Relationship between Clifford's work and scientific naturalism

0:00 This week we're going to have Michael Michael speaking on the relationship between mathematics and scientific naturalism. Shall I let you introduce how this fits into your research? Okay, so basically this is my M field dissertation, which I'm hoping to build on into a PhD, so I'll be interested in getting some feedback. So I guess like, I'll begin with like 3-2-1, I don't know anything about him. His dates are 1845 to 1879, so he died young at the age of 34, but not before he'd established quite a reputation, but as a mathematician and as one of the most outspoken scientific naturalists. he was educated here in Cambridge at Trinity College where he graduated in 1867 second wrangling mathematics tri-course and he was elected a fellow a year later and then he went on to become Professor of Applied Mathematics at University College London oh by the way here's a picture of him if anyone wants to have a look at that does anyone want to see a picture of you? great the beard's great Where does it end? Sorry One of his key mathematical interests was reminding geometry But he also developed what is now called clipped algebras Which is very popular amongst mathematicians, some mathematicians today He had a very good reputation as a populariser of his subject So he gave a series of popular lectures where he tried to explain mathematics to a non-mathematical audience And he was very successful at doing that And like I said, he was one of the most outspoken scientific naturalists So he was part of this inner circle of scientific naturalists Which included Huxley, Tindall, Spencer and Stephen who were united by their vision that science is going to solve the mysteries of mankind and science is going to be the only guide to man's moral and material progress. They also united in the

2:30 rejection of traditional theology and Turner argues they had a political agenda as well, promotion of professionalisation of science, promotion of scientists as a career, a secularization of society. So, what my dissertation was basically building on was a suggestion by Richards, who pointed out, this is Joan Richards, who pointed out that historians have treated WK Clippin separately, either as a scientific naturalist or as a mathematician, and haven't really drawn any links between the two. And Richards begins to draw out some of the connections scientific naturalism and I took that as my cue so that what I've been trying to do in my dissertation is to bring out more of the connections between his mathematics and his scientific naturalism. Now in the paper I submitted here, based on my dissertation, there are three general areas where I try to draw connections between his scientific naturalism and his mathematics, but I only have time to concentrate on one of them here because I can only talk for 20 minutes. So I'm going to talk about the boundaries of knowledge. Now, I'm going to talk about this because there's a particular difference between Clifford's agnosticism and that of some of his contemporaries, that of some of his fellow agnostics. It's a difference that is, I think, quite important, but Lightman doesn't make much of it in his book, The Regist of Gnosticism. But why it's particularly interesting for me is that it does demonstrate the direct influence of non-Euclidean geometry on Clifford's Gnosticism, especially of Riemannian geometry. So Clifford's, Gnosticism is about the limits of knowledge. And Clifford sets his limits to knowledge in a different way to the way that other agnostics were doing so. And he takes as his prime example non-Newfoundian geometry. So the idea for a long time had been that geometry contains absolute truths or necessary and universal truths. And that it reveals something about the underlying order of reality. So, for example, William Huell and John Herschel both had this view,

5:00 even though they were quite different philosophically. One was a nativist, one was an empiricist. They both shared the view that geometry had absolute truths, that it told you something about reality. But non-Euclidean geometry undermined this in that it showed that you can have alternatives to Euclidean geometry, that alternatives to Euclidean geometry were mathematically possible, and hence the people who developed non-Euclidean geometry and their supporters claim that this showed that Euclidean geometry, if it was true, was not necessarily true. The truths of geometry are not necessarily true, and they're actually a matter for empirical of investigation. Clifford used this example of non-euclidean geometry and the way it undermined the idea that there are absolute truths within the domain of geometry. He also used, in a broad sense, the example of history of science, he mentions the Copernican Revolution, as showing that what happens is that mankind has gradually become more humble, more cautious in the way that they extrapolate. So no longer claims like, do, does mankind extrapolate from this local knowledge that they have to these grand claims of universal knowledge of immensity and eternity. But extrapolations are much more cautious. We extrapolate onto the here and now based on our local knowledge. and he draws from this the lesson both from his version of the history of science and his example on nuclear geometry that the only knowledge that we can have is practically exact knowledge that is knowledge that is fallible, contingent and particularly it doesn't contain any of these absolute things it isn't necessary universal knowledge there isn't any absolute knowledge there so he's rejecting ideas of the absolute he's rejecting ideas of necessary universal knowledge and he's saying the only knowledge you can have is this fallible knowledge which is nevertheless reliable that is it can be used to guide to action so he's setting the limits in such a way as to exclude absolute knowledge and include only this fallible practically exact knowledge but when he concentrates on the practically exact fallible knowledge

7:30 that we can have he doesn't set any limits any prior limits to what knowledge you can get of this type he says that the only limits we have of this kind of knowledge are the limits of ignorance now this is where he differs from some of the other agnostics because what they were claiming that there are limits to the kind of knowledge we can have that are due to limits on our intellectual faculties. And they claim that there were positive arguments for saying that there were boundaries to what the human intellect can know, or boundaries to what is the knowledge that we can have or what is knowable. And they argued for these boundaries by talking about antinomies and this is this comes from Kant via people like William Hamilton and Mansell the idea being that when we try to think of certain things we hit against a contradiction which shows that we've reached the limit of our intellectual faculties so for example it's the famous antinomy of space the idea that we can't conceive space to being infinite nor can we conceive of spaces being bounded. So we hit against a contradiction which shows that we've hit against the limits of our intellectual faculties. And Herbert Spencer in particular used this idea of there being boundaries to what we can know to show that there is a realm out there beyond these boundaries that are noble, which we know exists, but we can't know in itself what it's like. This is essentially Kant's noumenal realm of things in themselves. And Spencer uses this as a way to try to reconcile science and religion. So his idea is basically that the unknowable is the domain of religion, and it represents the final stage in the evolution of religion, which began with lots of gods, down to one god, who was anthropomorphic, gradually became more abstract, and now the final stage, replaced god with the unknowable, which has a capital U in front. It's an infamous capital U, which he was criticised for, saying he can't turn the unknowable

10:00 into god just by having an initial capital initial letter. So, his objective, in some sense, was to redefine god the unknowable. So he had, in a sense, quasi-religious sayings. And Clifford doesn't like this idea of replacing God with the unknowable. So what he wants to do is he wants to reject the idea of the unknowable. And he does this by rejecting the idea that there are boundaries to what we can know, boundaries that we can know about to what we can know, boundaries to our knowledge. and he does this by attacking antinomies he's in a very good position to do this because Kant's antinomy of space Kant's famous antinomy of space contains an assumption that space is either infinite or bounded and Clifford knows for example that what comes out of Riemann's geometry actually be finite and bounded. It's a possibility that Riemann explicitly talks about in his famous 1867 paper, which Clifford translated into English. What this shows is that Kant has made an unwarranted assumption. And Clifford tries to diagnose why Kant made this unwarranted assumption. And what he says effectively is that he made the somewhat assumption because of his limited notion of conceivability. And he had a particularly limited notion of conceivability because he believed that we can have an absolute knowledge of space. This is basically the idea that we experience the world by bringing into it this transcendental intuition of And because we're the ones bringing this intuition into our experience, we can have an absolute knowledge of it. And this was the basis of what he went on to say about space, and the basis of his limited notion of conceivability. So Cliquid, in a way, is attacking this idea by using his own version of agnosticism, his rejection of absolute knowledge,

12:30 as a basis of attacking this Kantian version of agnosticism. And the key he has to do this is his expanded notion of conceivability. And his expanded notion of conceivability ties in to Riemann's work, Riemann's geometry, in two ways, really. So, I think what I'm going to talk about very briefly is what Riemann's geometry is about and show in what ways Clifford draws his notion of conceivability from Riemannian geometry So what Riemann did was step back from the idea that geometry is about physical space as such and develop the abstract concept of a manifold. So a manifold, most basically conceived, is a collection of points, either discrete or continuous, and it concentrates the continuous case. Some examples of which are, in the one-dimensional case, curves are manifolds, surfaces are two-dimensional manifolds, space is an example of a three-dimensional manifold, but they are higher-dimensional manifolds. With regard to three-dimensional manifolds, of which space is one, types of manifold we can have, characterised by different curvatures. So one possibility is that a three-dimensional manifold could have irregular curvature. And this is a possibility that Clifford considers. He says that physical space may be a three-dimensional manifold with irregular curvature. the idea being that this manifold has little wrinkles or little heels of curvature which are constantly being passed on like waves and this forms the base of his space theory of matter the idea that having this curvature that's being passed on like a wave can be used to explain the motion of matter and this has been taken to be an anticipation of Einstein's idea that we can do physics by doing geometry basically the geometrization of physics so that's one possibility another possibility is the one that Riemann raises that space could be a three-dimensional manifold with constant positive curvature and this is a possibility

15:00 which he talks about as having the consequence that we can that space could be both finite and unbounded. So the way of thinking about it is to consider the surface of a sphere, which has a finite area and yet doesn't have any boundaries, so it's unbounded. And so space could be the three-dimensional equivalent of that. So in raising these different possibilities, raising different possibilities for what physical space could be like. and this shows or Clifford Tapes is showing that we can conceive of alternatives to Euclidean geometry so this is the first aspect of his notion of conceivability, the idea that we can conceive through this process of abstract mathematical conceptualisation but there's a further aspect there's a much more concrete aspect to his notion of conceivability which is brought out in his lecture on the postulates of the science of space, which is basically a popular exposition of the last part of Riemann's paper, which is called Applications of Space, which is basically about five hypotheses that Riemann sets on a three-dimensional manifold by which we could recapture our intuition of Euclidean space. The idea is that if we add these five to our intuitive notion of Euclidean space. But these hypotheses are not necessarily true, they're just hypotheses, empirical hypotheses. And in his lecture, Clifford is really talking about these five hypotheses, he calls them the postulates of the science of space, and he reduces them to four, but they are essentially the same. But what's interesting about the lecture Is the way that he He sets out to present Each postulate To his Non-mathematical audience By showing how you can conceive Of each postulate as being proved But importantly also showing how you can conceive The negation of each postulate As holding And by showing That you can conceive the negation He's showing that these are not necessary truths of something it's not necessarily true and this tells us something about his notion of conceivability so for example one way he has a showing that the

17:30 postulate that space is continuous might not hold is by using a couple of analogies so he uses the analogy of the wheel of life so it's a picture taken Maxwell's letters the idea being that it's a wheel that goes round it's got pictures images attached to the side and when it goes round you get a continuous image, for example something juggling, but as you slow it down you find out that this isn't a continuous image but it's a series of discrete images our notion of continuous further breaks down to these discrete things he also used the example of water which appears to us as continuous but when we look at its substructure as it were we see it's got discrete substructure it's made up of molecules so he's showing through examples to analogies that what we initially think of as continuous might not be and therefore space which we think of as continuous might also not be so this is a way he has of conceiving the idea that space might not continuous. Another way he has of conceiving things is in his discussion of the possibility that space could have a constant positive curvature. And he conducts kind of a thought experiment where he says somebody could set off at a particular point in space, let's imagine, and set off in a straight line and keep going until they end up at the same place, but if they started off going up they'd come back from below so this is a thought experiment which can't be carried out in practice designed to show that a space of constant positive curvature is conceivable so what these examples show about his notion of conceivability is that he uses things like analogy and thought experiment to conceive of things And as he himself points out, these tools we have, conceiving things, can be increased as we learn new facts and new concepts. In other words, our notion of conceivability is not confined, but it expands as we learn new things. So putting these two different aspects of conceivability together, the more concrete aspect and the more abstract aspect,

20:00 We see that, in some way, Clifford's notion of conceivability is co-extended with science itself. It extends as far as abstract mathematical conceptualisation, that's a way of conceiving things, but also these very concrete ways of conducting analogies, like the thought experiment, analogies, is another way of conceiving things. It's a more expanded notion of conceivability, on which we cannot set any A4OI limits. And Paxton's showing that Our notion of conceivability Is not confined to some kind of Intellectual box Box of our mind And that we can't set these a priori limits On what is knowable Because we can't set these a priori limits On what is conceivable And in this way he undermines this idea That there are these boundaries To what is knowable Which are boundaries on our intellect and he's thereby able to reject this quasi-religious notion of the unknowable and unknowable that we can know about or we can know that it exists but we can't know what it is like and he thereby puts his emphasis on what is knowable and what is knowable is what we can know through doing science ok so that's basically what I'm going to talk about that's basically what I'm going to say like I said the emphasis here between his agnosticism and that of his fellow agnostics. It's a difference which shows direct influence of his mathematical preoccupations, which are with Riemann's geometry. And it shows how he drew important lessons from Riemann's geometry about the notion of conceivability. It gave him a much broader notion of conceivability that he was able to use in order to undermine a certain current thought amongst our Gnostics that we can confine what is knowable within a box and say the rest of it is unknowable and that's the domain of religion which is something he doesn't want to allow what he wanted to do was emphasise that science is the only guide as it were to giving us the answers and there's no way for anyone to consider what science can tell us ok, it's on the talk

22:30 give me a minute I've got some thoughts I just want to make sure I've got some things clear before I ask a question you're saying again that setting aside for the moment the difference of his agnosticism with others is that the variations in geometries are reminded of the same with generally scientific theories. It's shown that there was no such thing as absolute truths. Truth, per se. Which strikes me as interesting. Okay, I just want to make sure I have that clear. It's interesting because it seems to reveal, at least to me, that he's completely immune to Reformation theology. Because it's only in a Thomist, you know, world view that you would think that absolutely the truth would be evidence for God. The Reformation theology is based on a complete income. And so, it's striking that his agnosticism is based on a limited conception, theological conception. I don't know what his, you know, background was theologically. might have just been other agnostics portrayals of philosophical theology. But I'm wondering, you know, what would, what was, he might have liked to hear the idea of the complete providence of the willy of God and the fact that we have to, in a certain sense, recreate that image or build it up ourselves. what were his sources theological sources well first of all I guess did he have any training he was at one stage a high churchman and he had the idea of giving scientific justifications to various theological doctrines in the Catholic Church oh he was well he wasn't a high church

25:00 Anglican he was a high church you said high church when I thought you meant Anglican you mean that he was he was an Anglican you said Catholic oh Catholic, small c doctrines right, okay, sorry lots of bells So I don't know that much about the actual process of him losing his faith I don't know what that's looking for But I guess the general idea behind his agnosticism was that he's not rejecting as it were The idea that we can know that God exists What it's saying is that If we are going to make such a claim That that claim is going to be a scientific claim It's going to be a claim which is made In order to explain certain things So for example He talks about Our knowledge of morality The source of morality As being our conscious reasonable explanation for this, one reasonable hypothesis for this is the theistic hypothesis the idea that our conscious is the voice of God. Basically it's one that he rejects but he regards a kind of reasonable hypothesis. So he thinks that theism can in certain ways be a reasonable hypothesis and he's not rejecting that. But he has actually specifically rejected in the areas where he thinks that hypothesis is attempting to explain certain facts I don't know if that helps yeah I'm just wondering you know if he was kind of given a limited bag of goods theologically might have been interested in some other things that were around in a long time I don't think politically He was probably as philosophically and philosophically informed as most of his contemporaries, both because of his studies here and because of his reference to London. For example, one of his best friends is Morris, who is the founder of Christian socialism.

27:30 I think some of the oddities perhaps because he hasn't read the stuff but that's probably not what's going on I mean one thing that struck me in this paper that we've got in this version of the program is there's a very interesting relationship between this version of what Clifford's agnosticism and some then very well-known high church doctrines about the function of history. I think that's one of the really good things in this version of your talk. Because there's a group of high churchmen in the 19th century, led by Newman, certainly you are wants to say that the difference between high church i.e. Catholic religion and the errors of the low church and the evangelicals is the difference about what revelation is right so the low church revelation is singular and complete that's why it's pencil in that there is fixed boundary between secular and transcendental knowing. And that's set for all time. It happens at a revelatory moment. Spencers is pretty explicit about that. Whereas Clifford, and I think you've brought this out really, really, really well, has a completely historicist idea of what doctrine is. That it emerges, that it's a continuous change, potentially continuously advisable as it might seem to mere believers, right? Because revelation is a continuous process. Except that, for Clifford, revelation happens through science rather than through an established church or through the isolated soul of the individual believer, right? It's the collective, embodied, reliable knowledge of the scientific community that represents for all of us. the limits which are contingent to the changing and, of course, expanding to what it's now possible to conceive. I mean, I thought you did this more clearly here than in the Masters of the Threat, right? And it sounds like Newman. I mean, Newman has writings after writings in the 1850s and 60s, which I reckon could have known,

30:00 on the historical process of the revelation of doctrine, how it's an emergent process rather than a singular, sudden. I mean, roughly speaking, this is very rough, and enterprise, if you want to draw our attention away from the person of the living Christ, towards the collective of the church, except that, as I say, the church is silent, which is a lot of things as well. So I think that, I mean, there's a high churchiness in this version of Clifford, which I quite like, and the low churchiness in your version of Spencer, it seems to me, roughly. That's useful. Right. Thank you. But then I have a question, which is, okay, so if the truth is necessary, you can't conceive, it's opposite. If that's the definition of a necessary truth and conceivability is historical, that is to say it changes, then so does necessity. And that's pretty weird, right? I mean not even the pure things happen. So does Clifford really think that... That's not the definition of necessity. It's a criteria for showing that something is not necessary. If you can show that its negation is conceivable, then you've shown that it's not really necessary. He does give the normal definition of necessity as something whose negation is impossible. Nevertheless, it looks as though the number of necessary truths about Shakespeare to us is going down. The limits of conceivability are expanding. That's what the history of science is. Therefore, the number of necessary truths must be going down. in an absolute sense the number the number of truths we take the number of truths we take to be necessary is going down does he really think that

32:30 that's a very interesting thing to think isn't this an issue of the implication of it goes in one way though it's the conceivability could refute the necessity necessarily a necessity established in conceivability. Absolutely, but if conceivability is becoming a more and more corrosive tool, more and more powerful tool, the number of analogies and cases and exemplars that mathematics and science are providing us with corrodes the number of principles we hold that up till now we've taken to be necessary because they're in, because their antithesis is inconceivable. So the stock of principles which we recognize as necessary is for me. And I can't see in Clifford, in your version of Clifford, where if you like, new necessary truths are going to be coming from to make up the difference. I don't think he thinks there are going to be necessary truths. One of the things that doesn't happen in the history of science is the stuff we thought we could conceive as contingent turns out to be necessary. That isn't happening. Yeah. I mean, yeah, the truths that we tend to be necessary are dwindling in Clifford and the only real area left, I think, where he thinks that there might be something like necessary truths will be in areas like arithmetic and logic. But even in that case, because he's got this kind of neurological version of capitalism, they're not strictly necessary, as it were. He's got this evolutionary epistemology by which he thinks the truth of rhythm and logic pertains to the language of thought, as it were. And this language of thought evolved in a way that aided in our survival. it could have been the case that we could have had a different evolution environmental conditions could be different, could evolve a different language of thought in which case the statements, arithmetic logic as we now have them would be meaningless so what we now take of as truths, as necessary truths

35:00 wouldn't have been the case, so it's possible that they wouldn't have been the case so they don't have any kind of strict sense of necessity they have a sense of necessity in the sense that we can't actually conceive of them being false because they are so much part of our language of thought. So there is a kind of like ambiguity or split in his notion of necessity by which you could say the truth and logic are have a kind of weak necessity and that's the most we can say but they don't have this very strong necessity that it could not possibly be otherwise. So the necessary trees are dwindling and are being weakened as well. Okay, so the supplementary question is what do mathematicians do? That's always possible to be here. I mean, after all, a conventional model of what London Mathematical Society members are doing in the 1870s is that they're proving theories. Right. And one way of understanding what that activity is, is the revelation of the necessity of propositions we up to now have taken to be conjectures or merely empirical or something like that. whereas Traffordian mathematicians aren't doing that exactly there's two kind of things they're doing so the people working in geometry and mathematical analysis are actually proving results that apply to the physical world so the results are in a sense empirical about the physical world whereas people working on arithmetic and logic are looking at the consequences of our logic of thought of our language of thought so it's two different things they're doing and in particular the first part geometry and mathematical analysis Clifford is keen to show that both geometry and mathematical analysis are about the physical world because he wants to include them within the scientific naturalist scheme this composite vision that he has of science and he doesn't want pure mathematics to be left out and he also wants to show the value

37:30 mathematics so he wants to show that they really are about the physical world and therefore they tell us something about the kind of things that we'd like to know and would help us Does he not have any issues with making basically everything with completely getting rid of the necessary trees because the problem I have is that if you make thought was a necessary truth contingent upon environmental conditions as you were saying how are you getting over the fact that the environmental conditions might themselves be contingent upon other stuff what is it that we live in one world what is it that has established the laws which we have now if they're not necessary why do we have this particular set of laws what are they contingent upon is it not just Did he not get rid of God at the expense and just invoking chance? Or, I mean, is this a question which he doesn't raise at all? Well, not really, because what he's talking about is what we can know and the kind of questions you're asking about things that we might be able to know in the future, but at the moment we don't know. Yeah. Would you have to say something about the neurology, which you did in the paper, I mean you have to say more about that in the answer to Chris's point, that a lot of this material which may seem to be necessary or contingent insofar as it refers to something external, is actually, just as you said in reply to me, propositions which gain their strength from evolutionary adaptation. and the history of natural selection, and therefore propositions in fact, it seems to me, at least on your show, about psychological, physio, sorry, psychophysiological condition, that's just as historical. So we don't, I mean, in that sense, I guess what you might say is that, by my own premise, we don't necessarily have a lot of work. They could be other species. Okay, yeah.

40:00 I mean, is there I mean, is that right that Clifton's kind of answer to the problem of infinite regress is always to appeal to evolutionary development isn't that right? I'm not sure that you answer this No, I think it's a pathetic answer Yeah, he does appeal to this point of view that certainly in the case of rhythm and logic which talks about the logic of thought that is something that we can maybe investigate by doing neurology by looking at our psychology and finding out these necessary aspects of a language of thought, and that ultimately that depends on its evolution of history. I'm not sure what I can say. For example, take a physical proposition like, say, Newton's first law, which was a strong I suppose what Clifford would say, I don't know, is that evolutionary development is such that we are now hardwired to think that causes are proportional to effect. And that Newton's first law of motion looks like a necessary truth, because of natural selection, privileging folk who think that causes a proper proportion to effect. And Newton's first law is just a mathematical formalisation of that. So, I mean, even something like that, which is both empirical and potentially necessary, such that it's hard to imagine the negation. We don't have to imagine or conceive the negation now, we would then have to show the evolutionarily adaptive futures of that principle. So one could add to your list of stuff that it gets from science, all the evolutionist stuff too, and it's not just zoetropes and so on, it's also Darwin himself.

42:30 It seems to me that's how it works. And I would then say philosophically the reason why that is dodgy is because you can't get an account of why it's adaptive to think the causes are proportional to effects, unless, to put it bluntly, they are, which is Chris's question. I'm curious about the Wheel of Life. Did he ever mention his sources, like earlier sources, the same kind of thing he used. For example, the 18th century judge with Adam Matthews Kirchner, or Charbonne-Kirchner, perhaps. He strikes me as something that I've already seen in the 18th century. No, I don't think he actually mentions the source of when he talks about the revival, he just talks about it in terms of something that was well-known at the time. So I can't remember any particular source of that. Was he the only one using that particular thing, or was he also referring to this real-life? Well, this is Maxwell's real-life, so I guess other people are talking about this at the same time. It's just an animation machine, right? Yeah. I mean, similar objects would be used in Europe by collectors who are kind of interested in seeing how the natural world works. So that's why they also understand ways of life, but with totally different computers, of course. This one's in the Countess. Now. I mean, it's in their museum. you can go and see it and Duffin certainly saw it because Maxwell used to use it in his lectures to demonstrate vortex rings

45:00 because there are some drawings that Maxwell made of vortices moving and then you get the students to look through these so there's an immediate context but wasn't it Absolutely. Maxwell, I think, is the first person to use it in physics, which is not very surprising. This machine is invented in 1829, and it's one of dozens of similar devices exactly do so. For some reason, which I've never understood, in the 1820s and 30s, there's a sudden explosion in devices like this, especially here and in Paris and in Brussels. So Plato, who is probably the most famous person working as Joseph Plato, who is a physicist in Ghent, invented a machine with the wonderful name of the Phanekistoscope, which is this with a mirror in the middle. So instead of slits, what you do is you have a continuous strip. I think it's on display in the Prolizian underground at the moment. I'm sure. I'm pretty confident. So you have a continuous strip with the figures painted on the inside and then it spins and you have a spinning mirror in the centre and it's sort of looking through since you look over the edge into the mirror and what you see in the mirror is the dots and the figures. In the mirror So that was invented in 1831, which is three years after Zodra. And in 1826, Peter Roget, who was Secretary of the Royal Society, writes one of the first really serious papers on the phenomenon of resistance and vision. And in 1831, Michael Faraday invented his own version of this, right, made the lecture on it at the Royal Institution, which is called Faraday's Wheel, which is simply a mirror there, right, and a disc, which you hold vertically, and it has slips in it, right, and you spin the disc, and that's how you see the phenomenon.

47:30 So by Clifford Maxwell's design, this is coming everywhere. What was he doing with it? What was the principle that was demonstrated? Something continuous can be made outside of this. Can I just change back slightly? I was interested in your... So Clifford's link between kind of egocentrism or whatever, and going back to a more cautious extrapolation of things, and that seems to link in with sort of the idea that geocentrism is no longer an absolute truth or an absolute necessary truth or whatever, so you become. and this course does. Clifford or Woody actually have had a problem with the fact that you could argue that there were no absolute laws of nature and that they weren't founded or anything and that the whole court basis just kind of didn't exist. I mean, you can't that quote about crystallization of hand forces, but he seems to be wanting to be just absolutely open to everything. So, if you got rid of all laws in Asia and so on, you just adopted them on a convenience kind of basis, which I'm not sure if you can actually do that, but you're just open to everything. I guess the idea behind the crystallization thing is that he wants to avoid the idea that we stick to any kind of traditional source of authority, traditional views within science because then if we avoid doing that and we give science a free way we allow it to develop in certain that might not be readily useful but might have an application in the future so it just basically wants to encourage

50:00 the development of science by taking away restrictions we have so no part of science becomes codified solidified as it were so I mean you know, that we can remove all forms of visualization, or just the ancient authority type thing? The idea, I think, is basically once we have evidence that something that we believed in for a long time might not hold any longer, then we shouldn't stick to the, you know, conservatively stick to what we believed. that it's been believed for so long, we should allow that to go. Is that just evidence that that thing doesn't exist or she doesn't hold? Or just sufficient evidence that we can conceive that it might not hold? Which would get rid of her much greater... If we conceive that it might not hold, that would tell us that it doesn't necessarily hold. that doesn't say it's false then we have to do a few of them investigations to find out it's false so conceivability just works just acts against the idea of insensibly basically I was just going to say just as a point of curiosity when you say the naturalists needed to establish themselves as political thoughts I was wondering why, what were they actually trying to do I mean, secularise in some kind of no sense but related which is the point that if they hold it as a principle that it's not right to be proper, then that legitimately seems to be quite a subversive political force. I guess they were. One of the political points was that some of the early scientists actually, like Paxlandt and Tinker, find it quite difficult to get jobs. So they were trying to promote the idea of science career in order to be able to have a secure position for themselves. That was part of what they were trying to do. for the subversive element they were trying to subvert the non-conservative political status because they had to change something in order to give science a better footing and promote their own genesis I mean some of the later people in the 19th century

52:30 involved, Maxwell and Kelvin do have major issues with scientific naturalists and the materialists as well What were these guys like, socially, going around saying that it might not be the right to be proper, sounds like they might be the trickles and harsh that thing? Well, Clifford was particularly outspoken in that way. They were kind of a mixed bunch. Clifford was he was like a very social person a large group of friends and he would he would speak out against he would write his little poems attacking traditional theological views and stuff like that so he was like a free spirit they weren't all like that and even Leslie Stevens much more introvertly less open Sorry, having just mentioned materialism What were his use of materialism? Because there's a definite spectrum from naturalism to materialism He was actually an idealist Sometimes quite explicitly an idealist So his idea was basically that Reality or objects, as it were, are composed of feelings And that what makes these feelings objective, as it were Is the idea that other minds have this Our assumption that other minds have the same kind of feelings Gives them a sense of externality Which makes them objective And what we do, we do science We make inferences We're making inferences about these feelings Right he mentions Barclay as a source for his idealism that's quite different from Tyndall for instance isn't who's definitely kind of hard particles and forces that's about all that is really I guess I don't know how to think of someone like Huxley they were criticised the fact that they at times seemed to

55:00 be like and other times seem to be idealist, so there's also some kind of tension between these two aspects. But Clifton certainly does seem to be explicitly an idealist, and this actually in some ways helps in some of the things he says about geometry. For example, his idea that things like surfaces are boundaries, and lines are boundaries, and points are boundaries. He's able to assert that this means that they really exist in the physical world, because boundaries are just like any other object, just feelings that exist in our consciousness in terms of doing physics by doing geometry, again idealism helps there because the idea that matter and motion of matter are reducible to stuff we say about geometry it helps if you're an idealism in that sense, you know, what you're talking feelings, which is what you're talking about when you're doing geometry as well so because idealism does actually help specific aspects of this science that makes sense to me saying that, obviously you can then understand why he thinks that conceivability is such an important part to negate necessity because for him all necessity must be effectively mental anyway So, you know, by its very nature, if it's, if the opposite is conceivable, then it's not. Yeah. Yeah. Yeah, that's it. Did he, did he use the actual expression language of thought? Okay. Something in a church photo is called language of thought. Yeah. and issues whilst in language. Did he, it was language, not for him, in co-existence of spoken language? Or was there... No, no, it was internal language. Okay. It's a photo of plagiarism. Haha! I think perhaps we'd better Good, thank you very much. What's going on? What's going on? I'm going to get in there for a night to start. And now you're going to be eating. What time? I'll do it again.