 ... Jeremy Corbyn yn ei wneud yn erbyn i'r dynfodol meddwl y byddwch chi buddach chi'n bodan ynghyrchu i'w dynum... ... yn y brolin â hyd i gael eu rayon i'r dynfodol... ... mae nhw phoblu i'r dynnu'r dynnu'r wylio'r dynnu ei gwas cryf. O地 o dynnu ei wneud i'r dynnu'r dynnu'n dynu r Baeth yma gwyfodol 2 o Llyfrgell... ... mae gwrs hynny wedi gweld i'r dynnu... If you look at books on Hume, you will often find that no mention of this is made at all, or it is treated rather dismissively. I actually think that is probably fairly justified, but you will find plenty of Hume scholars who will argue the reverse, I will be referring to some of them. Now what Hume seems to be doing in this part of the treatise is applying his theory of ideas to draw conclusions mae'r nifiad i ddweithio arniwch gweithiaethol o ddiweddol yn dda, a dddiweddol yn dda fel yna. O'r ddigon ti'n mynd i ddigon a llwybraeth sydd yn ei ddeilig oedd hi wedi'i dod oedd o'r ddiweddol, dywedudio'n ddigon i'r ddyreu'r ddweithiau hyn o ddiweddol arniwch, yw'n mynd i'ch bod yn ddod o'r hunain, sechwan i ddweithio'r ddweithiau o ddiweddol o'r ddweithiau. er enghreifftodd cyfnodd, i'r bynd yn��라고요 i'r hyn Yaeth fallewch. Fe'r byd yn oedd pei wedi eumentsiwyll yn sicr, felly mae'r bynd mae'r bynd i'wmentsiwll balwod y bobl ei hynny a'r bynd yn y bydd yn phosio eu phasio i fynd flynydd Allez. gweld!學b yma yng ngNat Scotland mewn baggage Llyfr engylleteich духов read yn deilig 69-80 sydd Vedder o'r hyn ac roedden nhw'n nhw wedi'u gwneud y lleig o'r gweithio dechrau sydd eich fynd yw'r amser i gŷn a i wneud eich gwneud yn digwydd i digwydd i'r ll♡t y mawr. Felly mae'r ffwllfawn hefyd yn gweithio yn y ddad! Ystod nid yn ei ddweithio'r ddweithio, dyf yn yw yng nghyd Heli Gwysig o'r ddweithio'r ddweithio gŷn o gweithio'r ddweithio'r ddweithio'r ddweithio o gweithio'r ddweithio'r boblid, oes unrhyw union y line. Mae gyda gweithio. Mae'r idea ymlaen i gael eich gwahanol eich gwahanol eich gwahanol eich gwahanol, mae'n mynd i gael eu ddaf yn rhaid. Felly sy'n gael bod ydych chi'n gwneud gweithio'n meddwl i'r hyn sydd i'n gweithio Cymru y mynd i'w gwirio ag oed yn ymweld ymweld i'w gweithio'r idea'r byw, rydych chi'n mynd i'r gweithio'r bod yn ymddangos, yn y gyd, yn y gweithio'r gweithio'r minim. Rwy'n credu rwy'n deall, ydych chi'n yr argyfweld. Rwy'n credu'r unig o'r amgylcheddig o'r ddaeth yma. A'r cyfnodd ag ychydig i gyd yn dweithio'r gweithio. y gallwch yn ei wneud, mae'n bwysig yn gyfreIt. Ac wrth gwrs, y gallwch yn ymd�. Maen nhw'n ei wneud eich argument, o'i olywch â'r ysgrifennu, oedd y Bohr. Le yna'ch gynnwch ar y dyfodol, ydych yn uwch, drwy'n ei wneud yma. Rydych yn ymwysig rydych chi'r llyfrfer, yr uwch yn ymwyf. Ond yw'r llyfr yw'r ymwysig yn ymwysig. fel dill nid i chi'n rhaid i chi ddweud â'r rhaid, yn ddgynnais, gyda'n ddim rhaid, gyda'r dda chi'n rhaid i chi ddweud. That is the minimum visible quantity. So what you will see, Hume thinks, is a coloured point, a coloured extension-less point, because it will be indivisible, it will just be a point. You won't be able to distinguish the left side from the right side of it, ond rydyn ni'n ddweud yma'r ddweud. A mae'n ddweud yma'r unrhyw yma'r ffordd. Ond yn ffrindio'r ffordd yma'r cyffredinol, mae'n ffordd ffordd o'r ddweud yma'r ddweud, o'r ffordd cyffredinol yn ddweud. Felly, yn y rhan o ffordd ar gyfer y ddweud yma, yma'r Rolf George yn ymdwy'r ddweud yma'r ddweud yma'r ddweud. Y prynsibol yma'r ddweud yma'r ddweud. ac mae'n edrych yn dweud y dyfodol yma o'i allu allu arall. Ond yma yma'n ddysgu'r ffilosofi hwn o'r ddau hwn o'r ddau, mae'r prinsibol yma eich ymddangos o'r llwythu ar y llyfr. Yn y ddau hwn o'r ddau hwn o'r ddau hwn, mae'n ddau hwn o'r ddau. Yn y peth yw'r ddweud yw'r ddau yn ysgrifennu i'r argymwynt. Yn y peth yw'r ddau, mae'n ddau hwn o'r ddau hwn o'r ddau. Ond y gallwn i'n dweud yn bwysig y cyfnod o'r ffordd o'r dynnu'n dda'r cifrif, os yw'r dynnu'n dda'r cyfnod o'r dynnu'n ddangos cyfnodol. Fy gwrtheg, y chyfnodd o'r cynnig o'r cyfnodol yn bwysig o'r cyfnodol. Fy gwrtheg, y cwmpwysig cyfnodol yn ddysgwm. A oeddiw wedi'u bod yn ddysgwm arnynt yn y cyfnodol. y bod eich sylfa ar fy nifer ar gyfer o adrwyafn i ddau a rhagio cyntafol mewn ddweud o'r fag i chi'n responded o'r dda ni, o'i ddweud o ddweudio a ddweud o duodau am rhai gwasiol. Ieithaf, i'n rhan gorau, rydym wedi bod nifer o ddodd o dduhyw gwaddishwyme a phas daddiad. Rydym wedi bod wedi'u bod yn fod o bobl yw'r adrwyphau sôn, i'r cyffredinio gyda'n eu ddweud i ddweudio'i ddweud eu ddweud o erbyn iawn o'r ddweud o ddweudio. ond ymlaes ei wneud am y cyfnodd ymlaen i chi'r ystyried ymlaen i'r yrhwy�fynwyr. Yn ystod o ddod, mae'r cyfnodd yn iddyn nhw'n mynd i'r cyfnodd yn ymlaen i'r ymlaen i'r cyfnodd yn ymlaen i'r cyfnodd. Mae'n amser o adrecon iawn diwyddiant, mae'n adrecon iawn i chi wedi'i ei wneud o'r cyfnodd o'r cyfnodd ar y cyfnodd a'i ei ddysguŷu mewn cyfnodd. felly mae'n gweld yn gwneud o'r prinsiell cyfnod. Mae'n cael ei wneud. Ond yna'r eich cyfnod ymlaen, mae'n gweld yn gwneud o'r cyfnod. Rolf George yw'r ysgolwyd yn ymdweud y gallu'r ysgolwyd yn ymdweud. Yn 1738, James Dwyryn yn ysgolwyd yn ysgolwyd o'r ysgolwyd yn ymdweud. George's hypothesis is that this, as it were, awoke David Hume from his dogmatic slumbers. How could it do that? Here we have a line and here we have a dot. You will notice that the dot is greater diameter than the line is across. Now imagine retreating further and further away from that until the dot cannot be seen. Nevertheless you will still be able to see the line. Now that's an empirical claim. What James Durian was doing was making empirical investigations into human acuity. You can see that's a little bit of a problem for Hume. If you think that there are minima in our visual field of a certain fixed size, that as you go smaller and smaller you hit a limit like a computer pixel, just like the pixel on a computer screen. You cannot represent any image which is smaller than that. Well at the point when that dot has disappeared there should be no pixels at all left representing the line. So the line should disappear too but it doesn't. So as I say that's an interesting speculation. We don't know whether it's true but the dates are very suggestive. We have this investigation being published in 1738. The treatise was published in 1739. Highly plausible that Hume between then and 1748 came across this and George gives relevant evidence. OK, but let's now proceed and see what Hume does with his theory. Well, having established that there are these minima, Hume considers those. Now if we hit a minimum, if we actually think of a minimum possible point, it's extension-less. You cannot distinguish the left from the right. It's as small as anything could be. It follows that nothing can be more minute than some ideas which we form in the fancy. The fancy remember is another name for the imagination. And images which appear to the senses. Since these are ideas and images perfectly simple and indivisible. The only defect of our senses is that they give us disproportioned images of things and represent as minute and uncompounded what is really great and composed of a vast number of parts. Take that dot that we've drawn on a board. And maybe it's quite big. But we go further and further and further away until we can only just see it. And at that point it looks to us completely simple and uncompounded. We just see the dot. Now we might therefore have the erroneously draw the conclusion that the thing itself that we're seeing is totally simple. But what we can do at that point is pull out our binoculars or our telescope and take a look and we see, ah, it's bigger. So it's clear that there are a lot of light rays coming and if we use instruments we can see the thing in more detail. It ceases to be so simple. But what Hume wants to say is that that simple idea that we get correctly represents the smallest part of anything. Nothing can be smaller than that. So we get a famous image of a flea from Hooke's micrographia 1665 and Hume is clearly alluding to this. This however is certain that we can form ideas which will be no greater than the smallest atom of the animal spirits of an insect a thousand times less than a mite. Animal spirits think of what goes through the nerves. And we ought rather to conclude that the difficulty lies in enlarging our conception so much as to form a just notion of a mite or even of an insect a thousand times less than a mite. For in order to form a just notion of these animals we must have a distinct idea representing every part of them. So what's going on here, you might think that when we look at something from a distance, we're making an error in seeing the thing as simple. Our idea as it were is misrepresenting it. And Hume's saying we're thinking that way round is the wrong way. Actually we can form ideas which are adequate to the tiny parts of things because our ideas are pure and simple. They're just uncompounded. So they form an adequate idea of the very smallest parts of anything. What's actually difficult is forming an idea adequate to a whole mite. That's vastly complex. Or even a creature a thousand part of a mite. OK. So Hume has drawn here an important conclusion. And it's one that he's going to use now to conclude about space and time in themselves rather than just about our ideas. So we get that right at the beginning of Treaties 122. Wherever ideas are adequate representations of objects, the relations, contradictions and agreements of the ideas are all applicable to the objects. OK. That seems reasonable. If our ideas are faithful representations of the way objects are, then inevitably any conclusions that we draw from the ideas will be applicable to the objects. And I realise you're all wondering where the handout for this is. It'll come next week with stuff for next time because it didn't make up a complete handout. OK. So fair enough. If we've got adequate ideas, the ideas, as I say, faithfully represent what they are ideas of, then in reasoning about the ideas and drawing conclusions about those, those conclusions will inevitably follow to the things that the ideas represent. But here comes the crucial claim, the one he's been arguing for, but our ideas are adequate representations of the most minute parts of extension. And through whatever divisions and subdivisions we may suppose these parts to be arrived at, they can never become inferior to some ideas which we form. So the ideas are so simple, so uncompounded that no part of extension can possibly be less than those. The plain consequence is that whatever appears impossible and contradictory upon the comparison of these ideas must be really impossible and contradictory without any further excuse or evasion. Now notice that Hume here is not using what might seem to be his conceivability principle. He's arguing from inconceivability to impossibility. That's different from arguing from conceivability to possibility. We saw the conceivability principle last time. We'll be seeing lots more of the conceivability principle. Hume thinks quite generally that to conceive of something distinctly implies its possibility. You cannot distinctly conceive of something that's impossible. Okay, so conceivability implies possibility. But here he's saying that inconceivability implies impossibility. But he only wants to say that that applies where ideas are adequate. Now that's quite important. Remember Hume's an empiricist? He thinks our ideas are derived from impressions. He thinks for example that a blind man has no visual ideas. So he surely doesn't want to say that inconceivability quite generally implies impossibility. There may be all sorts of things of which we cannot conceive because we don't have the ideas. And he said that our minds are finite. There may be all sorts of things that we can't conceive of because we're just not capable of it. We don't want to conclude in general that that implies impossibility. But when our ideas are adequate, that's a different matter. So he's already said that our ideas are adequate representations of the most minute parts of extension. We've seen that our ideas are not infinitely divisible and it follows that the same is true of space. I first take the least idea I can form of a part of extension and being certain that there is nothing more minute than this idea I conclude that whatever I discover by its means must be a real quality of extension. I then repeat this idea once, twice, thrice. Imagine that tiny little atomic idea and now put another one next to it and another one next to that. And if it helps, think of them as differently coloured. You start off with a blue dot. Remember it's extension-less, you can't distinguish its parts but now you put a red dot next to it and maybe a yellow dot next to that. And what you do now is build up extension. The idea of extension comes to you as soon as you've got more than one of these. So each of our minimal ideas is indivisible and therefore not extended but as soon as you put two together you've got the minutest part of extension. Add another one, you've got a bit more extension. Add another one, you've got more. Carry on to infinity, where do you get? Well you're going to have an infinitely large extension. No way round it. Although each indivisible atom as it were is unextended, as soon as you put lots of them together you get a finite extension. If you put an infinite number together you'll get an infinite extension. So Hume goes as far as saying that the idea of an infinite number of parts is the same idea with that of an infinite extension. So he's proved to his satisfaction at any rate that space is not infinitely divisible because we've got these little ideas that are adequate to the minutest parts of space and if space were infinitely divisible then you'd have to be able to have an infinite number of these tiny parts within a finite amount of space but you can't because as soon as you get an infinite number of these little atoms you get an infinite extension. Now if you're familiar at all with mathematics an objection is likely to come to your mind. Imagine something that's finitely extended imagine dividing that extension in two and taking half of it then divide that in two and take half divide that in two and take half and go on and on and on and on and on you start with a half then a quarter then an eight then a sixteen on and on and on without stopping apparently. So what's wrong with that? Why can't you divide things infinitely? Well if you actually address this objection in a footnote he distinguishes between proportional and aliquot parts so proportional parts where you're dividing up again and again and again like this aliquot parts all of equal size and he just seems rather dogmatically to say well that doesn't deal with my argument because nothing, I've proved nothing can be inferior to those minute parts we conceive when I think of this idea of a simple nothing can be smaller than that so divide up as much as you like you cannot get smaller than that and if you can't get smaller than that then an infinite number of those is going to give you an infinite extension so there you are my argument stands. Later in the section Hume again comes back and deals with a potential mathematical argument so there are various mathematical arguments that seem to tell in favour of infinite divisibility that seem to try to prove it and Hume says these can't be right now he is appealing to the conceivability principle he's saying I have this notion of space made up of all these little atoms that's a conceivable picture of the way space could be since it's conceivable it's possible so any attempted proof that it's impossible must be fallacious so he's attacking the mathematical objection to his own view and he's attacking himself the argument of mathematicians that is claimed as a positive proof of infinite divisibility now these arguments don't seem to be ideal particularly his argument against infinite divisibility against proportional parts because when he says my idea is as simple as can be this atomic idea of a visual atom must correctly represent the smallest parts of space because nothing could possibly be smaller therefore when you finally get down to the ultimate bits of space they're going to be simple my idea is simple therefore the two must match that must be an adequate idea the obvious response is to say well I'm sorry Hume if space is infinitely divisible you never do get down to an ultimately simple part so when in claiming that the ultimate parts of space must match with this idea you're begging the question you're taking for granted that you do actually get to ultimate symbols and that's just assuming that space isn't infinitely divisible so there's a bit of a puzzle here Hume is generally a pretty acute philosopher as I've said book 1 part 2 is probably well almost certainly the weakest part of treatise book 1 the arguments aren't that great and maybe Hume just imagined himself to be better at mathematics than he really was later in life he did actually produce a treatise on geometry and he was persuaded by Lord Stanhope and noted mathematician not to publish it sadly it disappeared without trace it would be great if it turned up at some point but at any rate when he wrote the treatise he seems pretty confident doesn't he it is evident this is absolutely clear etc so is something going on that brought it about that he didn't see the problems that we see in his arguments well here we're reduced really to speculation Tom Holden a book published in 2004 he suggests that Hume is presupposing an actual parts metaphysic whereby anything that is divisible must in advance consist of the actual parts into which it is divided so contrast two different possible accounts of divisibility you've got the Aristotelian idea of potential infinities so suppose I take an extension divide it up divide that again again and again and again however much I divide it I can go on dividing further so in that sense there's a potential infinity it's like saying give me any number I can always add one you can always go further so there's a potential infinity but that's different from saying that there's an actual infinity you can say that the line is potentially divisible without claiming that it is already divided into parts that those separate parts already exist as it were prior to the division but Tom argues that at the time the actual parts metaphysic was very strongly in the air the thought that if something's divisible the parts already have to be there they have to exist prior to the division now that suggestion is somewhat supported by an argument that Hume uses in treatise 1-2-2-3 he borrows it from Nicholas de Malizio it is evident that existence in itself belongs only to unity and is never applicable to number but on account of the unities of which the number is composed it is therefore utterly absurd to suppose any number to exist and yet deny the existence of unities and as extension is always a number and so on the thought is if a group of people exist they exist only in virtue of the existence of each one of them take any number of things the ultimate existence are always the unities of which the group is composed now apply that to an extension the thought would be that unless there are ultimate parts of extension nothing exists so if you always can divide further you never hit the ground then ultimately metaphysically there's nothing another possible account of what's going on is due to Don Baxter he's written an article in the Cambridge companion to Hume quite recent and he suggests that Hume is pursuing a somewhat Kantian agenda so what Emmanuel Kant wanted to do was to say that our knowledge of space and time our knowledge of space and time in the phenomenal world in the world that we experience not in the world as it is in itself and so Baxter's suggestion is that Hume's aim is to find out about object as they appear to us by examination of the ideas that we use to represent them so it's less ambitious the thought is Hume's concern is with space and time within as it were the experienced manifold and within that realm the limits of space and time the limits of our ideas I'm not persuaded but it's an interesting suggestion Finally, notice that Hume draws the same conclusions about time that he draws about space all this reasoning he says takes place with regard to time and he adds an extra argument it's the essence of temporal moments to be successive time is of its nature successive in a way that space isn't so if time were infinitely divisible you'd get co-existent moments and that's not possible so time can't be infinitely divisible and then as soon as you think of motion something moving in time through space you can see that if infinite divisibility of time is impossible infinite divisibility of space must be as well okay we'll continue next time a little bit more on space and time and then we will be getting on to book 1 part 3 which is the most important part of the entire treatise see you then