". But do always ask-is this amount of scene-setting really necessary? Can't I assume that my audience (your supervisor, your examiner, the readers of the journal you are trying to write for) will already know at least that? Give your audience the benefit of the doubt and assume they are reasonably up-to-speed (a supervisor or editor will always tell you if you presuppose too much: but you are unlikely to do so).<br /><br />At different stages in your writing career, different material can be taken for granted. What you are expected to spell out as an undergraduate becomes background material at M. Phil. level; and some of what you need to spell out now will in turn become background material as you march on to the frontiers. But whatever level you are working at, do try to keep the basic scene-setting appropriate to that level to no more than (say) 25% of the whole. You will want to write about the background at greater length in your own notes: but when you are writing for others, be very selective. If in doubt, prune it out.<br /><br /><br /></span>Mikolkahttp://www.blogger.com/profile/06474496860871759825noreply@blogger.com0tag:blogger.com,1999:blog-2437165907915350480.post-7365520137206251132008-06-19T16:22:00.004+02:002008-06-22T20:48:49.667+02:00Getting published, Peter Smith<a href="http://www.phil.cam.ac.uk/teaching_staff/Smith/index.html">Peter Smith</a> est professeur de Logique à <span style="font-style: italic;">Cambridge University</span>. Il fut le directeur de la revue <a href="http://www.nottingham.ac.uk/journals/analysis/"><span style="font-style: italic;">Analysis</span></a>. Il donne des conseils pour permettre à quiconque de rédiger un texte qui a des chances d'être publié dans une revue. Le texte (version anglaise seulement) se trouve originellement <a href="http://www.phil.cam.ac.uk/teaching_staff/Smith/students/published.html">ici</a>.<br /><span class="fullpost"><br /><br /><span style="font-weight: bold;">Why rush to publish?</span><br /><br />Publish or perish? Well, like it or not (and I for one don't!-for I fear it encourages narrowness and scholasticism), having a track record of pieces accepted for publication is now more or less a sine qua non for getting a foot on the first rung of the profession, as a junior research fellow or temporary lecturer. And when it comes to applying for a permanent lectureship a good track record of publication and clear evidence that you are going to continue publishing is even more essential: UK departments attach a huge importance to their ratings in the Research Assessment Exercises, and good overseas departments place equal if not more weight on research promise.<br /><br />Note, though, the injunction "publish" certainly doesn't mean "publish as much as you can, without real regard to the quality of your work or to where it appears". Publishing a lot of third rate stuff (which is possible if you try hard enough) is highly counterproductive. It is much better to produce two or three pieces that make it into top-class journals than sprinkle third-division outlets with hack work. Go for quality, not quantity.<br /><br />There's a lot of useful information in the APA Guidebook for Publishing Philosophy, edited by Eric Hoffman (in the philosophy faculty library, F 12 HOF); so these brief notes don't aim to be comprehensive. They just try to distill one ex-editor's experience.<br /><br />The main route into publication is through professional journals, and below the emphasis will be on publishing articles in journals. But there are other kinds of publication -- and perhaps the key one to mention which is relevant to graduate students/JRFs is ...<br /><br /><br /><span style="font-weight: bold;">The book review</span><br /><br />You certainly won't build a career on the back of book reviews, but it is probably good to do one or two. But how do you get invited? One way is to put yourself around a bit at conferences, give a 'graduate paper' here and there so that you get recognized as someone working in your field. But also your research supervisor may be able to pass on an invitation to you, or use his or her own contacts with journal reviews editors to get you an invitation to review. In particular, if you know that a book is forthcoming on your own research topic, then you could ask your supervisor to put out feelers with some journals ahead of publication date (reviews editors are hard pressed to find enough people to review books, and will probably welcome the recommendation of a new reviewer).<br /><br />If you are asked to review a book, you will be given a word limit you should stick to. And remember that the readers will mostly want to know what is in the book and how it adds to the literature (do they have to read it?). Readers will be rather less interested in your views! You can be critical, of course, but if so be temperate and judicious: nobody likes a smart-arse! If you find what seem to you bad errors that you are going to focus your review on, then it might be worth contacting the author by e-mail and check that your reading of the text is a fair one (most authors are only too glad to find there is someone actually interested in their stuff!).<br /><br />Try out a draft of your review -- as indeed a draft of anything you want to submit for publication -- on a critical friend, asking for a frank judgement about clarity and readability. Another general point: if at all possible, put your final draft in a drawer for a fortnight or so before sending it off: a final re-read after a period away from the piece can often show up some glaring inelegances or clumsy passages.<br /><br />But as I say, reviews -- while worth doing -- don't count for much in the scheme of things, so let's turn to our central topic, the journal article.<br /><br /><br /><span style="font-weight: bold;">One journal</span><br /><br />First, some rather specific info about how one journal works, or at least worked while I was editing it (until 1999 in fact). In some ways, ANALYSIS is atypical -- but since it publishes shorter papers, it is often the first journal that a budding philosopher submits papers to. So the info is perhaps of especial relevance.<br /><br />When a paper arrives (the better part of 400 a year!) the editor will make an initial triage into "must publish", "send to referees", and "no thanks". Different journals will differ in the proportions in each category. When I was editing ANALYSIS, the proportions were something like 4%, 12%, 84%; and in the end about 11% of papers got published.<br /><br /><br /><span style="font-weight: bold;">Why, then, do papers get turned down, as most do? Some common reasons ...</span><br /><br /> -They are badly written at the micro-level-- too many sentences are clumsy, or even just don't make clear sense.<br /> -Even if the sentences make sense taken severally, they don't add up to very clear sections. The writing is bad at the macro-level.<br /> -Section by section things go quite well, but the sections don't add up to a well-structured, well organized paper.<br /> -The writing and structure is fine, the message is clear, but the paper re-invents the wheel (the point has already been made in the recent literature).<br /> -The final message is novel, but it comes after far too much scene-setting or exposition of familiar stuff (a very common mistake, especially it seems from USA grad students, who seem to think that ten pages of scene-setting are needed before they offer two pages of original stuff: not so!).<br /> -The message is novel, and put crisply, but is too trivial/obvious/doesn't really need saying. [The previous faults of bad writing, too much scene setting, or being old-hat are fairly objectively discernible -- now we are getting to the sort of things that will vary somewhat from editor to editor: that's why you shouldn't be too disheartened by a rejection first time around. Another editor may well take a different view. Still, editors will probably tend to share a view on what counts as a footnote or paragraph puffed up into a paper.]<br /> -The message is novel and non-trivial but a contribution to a 'dead' debate (no one much is interested: sorry, but philosophy is as fashion prone as other intellectual enterprises! if you do want to heat up some 1980s dish, you'll need to do it with extra zip and with exciting advertising spiel!).<br /> -The opposite fault: the message is novel but a contribution to a debate that is currently too over-exposed (so the editor is reluctant to print yet another article on [as it might be] externalism and self-knowledge, unless it is unusually striking).<br /> -The message is novel but the conclusion is just downright implausible. That's a judgement call, of course!-- true, a neat argument to a novel apparent paradox can be fun and instructive, but sheer perversity palls. If you do find yourself arguing for a highly heterodox view, then you need to sugar the pill in various ways (explain why your view isn't as mad as it might seem, or why it has really positive pay-offs, or ...).<br /> -Worthy but dull: the message is novel, there isn't too much scene-setting, the conclusion is interesting and well-argued, the prose is clear -- but it is just all too laboured and manages to produce boredom in the reader rather than interest (that's another judgement call, of course)! This is another frequent fault -- you must remember that not everyone will find your research topic riveting, so you need to sell your piece with some crisp prose, neat illustrations, nice turns of phrase.<br /> -The message is novel and interesting, the piece is well written, it has all the virtues, except that it comes in second -- it is pipped to the post by another piece making a similar contribution to the same debate (often happens in a journal like ANALYSIS).<br /><br />Presentation matters a lot then, then! You can't easily forestall the bad luck of being pipped to the post (though if you do think of writing a piece on a hot debate, best to do it quickly as soon as the idea strikes you!). But some of the other failings can be avoided by giving quite a bit of thought to how you package your arguments. Brevity is a great virtue, given the pressure on space in journals; and cutting your article down to the bones will almost always make for a zippier read.<br /><br />If the editor decides to publish or reject straight off, without consulting referees, then you should hear within four weeks (I'm still talking about ANALYSIS here). A straight rejection may well be unexplained (I took the line, as some editors do, that authors prefer speed to comments, unless the comments are extensive enough to be useful).<br /><br />If a paper is sent out to referees, then it could be more like eight weeks before you get a decision. You should, in the second case, get at least excerpts from the referees comments; but not necessarily (referees are allowed to write 'for the editor's eyes only', or to be very brisk if they are pushed for time). If what you receive is a reasoned rejection then you should take your medicine without complaint (unless the referee's comments are quite wildly off-key, e.g. based on an obvious misreading of your argument -- you can protest, but I think in my 12 years of editing, I only changed my mind in response to authors' protests very rarely).<br /><br />If you are asked to revise taking into account the referee's suggestions and worries than try to do just that (even if the referee's worries don't always seem terribly well-based to you, at least take this as an opportunity to fend of possible misunderstandings). Remember it is possible that the same referee will be asked again to read the revised version, so don't write something along the lines of "someone might object ...; but that is obviously naive and foolish because ..."! Explain in a covering letter how you have dealt with the referee's comments: if one of the referee's comments does seem off-beam, then do explain in a quietly reasoned way why you haven't changed anything in response to that comment. An invitation to resubmit is not a promise to publish, but indicates a high probability of publication if you deal with the referee's suggestions in a positive and constructive manner.<br /><br />If your paper is accepted, then, with luck, it should appear within nine months of acceptance.<br /><br /><br /><span style="font-weight: bold;">Other journals</span><br /><br />Some American journals send pretty much everything they receive (whether it initially looks rather good or pretty bad) out to two referees: so the proportions in their initial triage are more like 0%, 95%, 5%. But whatever the mechanism, the final result is much the same: most good journals publish no more than about 10% of the papers submitted to them (considerably less for the really prestigious journals).<br /><br />Journals should make it clear what the expected turn-around period is and it is quite in order to e-mail a query if the expected date for a decision has passed: but basically you have to be very patient -- many journals can take over six months to give you a decision. And the lead time to publication can be two years... (Some journals print acceptance dates: then you can tell how long it typically takes the journal to get papers into print.)<br /><br />Do try sensibly to match submitted paper to the journal you are sending it to. You need to do some homework: has the journal recently been publishing similar sorts of papers (construing 'similar' broadly)? In a similar sort of style? For example, some journals are much more receptive to very straight history of philosophy than others. Again, some journals are much more receptive to papers that straddle discipline boundaries than others. And even if you are writing straight analytic philosophy, ANALYSIS (say) has a rather different flavour to Philosophy, even though they are both mainstream analytic journals. Your own reading in your own area should make it pretty clear which journals are 'your' sort of journal.<br /><br />And there is a pretty well understood pecking order of journals in terms of quality and prestige: are you aiming sensibly? By common perception (and by difficulty of getting accepted) Journal of Philosophy trumps Nous or the Australasian Journal (say), yet the latter are highly respected. It is absolutely not done to send a paper to more than one journal at a time (you may be asked to confirm in your covering letter that the paper isn't under consideration with another journal). So it could be unwise to tie up a paper maybe for six months or so by aiming too high, when (for CV purposes) it would be pretty much as good to get a piece into a slightly less exalted home.<br /><br />You can get some information about relative acceptance rates of different journals, etc., from the APA Guidebook . Many journals also have web-pages these days, which may contain useful additional information.<br /><br /><br /><span style="font-weight: bold;">How to increase your chances of getting published!</span><br /><br />Let's assume that you've got something interesting to say. Something novel (even if only critically novel). Something that you've tried out on your supervisor and on the graduate seminar and it has stood up to criticism. Something that strikes you as worth saying and as moving the debate forward. You now need to package it for publication:<br /><br /> -Make sure the topic really is paper-sized (not a footnote inflated beyond its worth, as has already been said -- but also not too action-packed to be readily readable: some papers by beginners try to pack too much in, and or are short papers padded out to be longer). Keep it focused and tightly structured.<br /> -Make it absolutely clear from the start what the thesis of the paper is (opening paragraphs make a very big impression). What is the "take home message"?<br /> -Make it absolutely clear at every point what the structure of the paper is (it is surprising how often as an editor I had to read material two or three times to see whether, at some point, the author was stating her own view or presenting the view under attack).<br /> -Use absolutely clear and direct prose (use the 'does it sound well if read aloud' test -- and there are many more recommendations about style here). Be terse and crisp.<br /> -Use a professional tone (not over casual, no over flippant remarks, no abuse of your target!).<br /> -Make sure your paper is really well presented, well laid-out following the proper bibliographical conventions for references, well spell-checked, printed using a quality printer, etc. (If the author can't be bothered to make the paper look really good, that doesn't make a good impression!).<br /> -You needn't slavishly follow the finest details of the particular journal's style on first submission -- but if you don't, you should say in your covering letter 'If the paper is accepted. I will send a version formatted according to your style-sheet' (or some such).<br /> -Do conform if the journal insists on, or encourages, submissions prepared for 'blind' refereeing -- i.e. use detachable cover sheets giving the your name and affiliation, so that the main body of the paper which is sent out to referees is free (as far as possible) of indications of who the author is.<br /> -To repeat, do try sensibly to match submitted paper to the journal you are sending it to.<br /> -Good luck!<br /><br />Another relevant book that seems to get recommended (I don't have first hand acquaintance) is P.J. Hills (ed.) Publish or Perish (Dereham: Peter Francis): a guide to publishing papers in professional and academic journals.<br /><br /><br /></span>Mikolkahttp://www.blogger.com/profile/06474496860871759825noreply@blogger.com0tag:blogger.com,1999:blog-2437165907915350480.post-842013691430521092008-06-16T16:01:00.001+02:002008-06-16T16:01:02.106+02:00Notes on how to tackle the Essay Paper, Peter Smith"In these notes I offer some suggestions about how to tackle this paper, and try to answer some Frequently Asked Questions. The notes are based (in the second half, very closely indeed) on notes written by Jane Heal -- I'm very grateful to her for allowing me to snaffle some of her best suggestions, though she is not responsible for the final result. Do note, though, that the result is still just one view ... Consult other supervisors/directors of studies for additional advice." Peter Smith.<br /><br /><a href="http://www.phil.cam.ac.uk/teaching_staff/Smith/index.html">Peter Smith</a> est professeur de Logique à <span style="font-style: italic;">Cambridge University</span>. Il fut le directeur de la revue <a href="http://www.nottingham.ac.uk/journals/analysis/"><span style="font-style: italic;">Analysis</span></a>. Ce texte (version anglaise seulement) se trouve originellement <a href="http://www.phil.cam.ac.uk/teaching_staff/Smith/students/Essay_Paper.html">ici</a>. <span class="fullpost"><br /><br /><br /><span style="font-weight: bold;">What is the point of the paper?</span><br /><br />To see if you can write at length about some topic, in a focused and sustained way. Focused -- not rambling disconnectedly on "everything I know about X", but discussing a specific topic or cluster of interrelated topics in an integrated way. Sustained -- following through some clear line(s) of argument in some depth (e.g. discussing not just objections but objections to the objections).<br /><br />That still leaves options. You may go 'vertically' and dig more deeply into one particular issue; or you may go 'horizontally' and be concerned to make connections, and show how different parts of the philosophical landscape fit together -- or a bit of both. But whichever way you go, you should aim for a clearly structured story and some meaty arguments.<br /><br /><br /><span style="font-weight: bold;">But typical one-word questions like "Necessity" or "Scepticism" or "Justice" are not very focused!</span><br /><br />True. But they are intended as invitations to write on some specific topic that falls under the one-word heading. What the the Faculty Handbook says about Extended Essays and Dissertations applies here too. "The candidate in effect sets their own question [in the given area], and is expected to define this question and then write about it, not about its general philosophical environs." To emphasize again, you cannot construct a good extended essay merely by collecting a lot of points about a topic and setting them out one after the other. They need to be organized into an argument in favour of some particular conclusion, which you have specified as your target.<br /><br /><br /><span style="font-weight: bold;">How much should I aim to write?</span><br /><br />Quite a bit! If your essay is hardly longer than a typical answer to a single question on one of the other papers, then it is almost certainly too short. (Of course, you might be a Gettier, about to make a Major New Point in a couple of pages -- but then again, probably not ...!)<br /><br />On the other hand, you might well write rather less overall than in other three hour papers, because you need to spend somewhat more time in thinking out and planning your work. Don't just dive in -- plan your answer very carefully. And certainly, you should avoid padding your answer out with material irrelevant to your main theme (that way, you can well end up with lower marks than if you had stopped sooner).<br /><br /><br /><span style="font-weight: bold;">It's a lottery. How can I be expected to predict questions?</span><br /><br />You can't make reliable predictions way ahead of time. You need to have a few areas prepared. But it's no secret how the questions on the essay paper are chosen -- 'big' topics on the syllabus of other papers that don't get questions asked on them in the relevant paper are very likely to get a question on the essay paper, so that the syllabus is covered fairly. If your favourite topic is absent from its 'home' paper, then it is a very good bet that it will turn up on the Essay Paper. So you can and should do some detailed last-minute preparation of two or three sensibly chosen topics once you have seen the other papers.<br /><br /><br /><span style="font-weight: bold;">How should I prepare in general?</span><br /><br />Practice! Whatever style of extended essay you favour, it is important to try planning and writing some before it comes to the Tripos itself. The Easter vacation is a good time to do this. Look at the essay topics set in some previous years' papers, and sketch out in detail how you would write on three or four of them (it will be good revision for the other papers too). You should actually write at least one extended essay of at least 2,000 words, and preferably two. Get some feedback about them from your supervisor at the start of the Easter term.<br /><br /><br /><span style="font-weight: bold;">Am I expected to have something original to say?</span><br /><br />Yes and no. No, you are not expected (even at Part II!) to come up with a brand new idea of your own. But yes, an absolutely routine presentation of absolutely standard points, however clearly done, isn't enough to do well. We are looking for signs of reading a bit more widely than the basic three or four papers you'd have to read for a supervision essay on the topic. And we are looking for something that is original to you in the sense of bringing together your reading and thinking in an individual way that shows that you have thought through the ideas for yourself.<br /><br /><br /><span style="font-weight: bold;">But how do I give an individual twist to essays on what are, typically, very mainstream topics?</span><br /><br />Don't worry! You'd be surprised how different even regular supervision essays can be, even on a standard topic when everyone's essay is based on a standard reading list. If you have read more than the most basic literature (important!) and have thought about it a bit (even more important!), then you'll almost certainly write with more individuality than you realize.<br /><br />Still, if you find it difficult to kick-start your thought processes when faced with a numbingly general essay title like 'Pleasure', you might like to consider the following interesting advice from Jane Heal (what follows is from her notes, lightly edited):<br /><br /><br /><span style="font-weight: bold;">One method: one example</span><br /><br />It is a good thing to write in a way which shows that you can see the ramifications of the topic and are aware that there are many interesting questions, other than the most central and familiar ones, which can be asked about philosophical topics and many ways in which philosophical views interconnect.<br /><br />To be able to do this you need, to start with, to have your mind decently well stocked with philosophical questions and ideas. And there is no way of getting it well stocked except by reading and thinking steadily throughout the year, getting into the habit of trying to relate what you hear in lectures to supervision reading you have already done, keeping a file of interesting ideas which strike you and so forth. But, even if you have a well stocked mind, you also need a method of retrieving from the various comers of your memory all the things you know about a given topic, so that slightly less familiar connections of ideas come into view and so that you can in the examination make best use of everything you know, rather than just relying on those obvious ideas which come first to mind. Here is one way of proceeding:<br /><br /> -Construct a list of major philosophical areas or concepts, for example such things as: ontology, epistemology, ethics, logic, God, time, matter, mind, causation, God, everyday life, etc. (Other big categories could include history of philosophy, art, political life, science, love, necessity, hate, creativity, death, law, etc. etc.) Choose five or six areas/concepts which you feel you know about and/or which are of interest to you and/or which name big topics which you have strong opinions about.<br /> -Now take the essay title you want to tackle and juxtapose it in turn to all your chosen big concepts and see what questions and ideas present themselves.<br /><br />An example. Suppose the topic is 'Pleasure' -- and consider questions that might arise when you juxtapose this with the first five headings above<br /><br /> -Pleasure + ontology: What sort of thing is pleasure - is it just a subjective state of mind? Is it different from happiness or contentment? Does it come in higher and lower varieties?<br /> -Pleasure + epistemology: Can we know whether another is enjoying some pleasure and if so how, and how accurately? Can I know whether I am taking pleasure and if so how? Do issues about the epistemology of pleasure make obstacles for attempts to make pleasure the central notion in ethics?<br /> -Pleasure + ethics: Is pleasure the only valuable thing? If not why not, and what other sorts of valuable things are there? How should I (morally? rationally?) weigh my own pleasure in comparison with that of others when I am making decisions?<br /> -Pleasure + logic: What is the logical shape of claims about pleasure -- e.g. does a person always take pleasure in something or can a person just have pleasure but in nothing in particular? Can pleasure really be quantified? Does it make logical or conceptual sense to talk of 'units of pleasure' or one person having twice as much pleasure as another?<br /> -Pleasure + God: Could God and/or belief in God be a source of happiness or pleasure? If so, of what kind and why? (And does the notion of infinite bliss lasting for eternity make sense?)<br /><br />And 'history of philosophy' perhaps should also be on your list of headings, to lead you to think about what opinions notable philosophers of the past have held on Pleasure -- Plato, Aristotle, Hume or whoever.<br /><br />Thus far you can proceed mechanically, although you should take a few minutes over each pairing in this part of the process. If no questions or ideas present themselves at once when you juxtapose (say) 'pleasure' and 'logic' do not give up instantly, but persevere and try associating from the two concepts in various directions and stirring round in your mind and see if you cannot get them to link up somehow.<br /><br />The next stage is less mechanical and at this point your own creativity and individuality come into play. You should by now have notes of lots of questions (together perhaps with possible answers to them, reminders of opinions which others have held etc.). You should now consider which of these questions you are interested in. You should reflect also on which of them you have (or think you have) defensible answers to. And you should also (very important!) think which of the questions are linked together, so that giving a certain answer to one might commit you to giving a certain answer to another. From this kind of reflection, with any luck, you will begin to see a possible structure for an essay.<br /><br />For example suppose you are initially strongly inclined to think that there are higher and lower forms of pleasure. How then are you to distinguish the levels? One plausible move commits you to saying that pleasure must be taken in something (i.e. commits you to an answer to the question about the logical shape of talk about pleasure), precisely because it seems natural to distinguish the levels of pleasure by saying that higher pleasures are taken by contemplating or somehow interacting with the more valuable things. Butt now you find yourself committed to some kind of objectivism about value. Perhaps this does not seem to you at all congenial! Can you find a way out, by differentiating higher and lower pleasures in some other way? Yes! you remember that there are various proposals here ... But do they work to draw the line between higher and lower where you would like to draw it? Hm -- let's think about various cases ...<br /><br />(Note that in constructing this line of thought many, indeed most, of the questions and ideas generated by the juxtaposing process have been discarded. There is no need to think that you must use in your final essay everything assembled in the initial phase.)<br /><br />Now you can begin to start outlining your essay: an introduction in which you say that what you want to do is show how we can distinguish higher and lower pleasures without committing ourselves to implausibly strong views about the objectivity of value; a first section in which you point our how the various views seem to be connected: another section in which you explain your way out; perhaps there will be various subsections as well. (There will be plenty of scope for examining different kinds of case, comparing and contrasting examples of higher and lower, saying why, according to you, objectivity of value is not a plausible idea, etc. etc.)<br /><br /><br /><span style="font-weight: bold;">Another Example</span><br /><br />Let's consider another example, say 'Knowledge of God'. When faced with such a phrase it might be a good idea to look at each part of it separately, rather than moving instantly to consider the most obvious question which the phrase as a whole suggests.<br /><br /> -Knowledge + ontology: What ontological category does knowledge itself belong to - e.g. is it a state of mind? What ontological categories of things can we know about?<br /> -Knowledge+ epistemology: This looks a bit boring! Not every juxtaposition yields something interesting. But perhaps we are wrong here. Are there special problems in knowing about knowledge? There is indeed an issue about how and whether we can know about definitions of knowledge. When testing a definition we need agreed cases of the thing to be defined to provide tests, but the possibility of sceptical disputes, e.g. about whether we really do know about external objects, makes this sort of testing problematic in the case of knowledge -- so how can we test our attempted definitions?<br /> -Knowledge+ ethics: Should we take responsibility for our own opinions (remember Descartes' view that falling into error was always our own fault?) -- Can we know about values?<br /> -Knowledge+ logic: What is the logical shape of the concept of knowledge? How is knowledge to be defined - e.g. is it justified true belief or is it belief caused by what is known or is it belief acquired by a reliable method? How do we know about necessary truths (as some claims about God are supposed to be)?<br /> -Knowledge+ God: Can we know God exists? Can we know God's properties? It is at this point that the most obvious questions suggested by the phrase 'Knowledge of God' will appear - e.g. Does the ontological argument work? Does the argument from design work? etc.<br /><br />One line of thought which already emerges from this collection (even without going on to do more juxtaposing of 'God' and further concepts) is that consideration of the traditional arguments for the existence of God seem to operate against a background of a justified true belief account of knowledge, in that the object of these traditional arguments is to produce good reasons for believing in the existence of God and the implication of the discussions is that we do not have knowledge of God if all the arguments fail. But what if a causal theory or a reliable method theory of knowledge were correct? Then the failure of the traditional arguments would not show that believers do not have knowledge of God. Someone could have knowledge of God if they had belief in God caused by God or belief in God acquired by some reliable method, even if they couldn't produce any reasons for the belief. Does this make sense? It seems, somehow, to make things too easy for the believer to defend the claim that (perhaps) he/she has knowledge of God. In the case of the external world, many philosophers have fastened on a 'reliable method' account of knowledge as enabling us to defend the idea that we have knowledge of the external world, even when we cannot produce reasons for our beliefs and cannot disarm the sceptical Cartesian Demon arguments. And this has seemed a respectable philosophical position. But is the analogous position vis a vis knowledge of God equally defensible? Is the case of God importantly different from the case of the external world? If so how? Plenty of things could be suggested here ... (And perhaps a line of thought pursuing these issues could weave in the point about the difficulty of testing definitions of knowledge because of the difficulty of knowing which are cases of knowledge?) And so it goes ...<br /><br />Well, the direction your ideas would take is no doubt different. But this is an example of how juxtaposing headings can generate ideas.<br /><br /><br /><span style="font-weight: bold;">Summary</span><br /><br />Whether or not you find the suggested method for generating ideas for your essay useful, the headline points remain clear: Your essay should be<br /><br /> -focused -- don't ramble or offer a disconnected heap of points: plan the essay carefully<br /> -sustained -- at least some threads of argument need to be pursued in detailed<br /> -informed -- show that, on your chosen topic, you know more than the absolutely basic moves<br /> -individual -- show that you have thought for yourself.<br /><br />And if all that sounds daunting, let's finish by noting that (hard as though it might be to believe) quite a few find that -- once into the business and with the adrenalin flowing -- they quite enjoy the experience ...!<br /><br />Good luck!<br /><br /><br /><br /></span>Mikolkahttp://www.blogger.com/profile/06474496860871759825noreply@blogger.com1tag:blogger.com,1999:blog-2437165907915350480.post-18185146747203557212008-06-14T17:34:00.000+02:002008-06-14T17:34:00.724+02:00Comment écrire un article philosophique ? (Jim Pryor)Vous trouverez ici des conseils pratiques et méthodologiques pour écrire un article ou un ouvrage philosophique (version anglaise seulement). L'auteur de ces conseils est Jim Pryor.<span class="fullpost"><br />Le texte se trouve sur la page personnelle de <a href="http://www.jimpryor.net/">Jim Pryor</a>, à <a href="http://www.jimpryor.net/teaching/guidelines/writing.html">Guidelines on Writing a Philosophy Paper</a>, dans <span style="font-style: italic;">Teaching and Advice</span>.<br /><br />Philosophical writing is different from the writing you'll be asked to do in other courses. Most of the strategies described below will also serve you well when writing for other courses, but don't automatically assume that they all will. Nor should you assume that every writing guideline you've been given by other teachers is important when you're writing a philosophy paper. Some of those guidelines are routinely violated in good philosophical prose (e.g., see the guidelines on grammar, below).<br />Contents<br /><br /> * What Does One Do in a Philosophy Paper?<br /> * Three Stages of Writing<br /> * Minor Points<br /> * How You'll Be Graded<br /><br /><span style="font-weight: bold;">What Does One Do in a Philosophy Paper?<span style="font-weight: bold;"></span></span><br /><br /> 1. A philosophy paper consists of the reasoned defense of some claim<br /><br /> Your paper must offer an argument. It can't consist in the mere report of your opinions, nor in a mere report of the opinions of the philosophers we discuss. You have to defend the claims you make. You have to offer reasons to believe them.<br /><br /> So you can't just say:<br /><br /> My view is that P.<br /><br /> You must say something like:<br /><br /> My view is that P. I believe this because...<br /><br /> or:<br /><br /> I find that the following considerations...provide a convincing argument for P.<br /><br /> Similarly, don't just say:<br /><br /> Descartes says that Q.<br /><br /> Instead, say something like:<br /><br /> Descartes says that Q; however, the following thought-experiment will show that Q is not true...<br /><br /> or:<br /><br /> Descartes says that Q. I find this claim plausible, for the following reasons...<br /><br /> There are a variety of things a philosophy paper can aim to accomplish. It usually begins by putting some thesis or argument on the table for consideration. Then it goes on to do one or two of the following:<br /><br /> * Criticize that argument; or show that certain arguments for the thesis are no good<br /> * Defend the argument or thesis against someone else's criticism<br /> * Offer reasons to believe the thesis<br /> * Offer counter-examples to the thesis<br /> * Contrast the strengths and weaknesses of two opposing views about the thesis<br /> * Give examples which help explain the thesis, or which help to make the thesis more plausible<br /> * Argue that certain philosophers are committed to the thesis by their other views, though they do not come out and explicitly endorse the thesis<br /> * Discuss what consequences the thesis would have, if it were true<br /> * Revise the thesis, in the light of some objection<br /><br /> No matter which of these aims you set for yourself, you have to explicitly present reasons for the claims you make. Students often feel that since it's clear to them that some claim is true, it does not need much argument. But it's very easy to overestimate the strength of your own position. After all, you already accept it. You should assume that your audience does not already accept your position; and you should treat your paper as an attempt to persuade such an audience. Hence, don't start with assumptions which your opponents are sure to reject. If you're to have any chance of persuading people, you have to start from common assumptions you all agree to.<br /><br /> 2. A good philosophy paper is modest and makes a small point; but it makes that point clearly and straightforwardly, and it offers good reasons in support of it<br /><br /> People very often attempt to accomplish too much in a philosophy paper. The usual result of this is a paper that's hard to read, and which is full of inadequately defended and poorly explained claims. So don't be over-ambitious. Don't try to establish any earth-shattering conclusions in your 5-6 page paper. Done properly, philosophy moves at a slow pace.<br /><br /> 3. Originality<br /><br /> The aim of these papers is for you to show that you understand the material and that you're able to think critically about it. To do this, your paper does have to show some independent thinking.<br /><br /> That doesn't mean you have to come up with your own theory, or that you have to make a completely original contribution to human thought. There will be plenty of time for that later on. An ideal paper will be clear and straightforward (see below), will be accurate when it attributes views to other philosophers (see below), and will contain thoughtful critical responses to the texts we read. It need not always break completely new ground.<br /><br /> But you should try to come up with your own arguments, or your own way of elaborating or criticizing or defending some argument we looked at in class. Merely summarizing what others have said won't be enough.<br /><br /><br /><br /><span style="font-weight: bold;">Three Stages of Writing:</span><br /><br />1. Early Stages<br />The early stages of writing a philosophy paper include everything you do before you sit down and write your first draft. These early stages will involve writing, but you won't yet be trying to write a complete paper. You should instead be taking notes on the readings, sketching out your ideas, trying to explain the main argument you want to advance, and composing an outline.<br />Discuss the issues with others<br />As I said above, your papers are supposed to demonstrate that you understand and can think critically about the material we discuss in class. One of the best ways to check how well you understand that material is to try to explain it to someone who isn't already familiar with it. I've discovered time and again while teaching philosophy that I couldn't really explain properly some article or argument I thought I understood. This was because it was really more problematic or complicated than I had realized. You will have this same experience. So it's good to discuss the issues we raise in class with each other, and with friends who aren't taking the class. This will help you understand the issues better, and it will make you recognize what things you still don't fully understand.<br /><br />It's even more valuable to talk to each other about what you want to argue in your paper. When you have your ideas worked out well enough that you can explain them to someone else, verbally, then you're ready to sit down and start making an outline.<br /><br />Make an outline<br />Before you begin writing any drafts, you need to think about the questions: In what order should you explain the various terms and positions you'll be discussing? At what point should you present your opponent's position or argument? In what order should you offer your criticisms of your opponent? Do any of the points you're making presuppose that you've already discussed some other point, first? And so on.<br /><br />The overall clarity of your paper will greatly depend on its structure. That is why it is important to think about these questions before you begin to write.<br /><br />I strongly recommend that you make an outline of your paper, and of the arguments you'll be presenting, before you begin to write. This lets you organize the points you want to make in your paper and get a sense for how they are going to fit together. It also helps ensure that you're in a position to say what your main argument or criticism is, before you sit down to write a full draft of your paper. When students get stuck writing, it's often because they haven't yet figured out what they're trying to say.<br /><br />Give your outline your full attention. It should be fairly detailed. (For a 5-page paper, a suitable outline might take up a full page or even more.)<br /><br />I find that making an outline is at least 80% of the work of writing a good philosophy paper. If you have a good outline, the rest of the writing process will go much more smoothly.<br /><br /><br /><br />Start Work Early<br />Philosophical problems and philosophical writing require careful and extended reflection. Don't wait until two or three nights before the paper is due to begin. That is very stupid. Writing a good philosophy paper takes a great deal of preparation.<br /><br />You need to leave yourself enough time to think about the topic and write a detailed outline. Only then should you sit down to write a complete draft. Once you have a complete draft, you should set it aside for a day or two. Then you should come back to it and rewrite it. Several times. At least 3 or 4. If you can, show it to your friends and get their reactions to it. Do they understand your main point? Are parts of your draft unclear or confusing to them?<br /><br />All of this takes time. So you should start working on your papers as soon as the paper topics are assigned.<br /><br />2. Write a Draft<br />Once you've thought about your argument, and written an outline for your paper, then you're ready to sit down and compose a complete draft.<br />Use simple prose<br />Don't shoot for literary elegance. Use simple, straightforward prose. Keep your sentences and paragraphs short. Use familiar words. We'll make fun of you if you use big words where simple words will do. These issues are deep and difficult enough without your having to muddy them up with pretentious or verbose language. Don't write using prose you wouldn't use in conversation: if you wouldn't say it, don't write it.<br /><br />You may think that since your TA and I already know a lot about this subject, you can leave out a lot of basic explanation and write in a super-sophisticated manner, like one expert talking to another. I guarantee you that this will make your paper incomprehensible.<br /><br />If your paper sounds as if it were written for a third-grade audience, then you've probably achieved the right sort of clarity.<br /><br />In your philosophy classes, you will sometimes encounter philosophers whose writing is obscure and complicated. Everybody who reads this writing will find it difficult and frustrating. The authors in question are philosophically important despite their poor writing, not because of it. So do not try to emulate their writing styles.<br />Make the structure of your paper obvious<br />You should make the structure of your paper obvious to the reader. Your reader shouldn't have to exert any effort to figure it out. Beat him over the head with it.<br /><br />How can you do this?<br /><br />First of all, use connective words, like:<br /><br /> * because, since, given this argument<br /> * thus, therefore, hence, it follows that, consequently<br /> * nevertheless, however, but<br /> * in the first case, on the other hand<br /><br />These will help your reader keep track of where your discussion is going. Be sure you use these words correctly! If you say "P. Thus Q." then you are claiming that P is a good reason to accept Q. You had better be right. If you aren't, we'll complain. Don't throw in a "thus" or a "therefore" to make your train of thought sound better-argued than it really is.<br /><br />Another way you can help make the structure of your paper obvious is by telling the reader what you've done so far and what you're going to do next. You can say things like:<br /><br /> * I will begin by...<br /> * Before I say what is wrong with this argument, I want to...<br /> * These passages suggest that...<br /> * I will now defend this claim...<br /> * Further support for this claim comes from...<br /> * For example...<br /><br />These signposts really make a big difference. Consider the following two paper fragments:<br /><br /> ...We've just seen how X says that P. I will now present two arguments that not-P. My first argument is...<br /> My second argument that not-P is...<br /> X might respond to my arguments in several ways. For instance, he could say that...<br /> However this response fails, because...<br /> Another way that X might respond to my arguments is by claiming that...<br /> This response also fails, because...<br /> So we have seen that none of X's replies to my argument that not-P succeed. Hence, we should reject X's claim that P.<br /><br /> I will argue for the view that Q.<br /> There are three reasons to believe Q. Firstly...<br /> Secondly...<br /> Thirdly...<br /> The strongest objection to Q says...<br /> However, this objection does not succeed, for the following reason...<br /><br />Isn't it easy to see what the structure of these papers is? You want it to be just as easy in your own papers.<br /><br />A final thing: make it explicit when you're reporting your own view and when you're reporting the views of some philosopher you're discussing. The reader should never be in doubt about whose claims you're presenting in a given paragraph.<br /><br />You can't make the structure of your paper obvious if you don't know what the structure of your paper is, or if your paper has no structure. That's why making an outline is so important.<br /><br />Be concise, but explain yourself fully<br />To write a good philosophy paper, you need to be concise but at the same time explain yourself fully.<br /><br />These demands might seem to pull in opposite directions. (It's as if the first said "Don't talk too much," and the second said "Talk a lot.") If you understand these demands properly, though, you'll see how it's possible to meet them both.<br /><br /> * We tell you to be concise because we don't want you to ramble on about everything you know about a given topic, trying to show how learned and intelligent you are. Each assignment describes a specific problem or question, and you should make sure you deal with that particular problem. Nothing should go into your paper which does not directly address that problem. Prune out everything else. It is always better to concentrate on one or two points and develop them in depth than to try to cram in too much. One or two well-mapped paths are better than an impenetrable jungle.<br /><br /> Formulate the central problem or question you wish to address at the beginning of your paper, and keep it in mind at all times. Make it clear what the problem is, and why it is a problem. Be sure that everything you write is relevant to that central problem. In addition, be sure to say in the paper how it is relevant. Don't make your reader guess.<br /><br /> * One thing I mean by "explain yourself fully" is that, when you have a good point, you shouldn't just toss it off in one sentence. Explain it; give an example; make it clear how the point helps your argument.<br /><br /> But "explain yourself fully" also means to be as clear and explicit as you possibly can when you're writing. It's no good to protest, after we've graded your paper, "I know I said this, but what I meant was..." Say exactly what you mean, in the first place. Part of what you're being graded on is how well you can do that.<br /><br /> Pretend that your reader has not read the material you're discussing, and has not given the topic much thought in advance. This will of course not be true. But if you write as if it were true, it will force you to explain any technical terms, to illustrate strange or obscure distinctions, and to be as explicit as possible when you summarize what some other philosopher said.<br /><br />Comment: In fact, you can profitably take this one step further and pretend that your reader is lazy, stupid, and mean. He's lazy in that he doesn't want to figure out what your convoluted sentences are supposed to mean, and he doesn't want to figure out what your argument is, if it's not already obvious. He's stupid, so you have to explain everything you say to him in simple, bite-sized pieces. And he's mean, so he's not going to read your paper charitably. (For example, if something you say admits of more than one interpretation, he's going to assume you meant the less plausible thing.) If you understand the material you're writing about, and if you aim your paper at such a reader, you'll probably get an A.<br />Use plenty of examples and definitions<br />It is very important to use examples in a philosophy paper. Many of the claims philosophers make are very abstract and hard to understand, and examples are the best way to make those claims clearer.<br /><br />Examples are also useful for explaining the notions that play a central role in your argument. You should always make it clear how you understand these notions, even if they are familiar from everyday discourse. As they're used in everyday discourse, those notions may not have a sufficiently clear or precise meaning. For instance, suppose you're writing a paper about abortion, and you want to assert the claim "A fetus is a person." What do you mean by "a person"? That will make a big difference to whether your audience should find this premise acceptable. It will also make a big difference to how persuasive the rest of your argument is. By itself, the following argument is pretty worthless:<br /><br /> A fetus is a person.<br /> It's wrong to kill a person.<br /> Therefore, it's wrong to kill a fetus.<br /><br />For we don't know what the author means by calling a fetus "a person." On some interpretations of "person," it might be quite obvious that a fetus is a person; but quite controversial whether it's always wrong to kill persons, in that sense of "person." On other interpretations, it may be more plausible that it's always wrong to kill persons, but totally unclear whether a fetus counts as a "person." So everything turns here on what the author means by "person." The author should be explicit about how he is using this notion.<br /><br />In a philosophy paper, it's okay to use words in ways that are somewhat different from the ways they're ordinarily used. You just have to make it clear that you're doing this. For instance, some philosophers use the word "person" to mean any being which is capable of rational thought and self-awareness. Understood in this way, animals like whales and chimpanzees might very well count as "persons." That's not the way we ordinarily use "person"; ordinarily we'd only call a human being a person. But it's okay to use "person" in this way if you explicitly say what you mean by it. And likewise for other words.<br /><br />Don't vary your vocabulary just for the sake of variety<br /><br /> If you call something "X" at the start of your paper, call it "X" all the way through. So, for instance, don't start talking about "Plato's view of the self," and then switch to talking about "Plato's view of the soul," and then switch to talking about "Plato's view of the mind." If you mean to be talking about the same thing in all three cases, then call it by the same name. In philosophy, a slight change in vocabulary usually signals that you intend to be speaking about something new.<br /><br />Using words with precise philosophical meanings<br /><br /> Philosophers give many ordinary-sounding words precise technical meanings. Consult the handouts on Philosophical Terms and Methods to make sure you're using these words correctly. Don't use words that you don't fully understand.<br /><br /> Use technical philosophical terms only where you need them. You don't need to explain general philosophical terms, like "valid argument" and "necessary truth." But you should explain any technical terms you use which bear on the specific topic you're discussing. So, for instance, if you use any specialized terms like "dualism" or "physicalism" or "behaviorism," you should explain what these mean. Likewise if you use technical terms like "supervenience" and the like. Even professional philosophers writing for other professional philosophers need to explain the special technical vocabulary they're using. Different people sometimes use this special vocabulary in different ways, so it's important to make sure that you and your readers are all giving these words the same meaning. Pretend that your readers have never heard them before.<br /><br />Presenting and assessing the views of others<br />If you plan to discuss the views of Philosopher X, begin by figuring out what his arguments or central assumptions are. See my tips on How To Read a Philosophy Paper for some help doing this.<br /><br />Then ask yourself: Are X's arguments good ones? Are his assumptions clearly stated? Are they plausible? Are they reasonable starting-points for X's argument, or ought he have provided some independent argument for them?<br /><br />Make sure you understand exactly what the position you're criticizing says. Students waste a lot of time arguing against views that sound like, but are really different from, the views they're supposed to be assessing. Remember, philosophy demands a high level of precision. It's not good enough for you merely to get the general idea of somebody else's position or argument. You have to get it exactly right. (In this respect, philosophy is more like a science than the other humanities.) A lot of the work in philosophy is making sure that you've got your opponent's position right.<br /><br />You can assume that your reader is stupid (see above). But don't treat the philosopher or the views you're discussing as stupid. If they were stupid, we wouldn't be looking at them. If you can't see anything the view has going for it, maybe that's because you don't have much experience thinking and arguing about the view, and so you haven't yet fully understood why the view's proponents are attracted to it. Try harder to figure out what's motivating them.<br /><br />Philosophers sometimes do say outrageous things, but if the view you're attributing to a philosopher seems to be obviously crazy, then you should think hard about whether he really does say what you think he says. Use your imagination. Try to figure out what reasonable position the philosopher could have had in mind, and direct your arguments against that.<br /><br />In your paper, you always have to explain what a position says before you criticize it. If you don't explain what you take Philosopher X's view to be, your reader cannot judge whether the criticism you offer of X is a good criticism, or whether it is simply based on a misunderstanding or misinterpretation of X's views. So tell the reader what it is you think X is saying.<br /><br />Don't try to tell the reader everything you know about X's views, though. You have to go on to offer your own philosophical contribution, too. Only summarize those parts of X's views that are directly relevant to what you're going to go on to do.<br /><br />Sometimes you'll need to argue for your interpretation of X's view, by citing passages which support your interpretation. It is permissible for you to discuss a view you think a philosopher might have held, or should have held, though you can't find any direct evidence of that view in the text. When you do this, though, you should explicitly say so. Say something like:<br /><br /> Philosopher X doesn't explicitly say that P, but it seems to me that he's assuming it anyway, because...<br /><br />Quotations<br /><br /> When a passage from a text is particularly useful in supporting your interpretation of some philosopher's views, it may be helpful to quote the passage directly. (Be sure to specify where the passage can be found.) However, direct quotations should be used sparingly. It is seldom necessary to quote more than a few sentences. Often it will be more appropriate to paraphrase what X says, rather than to quote him directly. When you are paraphrasing what somebody else said, be sure to say so. (And here too, cite the pages you're referring to.)<br /><br /> Quotations should never be used as a substitute for your own explanation. And when you do quote an author, you still have to explain what the quotation says in your own words. If the quoted passage contains an argument, reconstruct the argument in more explicit, straightforward terms. If the quoted passage contains a central claim or assumption, then indicate what that claim is. You may want to give some examples to illustrate the author's point. If necessary, you may want to distinguish the author's claim from other claims with which it might be confused.<br /><br />Paraphrases<br /><br /> Sometimes when students are trying to explain a philosopher's view, they'll do it by giving very close paraphrases of the philosopher's own words. They'll change some words, omit others, but generally stay very close to the original text. For instance, Hume begins his Treatise of Human Nature as follows:<br /><br /> All the perceptions of the human mind resolve themselves into two distinct kinds, which I shall call impressions and ideas. The difference betwixt these consists in the degrees of force and liveliness, with which they strike upon the mind, and make their way into our thought or consciousness. Those perceptions, which enter with most force and violence, we may name impressions; and under this name I comprehend all our sensations, passions, and emotions, as they make their first appearance in the soul. By ideas I mean the faint images of these in thinking and reasoning.<br /><br /> Here's an example of how you don't want to paraphrase:<br /><br /> Hume says all perceptions of the mind are resolved into two kinds, impressions and ideas. The difference is in how much force and liveliness they have in our thoughts and consciousness. The perceptions with the most force and violence are impressions. These are sensations, passions, and emotions. Ideas are the faint images of our thinking and reasoning.<br /><br /> There are two main problems with paraphrases of this sort. In the first place, it's done rather mechanically, so it doesn't show that the author understands the text. In the second place, since the author hasn't figured out what the text means well enough to express it in his own words, there's a danger that his paraphrase may inadvertently change the meaning of the text. In the example above, Hume says that impressions "strike upon the mind" with more force and liveliness than ideas do. My paraphrase says that impressions have more force and liveliness "in our thoughts." It's not clear whether these are the same thing. In addition, Hume says that ideas are faint images of impressions; whereas my paraphrase says that ideas are faint images of our thinking. These are not the same. So the author of the paraphrase appears not to have understood what Hume was saying in the original passage.<br /><br /> A much better way of explaining what Hume says here would be the following:<br /><br /> Hume says that there are two kinds of 'perceptions,' or mental states. He calls these impressions and ideas. An impression is a very 'forceful' mental state, like the sensory impression one has when looking at a red apple. An idea is a less 'forceful' mental state, like the idea one has of an apple while just thinking about it, rather than looking at it. It is not so clear what Hume means here by 'forceful.' He might mean...<br /><br /><br /><br />Anticipate objections<br />Try to anticipate objections to your view and respond to them. For instance, if you object to some philosopher's view, don't assume he would immediately admit defeat. Imagine what his comeback might be. How would you handle that comeback?<br /><br />Don't be afraid of mentioning objections to your own thesis. It is better to bring up an objection yourself than to hope your reader won't think of it. Explain how you think these objections can be countered or overcome. Of course, there's often no way to deal with all the objections someone might raise; so concentrate on the ones that seem strongest or most pressing.<br /><br />What happens if you're stuck?<br />Your paper doesn't always have to provide a definite solution to a problem, or a straight yes or no answer to a question. Many excellent philosophy papers don't offer straight yes or no answers. Sometimes they argue that the question needs to be clarified, or that certain further questions need to be raised. Sometimes they argue that certain assumptions of the question need to be challenged. Sometimes they argue that certain answers to the question are too easy, that is, they won't work. Hence, if these papers are right, the question will be harder to answer than we might previously have thought. These are all important and philosophically valuable results.<br /><br />So it's OK to ask questions and raise problems in your paper even if you cannot provide satisfying answers to them all. You can leave some questions unanswered at the end of the paper. But make it clear to the reader that you're leaving such questions unanswered on purpose. And you should say something about how the question might be answered, and about what makes the question interesting and relevant to the issue at hand.<br /><br />If something in a view you're examining is unclear to you, don't gloss it over. Call attention to the unclarity. Suggest several different ways of understanding the view. Explain why it's not clear which of these interpretations is correct.<br /><br />If you're assessing two positions and you find, after careful examination, that you can't decide between them, that's okay. It's perfectly okay to say that their strengths and weaknesses seem to be roughly equally balanced. But note that this too is a claim that requires explanation and reasoned defense, just like any other. You should try to provide reasons for this claim that might be found convincing by someone who didn't already think that the two views were equally balanced.<br /><br />Sometimes as you're writing, you'll find that your arguments aren't as good as you initially thought them to be. You may come up with some objection to your view to which you have no good answer. Don't panic. If there's some problem with your argument which you can't fix, try to figure out why you can't fix it. It's okay to change your thesis to one you can defend. For example, instead of writing a paper which provides a totally solid defense of view P, you can instead change tactics and write a paper which goes like this:<br /><br /> One philosophical view says that P. This is a plausible view, for the following reasons...<br /> However, there are some reasons to be doubtful whether P. One of these reasons is X. X poses a problem for the view that P because...<br /> It is not clear how the defender of P can overcome this objection.<br /><br />Or you can write a paper which goes:<br /><br /> One argument for P is the 'Conjunction Argument,' which goes as follows...<br /> At first glance, this is a very appealing argument. However, this argument is faulty, for the following reasons...<br /> One might try to repair the argument, by...<br /> But these repairs will not work, because...<br /> I conclude that the Conjunction Argument does not in fact succeed in establishing P.<br /><br />Writing a paper of these sorts doesn't mean you've "given in" to the opposition. After all, neither of these papers commits you to the view that not-P. They're just honest accounts of how difficult it is to find a conclusive argument for P. P might still be true, for all that.<br /><br />3. Rewrite, and Keep Rewriting<br />Now you've written a complete draft of your paper. Set the draft aside for a day or two.<br /><br />Then come back to the draft and re-read it. As you read each sentence, say things like this to yourself:<br /><br /> "Does this really make sense?" "That's totally unclear!" "That sounds pretentious." "What does that mean?" "What's the connection between these two sentences?" "Am I just repeating myself here?" and so on.<br /><br />Make sure every sentence in your draft does useful work. Get rid of any which don't. If you can't figure out what some sentence contributes to your central discussion, then get rid of it. Even if it sounds nice. You should never introduce any points in your paper unless they're important to your main argument, and you have the room to really explain them.<br /><br />If you're not happy with some sentence in your draft, ask yourself why it bothers you. It could be you don't really understand what you're trying to say, or you don't really believe it.<br /><br />Make sure your sentences say exactly what you want them to say. For example, suppose you write "Abortion is the same thing as murder." Is that what you really mean? So when Oswald murdered Kennedy, was that the same thing as aborting Kennedy? Or do you mean something different? Perhaps you mean that abortion is a form of murder. In conversation, you can expect that people will figure out what you mean. But you shouldn't write this way. Even if your TA is able to figure out what you mean, it's bad writing. In philosophical prose, you have to be sure to say exactly what you mean.<br /><br />Also pay attention to the structure of your draft. When you're revising a draft, it's much more important to work on the draft's structure and overall clarity, than it is to clean up a word or a phrase here or there. Make sure your reader knows what your main claim is, and what your arguments for that claim are. Make sure that your reader can tell what the point of every paragraph is. It's not enough that you know what their point is. It has to be obvious to your reader, even to a lazy, stupid, and mean reader.<br /><br />If you can, show your draft to your friends or to other students in the class, and get their comments and advice. I encourage you to do this. Do your friends understand your main point? Are parts of your draft unclear or confusing to them? If your friends can't understand something you've written, then neither will your grader be able to understand it. Your paragraphs and your argument may be perfectly clear to you but not make any sense at all to someone else.<br /><br />Another good way to check your draft is to read it out loud. This will help you tell whether it all makes sense. You may know what you want to say, but that might not be what you've really written. Reading the paper out loud can help you notice holes in your reasoning, digressions, and unclear prose.<br /><br />You should count on writing many drafts of your paper. At least 3 or 4!! Check out the following web site, which illustrates how to revise a short philosophy paper through several drafts. Notice how much the paper improves with each revision:<br /><br /> * Writing tutor for Introductory Philosophy Courses <http:>.<br /><br /><br /><br /><span style="font-weight: bold;">Minor Points:</span><br />Beginning your paper<br />Don't begin with a sentence like "Down through the ages, mankind has pondered the problem of..." There's no need to warm up to your topic. You should get right to the point, with the first sentence.<br /><br />Also, don't begin with a sentence like "Webster's Dictionary defines a soul as..." Dictionaries aren't good philosophical authorities. They record the way words are used in everyday discourse. Many of the same words have different, specialized meanings in philosophy.<br />Grammar<br /><br /> * It's OK to end a sentence with a preposition. It's also OK to split an infinitive, if you need to. (Sometimes the easiest way to say what you mean is by splitting an infinitive. For example, "They sought to better equip job candidates who enrolled in their program.") Efforts to avoid these often end up just confusing your prose.<br /><br /> * Do avoid other sorts of grammatical mistakes, like dangling participles (e.g., "Hurt by her fall, the tree fell right on Mary's leg before she could get out of the way"), and the like.<br /><br /> * You may use the word "I" freely, especially to tell the reader what you're up to (e.g., "I've just explained why... Now I'm going to consider an argument that...").<br /><br /> * Don't worry about using the verb "is" or "to be" too much. In a philosophy paper, it's OK to use this verb as much as you need to.<br /><br />Secondary readings<br />For most classes, I will put some articles and books on reserve in Bobst Library for additional reading. These are optional, and are for your independent study.<br /><br />You shouldn't need to use these secondary readings when writing your papers. The point of the papers is to teach you how to analyze a philosophical argument, and present your own arguments for or against some conclusion. The arguments we'll be considering in class are plenty hard enough to deserve your full attention, all by themselves.<br />Can you write your paper as a dialogue or story?<br />No. Done well, these forms of philosophical writing can be very effective. That's why we read some dialogues and stories in Philosophy 3. But these forms of philosophical writing are extremely difficult to do well. They tempt the author to be imprecise and to use unclear metaphors. You need to master ordinary philosophical writing before you can do a good job with these more difficult forms.<br /><br />Mechanics<br />Aim to make your papers less than or equal to the assigned word limit. Longer papers are typically too ambitious, or repetitious, or full of digressions. Your grade will suffer if your paper has these defects. So it's important to ask yourself: What are the most important things you have to say? What can be left out?<br /><br />But neither should your papers be too short! Don't cut off an argument abruptly. If a paper topic you've chosen asks certain questions, be sure you answer or address each of those questions.<br /><br />Please double-space your papers, number the pages, and include wide margins. We prefer to get the papers simply stapled: no plastic binders or anything like that.<br /><br />Include your name on the paper. And don't turn in your only copy! (These things should be obvious, but apparently they're not.)<br /><br /><br /><br /><span style="font-weight: bold;">How You'll Be Graded:</span><br /><br />You'll be graded on three basic criteria:<br /><br /> 1. How well do you understand the issues you're writing about?<br /> 2. How good are the arguments you offer?<br /> 3. Is your writing clear and well-organized?<br /> We do not judge your paper by whether we agree with its conclusion. In fact, we may not agree amongst ourselves about what the correct conclusion is. But we will have no trouble agreeing about whether you do a good job arguing for your conclusion.<br /><br /> More specifically, we'll be asking questions like these:<br /> o Do you clearly state what you're trying to accomplish in your paper? Is it obvious to the reader what your main thesis is?<br /><br /> o Do you offer supporting arguments for the claims you make? Is it obvious to the reader what these arguments are?<br /><br /> o Is the structure of your paper clear? For instance, is it clear what parts of your paper are expository, and what parts are your own positive contribution?<br /><br /> o Is your prose simple, easy to read, and easy to understand?<br /><br /> o Do you illustrate your claims with good examples? Do you explain your central notions? Do you say exactly what you mean?<br /><br /> o Do you present other philosophers' views accurately and charitably?<br /><br /> Comment: The comments I find myself making on students' philosophy papers most often are these:<br /><br /> o "Explain this claim" or "What do you mean by this?" or "I don't understand what you're saying here"<br /> o "This passage is unclear (or awkward, or otherwise hard to read)" "Too complicated" "Too hard to follow" "Simplify"<br /> o "Why do you think this?" "This needs more support" "Why should we believe this?" "Explain why this is a reason to believe P" "Explain why this follows from what you said before"<br /> o "Not really relevant"<br /> o "Give an example?"<br /><br /> Try to anticipate these comments and avoid the need for them!<br /><br /> Your paper should do some philosophical work<br /> A kind of complaint that is common in undergraduate philosophy papers goes like this:<br /><br /> Philosopher X assumes A and argues from there to B. B seems unattractive to me. Philosopher X just assumes A and doesn't give any argument for it. I don't think A is true. So I can just reject A and thereby avoid B.<br /><br /> This line of thought may very well be correct. And the student may very well be right that Philosopher X should have given more argument for A. But the student hasn't really philosophically engaged with Philosopher X's view in an interesting way. He hasn't really done much philosophical work. It was clear from the outset that Philosopher X was assuming A, and that if you don't want to make that assumption, you don't need to accept X's conclusion. If this is all you do in your paper, it won't be a strong paper and it will get a mediocre grade, even if it's well-written.<br /><br /> Here are some more interesting things our student could have done in his paper. He could have argued that B doesn't really follow from A, after all. Or he could have presented reasons for thinking that A is false. Or he could have argued that assuming A is an illegitimate move to make in a debate about whether B is true. Or something else of that sort. These would be more interesting and satisfying ways of engaging with Philosopher X's view.<br /> Responding to comments from me or your TA<br /> When you have the opportunity to rewrite a graded paper, keep the following points in mind.<br /><br /> Your rewrites should try to go beyond the specific errors and problems we've indicated. If you got below an A-, then your draft was generally difficult to read, it was difficult to see what your argument was and what the structure of your paper was supposed to be, and so on. You can only correct these sorts of failings by rewriting your paper from scratch. (Start with a new, empty window in your word processor.) Use your draft and the comments you received on it to construct a new outline, and write from that.<br /><br /> Keep in mind that when I or your TA grade a rewrite, we may sometimes notice weaknesses in unchanged parts of your paper that we missed the first time around. Or perhaps those weaknesses will have affected our overall impression of the paper, and we just didn't offer any specific recommendation about fixing them. So this is another reason you should try to improve the whole paper, not just the passages we comment on.<br /><br /> It is possible to improve a paper without improving it enough to raise it to the next grade level. Sometimes that happens. But I hope you'll all do better than that.<br /><br /> Most often, you won't have the opportunity to rewrite your papers after they've been graded. So you need to teach yourself to write a draft, scrutinize the draft, and revise and rewrite your paper before turning it in to be graded.<br /><br /><br /><span style="font-weight: bold;">Acknowledgements</span><br />I don't want to claim undue credit for this work. A lot of the suggestions here derive from writing handouts that friends and colleagues lent me. (Alison Simmons and Justin Broackes deserve special thanks.) Also, I've browsed some other writing guidelines on the web, and occasionally incorporated advice I thought my students would find useful. Peter Horban's site deserves special mention. Thanks to Professor Horban for allowing me to incorporate some of his suggestions here.<br /><br />Naturally, I owe a huge debt to the friends and professors who helped me learn how to write philosophy. I'm sure they had a hard time of it.<br /><br />If you're a teacher and you think your own students would find this web site useful, you are free to point them here (or to distribute printed copies). It's all in the public good.<br /><br /><br /></http:></span>Mikolkahttp://www.blogger.com/profile/06474496860871759825noreply@blogger.com0tag:blogger.com,1999:blog-2437165907915350480.post-86862003209248604562008-06-11T17:17:00.000+02:002008-06-11T17:34:50.157+02:00Comment lire un article philosophique? (Jim Pryor)Vous trouverez ici des conseils pratiques et méthodologiques pour lire un article ou un ouvrage philosophique (version anglaise seulement). L'auteur de ces conseils est Jim Pryor.<span class="fullpost"><br />Le texte se trouve sur la page personnelle de <a href="http://www.jimpryor.net/">Jim Pryor</a>, à <a href="http://www.jimpryor.net/teaching/guidelines/reading.html">Guidelines on Reading Philosophy</a>, dans <span style="font-style: italic;">Teaching and Advice</span>.<br /><br /><br /><span style="font-weight: bold;">Skim the Article to Find its Conclusion and Get a Sense of its Structure:</span><br />A good way to begin when you're trying to read a difficult article is to first skim the article to identify what the author's main conclusion is. Pay special attention to the opening and closing paragraphs, since authors will often tell you there what they intend to be arguing for. When you do figure out what the author's main conclusion is, try to restate it in your own words. This will help you to be sure that you really understand what the author is arguing for.<br />When you're skimming the article, try also to get a general sense of what's going on in each part of the discussion. What is the structure of the article? Sometimes authors will tell you, early in the paper, what their argument will look like. This makes your job easier.<br />The articles we read won't always have a straightforward structure. They won't always be of the form: "This is the conclusion I want you to accept. Here is my argument for that conclusion... "<br />Philosophers often provide auxiliary arguments, arguments for important premises they appeal to in support of their main conclusion. For instance, the author's discussion may have the form:<br /><br /> "The conclusion I want you to accept is A. My argument for this conclusion is as follows: B and C are true, and if B and C are true, then A must also be true. It is generally accepted that B is true. However, it is controversial whether C is true. I think you ought to accept C for the following reasons... "<br /><br />Here the author's main argument is for the conclusion A, and in the process of arguing for A he advances an auxiliary argument in support of C. Try to identify these auxiliary arguments, and the claims they're intended to support; and try to avoid mistaking one of these auxiliary arguments for the author's main argument.<br />Articles can be complex in other ways, too. Not everything the author says will be a positive conclusion or a premise in support of his conclusion. Sometimes he'll be supporting his view with a thought-experiment. Sometimes he'll be arguing for a distinction which his positive view relies on. Sometimes he'll be arguing that another philosopher's views or arguments ought to be rejected. Sometimes he'll be defending a view against somebody else's objections.<br />Keep an eye out for words like these when you're reading:<br /> * because, since, given this argument<br /> * thus, therefore, hence, it follows that, consequently<br /> * nevertheless, however, but<br /> * in the first case, on the other hand<br />These are signposts which help you keep track of the structure of the discussion. For example, one philosophy article might run as follows:<br /> Philosopher X advanced the following argument against dualism...<br /> The dualist has two responses to X's argument. First...<br /> However, this response runs into problems, because...<br /> A better response for the dualist says...<br /> X might be tempted to counter as follows... However...<br /><br />and so on. The words "first" and "however" and "a better response" make it easy to see where the discussion is going. You'll also want to put signposts like these in your own philosophical writing.<br /><br />Here's another example:<br /> The skeptic says that we can't tell whether we're seeing things as they really are, or whether we're brains in vats being force-fed false experiences, like the inhabitants of The Matrix.<br /> Y raised the following objection to the skeptic... Hence, Y concludes, we have no reason to think our situation is as bad as the skeptic makes it out to be.<br /> This is an attractive response to the skeptic, but I don't think it can really work, for the following reason...<br /> Y might respond to this problem in one of two ways. The first way is... However, this response fails because...<br /> The second way Y might respond is... However, this response also fails because...<br /> So in the end I think Y's objection to the skeptic can not be sustained. Of course, I'm not myself a skeptic. I agree with Y that the skeptic's conclusion is false. But I think we'll have to look harder to see where the flaw in the skeptic's reasoning really is.<br />In this article, the author spends most of his time defending the skeptic against Y's objections, and considering possible responses that Y might give. The author's main conclusion is that Y's objection to the skeptic does not work. (Notice: the main conclusion isn't that skepticism is true.)<br /><br /><br /><br /><span style="font-weight: bold;">Go Back and Read the Article Carefully:</span><br />When you've figured out what the main conclusion of an article is, and what the overall structure of the article is, go back and read the article carefully. Pay attention to how the various parts fit together.<br /> * Most importantly, figure out what the author's central argument(s) are. What reasons does he offer in support of his conclusions? Where in the article does he put these reasons forward?<br /><br />Also keep an eye out for the following:<br /> * Notice where the author says explicitly what he means by a certain term.<br /> * Notice what distinctions the author introduces or argues for.<br /> * Take special notice of any unargued assumptions you think the author is relying on.<br /> * Consider various interpretations of what he says. Are there any important ambiguities that his argument fails to take account of?<br /><br />All of these things will help you to understand the article better. And they'll be crucial when you're trying to evaluate the author's argument, and deciding whether or not you should accept his conclusion.<br />In your notes, you might make a quick outline of the article's major argumentative "pieces." Draw arrows to diagram how you think those pieces fit together. If you can't do this, then you need to go back and look at the article again to get a better understanding of what the author is up to.<br />You should expect to read a philosophy article more than once. I've been doing philosophy for more than ten years and I still have to read articles many times before I fully understand them. Intellectually digesting a philosophy article takes time, effort, and concentration. You definitely won't understand everything in the article the first time you read it, and there may be some parts of the article you don't understand even after reading them several times. You should ask questions about these parts of the article (in class or after class or in section, as you judge appropriate). You could say:<br /> What is going on on p. 13? Descartes says X, but I don't see how this fits in with his earlier claim Z. Is X supposed to follow from Z? Or is he trying here to give an argument for Z? If so, why does he think that X would be a reason in favor of Z?<br /><br /><br /><br /><span style="font-weight: bold;">Evaluate the Author's Arguments:</span><br />Obviously, you're only in a position to evaluate an author's argument when you've done the work of figuring out what it is he's really saying, and how his arguments work.<br />When you come to that point, you can start asking questions like these: Do you agree with the author? If not, what do you think is wrong with his reasoning? Does he appeal to some premise which you think is false? (Why do you think it is false?) Is there some assumption which the author does not make explicit, but which you think is false? Does his argument equivocate or beg the question?<br />You will often feel that the debates we examine are tangled messes and you don't know whose argument to believe. There's no escaping this. I feel this way all the time. All I can say is, if you work hard, you will be able to make some sense of the mess. You'll start to get a sense of how the different views relate to each other and what their pros and cons are. Eventually, you may realize that things are even messier than you thought, which will be frustrating, and you'll have to go back to the drawing board. This can happen over and over again. You may never reach any definitive conclusion. But each time you try to make sense of the debate, you'll find you understand the issues a little bit better. That's the way we make progress in philosophy. It never gets easier than that.<br />Sometimes one philosophical issue leads into three other issues, which themselves lead into yet other issues... and you can't possibly explore all of the relevant connections right then. So you'll have to learn to make do without definitive answers. You may not be able to come to a settled view about whether you should accept some philosopher's argument, because that turns on further issues P, Q, and R, which you haven't figured out yet. That's perfectly normal. Your philosophy professors often feel this way themselves, about many of the arguments they read.<br />Other times, you may be sure that some argument is flawed, but you won't have the time and resources to figure out, or explain and argue for, everything you think is wrong with the argument. In such cases, you may want to provisionally accept one of the argument's premises, and move on to focus on other premises, which you think are more important or which are easier to criticize. (This is why you often hear philosophers saying, "Even if we assume such-and-such for argument's sake, I still think X's argument fails, because...").<br /><br /><br /></span>Mikolkahttp://www.blogger.com/profile/06474496860871759825noreply@blogger.com0tag:blogger.com,1999:blog-2437165907915350480.post-70121238858540921422008-05-17T14:21:00.000+02:002008-05-17T14:44:48.302+02:00Le Mathématicien et l'histoire des mathématiquesDans ce billet, je propose la structure d'un traitement du sujet "Le Mathématicien et l'histoire des mathématiques".<br />La méthodologie n'est pas respectée à la lettre. En effet, cette dissertation a plus d'exemples que l'usage ne le veut et les exemples sont amplement développés. Le lecteur trouvera ici des éléments d'histoire des mathématiques.<br /><br /><span class="fullpost"><br /><br /><br /><br /><br /><br /><span style="font-weight: bold;">Introduction :</span><br /><br />Les mathématiques sont un ensemble de disciplines qui se concentre sur des objets spécifiques (nombre, figure, structure) et qui a un ensemble de méthode qui leur sont propres (démonstration par récurrence, par l’absurde, déduction…). À la différence des autres sciences, les objets des mathématiques sont a priori. Les autres sciences, comme la physique ou la biologie, présupposent toujours l’existence d’un objet, même si cette existence est implicite et non démontrée. Elles s’efforcent de rendre compte par des lois des phénomènes réels. En revanche, les mathématiques ne sont pas une physique du nombre ou de la figure. Ces objets sont a priori, c’est-à-dire qu’ils sont indépendants de tout contenu sensible et sans position d’existence. Par conséquent, le mathématicien n’exerce son activité sans se poser la question du fondement réel ou de l’adéquation de ses objets avec la réalité.<br />Toutefois, l’histoire des mathématiques dément l’uniformité de la méthode et des objets des mathématiques. Autrement dit, le mathématicien n’a pas toujours utilisé la même méthode et n’a pas toujours calculé sur les mêmes types d’objets. Des objets sont apparus (la probabilité au 17ème siècle, les géométries non planes au 19ème siècle), des méthodes ont été discutées (la crise des fondements et de l’axiomatisation au début du 20ème siècle). Par conséquent, les mathématiques sont à la fois anhistoriques et soumises aux déterminations historiques. Le mathématicien n’est pas celui qui a accès à un monde intemporel, uniforme et homogène. Le mathématicien est soumis à une histoire et il peut avoir divers rapport avec l’histoire de sa propre discipline. Quels sont les rapports du mathématicien à l’histoire de sa discipline ? L’histoire des mathématiques peut-elle apporter quelque chose au mathématicien ?<br />L’enjeu est de savoir si l’histoire des mathématiques peut être un moyen, pour le mathématicien, de mieux connaître les forces et les faiblesses de sa discipline, afin d’obtenir des résultats consistants. Pour répondre à cette question, on se demandera si le mathématicien peut se rapporter de manière totalement anhistorique au passé de sa discipline, en n’y voyant que des systèmes formels plus ou moins bien réalisés. Toutefois, ce que l’histoire des mathématiques lui montre, ce n’est pas seulement l’absence d’achèvement de la raison dans des œuvres mathématiques du passé, mais les ruptures, les genèses manquées, repoussées, qui peuvent le conduire à douter de la validité de sa discipline. Enfin, puisque le mathématicien n’est pas intéressé par la narration de la genèse des propositions mathématiques, mais par les manières de résoudre des problèmes, il aura tendance à avoir un rapport sélectif ou éliminatif au recueil des faits mathématiques.<br /><br /><br /><br /><span style="font-weight: bold;">A) Le mathématicien peut-il se rapporter de manière anhistorique à l’histoire des mathématiques ? </span><br /><br /> a) Un mathématicien a-t-il besoin des déterminations historiques d’une œuvre d’un collègue pour s’en servir ?<br /><br />-Il semblerait qu’un mathématicien puisse produire des résultats pertinents à partir de données empruntées à un autre mathématicien sans tenir compte des déterminations, des conditions historiques de la production mathématique.<br />-Exemple : le lyonnais Girard Desargues (1591-1661) publie en 1639 son <span style="font-style: italic;">Brouillon project d’une atteinte aux événements des rencontres du cône</span> avec un plan en 50 exemplaires. Il n’est pas un mathématicien professionnel et ne s’intéresse principalement qu’aux applications des mathématiques. Il entend faire profiter les peintres, les architectes, les ingénieurs et les tailleurs de pierre de ses découvertes dans les coniques. Pascal, en revanche, ne s’intéresse pas aux applications de la géométrie projective ou en perspective. Toutefois, il va rapidement assimiler les méthodes et les résultats de Desargues pour rédiger son petit traité sur les coniques (perdu, mais mentionné par Leibniz dans une lettre au neveu de Pascal) et son <span style="font-style: italic;">Essai sur les coniques</span> (retrouvé en 1779) écrit en 1640. Il s’en sert pour établir la démonstration de l’hexagramme mystique.<br />-Par conséquent, sans culture historique, sans tenir compte des conditions de la production, Pascal s’empare des travaux d’un prédécesseur pour résoudre les problèmes mathématiques qu’il se pose.<br /><br /><br /> b) Si un mathématicien peut s’emparer des méthodes et des résultats d’un autre, cela implique-t-il que le pillage est le mode principal du rapport entre les mathématiciens et leur histoire ?<br /><br />-Au contraire, le mathématicien ne s’intéresse qu’aux travaux des grands mathématiciens dans l’histoire qu’il tente de continuer. Le mathématicien entreprend un dialogue avec ses prédécesseurs.<br />-Kant, <span style="font-style: italic;">Critique de la faculté de Juger</span>, §32 : « Que l’on vante à bon droit les œuvres des Anciens comme des modèles et qu’on désigne leurs auteurs comme s’ils constituaient parmi les écrivains une certaine noblesse qui, par l’exemple qu’elle donne, fournit au peuple des lois, cela semble faire référence à des sources a posteriori du goût et réfuter l’autonomie de celui-ci en chaque sujet. Seulement, on pourrait tout aussi bien dire que les anciens mathématiciens, tenus jusqu'à aujourd’hui pour des modèles quasi indispensables de la radicalité et de l’élégance souveraine de la méthode synthétique, prouvent que, de notre côté, la raison est là aussi imitatrice et témoignent de son impuissance à produire d’elle-même des démonstrations rigoureuses procédant avec la plus haute intuition par construction de concepts. Il n’existe absolument aucun usage de nos forces, si libre qu’il puisse être, ni même de la raison (laquelle doit puiser a priori tous ses jugements à la source commune), qui ne s’engagerait dans des tentatives manquées si chaque sujet devait toujours partir intégralement des dispositions brutes, et si d’autres ne l’avaient précédé à travers leurs propres recherches ; non pas pour faire que leurs successeurs deviennent de simples imitateurs, mais pour en mettre d’autres sur la voie de leur démarche, afin qu’ils cherchent en eux-mêmes les principes, et suivent ainsi leur chemin propre, souvent meilleur. »<br />-Quand un mathématicien étudie les travaux d’un autre, il ne vient pas nécessairement s’emparer, piller des résultats et des méthodes. Selon Kant, il vient y chercher le moyen de « suivre son chemin » en imitant l’esprit, la raison à l’œuvre dans l’histoire.<br /><br /><br /> c) Si le mathématicien ne voit que la raison à l’œuvre dans le passé des mathématiques, cela implique-t-il que le mathématicien ne s’intéresse pas aux problèmes mathématiques du passé ?<br /><br />-Les problèmes mathématiques ne sont pas envisagés d’un point de vue historique, mais d’un point de vue anhistorique. Les mathématiciens s’intéressent donc aux problèmes du passé sans chercher à accroître leur érudition ou établir fidèlement l’ensemble du corpus mathématique. Les mathématiciens reprennent les problèmes du passé, les formalisent autrement, tentent d’en apporter de nouvelles démonstrations.<br />-Exemple : le 5ème postulat d’Euclide (<span style="font-style: italic;">Les Éléments</span>, Livre I) : par un point pris hors d'une droite il passe une et une seule parallèle à cette droite. C’est l’un des axiomes géométriques qui permettent de construire la géométrie plane. De l’Antiquité au 19ème siècle, ce postulat est continûment pris dans une tentative de clarification. Deux tentatives principales concurrentes sont présentes : a) celle qui tente de se débarrasser de ce postulat et de le remplacer par un autre, plus intuitif ; b) celle qui tente de le déduire des 4 autres postulats.<br />La naissance des géométries non-euclidiennes est liée à la tentative de démontrer la vérité du 5ème postulat par la méthode par l’absurde (Lobatchevski, 1792-1856) : en faisant l’hypothèse que par un point pris hors d’une droite, il ne passait pas de droite parallèle, les mathématiciens voulaient démontrer qu’on aboutissait à des résultats contradictoires. Or leurs résultats étaient consistants. C’est la naissance d’un type de géométrie non euclidienne : la géométrie de Lobatchevski (Gauss, Bolyai, Lobatchevski) : par un point pris hors d'une droite il passe une infinité de parallèles à cette droite. La démonstration a permis de passer d’un postulat à un autre postulat.<br />-Le mathématicien ne tire pas un grand trait sur ce qui l’a précédé. Cependant il ne tient pas compte du laps de temps qui le sépare de la formulation première du problème, de la différence des méthodes. Il s’appuie sur la continuité de la méthode rationnelle pour traiter des problèmes formulés dans le passé et néglige les aspects contingents de la formulation première.<br /><br /><br /><br /><span style="font-weight: bold;">Transition :</span><br />le mathématicien peut se rapporter de manière totalement anhistorique à l’histoire des mathématiques. Il peut employer des méthodes prises dans un cadre précis à d’autres fins. Il peut négliger le temps qui le sépare d’une formulation d’un problème. Car il s’appuie sur la puissance universelle de la raison. Mais l’histoire des mathématiques n’est pas l’histoire de la raison des mathématiciens. Elle ne vise pas à exclure les déterminations, les contingences, les événements, les ruptures. Elle ne s’appuie pas sur l’uniformité de la raison, mais sur l’étude des conditions de production des faits. Est-ce que le fait de se pencher sur la genèse des faits introduit chez le mathématicien une modification dans son rapport à sa discipline ?<br /><br /><br /><br /><span style="font-weight: bold;">B) Comment le mathématicien se rapporte-t-il à l’histoire des mathématiques telle qu’elle est vue par les historiens ?<br /><br /></span><br /> a) Y a-t-il toujours correspondance, identité entre les faits de l’histoire mathématique et la raison mathématique ?<br /><br />-Il n’y a pas toujours une adéquation stricte entre les faits mathématiques établis par l’histoire et la raison mathématique. L’histoire des faits mathématiques se trouve face à un ensemble de travaux dont un grand nombre sont inachevés, esquissés dans des correspondances, suggérés dans des brouillons.<br />-Exemple : en 1621, Bachet de Meziriac publie le texte grec de Diophante accompagné par une traduction latine des Arithmétiques. Fermat travaille sur cette édition. C’est dans les marges de cette édition qu’on trouve le fameux : « J’ai une démonstration véritablement merveilleuse de cette proposition, que cette marge est trop étroite pour contenir, hanc marginis exiguitas non caperet » (page 85 de l’édition de Diophante). La proposition concernait ce qu’on appelle le « grand théorème de Fermat » :<br />« Pour n entier plus grand que 2, l’égalité xn + yn = zn est impossible dans l’ensemble des entiers naturels (Z) et dans l’ensemble des nombres rationnels (Q) » (voir Fermat, Varia Opera Mathematica, Toulouse, 1679).<br />Soit n=1, x=1, y=2, alors 11 + 21= 31. L’égalité est valide. Pour n=1, il existe une infinité de solutions.<br />Soit n=2, x=3, y=4, alors 32 + 42= 52. L’égalité est valide. Au-delà de 2, l’égalité n’est plus possible.<br />L’histoire permet d’établir que, jusqu’à ce jour, cette proposition n’est rien de plus qu’une hypothèse, car nous ne possédons aucune trace d’une démonstration de Fermat. Mais l’histoire permet aussi d’établir que le mathématicien de Cambridge Andrew Wiles, avec l’aide de Richard Taylor, en 1994, a établi la démonstration de la conjecture de Fermat (Andrew Wiles, « Modular elliptic curve and Fermat’s last theorem », in Annals of Mathematic, 141 (3), 1995, pp 443-551).<br />-L’histoire permet donc d’établir deux grands moments dans la démonstration du « grand théorème de Fermat », mais elle peut établir aussi la démonstration de l’impossibilité dans le cas où n=3 (Eisenstein), où n=4 (Euler), où n=5 (Dirichlet). Le mathématicien qui a besoin, pour ses nombres, du denier théorème de Fermat se plongera-t-il dans l’ensemble de ses travaux ? Certainement pas, à moins que son travail ne l’exige. S’il le faisait, il se rendrait compte qu’il peut y avoir un décalage entre la formalisation mathématique (théorème Fermat-Wiles) et l’histoire des mathématiques (ensemble des tentatives de démonstration).<br /><br /><br /> b) Est-il possible que la raison mathématique, si homogène selon Kant, puisse introduire des ruptures ?<br /><br />-Le mathématicien peut faire l’expérience des « antinomies » de la raison mathématique.<br />-Exemple, dans son traité <span style="font-style: italic;">Della pictura</span>, Alberti (1404-1472) avait remarqué empiriquement que la perspective transforme un système de droites parallèles en un système de droites concourantes. Girard Desargues, dans le <span style="font-style: italic;">Brouillon project d’une atteinte aux événements des rencontres du cône avec un plan</span>, sus-mentionné, formalise certains aspects de la perspective : la perspective est une projection centrale faite d’un point O, le point de vue, sur un plan P, le plan de projection donné, qui à tout point M de l’espace fait correspondre un point M’, intersection de la droite OM avec le plan P. Le point de départ de Desargues, pour les coniques, est le cercle. Il imagine de transférer les propriétés du cercle au cône en interprétant le cône comme une projection du cercle à partir du sommet du cône sur le plan coupant. Il suffit de donner les propriétés du cercle et de les étendre. Il forme donc une théorie générale des coniques. Afin de compléter la correspondance entre le système des droites parallèles et le système des droites concourantes, Desargues introduit un point nouveau : « le point de l’infini ». Si x est le point de l’infini, alors il appartient à chacune des droites des deux systèmes. Il est le point de concours des droites parallèles, le point par lequel il affirme qu’il y a une identité en perspective entre les droites parallèles et les droites concourantes. Mais ce point est rejeté à l’infini.<br />-Affirmer comme le fait Desargues que les droites concourantes et les droites parallèles sont identiques dans la géométrie projective est une thèse incompatible avec la géométrie plane. En ce sens, la méthode mathématique a introduit un conflit au cœur de la raison et une rupture dans l’histoire.<br /><br /><br /> c) S’il y a un si grand décalage entre l’histoire des mathématiques et la raison mathématique et un conflit possible au sein de la raison mathématique, le mathématicien observant l’histoire des mathématiques ne perdra-t-il pas confiance en la valeur de sa discipline ?<br /><br />-L’histoire des mathématiques semble montrer que l’accumulation des obstacles serait plutôt un stimulant. Les obstacles ne remettent pas en question la validité comme telle des mathématiques, ils font simplement douter de la validité des méthodes employées.<br />-Exemple : dans les<span style="font-style: italic;"> Éléments</span> d’Euclide, les démonstrations de l’égalité des triangles ABC et DEF (Livre I, propositions 1-4) allient à la fois des aspects formels et des aspects matériels. Euclide ou l’auteur de la démonstration fait appel au sens commun, à la possibilité de superposer un triangle sur l’autre. Cet aspect matériel n’est ni nécessaire ni suffisant pour un mathématicien contemporain. Pour débarrasser la géométrie de son aspect matériel, David Hilbert (1862-1943), dans Les <span style="font-style: italic;">Fondements de la géométrie</span> (1899), propose d’axiomatiser la géométrie de manière formelle et irréfutable. Il met de côté toute référence à une figure ou à une quelconque expression pouvant rappeler un aspect sensible. Il se donne trois objets non définis : le plan, le point, la droite. Les axiomes (au nombre de 21) sont regroupés en catégories : l'association, l'ordre, la congruence, la continuité et les parallèles. Les trois premiers sont des concepts qui définissent des types de relation. Résultat : un triangle n’est pas une figure à trois côtés, mais trois points non alignés. Cette volonté d’axiomatisation est révolutionnaire dans les mathématiques d’alors.<br />-La tentative de Hilbert, alors que <span style="font-style: italic;">Les Éléments</span> d’Euclide sont l’objet de discussion et réfutation nombreuses, montre que les erreurs ou les maladresses des mathématicien n’ébranlent aucunement leur confiance dans la validité et la pertinence de leur discipline. En un sens, l’axiomatisation de la géométrie de Hilbert n’est pas en rupture avec Euclide. Car il cherche à réorganiser les objets euclidiens et à leur donner une meilleure assiette, sans se départir de l’idée que les résultats doivent être conservés.<br /><br /><br /><br /><span style="font-weight: bold;">Transition :</span><br /> l’histoire des mathématiques introduit un rapport spécifique du mathématicien avec sa discipline. Elle introduit deux changements notables. Le premier changement est d’ordre psychologique : elle le met en face des hésitations, des inachèvements de ces prédécesseurs. Elle peut conduire au doute ou à la volonté de surmonter les obstacles. Le second changement est rationnel : méthodologique, s’il concerne la réorganisation des données ; fondamental, s’il introduit de nouvelles branches. Mais, comme on l’a vu, ce qui intéresse le mathématicien dans ses travaux, ce n’est pas la genèse des propositions mathématiques ou la narration historico-épique des grandes prouesses des génies de la science, mais le recueil des démonstrations, des théorèmes. Comment le mathématicien utilise-t-il la collection des faits mathématiques ?<br /><br /><br /><br /><span style="font-weight: bold;">C) Comment le mathématicien se rapporte-t-il au catalogue des faits de sa discipline ? </span><br /><br /> a) Un mathématicien s’intéresse-t-il à tous les faits ?<br /><br />-Un mathématicien ne s’intéresse pas à tous les faits, non pas simplement parce qu’il lui faudrait plus qu’une vie pour s’intéresser à toutes les propositions mathématiques, mais parce que son attention est attirée proportionnellement à la hauteur de l’enjeu.<br />-Exemple : au cours de la 2ème partie du 19ème siècle, l’idée qu’il était possible de fonder les mathématiques a vu le jour. Plusieurs voies se sont manifestées :<br />*Le psychologisme (Brentano-Husserl) : il consistait à démontrer que, dans le domaine arithmétique, les nombres peuvent être fondés sur l’acte de compter, puis à étendre cette propriété à tous les objets mathématiques.<br />*L’intuitionnisme (Brouwer) : appuyé sur Kant et Schopenhauer, il consistait à démontrer que les mathématiques ne sont pas un langage et un système hypothético-déductif, mais une expérience d’un type de vérité par un sujet.<br />*Le formalisme (Pasch, Hilbert et Peano) : il consiste a) à formaliser totalement les mathématiques en un système hypothético-déductif où les propositions mathématiques sont interprétées comme des relations ou des chaînes de signes ; b) à déterminer les axiomes prouvés et en nombre réduit sur lesquels reposent l’ensemble de l’édifice.<br />Les axiomes de Peano pour l’arithmétique :<br />1. L'élément appelé zéro et noté « 0 », est un entier naturel.<br />2. Tout entier naturel n a un unique successeur, noté s(n) ou Sn.<br />3. Aucun entier naturel n'a 0 pour successeur.<br />4. Deux entiers naturels ayant même successeur sont égaux.<br />5. Si un ensemble d'entiers naturels contient 0 et contient le successeur de chacun de ses éléments, alors cet ensemble est égal à l’ensemble des entiers naturels (Z).<br />*Le logicisme de Frege, Russell et Whitehead : il consiste à démontrer que toutes les propositions mathématiques peuvent être dérivées des principes de la logique formelle.<br />-Cette énumération est évidemment incomplète et ne saurait prendre en compte les variantes de ces branches. Elle a seulement pour but de montrer qu’institutionnellement et historiquement, cet épisode se caractérise par une convergence soudaine d’une partie très importante de la communauté des mathématiciens. Plusieurs causes ont pu présider à cette convergence : a) psychologique : l’espoir d’accéder à une science indubitable où l’erreur n’a pas sa place ; b) sociologique : le défi entraîne le désir d’être compétiteur et, surtout, vainqueur. L’histoire fournit un thème sur lequel il peut exercer son goût de l’invention, de l’élégance scientifique, de la parcimonie ou de la simplicité. Ainsi, plus l’enjeu est grand, plus le mathématicien peut recourir à des procédures inédites.<br /><br /><br /> b) Mais tous les grands enjeux de l’histoire des mathématiques suscitent-ils l’intérêt du mathématicien ?<br /><br />-Le mathématicien sélectionne parmi les grands enjeux des mathématiques en fonction de la possibilité ou de l’impossibilité de la résolution des problèmes.<br />-Exemple : la recherche des fondements a donné lieu à la crise des fondements des mathématiques.<br />*La première secousse eut lieu en 1903. Elle ébranle le logicisme de Frege. Dans une lettre à Frege de novembre 1903, Russell se demande : soit x un barbier qui rase ceux et uniquement ceux qui ne rasent pas eux-mêmes, lui-même se rase-t-il ? S’il se rase, alors il ne fait pas partie de ceux qui ne se rasent pas eux-mêmes. Sinon, il ne rase pas l’ensemble des personnes qui ne se rasent pas elles-mêmes. Pour Russell, le barbier n’existe pas. Il s’agit de la formulation imagée du « paradoxe de Russell » qui peut être formulé ainsi : si x est l’ensemble de tous les ensembles qui ne s’appartiennent pas à eux-mêmes, l’ensemble de ces ensembles doit-il s’inclure lui-même ? Si oui, alors il n’appartient pas à lui-même et il faut supposer ad infinitum un autre ensemble. Sinon, alors il ne contient pas tous les ensembles. Ce sont deux contradictions. Or, elles sont tirées des <span style="font-style: italic;">Fondements de l’arithmétique</span> (1884) de Frege. Russell essaiera de résoudre ce paradoxe par la théorie des types. Mais le logicisme est profondément ébranlé.<br />*Seconde et dernière secousse : « Sur les propositions formellement indécidables des Principia mathematica et des systèmes apparentés », Kurt Gödel, 1931. Le mémoire de Gödel consiste à démontrer l’impossibilité de démontrer certaines propositions dans un système donné. La démonstration aboutit à plusieurs théorèmes :<br />1) Les théorèmes 1-6 ont la conclusion suivante : « Par conséquent, dans tout système formel qui remplit les conditions 1 et 2 et qui w-consistant, il existe des propositions indécidables de la forme (x)F(x), où F est une propriété des nombres naturels récursivement définie… » (Ernest Nagel, James R. Newman, Kurt Gödel et Jean-Yves Girard, <span style="font-style: italic;">Le Théorème de Gödel</span>, Seuil, Paris, 1989, pages 131-132).<br />2) Les théorèmes 7-11 ont la conclusion suivante : soit T une théorie consistante ; la consistance de T, qui peut s’exprimer en T, n’est pas démontrable dans T.<br />C’est une attaque directe envers les tentatives de fonder les mathématiques : le logicisme, le formalisme et les deux variantes du subjectivisme. Ce mémoire met en cause la possibilité de démontrer la consistance des axiomes dans des systèmes hypothético-déductifs. Autrement dit, toute tentative de fonder les mathématiques génèrera des paradoxes, des contradictions…<br />-Il y a aujourd’hui des tentatives de fonder les mathématiques, notamment le néologicisme (Crispin Wright), qui affirme qu’on peut aboutir à des démonstrations consistantes si l’on écarte le principe de compréhension non restreint (« il existe un ensemble B tel que ses membres sont ceux dont les propriétés satisfont le prédicat P ») qui a généré le paradoxe de Russell. Mais c’est un mouvement philosophique, ce n’est pas l’œuvre de mathématiciens. Les mathématiciens ont quitté ce champ, ont approfondi, précisé certains aspects (Jean-Yves Girard, Alan Turing…) de la démonstration de Gödel, mais ils ne l’ont pas remise en question. Autrement dit, la tentative de fonder les mathématiques, si elle porte un enjeu appréciable, n’est plus un choix de travail pour les mathématiciens parce qu’elle ne génère pas un problème auquel les réponses peuvent être consistantes. Autrement dit, la recherche du mathématicien est orientée par la possibilité d’obtenir des conséquences nécessaires et logiques.<br /><br /><br /><br /><span style="font-weight: bold;">Conclusion :</span><br /><br />Les mathématiques sont à la fois anhistoriques, au sens où le contenu des propositions est indépendant de conditions matérielles de production, et historiques, puisque les méthodes et les objets mathématiques ont changé au cours de l’histoire. Le mathématicien est à l’intersection entre l’anhistoricité et l’historicité des mathématiques. Concernant la question de déterminer les relations entre le mathématicien et l’histoire des mathématiques, il semble que le mathématicien ne se rapportera que sous certaines formes et conditions à celle-ci. La condition principale est la suivante : le mathématicien présuppose toujours la rationalité dans l’œuvre de son prédécesseur. Ainsi, le mathématicien s’intéresse peu à la dimension narrative ou génétique des faits mathématiques répertoriés par l’histoire. La forme du rapport du mathématicien à l’histoire des mathématiques est en grande partie sélective : le mathématicien ne se rapporte pas à l’ensemble des faits mathématiques, mais à ceux qui peuvent générer des problèmes dont les solutions sont consistantes. Par conséquent, rien ne l’empêche de naviguer d’une période à une autre de l’histoire des mathématiques pour trouver une formulation complète d’un théorème. Cela implique que le rapport du mathématicien à l’histoire des mathématiques n’est pas mythologique, mais essentiellement pragmatique. Le mathématicien, dans sa pratique des mathématiques, ne cherche pas à faire le roman des grands faits de sa discipline, mais à répondre à des problèmes, à vérifier des conjectures et des hypothèses ou à établir des théorèmes précis. L’utilité vis-à-vis du but est le critère déterminant du choix du rapport à l’histoire de sa discipline.<br /><br /><br /><br /><br />BIBLIOGRAPHIE :<br />Dahan-Dalmedico et Peiffer, <span style="font-style: italic;">Une Histoire des mathématiques</span>, Seuil, Paris, 1986 (2ème édition).<br />Euclide, <span style="font-style: italic;">Les Éléments</span>, vol 1, ed Vitrac, PUF, Paris, 1990.<br />Fermat, <span style="font-style: italic;">Varia Opera Mathematica</span>, Berlin, 1861.<br />Frege, <span style="font-style: italic;">Écrits logiques et philosophiques,</span> Seuil, Paris, 1971.<br />Frege, <span style="font-style: italic;">Fondements de l’arithmétique</span>, Seuil, Paris, 1969.<br />Girard Desargues, <span style="font-style: italic;">Brouillon project d’une atteinte aux événements des rencontres du cône avec un plan</span>, 1639.<br />Hilbert, <span style="font-style: italic;">Les Fondements de la géométrie</span>, ed Rossier, Dunod, 1971.<br />Kant, <span style="font-style: italic;">Critique de la faculté de Juger,</span> ed Renaut, GF, Paris, 1995.<br />Lobatchevski, <span style="font-style: italic;">Pangéométrie</span>, 1856.<br />Nagel, Newman, Gödel, Girard, <span style="font-style: italic;">Le Théorème de Gödel</span>, Seuil, Paris, 1989.<br />Singh, <span style="font-style: italic;">Le Dernier Théorème de Fermat</span>, Hachette, Paris, 1999.<br />Wiles, « Modular elliptic curve and Fermat’s last theorem », in Annals of Mathematic, 141 (3), 1995, pp 443-551.<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/2.0/fr/"><img alt="Creative Commons License" style="border-width: 0pt;" src="http://i.creativecommons.org/l/by-nc-nd/2.0/fr/88x31.png" /></a><br /><span dc="http://purl.org/dc/elements/1.1/" href="http://purl.org/dc/dcmitype/Text" property="dc:title" rel="dc:type">Le Mathématicien et l'histoire des mathématiques</span> by <span cc="http://creativecommons.org/ns#" property="cc:attributionName">Mikolka</span> est mis à disposition selon les termes de la <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/2.0/fr/">licence Creative Commons Paternité-Pas d'Utilisation Commerciale-Pas de Modification 2.0 France</a>.<br /></span>Mikolkahttp://www.blogger.com/profile/06474496860871759825noreply@blogger.com0tag:blogger.com,1999:blog-2437165907915350480.post-68865682487359822292008-04-24T20:44:00.001+02:002008-06-11T18:02:54.372+02:00Perles trouvéesQuelques perles trouvées dans des copies de terminale ES, sur le sujet "L'État restreint-il la liberté individuelle?" <span class="fullpost"><br />Les voici, sans aucune modification:<br /><br />- "Au IIXXè sciecle..."<br /><br />- "Les hommes éprouvent de la pitié, qui est comme une compensassion..."<br />("Compensassion" à la place de compassion)<br /><br />- "D'autre part, toute société a des lois, qui permettent de contenir la volonté expensive des hommes. Comme le dit Caliclès, personnage soffiste imaginé par Socrate et arborant toutes leurs convictions, les lois sont faites pour proteger les faibles des plus forts..."<br /><br />-Une autre à propos des sophistes: "D'après Protagoras (sphosite), "l'homme est la mesure de toute chose", à partir de son désir renouvelé."<br /><br />- "Le souverain est absolu et l'état artificiel est appelé par Hobbes le Léviathan (du nom du monstre Job)."<br /><br />-Première phrase d'une introduction: "L'État, c'est la représentation immatérielle ultime d'une société."<br /><br />-Dernière phrase d'un développement: "Ainsi est-ce l'État qui offre aux individus la seule liberté possible, puisqu'il n'existe pas de liberté individuelle, et qu'il n'y a nulle liberté hors de l'État."<br /><br />- "L'homme est alors naturélement objectivé a se mefier de l'autre puisqu'il est mis en concurence avec d'autres pour parvenir a ses desirs."<br /><br /></span>Mikolkahttp://www.blogger.com/profile/06474496860871759825noreply@blogger.com1