Does Math Point to God? William Lane Craig + Graham Oppy

hello and welcome to capturing christianity my name is cameron Bertuzzi I'm exposing you to the intellectual side of Christian belief that's what I do on my channel I think it's safe to say that in today's episode we are possibly making history I've received so many messages from people saying that they've been waiting years and years to see a discussion alive to debate or discussion or whatever it is between these two guys that I have on with me today dr. William Lane Craig and dr. Graham moppy and today's that day so dr. Craig and dr. Opie are joining me on the show today to discuss an argument from mathematics for God's existence dr. Craig things that say a good argument part of a cumulative case for Christianity and dr. Opie doesn't think that he well anyways thank you guys for coming on the show today it's so great to have you back well both of you guys have been on the show before and it's so it's we were talking about this right before we went live dr. Graham Oppie has been on the show this is his fifth appearance if you can believe that that's crazy he's been on a bunch of times and dr. Craig this may be your fifth appearance actually I don't know I'd have to go back in and check right well let me give a brief introduction of my guess if you don't know who they are dr. Craig is a Christian philosopher he holds two PhDs one in philosophy from the University of Birmingham in England and the other in theology from the University of munchin is that how that how do you know that music there you go in Germany he's written over 40 books many of which we actually featured in a recent interview if you want to go check that out he's authored dozens of peer-reviewed articles he runs an online ministry called reasonable faith the link to that ministry is in the description of the video dr. Graham moppy he's our atheist guess he's been on the show several times like I mentioned including to discussions with dr. ed fazer he holds a PhD in philosophy from Princeton University his dissertation was on semantics for propositional attitude ascriptions in philosophy language most of his recent publications have been in philosophy of religion though he's also published in metaphysics epistemology and philosophy of science if you guys want to learn more about apologetics and see intelligent conversations between Christians and non-christians like the show you're going to see today make sure to subscribe to the channel and turn on a little bell you can get notifications when we post new videos alright with that let's get into it the format's for tonight is going to be pretty simple we'll have one hour of dialogue followed by 30 minutes of Q&A so we'll get a total of 90 minutes and we won't go any longer than that at all well let's start with a quick explanation of why the two of you have decided to discuss this particular topic rather than what I think most people were expecting or hoping for perhaps the Kalam cosmological argument let's pass it over to you dr. Craig well I think that we both felt that that topic had been pretty exhaustively discussed and that it would be much more fresh and interesting to tackle a new topic that we haven't discussed previously right so that's that's the basic idea there they've done they've gone back and forth in the literature on the Kalam cosmological argument several times and so if you want to see a discussion on that between them two then go go check out some of the articles that they've written well let's get into it so dr. Craig spend however long you'd like to take to lay out the argument and I was I was we talked about this too I was listening to your discussion with Daniel came on unbelievable and one of the things that I wished had happen in that discussion was to give some some concrete examples of how the applicability of math to the physical universe provides evidence for God so like what are some concrete examples but give the examples after you lay out the argument sure we agreed to use as a springboard for our discussion today an article published by Eugene Wigner in 1960 entitled the unreasonable effectiveness of mathematics in the physical sciences Vigna was a Hungarian born physicist and mathematician who emigrated to the United States prior to the rise of Hitler's Third Reich and he went on to become one of the greatest physicists of the 20th century earning the Nobel Prize in Physics in 1964 for his contributions to the mathematics of quantum mechanics and in this article vikner argues that the applicability of mathematics to the physical world is a mystery that cries out for some sort of explanation now what do we mean by applicability of mathematics applicability has to do with mathematics reliability or utility in successfully navigating the physical world physicists find that the laws of nature can be expressed as mathematical equations which describe physical phenomena to an astonishing degree of accuracy and so Victor's main point in this article was and I quote mathematical concepts turn up in entirely unexpected connections in physics and often permit an unexpectedly closed and accurate description of the phenomena in these connections so with respect to mathematics role in physics vikner notes that mathematics plays an important and what he called sovereign role in physics which enables us to formulate the laws of nature in the language of mathematics in order for them to then be an apt object for the use of applied mathematics and vikner argues that the mathematical formulation of the physicists often crude experience leads in an uncanny number of cases to an amazingly accurate description in a large class of phenomena and he gives three examples in support the first example is Newton's second law of motion F equals M a where F is the force of an object M is the mass of the object and a is the acceleration of the object second example is the use of so-called matrix mechanics in the formulation of ordinary elementary quantum mechanics and his third example is quantum electrodynamics which is a theory which unites quantum mechanics with special relativity in order to describe electromagnetism and these examples which grow in complexity as you go through them and which he says could be multiplied almost indefinitely illustrate the appropriateness and the almost fantastic accuracy of the mathematical formulation of the laws of nature at this point vikner then muses it is difficult to avoid the impression that a miracle confronts us here he thinks that the success of mathematics in physical theories is truly surprising and he gives one reason for that and then I would like to add one his reason is the opry or e nature of mathematical theorizing big nurse stresses the a priori nature of mathematical inquiry especially the mathematics that's so valuable in physics I quote whereas it is unquestionably true that the concepts of elementary mathematics and particularly elementary geometry were formulated to describe entities which are directly suggested by the actual world the same does not seem to be true of the more advanced concepts in particular the concepts which play such an important role in physics most more advanced mathematical concepts such as complex numbers algebra linear operators Borel sets and this list could be continued almost indefinitely we're so divided that they are apt subjects on which the mathematician can demonstrate his ingenuity and sense of formal beauty and big nur finds a particularly striking example in complex numbers these are numbers which are multiples of the square root of negative 1 he says and I quote certainly nothing in our experience suggests the introduction of these quantities indeed of a mathematician is asked to justify his interest in complex numbers he will point with some indignation to the many beautiful theorems in the theory of equations of power series and of analytic functions in general which oh their origin to the introduction of complex numbers the mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius end quote so who would have ever anticipated them the centrality and the usefulness of complex numbers in physical theory the second reason I think it's surprising and unexpected is because of the causal impotence of mathematical objects I would add to bigness point the fact that mathematical objects even if they exist have no causal impact upon the physical world so that their applicability in the physical world is I think surprising so the following would seem to be I think a suitable formulation of big nurs argument in his paper it consists of four premises number one mathematical concepts arise from the aesthetic impulse in humans and have no causal connection to the physical world premise two it would be surprising to find that what arises from the aesthetic impulse in human and has no causal connection to the physical world should be so significantly effective in physics from those premises it follows that it would be surprising to find that mathematical concepts should be so significantly effective in physics the third premise states that the laws of nature can be formulated as mathematical descriptions which are often significantly effective in physics and then for therefore it is surprising that the laws of nature can be formulated as mathematical descriptions that are often significantly effective in physics so given this unexpected applicability of mathematics to the physical world it seems to me that the applicability of mathematics does cry out for some sort of explanation and that's where big nerds article end he has no explanation for the applicability of mathematics as a naturalist he simply left with a mystery he says the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve and that is where his article finishes all right would you like to come in here Krim sure so that's really interesting and I like the formulation of the argument I tried to write it down while you're saying it and I thought it think that it's helpful because it points to a couple of the point of places where I would question what Vigna says so you're the the first premise was something like that mathematical concepts at least certain advanced mathematical concepts come from aesthetic impulse and the idea was that the complex numbers one of the ideas was that the complex numbers an illustration of this I think that that's probably not right so I remember doing studying some complex analysis when I was doing my maths degree and one of the interesting things about the complex numbers is what you can do with them so you can start with real valued equations that you can't solve analytically using real analytic techniques but by making a transformation into the complex plane you can do some complex analysis and then of by purely analytic techniques out pop some real numbered answers so that the utility of the complex numbers at least initially and the reason why mathematicians were interested in them was anaesthetic it was because there were practical problems that they wanted to solve they wanted to be able to give exact solutions to these real numbered equations and it turns out that the only way that you can do that is by taking a detour through complex analysis I think more generally that Vigna underestimates the extent to which mathematics is about problem solving and overestimates the stuff about aesthetic impulse I think that typically mathematicians are interested in puzzles especially long-standing puzzles but puzzles that they want to solve and then they're looking around for ways to make advances and when when a long-standing puzzle does get solved the expectation is that lots of new mathematics will follow on its train you'll remember when Wiles proved Fermat's Last Theorem some time back there were some expressions of disquiet amongst some in the mathematical community because they couldn't see that there was lots of new mathematics that was going to be coming out of it but but the general point I think is that figner is kind of talking up the wrong thing when he's talking about the reliance on aesthetic considerations because I think that mathematics is much more about problem solving anyway that's the first thought that you might want to say something about I think that it's certainly true that these mathematical concepts do find very practical applications for example in something as simple as electrical engineering complex numbers turn out to be critical and very useful but I don't think it's true that what drives the working mathematician is scientific utility the philosopher of mathematics Penelope Maddy has written eloquently on what she calls maximizing principles in mathematics which he says are of a sort that is quite unlike anything that turns up in the practice of the natural sciences she says and I quote crudely the scientist deposits only those entities without which she cannot account for our observations while the set theorist deposits as many entities as she can short of inconsistency and Mattie identifies quite a few of these what she calls rules of thumb that are followed by mathematicians in choosing their axioms and constructing your theory such as maximize richness diversity one step back from disaster etc and in a similar way big nur in his article observes and I quote the great mathematician fully almost ruthlessly exploits the domain of the permissible reasoning and skirts the impermissible so it does seem to me that mathematics is driven by this a priori quest for mathematical fruitfulness the sort of fruitfulness that you said disappointed some mathematicians when Wiles proved Fermat's Last Theorem they want to see mathematical richness but scientific applicability isn't what drives the mathematician and and and and therefore these disciplines it seems to me are very different in the way in which they operate so I don't think anything I said contradicted what you just said then so I wasn't suggesting that what was driving the mathematicians was applicability to the Natural Sciences or to the sciences generally but it's mathematical problem solving which is not an aesthetic consideration it's all I want to work out what the answers are right so I know these I've got these real valued equations right I want to be able to solve them it turns out the only way you can solve them analytically is by making this detour through the complex plane so I one way of explaining how complex numbers get into mathematics in the first place is from a desire to solve puzzles of another kind how do I solve these equations these real value equations how do I give exact solutions to them and so I would and I'm thinking that's not aesthetic it's something else it's a challenge you're trying to get the right answers that drives mathematical innovation and that Vigna is stuff about I kind of in utility and beauty and things like that isn't the primary consideration for mathematicians generally that was my thought so I just wanted to do disagree I feel quite certain having digested big nourish article that he understands aesthetic you know broad sense that would include mathematical problem solving he often talks about how the mathematician chooses concepts on which he can exercise his mathematical ingenuity and develop formal beauty so certainly mathematical problem solving would be included in this and I think Vigna would call that broadly aesthetic I myself prefer to refer to it as a priori it's it's not an investigation of the empirical world but it's a purely a priori discipline that then finds unexpected application in many cases in the laws of nature can I jump in here real quick and can I get like an explain it to me like I'm five of this of where we're at so far in this argument because everything that's happened so far is just right over my head so how does how does this apply to the to the argument from the applicability of math to the universe okay so let's go back maybe I'm in viable to build to read out his first premise again yeah that would be that kind of most automatic akan ceps arise from the aesthetic impulse in humans and have no causal connection to the physical world right so I'm thinking about the first bit just the mathematical concepts arise from an aesthetic impulse the way that I would understand that that just sounds false it just sounds way too narrow so that's what I was worrying about because it was the first premise in that argument but what Bill's been saying is that maybe we should understand the aesthetic impulse in a fairly general you know a more extended a sense than you ordinarily would so that would pick up what I think is what much of mathematics is motivated by is unsolved problems in mathematics and you're trying to work out what the answers are and that doesn't feel to me like it's an aesthetic impulse right it's it's something much more truth directed because you want to work out what the right answers are well okay now I would be cautious there Graham because for example you know there are alternative set theories and set theorists are very happy to adopt more restricted axiom sets and explore the consequences or to adopt additional axioms and to see what those consequences would have ordered it to opt for an entirely different set of axioms and so there's a variety of different theories and the question isn't are they true it is rather as you say the sort of mathematical problem solving so I would be cautious about saying that mathematicians are motivated by a desire to figure out what is true so I I think yes and no sorry there's a controversy amongst set theorists about whether there's one true set theory or not and there are people like who wouldn't who say yes and then there are many people on the other side who say no but if you look at some of the things that are controversial in set theory so where you can take an alternative route and develop an alternative set theory so you can do cert 3 with that choice or without the continuum hypothesis to pick two examples you're most working mathematicians are perfectly happy to accept both choice and the continuum hypothesis and sure you can you can explore what happens if you gave them up but if you look at what so it's so for example to go back to the example that we were talking about before Wiles is proof requires that is his proof of Fermat's Last Theorem requires the axiom of choice very few people have objected to the proof on the grounds that it assumes choice most working mathematicians think that's just fine and that view is consistent with thinking okay what would happen if you gave up choice what would set theory look like right but that's just a different kind of you know problem that you know a politicians might be interested in which doesn't undermine the idea that if Wiles is proof is a proof it shows that what Fermat said was truly right that's me so I'm not sure whether that's entirely satisfactory anyway maybe we should move on to another well let me get to Cameron's question about how would we explain this to a five-year-old suppose you're trying to figure out how many gallons of paint you need to paint the floor of the playroom well what you would do is you would as I say the playroom is square or rectangular you would measure the distance in feet one way and then the distance in feet the other way and then you would multiply these together to figure out how many square feet are in the room and then you would find out how much paint you need say per square foot and that will then tell you how much paint you need to paint your room that's an example of the applicability of mathematics you can figure out how much paint you need by mathematics now that is but that's what you asked for vendors point is that when you get into relativity theory quantum mechanics quantum electrodynamics there you have mathematical equations of breathtaking complexity and astonishing accuracy in describing the physical phenomena is that clear yes that yeah that's that's very clear but but it's not clear where the disagreement was was happening how that relates to the example that you just gave and it it'll be hard to bring it out in respect of that example because it's quite plausible that the mathematics that we're using there was originally developed for practical applications so if you think about elementary arithmetic and elementary geometry it was precisely because we wanted to do bookkeeping and work out how to apportion odd shape plots of land equally amongst the heirs and things like that that elementary mathematics developed so it was designed precisely for its application to real world problems and you don't I mean big news worries don't come up in connection with elementary arithmetic for example radio he branched that point yeah yeah so because so you want a different example you want one Cameron you want an example where there's something a bit more uncanny about the applicability so I go back to the concepts that Vigna picks out so the complex numbers when you think about the square root of -1 right the kind of defining thing for the complex numbers and then you think about electrical circuit theory and you wonder what on earth could the square root of -1 have to do with the equations that we use to describe current flow in electrical circuits or a bunch of other applications to the natural world of the complex numbers then it's puzzling you might think in a way that the applicability of elementary arithmetic or geometry isn't build a certain sound about I like that I thought that was quite clear and then what's the know what's the next step well the other thing was that mathematical objects have no causal connection with the physical world even if you think they exist they exist as abstract objects usually beyond time and space but which are causally a feat they have no causal powers and therefore have no causal impact upon the physical world if param posible all of the mathematical objects were to vanish overnight it would have no impact upon the physical universe in which we live now given that oh and that's if they if they exist of course if they don't exist if you're a nanny realist about mathematical objects then obviously they don't have any causal impact upon the physical world so given that absence of a causal connection between mathematical objects and the physical world it does seem really surprising that the physical world should be describable in such detail and complexity by these mathematical objects Graham is there anything that you disagree with so far say the thing that bill was just saying isn't in the Vigna paper this is his own edition and I'm not sure oh then there's a big dispute to be had about whether the objectivity of mathematics requires objects and you might think that you can not tread the path of the fictionalist but also not be applied missed and there would it would require some argument which we I surely we don't have time to go into to consider whether that's an option or not and so unless it's it comes up in the later discussion I would prefer to put aside the dispute between platon is fictionalist and all the other sort of accounts of the ontology of mathematics because our question is more about the application of mathematical theories to the world and that may not turn on any questions about whether there are mathematical objects well yeah I agreed with that Graham because my point was that whether you are a plate inist and a realist or you are an anti realist in either case there's no causal connection of mathematical entities with a physical world they can't influence the way physics were operates and so it's astonishing then that you would have these mathematical descriptions that enable you to describe and to predict how the physical world is going to behave so I think we should go on a beat and we'll kind will come to this point yeah the other so the other thing that I in so I'm hoping that we're going to have time to get to the that argument about God I'm a bit worried that we won't they're right this is going the other thing in the argument that you attributed to vino that I wanted to ask about it was the claim that the laws of nature can be formulated in the language of mathematics that seems to suppose that we know what the laws of nature are that seems to me not to be so it's true that we formulate scientific theories and they have principles in them but almost always it turns out that we end up thinking that those principles are false if those principles are false then they're not laws of nature here big neurs brilliance emerges in his paper I am just amazed when I read the paper how he anticipates these objections and preempts them he makes a point himself in the paper that he is not claiming that there is a unique description of the physical laws that govern our universe what he says is that the that we can formulate these mathematical laws of nature and there could be different formulations of them there could be he's not claiming that they're unique but we can formulate these laws of nature and then apply them test them and they turn out again and again and again to be accurate in describing the physical phenomena the way the world appears to us so I think that that premise is formulated by big nur in such a way as to preempt the objection that we don't know the final form of the laws of nature that they could be variously formulated or that they may not even describe the physical world in itself but simply the phenomena the physical phenomena as we apprehend them in science ok so let let's think about an example so maybe this will make Cameron happy right a concrete example so think about classical mechanics and think about what happened in the very early 19th century so there is Adams in England and there's lavarro in France doing calculations using classical mechanics and eventually levare says to Gailey point your telescope at this point in the sky and you will see a planet that's perturbing the orbit of uranus it's their explanation for why you know and so Galle goes and points his telescope there and lo and behold there is Neptune oh this was how Neptune was discovered it was a prediction of classical mechanics but the problem is that classical mechanics is a false theory Ryan use it to try to predict the the precession of the perihelion of mercury it gives you the wrong answer right so presumably it can't be that this Theory's accuracy was due to its getting the laws right right it's a false theory it's not just that it's that it's accurate the puzzle is that the theory is false and it's still giving accurate results it can't you can't explain the accuracy of the results in terms of its hooking on to the true structure of the world or hooking onto the laws or anything like that because we know it doesn't so back to you what what is correct I think is to say that the laws of classical mechanics are approximately true that they are true within a certain range and this is not so much falsified as made more precise than by special in general relativistic laws and there's no claim here that we've got the final formulation of physical laws rather with increasing accuracy to often astonishing degrees we seem to be able to describe the physical phenomena in other cases the descriptions might be more approximate but this is this is no more problematic than saying that I have a watch without a second hand that will accurately tell me the hour and the minute of the day but it won't give me the second and that to get the second I need a more accurate watch and if I have a watch with the second hand that still isn't going to give me the current nanosecond I'll need an atomic clock for that so the laws of nature can approximate accuracy with different degrees of specificity okay so that sounds sort of right the relationship between mathematics and the physical world is one of fit to within acceptable limits of Tolerance of empirical predictions in some cases but not all and that's general so whatever Theory we're talking about it's got a range of application and outside that range of application it doesn't give you the right results and so on then the questions going to be at least one questions going to be what's uncanny about that why not just think that that's what you'd expect given the power and flexibility of mathematics because now we're not talking about some amazing fit between the mathematics and the true structure of the world we're talking about our ability to make models that will give you the right results across some domain to within some specified tolerance some you know limits of accuracy so when gully points his telescope to the sky Lavar EA's calculations accurate within one second of Arc but when you care like the precision of the perihelion of mercury using Newtonian theory it's just wrong it's out by so much mm-hmm yeah III guess I just don't see the problem there I mean the equations were sufficiently too precise to yield a real-world result the discovery of the planet Uranus that is out there it is a real-world result that was possible because these mathematical occasions were accurate to a sufficient agreed to be able to predict such a phenomenon and the equations of quantum mechanics and general relativity theory are more accurate two orders of significance in terms of how accurate these theories are so there is a significant fit that enables us to get along in the universe to get along in the world because of mathematical applicability okay maybe now would be a good time to advance to the argument for God that you want to make sure so can we can we move on yes yes now you remember vikner ended his essay by saying that the applicability of mathematics is a miracle which we neither understand nor deserve but bickner never actually considered theism in his essay as to whether or not that might not furnish a good explanation of the applicability of mathematics and my view is the theist will have a considerably easier time The Naturalist in explaining the applicability of mathematics to the physical world and this will be the case whether one is a realist about mathematical objects or whether one is an anti realist about mathematical objects on the one hand if you are a realist than the fact that reality would behave in a cool with these causally a feat abstract objects beyond space and time is in the words of philosopher mathematics Mary Lang a happy coincidence which just seems incredible mark Bala Guerra who is another philosopher of mathematics has said the idea here is that in order to believe that the physical world has the nature that empirical science assigns to it I have to believe that there are causally inert mathematical objects existing outside of space-time which is just inherently implausible now by contrast the theistic realist can argue that God has fashioned the physical world on the structure of the mathematical objects that he has chosen and this is essentially the view the Plato defended in his dialogue the Timaeus on the other hand suppose you're in anti-realist about mathematical objects then again it becomes inexplicable as to why the physical world would behave in accordance with these pretend entities that don't really exist but if you're a theist what you can say is that God has fashioned the physical world on the mental plan that he had in mind so that the physical world has the structure that God had conceived prior to creation and this is the view that was defended by the Jewish philosopher Philo of Alexandria so whether you go with Plato or with Philo it seems to me that the theist has a much easier time of explaining the applicability of mathematics to the physical world than does the to lust and so the applicability of mathematics counts in favor of a theistic view of the world okay so to check that I understand what's going on here and maybe I don't there's it sounds as though the story is committed to something like this mathematical theories apply to the physical world because the structure of the physical world is an instantiation of mathematical structures described by those mathematical theories so God makes the world with a certain physical structure because there's a certain mathematical structure that God wants to have the physical world instantiate that's right so that's the kind of Pythagorean idea right number is really fundamental fundamentally the structure of the world is mathematical structure is that part of the idea or not because I'm trying to think you know what wait what does God do here right yes the idea it's part but only part gram and that's really important to see even if you say that the physical world exhibits this complex mathematical structure that it does and that's why mathematics is applicable to it that leaves unexplained on a naturalistic metaphysics why the world should have the fantastic complex mathematical structure that it does that is described by general relativity and quantum mechanics so that's part of it but that's not the whole story by choosing examples like complex numbers and infinite dimensional hilbert space vinner implicitly precluded the explanation that the reason mathematics is applicable is simply because the physical world instantiates these structures because these kinds of structures cannot be physically instantiated and this is the burden of mark Steiners book the problem of the applicability are pardon me the applicability of mathematics as a physical problem Steiner gives example after example of applicable mathematical concepts which cannot be physically instantiated and so what you've expressed is only a part of the story and here again is where theism emerges I think is a better explanation than naturalism because God can create a world that will operate in such a way that the use of hilbert spaces and complex numbers and other unintentional mathematical structures can be useful in describing and predicting physical phenomena okay so I'm not sure I'm following these now so we've so I'm still trying to work out on your theory what what God's doing so part of it is that God makes the physical world to instantiate a certain kind of mathematical structure but God also picks the structure so that it in stands it so that you can use other mathematical theories to investigate that structure but we don't suppose that those other theories instantiate the structure there's some other relationship that holds between them yeah tween the yes okay now we're in that picture so know that maybe it's now becoming clearer what what the idea is in relation to say the example of Neptune the discovery of Neptune right the the theory doesn't latch on to the structure the Theory's false right so it definitely doesn't latch to the physical structure that the world exemplifies again I would say that it does to certain degrees of approximation that I'm not sure that I understand that right all right maybe there's a few gives you an exacta mately true description of our solar system so there's a view that some people have about say the relationship between general relativity and Newtonian mechanics or between quantum mechanics and Newtonian mechanics that there's a there's a kind of quantity and you let it go to infinity or you let it go to 0 and the other theory falls out then you know Newtonian mechanics falls out as a special case and that's how you explain how the one theory is an approximation to the other it's not clear that that's right but it's also not clear how we're going to understand this idea that the theories and approximation that the one of theories an approximation to the other so let me try something else consider what Michael Friedman says in his book on space and time about the relationship between general relativity and Newtonian theory it turns out that I we can write both these theories in the language that was originally the mathematical language that was originally invented in order to make it possible to represent general relativity but you can rewrite Newtonian mechanics in that language as well and when you compare the two theories the difference between the theories is that Newtonian mechanics postulates some extra structure it's not that it postulates less it postulates more right now how can it be that that's ok how are we going to think about that as an approximation to the truth right when what it's done is its postulated extra stuff that meant that it went I think it would depend on whether or not that extra structure needs to be excised to get a more accurate description of the physical phenomena and to predict future results of experiments as you may know I myself think that the general relativity is wanting in structures space-time structures that they deleted some important things like hyper surfaces of absolute simultaneity that tend to be restored in I think Astrophysical cosmology but be that as it may whether the structures are additional or deleted it would be a matter of the degree to which the mathematical laws give us an accurate description of the phenomena and enable us to predict future phenomena as you say the very A's theory didn't allow us to predict the perihelion of mercury we needed relativity theory general relativity theory to make that prediction so I think the theism has more explanatory power than naturalism with respect to this unexpected applicability of mathematics okay so maybe now I should address that question because I'm I mean in a way I feel like I have enough physics really to kind of assess bigness claims about whether there's this unreasonable effectiveness there or not and I thought it taught about lots of examples and wondered you know there's lots of examples of for example simple physical problems in classical mechanics where you set up an equation and you to model some situation and you solve it and then you notice that there are solutions to the equations that just don't make any sense and so you ignore them right on the grass and then on physical but there are all these kind of interesting questions about the ways in which we and so so an example imagine a cliff top and you're throwing a rock into the ocean right and they and they so you've got you know you set up your your model have sea level at zero the height of the cliffs H there's some angle that you project the rock you get an equation of motion and you work out some time at which the rock intersects with the water now your equation is a parabola and so there's another solution where it intersects the exit you know x equals 0 the y axis and at some negative time some earlier time and when you look at that you don't think mmm so maybe there was an anti rock and it tunneled up through the cliff and it was annihilated when what you do is you say that's not a physical solution yes alright and and that's the kind of universal thing in physical in in kind of modeling physical modeling of the universe and so I mean I wondered about the bearing of that on some of the examples that that you've used previously and some of the examples that Vigna gives in his paper for example right there's there's direct prediction of the positron but direct also predicted magnetic monopoles which we haven't yet found what if we never do what if there aren't any yeah right then presumably the magnetic monopole monopole is just going to go the way that the in in my simple example we just say well it was an artifact in the model didn't correspond to anything in physical reality once you start thinking about all of the many many failed predictions from physical theories right that correspond to the success where there's the positron you might wonder it whether it's really true that there's any uncanny effectiveness here or whether it's what's rather the case is just that we forget about all the successes and remember the one or two successful cases so so so I'm kind of worried about it I mean again I don't have any data I don't know he keeps a record of all the failed physical productions physical theories I don't know if there's anything uncanny there or not well both ignorant and Steiner discussed this fact I mean the the failures the mathematical failures outnumber the successes there's no doubt about that when you think about it the realm of mathematics is infinite the physical world is finite so of course the most mathematical concepts of formulations will fail to apply but I don't see that cases in which mathematics fails to apply does anything to explain the cases in which you do have this breathtaking accuracy and detail of mathematical descriptions of the universe I think you can acknowledge the failure of many mathematical concepts to apply and of laws of nature that are false but that just doesn't do anything to render it likely that on naturalism you would have this sort of mathematical precision characteristic of the physical phenomena so I'd like to jump in just real quick well first of all got to mention that we're about to move to QA like in just a few minutes okay so but I do have one one thought on this is that gram it sounds like if we could split the argument into stages or stage one being about whether or not the universe for math does apply or does have this sort of uncanny applicability to the universe if we labeled that stage one and then stage two is how do we explain this is it evidence for theism it sounds like you're wanting to back to stage 1 and say well I don't really know if mathematics does have this uncanny applicability right so that's all I've argued about so far but let me say something about the argument right because I think that it's not true that Naturals have no resources here so I suppose it's true that there's this fit between mathematics and physical structure right of the kind that we're imagining there are versions of naturalism that can explain this in a very straightforward way and so one of the versions of naturalism can do this is one that I've been playing around with for about a decade now and so let me give you the kind of tenants of the theory that you need in order to explain the effectiveness you may when I get to the end of it you may think it's I don't know disappointing that it turns out that this is the way the explanation goes but it's definitely an explanation so start with this a theory of modality so every possible world shares some history initial history with the actual world diverges from it only because chances play out differently right so that's all the possibilities there are the only possibilities that you need really of a chance only talking metaphysics here we're not talking docks axes possibilities or epistemic possibilities we're talking metaphysical possibilities so that's all the possibilities that there are the laws are necessary the boundary conditions are necessary these will be this is true it doesn't matter whether we're thinking about one universe or many universe model so we're supposing that we're contingency comes in is in the outplaying of chances that's that's the only place that contingency comes in we suppose also and this is the only kind of new assumption that we're going to make to go along with the kind of metaphysical picture that we've already outlined which is going to be a naturalistic picture is that the laws and the boundary conditions are amenable to mathematical formulations on that assumption and giving given the other assumptions it just turns out that it's necessary that that's the case it couldn't possibly have failed not to be so now adding a couple of other things that I don't really need just but that are also part of this picture that I developed when I was thinking about the origins of the universe had nothing to do with the applicability of mathematics there's no explaining why something's necessary once you get to the postulation of necessities you've reached the end of the explaining that you can do and last of all if you've got a non-modal claim P net and you believe that oh you accept that necessarily P then it's being necessary that P explains why P okay so now given that we have an explanation for the the effectiveness of mathematics which is that it had to be because it had to be it's so right and it just falls out of the picture now that's a naturalistic story that has an explanation you might not like the explanation but at least for me it comes for free from things that I've said elsewhere I well I hope that our listeners have understood your alternative because honestly Graham I think it takes you more faith to believe that than it does to believe in God the claim for example that the mathematical formulation of the physical world is necessarily true that just doesn't seem to be correct at all there might have been no physical universe whatsoever in which case mathematics would not be applicable because there would be no physical universe or there might have been a sort of chaos Albert Einstein wrote to Maurice Sullivan in 1952 one should expect a chaotic world which cannot be grasped by the mind in any way one could yes one should expect the world to be subjected to law only to the extent that we order it through our intelligence by contrast the order created by Newton's theory of gravitation for instance is wholly different even if the axioms of the theory are proposed by man the success of such a project presupposes a high degree of ordering of the objective world and thus could not be expected a priori that is the miracle which is being constantly reinforced as our knowledge expands so even so great a mathematical physicist this Einstein thought that it would it was a contingent matter that the the world should exhibit this sort of mathematical order that we should have expected on the contrary a chaotic world well let's say let's get let's get a response from dr. avi and then we'll move to some Q&A so unfortunately we do have to move on so when you talk about expectation you may be talking about something epistemic or Doc's asti I was talking about metaphysics I was doing metaphysics and and my claim is that this is the best metaphysical theory I'm not saying that it's true our priori I'm saying that it's the best metaphysical theory when you take everything into account can you specify gram force in a sentence or two why is it the best metaphysical theory in your view because it's if you think about the goal of theorizing what you're trying to do is strike the best balance between minimizing all of your theoretical commitments and maximizing the explanation that you can do and I think that this theory strikes that sweet spot that's that's the reason but there's a lot of data and there are hundreds of data points that you have to think about if we're going to compare this theory say with a theistic theory so I've written elsewhere at considerable length about why I think that you should prefer the naturalistic story to the theistic story it just turns out that the naturalistic story so because this is the point when you formulate in your theory you said naturalist just have no explanation that's not true he is a naturalistic theory that does have an explanation and what needs to be argued is about which one is the better theory and that's not something that's settled by these considerations it's settled by general considerations okay sound very explanatory to me but we'll leave it at that well do you think that you can't explain why something's the case by pointing out that it's necessary because that's all that's going on here yeah I mean it's really a way of avoiding explanation by just begging the question and assuming that it's necessarily the case and that is implausible and certainly not incumbent or or there's nothing that would lead us to think that that's true which is why I you thought it was the best it's certainly an exercise so that's not right though it's not assuming right we've got two theories and we're comparing their virtues the theories are what they are they say what they say it turns out that on this naturalistic theory there is an explanation the explanation is that this stuff's necessary right that's right so now you have to compare the two theories right but but this is the point you have to compare them on the total data in order to see which one's the best theory and I when you do that I say what you find out is that the naturalistic theory is better than the theistic theory all right and in order to argue that you can't point to your dissatisfaction with this particular you know I my theory explains it differently from the way you do so I'm not satisfied with what you do you have to look at the top of the big picture alright let's move on to some to some Q&A here so there's a lot of different questions on this topic so it'll it will open up some new things talked about from Indira she says dr. Wahby isn't the relative disdain of the four-color theorem and Fermat's Last Theorem and exemplifying exactly what dr. Craig is claiming and this happened earlier it in the discussion this the super chat came in earlier that beautiful proofs are more important in the applications are secondary and I think that this disdain for the full-color proof right it was a proof the problem was that it was an abuse I mean the the thing that's true is it's not a beautiful proof it was a computer proof it was done by kind of an exhaustive consideration of cases but that doesn't undermine the result right there was a serious question that people wanted to solve and we want the important thing was we wanted to know the answer now we do so I don't think that the that there's disdain for the four-color proof there's regret perhaps that we haven't come up with a complete analytic solution for it all right we have another super chat from I'm not even gonna try to pronounce that name he says dr. Craig if mathematical concepts arise from the aesthetics of the mathematician would there be causation if so does the applicable clickability this it looks like English might not be his his or the first language so it's difficult to this and worse if so does the applicable causation of at least one abstraction for example beauty not apply to the number seven no Vig neurs argument is quite independent of the concern I have about no causal connection between mathematical objects and the physical world his argument concerns simply the operatory way in which mathematicians pursue their discipline you wouldn't expect it to be so physically applicable when it's pursued in that way my point was that whether you're a realist or an anti realist mathematical objects don't have any causal impact upon the world and that would be the case with beauty too if you think that beauty is a sort of platonic form if it's an abstract object it doesn't come into contact with or or do anything I think what he means is that mathematicians seek beautiful theorems or proofs but that that's not to say that the abstract object beauty is causing them to do this is there anything you'd like to add Graham okay next super chat from Cranham in photo cinema and he is our videographer he sends in super chats all the time as John he says well he does he says why would the surprise of the applicability of applicability hinge on aesthetic impulse but not problem solving seems that it would still be surprising on the ladder no that's for Graham would you like me to repeat it I think that that's the kind of misunderstanding what what was happening in the earlier part of the discussion because we had an argument and the first premise of the argument was a premise about aesthetic impulse and so the question was was that premise true because when you evaluate an argument you kind of dull you know you think is invalid other premise is true it may be true that you can rewrite the argument in terms of something else and that would be fine that doesn't mean that you go back and try to get the premises right so that was that was the point of at which that is that is that clear or do I need to repeat what I said okay so I'm bill gave an argument and the first premise was I mean I can't remember the second part of it about causal impact but the first bit was magic mathematical concepts arise from an aesthetic impulse and I thought that's just false right so the premise is false at the very least we need to reformulate the argument to make it work now it might be true that you know if mathematical concepts arise from problem solving you can make the argument go through that would be fine that what it wasn't we were trying to we're trying to understand what the argument should be at that point that was the point of the discussion it did seem to me dr. Craig that that part of the argument was was not necessary well this is Vig neurs attempt to justify why the applicability of mathematics cries out for explanation and I took it that that would be the point that Graham would dispute most vociferously that he would say that the applicability of mathematics to the physical world isn't something that cries out for explanation and if the critic takes that point of view then these two arguments as to why it is surprising that mathematics should be so applicable in describing the physical phenomena so accurately do become very important namely the AA priori nature of mathematics and then secondly the lack of a causal connection all right let's move on to another question from Chris he says does the fact that mathematics always describes physical laws instead of randomly describing them mean anything for the design of the universe well there is the argument from fine-tuning for example which tends to be related to this namely that when you look at the mathematical equations that describe our universe you find appearing in them certain constants that fall within an exquisitely narrow life-permitting range and that cries out for explanation as well so this would be an example of where it's not just the mathematical applicability of the equation but it's also the values of the constants that are in those equations that reinforce your impression that there's something here that needs to be explained would you like to say anything else on that Graham and I'm by the way would you mind Graham would you mind like step taking off slightly sorry beautiful I knew that was gonna happen can I want ask Bill a question is that okay all right so it's it's it's it's related to this okay point but slightly tangentially so the question is this could God have freely chosen chosen to make a physical world in which it was not the case that mathematical theories apply to the physical world because the structure of the physical world is an instantiation of mathematical structures described by those mathematical theories well I got us really chosen yeah to make a world in which that was not the case well we'd say so let me yeah okay so there are two options right if not then it seems that what you're going to end up saying is that it's necessary that if there's a physical world mathematical theories apply which means you just end up agreeing with what the naturalist said right that will be the explanation on the other hand if it's true then it looks as though it's just now a brute contingency that mathematical theories apply to the physical world and for the reason given because it's brutally contingent that God chose to make this world rather than other worlds that he could have made instead we don't have an X nation right when you get to free choice and you think why this rather than that there's no explanation now to be given of why you ended up with one rather than the other so it looks as though either you're going to accept the necessity or you're going to end up with ultimately it's a brute contingency which was the problem that was the thing that was objectionable so don't wait quick response to that and then we'll move through some more questions I have no problem with saying that God has free choices that are ultimately inexplicable I think that that's unproblematic that theory still has greater explanatory depth than simply postulating the necessity of the mathematical structure in the world but youth in and out yeah yeah sorry sorry I was trying to be short cuz we have a lot of questions to get through is that okay if we keep moving on okay sure and this one is from a very good friend of mine his name is Ollie it's his screen name is different but anyways his very good friend it's like a brother to me says among physicists is there's actually a quote quote among physicists when it turns out that mathematically beautiful ideas are actually relevant to the real world we get dot there is dot dot some deeper truth what do you make out of Weinberg's view and maybe this can go to two either one I don't understand the question so Graham if you if you understand that go ahead I'm not thinking I'm not sure that I understand it either what's the dot dot dot referred to oh that's an ellipsis so he's taking some some later part out of it so let me just repeat any radio without the ellipses that one yeah it among physicists when it turns out that mathematically beautiful ideas are actually relevant to the real world we get there is some deeper truth what do you make out of Weinberg's view so what's he saying that when you find cases where there's the applicability of kind of surprising applicability of mathematics in the world that we suppose that there must be some deeper explanation for why it's applicable or something like that is that what the quotes supposed to be saying so I mean let me let me let me try a different example what kind of example we haven't discussed so far so Vigna mentions Borel sets as something that it's very surprising that we get applicability to the physical world but think about Borel algebra right we're in the same ballpark here Calma gaurav's theory of probability is couched in terms of Borel algebra and we use the theory of probability to do things like explain the behavior of bookmakers right so is there some deep explanation for why the theory of Borel algebras has some application to explanation of the behavior of bookmakers I mean it's I mean the quote that we were just given suggests that we should be thinking there's gotta be some deeper explanation here of how it turns out that that bit of rather abstruse mathematics ends up having application to the behavior of human being so it's got nothing isn't an example it's got nothing to do with physics this is another question that I had about Fitness paper that you can find these kinds of mathematical things applied to mass human behavior for example but anyway I don't know any thoughts on that dr. Craig rashon as Graham said I be a big newspaper is restricted to the mathematical laws of characterized physical phenomena in physics and he's not speaking to other disciplines areas such as biology or human behavior that's an open question that is another day to discuss alright so another super chat from david larosa and i apologize i can't get to every single super chat that was sent in some of them are a little off topic so i'm skipping over those to try to cover the ones that are very pertinent to what we're discussing tonight so this one is should reality be interpreted solely on calculations or is there a deeper meaning in physics and intuition plays a fundamental role in the final decision as to what route to follow okay let me say something controversial about that so before you can accept a physical theory what you need to have is some empirical predictions that have been successfully tested in accordance with the theory right we have lots of people have been working away on string theory for a long time it's controversial among physicists I believe whether we should even count it it's physics at this stage because it hasn't been able to generate any testable predictions right so it can't be that way and it won't be that we end up deciding that we've hit the ultimate theory because it's beautiful if we end up hitting the ultimate theory it will be because every you know there's nothing that we can't predict using it or something like that nothing relevant that we can't predict that it's fit to experimental results it's perfect I don't know does that answer the question I think so and string theory could be a great example of mathematical equations that are not applicable to physical phenomena and as we don't know you need to do some testing to find out okay so we have another question from cross-examined in espanol the Spanish channel for cross-examined they say if the universe has a mathematical ontological structure how can we postulate God as the best explanation if we do not yet have a theory that gives us a piston access to mathematical objects because the mathematical objects are not playing a role in the explanation mathematical objects even if they exist are non causally connected are causally non connected with the world so the explanation is that whether you're a realist or an a/d realist if you're a theist you have a causal explanation for why the physical world exhibits the mathematical structure and describe ability that it does and that explanation doesn't need to appeal to any kind of causal input of mathematical objects Graham is there anything you'd like that so I said earlier that I would kind of want to bracket the question about the ontology it doesn't seem that that's important it's that what really matters is something more like the objectivity of mathematics which is not their understanding of that objectivity is not helped by postulating objects in my view well which we agree yeah I know it's one of many points of all right from YT does the argument assume scientific realism you know I I don't think it does because again Vigna is very careful he says that it allows the the mathematical equations allow us to describe with an amazing accuracy in an uncanny number of cases the physical phenomena so he's talking about the way the world appears to us and he's not taking a kind of naive realistic view of science of the world day it could be scientific realism but it need not be for his argument to go through what do you think Graham do you think it has to it can only go through on scientific realism so so this is kind of tricky right sometimes people will be good so it sort of interrupted what it perhaps would be good to just define what scientific realism is well that's gonna be controversial too because some people think that scientific realism physiography it's just going to be realism about the entities that are postulated by science so a scientific realist believes in electrons and black holes and things like that whereas other people are going to think that you need a lot more for scientific realism than that what you need is that your scientific theories give a true account of the world so it's not just that they postulate the right entities but they say the right things about them as well and if you're kind of not inclined to think that our current scientific theories are true that they're true in every respect you might be a scientific realist in the first sense and think that the entities black holes and electrons and so on exist without going that to the second step I agree that Vigna is a bit canny about scientific realism in his paper but some people who present the kind of discussion that we're having today are kind of less cautious and they take the kind of important things that Vigna is talking about to be things like Dirac's prediction of the existence of positrons or Hawking's prediction of the existence of black holes or Higgs as prediction of the Higgs boson whereas in some ways that's not what bothers Vigna most right I mean it's closer to something that bill was talking about so here's the sort of thing that really I think really bothers Vigna and I'll give you two examples there different ways of formulating quantum mechanics you can get from a trix formulation you can give a wave formulation you can give a Hilbert space formulation the mathematical apparatus is completely different in each case what's the same is the empirical predictions so these theories are empirically equivalent but mathematically very different second example which he also mentions is Newtonian mechanics you can give action at a distance formulation you can give a local field formulation you can give a least action formulation the mathematics is very different in each case and as Vigna points out and fireman says if you want to take one of these theories and apply it elsewhere it makes a big difference which formula it can make a big difference which formulation you pick but in Newtonian mechanics there they give exactly the same empirical predictions that makes it sound as though to say that Vigna is really not that interested in the question about scientific realism what he's really interested in is just the empirical outputs I mean he could be an instrumentalist about scientific theories for all that we've been I think that's right okay two more questions and then we'll close it out so from Jonathan Thompson he says take the question yep why is God necessarily perfect and this one is for you dr. Craig take the question why is God necessarily perfect it seems that in answering that question we can't get past the fact that that's a necessary truth doesn't this lend support to AA peace point well I would say that God is by definition worthy of worship anything that is not worthy of worship just is not what we mean by the word God and from that it follows that God must be perfect he must be morally perfect because something that is not morally perfect something that's morally flawed would be not worthy of worship so while I'm certainly willing to postulate ultimate facts like free choices on God's part that have no deeper explanation I think that what Graham did in his alternative theory was to just postulate necessarily that which is crying out for explanation and that is a theory that has no explanatory depth I mean we can if we're presented with data that require an explanation rather than offer a hypothesis we can say well my explanation is just and then you just state the data you just state it again and that would that would be adequate to the data right because it's just a restatement of them but it wouldn't have any explanatory depth and I think that's what Graham has done with his naturalistic alternative whereas theism has greater explanatory depth even if it ultimately arrives at a free being who freely chooses to create a world that is constructed on the mathematical blueprint that he has in mind okay so I think that's not quite true right because if I just restated the data I would have just said here's my explanation for the ANA cannae efficacy of mathematics the uncanny accuracy of mathematics but that's not what I did I did something else I said look there's this long discussion that we've been having about the origins of the universe and I've developed a view about how Naturalist should think about this and look it falls out of that story that the explanation for the only candy efficacy of mathematics is that it's necessary and that's that strikes me is completely different from the way that you're describing what I did okay all right here's the last question would you be able to explain the arguments like I'm five years old I'm totally lost with the Briggs Big Brain vocabulary yeah I presented the argument in a very simple easily memorized way premise 1 if God does not exist the applicability of mathematics to the physical world is just a happy coincidence to the applicability of mathematics to the physical world is not just a happy coincidence from which it follows 3 therefore God exists right so one thing I did want to ask about this is whether you were happy to replace happy coincidence with brute contingency because that because happy coincidence is kind of vague brute contingency is a more familiar philosophical term yeah yeah and then what we disagree about is the first premise if God didn't exist the applicability of mathematics to the physical world suggests a brute contingency obviously I say if naturalism is true the applicability of mathematics in the physical world is not just a very contingency so it so far but not engine it's not a brute contingency right and so they and so that first premise is false and that's where we disagree all right well let's leave it there I really appreciate both of you guys coming on and having this discussion as I mentioned at the very beginning of this this has been a long time coming and it was a fascinating discussion I'm sure that it was over a lot of people's heads including my own at certain points but either way it was it was a fun discussion time I have to go back and listen to it a few times through but I really appreciate you two coming out taking the time to have this discussion it really means a lot so I appreciate you coming on it's a privilege to discuss these things with Graham IO is a pleasure it's a been a long time since we last had such a discussion sigh it's been good yeah all right well if you guys would like to support capturing Christianity and you want to help support this ministry make sure that these things can continue happening then the best way to do that is to go to patreon.com/crashcourse aport their monthly donations are the thing that keep this ministry up and running so I really appreciate it if you want to help us out there and until next time we'll see you guys later so have a good night [Music] [Music]

Channel: Capturing Christianity

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Length: 91min 42sec (5502 seconds)

Published: Thu May 14 2020