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Jeremiah Joven Joaquin and James Franklin eds., "The Necessities Underlying Reality: Connecting Philosophy of Mathematics, Ethics and Probability" (Bloomsbury, 2025)
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Gregory McNiff
Welcome to the New Books Network. I'm your host, Gregory McNiff, and I'm excited to be joined by James Franklin, the author of the Necessities Undermine Reality Connecting Philosophy of Mathematics, Ethics, and Probability. The book is published by Bloomsbury Academic and will be available in the United States in January 2026. Professor Franklin is an emeritus professor of mathematics and statistics at the University of New South Wales and a leading figure in Australian realist philosophy. Trained as a mathematician, his work spans the philosophy of mathematics, probability, ethics, and the history of ideas. He is the author of several books, including An Aristotelian Realist Philosophy of Mathematics, the Science of Conjecture, and the Worth of Persons. I selected this book because it tackles a question that contemporary philosophy often avoids, whether there are truths about the world that could not be otherwise. Professor Franklin connects mathematics, probability, ethics, and theology through a unified realist framework resisting both relativism and reductionism. The book is ambitious. It's very synthetic and unusually grounded in concrete examples rather than abstraction alone. It is dense, but it pays off wonderfully. If you invest the time, you will come out with a much better understanding of mathematics, ethics and the relation between the two. Thank you for joining me today, James.
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James Franklin
Thank you, Greg.
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Gregory McNiff
James, why did you write this book and who is the target audience?
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James Franklin
Like any author, I hope to tell readers something they don't know. In this case, it's that the world contains absolute necessities as well as things and facts. There are necessary connections between things. Let me give three quick examples. First, a simple mathematical one. In any lot of four things, there are six different pairs. Not a very exciting fact, maybe, but very general and absolutely certain. True in all possible worlds. The second example is the logical relation of evidence to conclusion. If an experiment goes as a scientific theory predicts, that makes the theory more probable. That's a necessary connection. And a third example is ethical necessity. Humans being what they are, they're ethically valuable and hence killing them is wrong. That's also necessarily how things are. Now, who the book is for? Well, in my view, it's for anyone intelligent who wants to hear about some neglected facets of reality. Some of the book has philosophical argument, so some philosophy training would help there. But anyone can get the basics. And anyway, it's open access, so anyone can try the beginning without spending money, see how it goes.
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Gregory McNiff
No, that's. That's wonderful precedent. James, I want to drill in a bit to your answer there to my first question by asking you, what do you mean by absolute necessities and how, how does that differ from analytic or linguistic truths?
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James Franklin
Well, analytical linguistic truths are things like all bachelors are unmarried or what I've written, I've written, they're just. They are necessary, but they're trivially so because they're just the way we use language, the meaning of words. But the necessities I'm talking about are nothing to do with linguistics or words. The fact that humans are valuable because of what they are, or that the bearing of evidence on conclusion or mathematical truths, they're not about language at all. They're about things. But on the other hand, they're necessary. They're not like they're much more necessary than scientific laws or historical facts. They absolutely must be so and true in all possible worlds.
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Gregory McNiff
Okay, I want to read you a quote here where you say, compared to other views, blatant, anomalous, for example, Aristotelian realism provides the best and most coherent account of the objectivity and the contentfulness of such necessities. This means that mathematical and ethical necessities, if they are truly absolute necessities, share the same objective mind and language independent nature. They only differ in contents. Mathematical necessities are about mathematical facts found in the world. Ethical necessities are about ethical facts grounded in our worth as human. Persons A are mathematical necessities universal and available to all people, and then B, are you suggesting we can design or discover an ethical framework that is similar to mathematical truth, sort of standing outside us and sort of independent of culture?
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James Franklin
Yes to both questions. So the mathematical truths are accessible to everyone. The fact that there's whatever number of primes there are between 1 and 100 is locked in. And the digits of PI, they're locked in, true in all possible worlds and accessible to everyone by pure thought. Yeah, please take a course in mathematics and a proper one with proofs and you'll understand why those things must be so yeah, and I saying it's exactly the same with ethics. If you understand the nature of humans, that they're rational or have emotional structure conscious and so on, then you'll see that that kind of person is value, that kind of entity is morally valuable in a way that just atoms or something are not. And hence it's important what happens to them. And yes, I'm saying that is absolute and accessible to everyone in exactly the same way as mathematical truths.
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Gregory McNiff
And what is the uniqueness of the Aristotelian realism? Why wouldn't you know Plato for yeah. Had map standing outside its own form, its own being, so to speak. Why?
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James Franklin
Yeah, so I have to explain in a couple of words the alternative Platonist and nominalist views. The nominalist views coming from the Latin phenomena, just names says that necessities, the only necessities there are ones due to language like we were talking about before, that all bachelors are unmarried and that it has to claim that mathematics is a vast structure of just tautologies like saying A is A. And that is not true because we understand the kind of things that mathematics is about, numbers and so on. Platonism has an alternative view on that. It says that mathematical truth are absolutely necessary, but only because they deal with a Platonic realm that's non physical, that's somewhere else, a realm of numbers or sets or groups or what have you, and that these are not part of the real world, they're part of some other world. Whereas the Aristotelian view contrasts with both of them in saying that mathematical necessities are implemented in this world.
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Gregory McNiff
So.
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James Franklin
So in the example I gave any set of four things, real things, books or people or whatever, you can find six different pairs in them. Well, that's not in another world, it's about anything physical things in this world.
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Gregory McNiff
Okay, I want to drill down into that a little more. But first you talk about modern education, leaving students with little exposure to Genuine necessity. Why is that? Today it seems like there's such an emphasis on specificity and technical expertise and including math. You would think there would be some connection there.
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James Franklin
That's right. Well, there's lots of things. The history of what's gone wrong with modern education is so long it's hard to know where to start. But a lot of it is if exam driven in that you want to give simple questions, they'll have simple answers and you can mark. But then there's the divergence between humanities and scientific education. Humanities can lead you to necessities in theory, but it tends to be more historicist, meaning it gives the impression that what happened, happened, and that's about all you can say about it. There's also been a certain neglect in mathematics education of the hard stuff, like proofs. So when I was a kid, which is the 60s, we learned math. Our main training in necessities was you proof in the style of Euclid in geometry. And that's unfortunately been neglected in years since. So there's many causes. But all in all, necessities have become hidden in modern education.
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Gregory McNiff
Okay, that leads to my next question. How do we perceive these necessities? And what role does intuition play here?
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James Franklin
Intuition is important, but it's a rather vague term and you don't quite know what it means or whether you can rely on it. It's better to just sit down and with Euclid's elements, why not take the original and read the definitions and go through his proof of book one, proposition one, and then you don't need to talk in the abstract about intuition. You really understand why that must be so. And if you work harder, you'll get to book one, proposition 47, Pythagoras theorem, that the square on the diagonal is the of a right angle triangle, is the sum of the squares on the other two sides, and you'll think, now I really understand why that must be so. It looks unlikely. How could that be true all the time? But now I understand by those proofs why that is so. And then if you train properly in that way, you can get around to seeing ethical necessities and logical necessities and all the others, and you'll be attuned to them. At the same time as I was studying Euclid, I was studying Thucydides, and the way we studied it was that we had gobbits, as they call them, because examined by us, giving a couple of sentences or a small paragraph of Thucydides. And the question was explain where that comes in the story and what it tells us, what evidence it is. What it is tells us about where the story is going, what propositions it's evidence for. And that was my training in that aspect of necessity, the relation of evidence to proof. We could do that too.
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Gregory McNiff
Okay, I want to hit you with a follow up here. You write in Ethics I became more convinced of its objective nature, but less than happy about existing foundations efforts to explain why. The parallel between mathematics and ethics, in that both are abstract, non experimental disciplines whose central truth are evident to intuition, evidently gave support to the objectivity of ethics. And few doubted the solidity of mathematics on the foundation of ethics. Aristotle and Aquinas were not as satisfactory on metaphysics. Like many other philosophers of ethics, they were misled by seeing ethics as fundamentally about what to do. And this is an aspect of ethics, but not the deepest one. What is more important is what entities are inherent. What is more important is what entities are inherently valuable or of worth. Is that your definition of ethics? Or what are you building this realist notion of ethics on?
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James Franklin
Yes, it seemed to me that objectivist people like as you suggest, Aquinas, failed to find the correct principles, even though everything they said was perfectly fine. If you think about an ethical rule, like what's wrong with killing people? And you ask yourself, well, maybe sometimes that's not always true. What about self defense? Where do you say why is it that self defense could be all right, at least in some circumstances? And you think, well, the basic thing is that being dead is bad. And that's not about rules or commands with God or anything or the benefit of society or something. It's about the nature of humans. Because humans are of inherent worth, then their existence is good, so their non existence or death is bad. So that's why thinking about what you ought to do, the objectivity of rules, or what you ought to do leads you back to something that's not about rules, but is about the inherent worth of persons.
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Gregory McNiff
What about, for example, volunteer work or alms, giving to the poor? If we were to think being poor is bad, do those who have more have an ethical obligation to give and if so, how much?
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James Franklin
Well, it's true they do have an opportunity to give because an obligation to give because. I mean, what is wrong about being poor? Well, in some aspects of being poor are maybe not very bad, but extreme poverty prevents you realizing your humanness. So you're in a child laborer 10 hours a day in a factory, when you can't become properly human, you can't develop the important aspects of yourself like rationality or even being fed properly. And so that is an evil because. And it's a violation of your rights as a human being. So in that case, those who are in a position to do something about it or to do something about it, and the reason is that they have the opportunity to enable someone to become, to realize their humanness. And how much? Yeah, well, it's hard to say that the principles of ethics are going to tell you exactly how much. That's maybe a problem we'll get to at the end once you work out how much superfluity you've got and so on. But I think we can leave those detailed questions for the individual conscience. It's in the same sense that the principles of geometry aren't supposed to tell you how far it is to the shops, but they give you some principles on how you might work it out if you got a map. And it's the same with the principles of ethics. Well, first things first, we'll get the principles right and then detailed casuistry we can get. Sure, we can get to later, but we need to have the principles right before we get there.
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Gregory McNiff
Okay. We've talked about Aristotelian realism. I want to go a little deeper into the mathematics portion of this. You write, mathematics itself stands as an unanswerable challenge to any relativist undermining of truth, but humanities scholars show little interest in it. Why do you think mathematics can stand against any relativist critique? And why wouldn't humanities or anyone really embrace mathematics as a means of certainty?
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James Franklin
Because it's the easiest way into understanding certainty and has been since ancient times, because it's so clear and precise that there's no opportunities for heading off into other directions and thinking in relativist ways or anything. If you understand matters like symmetry or ratio, that they're some of the basic subjects of mathematics, you can easily see free of any distractions, why there are necessary truths there. So it's been the reason mathematics has been so central to Western, especially education, but also Chinese education, is that it is a training in necessities. So in the 19th century, people, they trained the people, colonialists who were going to govern India in Greek and mathematics, because they thought these would teach them precision and details about the local laws or anything. They can pick up those as they go along. But if you understand how to deal with principles and necessary principles, that will give you a good grounding to think about anything. And yeah, it will make you have no temptation to go down the Paths of historicism, postmodernism, relativism, and so on.
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Gregory McNiff
Got it. Is it fair to say, James, mathematics will teach you to think?
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James Franklin
Yes, that's right. And it teaches you to think in itself, not about everything, but it teaches you how to think in a principled way.
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Gregory McNiff
Yeah. And is it fair to say humanity scholars, quote, unquote, lack that ability or have no desire to think?
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James Franklin
Because often, often, of course, I've met you meet humanity scholars that do do that. But still, there is a break between humanities scholars and other people that I think leads to a certain shallowness. Of course, the humanities scholars say that scientific people are shallow and don't understand literature, and often that is true as well. But we do need both sides of the humanities and the scientific worldview to be properly human and properly educated.
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Gregory McNiff
Yeah, I appreciate that. I should say in your book you make references to literature, including Dostoevsky, as well as, I think, offering some sense of ethical norms or ethical light.
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James Franklin
Well, that's right. I mean, if you want to understand what is the nature of humans and what it is that makes them valuable, then you can list things like rationality and consciousness. But if you want a kind of a more rounded and detailed view of what it really comes to, then the great novelists and Shakespeare and so on will really round that out and give you a much better sense of what it is really to be human and the possibilities, the remarkable possibilities of being human.
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Gregory McNiff
Okay, I want to just continuing on the steam of mathematics, you cite yours, Koenigsberg bridges proof, several times throughout your work. Why is that so central to your argument about real world necessity?
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James Franklin
Okay, it's harder to do this on audio. I wish we had a diagram. But perhaps I could ask your listeners who are interested in this to go and look at a diagram of Euler's Konigsberg bridges. So it was a problem in the 18th century that the citizens of Konigsberg in East Prussia realized that it was impossible to walk around the seven bridges of the city once and once only. So the city had two riverbanks and two islands, and they were connected by a system of seven different bridges. And they're arranged so that you can't get around all of them without going over one of them twice. This is a real system of real bridges, but it's a mathematical necessity, which Euler proved, that you couldn't do that. So I think it's a great example of being able to see very directly mathematical necessity in the real world, not in some abstract world, not in some linguistic world, not in some world of shuffling symbols, but in a system of actual bridges in an actual city. So I take that I refer to that several times in the book because it's such a clear example of necessities, absolute necessities existing in the world, so absolute. It's not as if any change in the laws of nature, for example, could make it possible to go over the bridges once and once only. It's a necessity much stronger than any scientific or linguistic or any other necessity. But it's in the real world.
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Gregory McNiff
Okay, And I want to move to that part two, labeled mathematical necessities. We've been talking about part one, which I believe is absolute necessities. I want to move to part two here. And you have a quote that says the problem is not so much that mathematics is true, but that its truths are absolutely necessary and that the human mind can establish those necessities and understand why they must be so. It is very difficult to explain how a physical brain could do that. How can a physical brain do that, James?
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James Franklin
We don't see how any physical object could truly understand. We don't know how they could be conscious either. And the only way we know that it's possible is that we have a physical brain and it does it. But it must have some mysterious properties that are beyond the physical. And we understand these a lot better now that we have AI doing things that appear to be intelligent. So AI clones all the human language there is and gives results that are much like what you get by acquiring an intelligent human. But we know it's just software with statistical methods. There's nothing, no gremlin, no mind in there understanding anything. So this has given us a much better understanding of the difference between human thinking and what physical things, including computer systems, can do. Somehow there's a vast difference. It's not to say I wouldn't say we understand it, but we're brought up against something that there's a hard problem of consciousness, but there's an even harder problem of genuine understanding. We have no idea how to start putting genuine understanding in a computer system. The animals hopeless at modality. Animals are very poor at even the simplest things about necessity. So, for example, if animals have to have a system where a pellet can that they would like, can come out of either of two holes, they don't get that to make sure that it must come out of one of them. So you've got to cover both of them. They're very hopeless. Even the very simplest thing about necessity, understanding necessities like that. But our Understanding of understanding why Pythagoras theorem must be true after following the proof. It's something completely different to anything we can imagine physical things doing.
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Gregory McNiff
Do you think AI will eventually be able to think on its own? And will it eventually have consciousness?
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James Franklin
I don't. Well, I don't think so, but. But then we don't really understand. The reason, when it's hard to be sure about, is that we don't really understand how human embryo develops physically and then consciousness emerges in it. Are we absolutely sure that something that's, that's non biological couldn't do that? Well, we're at square one because we have no idea how. How the embryo does that.
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Gregory McNiff
Yeah, it seems like they're still struggling with emergence and to what extent this is a function of austere physicalism or some kind of, I guess metaphysical or emergent property. But interesting. Your thoughts on AI in the book as well. I want to finish this section on mathematic necessities and proofs. Specifically, I want to ask you what has gone wrong and how proofs are taught and understood in contemporary mathematics education. I'm going to read you another quote here. A written proof should communicate a sequence of insights to the reader. Insights into necessary connections between the quantitative or structural universals dealt with by mathematics. That is so irrespective of whether individual proofs can be fitted into an overarching deductive scheme of axioms and theorems, or whether they can be expanded into purely syntactic form, why aren't proofs taught better and how should we be doing that?
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James Franklin
Well, I can answer the problem about how we should be doing it because my first book was called Proof in an introduction. And I wrote it because standard mathematics, where I was and everywhere else was not doing it. And the way mathematics education works, it's expected that smart mathematicians pick up how to do proof and the others just look at a problem saying prove this and they take it to mean move to the next question. It's very simple to give techniques of how to prove things in mathematics. And so I wrote a book on how to do it. Now why isn't it being done? I just can't answer that question because we used to do it by putting Euclid at the center of mathematics education. But since then there's too much computation, there's too much rules, there's too much, Too much content without concentrating on proof techniques. Let me give a simple proof technique. If you're going to where to start. If you're going to prove that the square of Every even number is even, let's say simple enough. Well, you start out by saying let X be an even number. So it's two times something, it's twice some other number. How simple can you get to explain that? But it's very hard to see that in mathematics education.
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Gregory McNiff
If I can hit you with a quote on Western philosophical thought that may be relevant here. You know, Western philosophical thought has an ingrained tendency to ignore or downplay the reality of relations. From ancient views that attempted to regard relations as properties of the individual, related terms to early modern ones that they were purely mental. But a solid grasp of the reality of relations such as ratio and symmetry is essential for understanding how mathematics especially can directly apply to reality. Has that been an issue here? That philosophy has somewhat distorted our view of mathematics as a universal objective basis for truth?
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James Franklin
I think so, yeah. Philosophy hasn't affected mathematics education. Mathematicians are very anti philosophical lot. But somewhere in the wider appreciation of mathematics something has gone wrong in people's not really grasping the, the relational aspects of what mathematics is about. So yeah, like I say, ratio and symmetry are good things to think about. So if you and I stand next to each other, there's a ratio of our heights that is easily perceived. So a ratio is a relation. Yeah, there's a relation of your height and mine and that ratio is something very abstract. So for example, two time intervals or two volumes could have the same ratio. So just ratio in itself is very abstract, easy to say necessary truths about, but somehow people are not focusing on it as a topic. You don't hear people kind of talk about let's talk about ratios or let's have some abstract truth about ratios. It's just missing somehow it's fallen between the cracks and the same really with symmetry. People know that symmetry is important to art and you know, architecture and the symmetry of molecules is important in chemistry, but as an overall topic it's not in people's minds. But nevertheless a branch of pure mathematics. Group theory tells you about all the different kind of symmetries there are. And it's a remarkable, it's a great topic to learn by itself in mathematics.
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Gregory McNiff
And Jim, I'm trying to figure out where you might assign the blame here. Is it not that mathematics is being taught properly? Non Euclidean geometry has replaced Euclidean geometry? Or is the Western philosophical approach which doesn't recognize these issues or has a correct understanding of ethics? I mean, I don't want to start pointing fingers here, but I think we're at that point in the interview.
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James Franklin
I blame everyone that's the second. That's the simplest answer to that. Everyone has got something wrong, but a different thing. So I'm writing a book that's got so many different aspects to it, ethical, logical, mathematical and so on, to try and bring it all together and get people to focus on this matter of absolute necessities that's kind of got lost in the sand in so many different directions.
- [31:01]
Gregory McNiff
Well, okay, I understand your desire to pass on that. I'll ask you about this, your personal background, the book you talk about, your exposure growing up. And to some extent, this is an intellectual biography here. And you obviously were exposed to the Greeks, Aristotle, Plato, also Aquinas as well. And at one point, I think you edited the Catholic Journal. I'm going to blank on the name, but you edited a Catholic journal.
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James Franklin
I'm editor of the journal of the Australian Catholic Historical Society. So, yes, I do think that Catholics have a. A little bit of a head start over the rest of the culture in this matter because of the background in natural law philosophy, especially that a Catholic upbringing will give you. Some sort of training in the idea that ethics is objectively true and not because of divine commands, but because of that's how humans are. So that is certainly a start. And I suppose you'd say that Catholic education, even if it's dumbed down in some places now, does give you some sense of other times and sense of the world of the New and Old Testament that gets you out of yourself. So in the history of ethics, the Psalms are very important, for example, that they think that the widow and orphan are people whom God specially favors and that everybody else should look after them as well. Well, that is not found in other ethical traditions much. So that is something that we can take, and that certainly I did take from having a Catholic upbringing, but it's not really specific to Catholicism. Some of the things that you get in the American Declaration of Independence, for example, about rights, well, that's not strictly religious, but is a background that will give you some sense of ethical necessity that you might get in other parts.
- [33:14]
Gregory McNiff
Of the culture, but somewhat consistent with your belief that ethics reflect every individual's inherent dignity, regardless of, and that our actions to that individual should be determined by how it impacts their dignity or their worth.
- [33:33]
James Franklin
That's right. So even in a very simple way, if you're polite to the receptionist at the doctor, it's not a very big deal ethically, but it is required. And it's just because they're humans, you should be behave like that to them. But in other cases, There are humans that are struggling from one way or another. Well, yeah, you should do what you can for them, given your limitations.
- [34:03]
Gregory McNiff
Have you ever been to New York City, James?
- [34:07]
James Franklin
Just for a few weeks.
- [34:09]
Gregory McNiff
I would like to be a real world test case here, but maybe in the next book. Yeah, all seriousness, I want to move to part three, Logical Necessities Probabilistic and Deductive. Again, another dense section, but definitely rewards the attentive reader. James, what is logical probability and how does it differ from Bayesian probability?
- [34:32]
James Franklin
Logical probability is the conception that something like proof beyond reasonable doubt or experimental evidence in science, or historical evidence based on. Based on texts, textual evidence is a matter of logical necessity, absolutely necessary logical necessity between evidence and conclusion. So if you say, let's say that in a certain civil case in law, the evidence favors a certain person owning something on the balance of probabilities, the suggestion is that that is not a subjective matter, like subjective Bayesianism might say, or postmodernism might say that anything goes but is an absolutely certain fact. So it's not certain that the outcome is not certain. I mean, it's not certain that somebody owns it. What is certain is that on the actual facts presented, ownership belongs to this person on the balance of probabilities. And so let's. So in many cases, scientific evidence is very convincing. So, for example, the evidence for the causation of flu by viruses is overwhelming. Now, the phrase overwhelming is a matter of logic. And it's a matter of. Yeah, it's a matter of logic. And hence it's one of the necessities that are out there in the real world. In this case, not the physical real world, but the world of propositions and evidence. And it's not a linguistic world. It's got nothing to do with language. It's that the evidence being what it is, the probability of the conclusion is whatever that is. So let me take a final example. A famous example in science is that Einstein's theory of general relativity implied that unexpectedly that if you went out to West Africa and observed the stars, you'd see that they appeared to be closer to the sun than they ought to be. And they went out to West Africa and sure enough they found that. And that was a remarkable, very solid confirmation of the theory of general relativity. So that relation of the experimental evidence to the hypothesis or theory is said on the theory of logical probability to be an absolute necessity, absolutely necessary matter.
- [37:05]
Gregory McNiff
Okay, I want to move to again, part 4. Absolute necessities Constrain even God. And I found this interesting. Why first of all, why are the discrete continuous? I guess that's dichotomy. And local global distinctions so fundamental to our understanding of math and yet neglected.
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James Franklin
Yeah. I wrote separate pieces on two of the big themes of mathematics, local versus global and discrete versus continuous. I think discrete versus continuous is better known. We understand that there's a division in mathematics between discrete things that go 1, 2, 3, or connections between nodes in a network. And on the other hand, the continuous aspect of mathematics, flow velocities, the things studied by calculus. It's strange that even though this is such a big theme, hardly anyone writes about it. I don't understand that. There's some mistake about people not looking into the big themes. And the other one was local versus global. It's that things that can happen locally can't happen globally. So let's go back to the Koenigsberg bridges. There are seven bridges, and it's easy to go over a few of them once and once only. But you can't fit together those local paths to find a global path that satisfies the constraint that you should go over all the bridges only once. So there's. Or to take another example, it's easy to have a spiral staircase that goes up in parts, but you can't have a spiral staircase that goes up all the way around and comes back to where it started. The local thing is easy. The global thing is fitting together. It can't be done.
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Gregory McNiff
I want to move to a related point here. How do these mathematical necessities constrain even divine omnipotence?
- [39:14]
James Franklin
Yeah. So it's normally thought, and I agree with that, that God cannot do the mathematically impossible. So God can't do the logically impossible. But surely God can't make any of the digits of PI other than what they are. It's just an absolute necessity. So where I say absolute necessities, they should be not subject to divine omnipotence because they're absolute. So God, in creating a world, will have to allow for those or be constrained by those. Perhaps the word constrain is not quite right. It's more that if you ask why shouldn't God make PI equal to 4? Is that there's, so to speak, no real possibility on which he could confer being. But, Mark. But then having thought that, I think that once you come to understand mathematical necessities, you'll understand that there are a lot more of them out there than you'd at first think. Because, well, that's what mathematicians do. They find things that are Unexpected, like Pythagoras theorem. So you might think Pythagoras theorem is something that will be easy to create exceptions to because it looks almost, you might say it looks contentious. It looks like it might be otherwise, but it couldn't be otherwise. So God will have to be constrained by that in creating a world.
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Gregory McNiff
Follow up to that. How does your view or approach to ethics relate to Leibniz theory of God and the best possible world?
- [40:53]
James Franklin
Leibniz had a good being a mathematician, had a good sense of this when other people, other philosophers didn't. And he said the reason God doesn't create a better world than the one we see is that there isn't one because of all these connections between global and local. Initially that looks like a crazy idea. I mean, everybody thinks they could create a better world by removing some fused toe stubbings or something and leaving everything as it is. But you can't leave everything as it is. There is no world that removes a lever like a toe stubbing and leaves everything as it is. For a start, the laws of nature are different because the laws that the natural process that created the stubbing are now not creating them. And I think although it looks like an initially very implausible idea, it is possible to solve the problem of evil about why God allows evil by thinking of how, by understanding how hard it is in a purely mathematical sense to create a universe. I mean, in the fine tuning argument we discovered that even to get the universe out of bed, to have a physical universe and life possible, there needs to be extremely fine tuning of the physical constants. You could try create, try changing all sorts of things, but it gives a sense of how hard mathematically creating universes is.
- [42:28]
Gregory McNiff
Yeah, it's interesting. Leibniz really pushed the very thoughtful argument and being a mathematician, not surprising based on your own work here. Turning to part five, ethical necessities are absolute. Why do you see ethics as closer to mathematics than to empirical science?
- [42:48]
James Franklin
Well, because mathematics and ethics are both sciences where you can act by pure thought and understand why things must be true. Whereas in empirical science, while understanding can be helpful, especially in physics, you do need to get out in the wet and observe some facts, because otherwise you can't start. So ethics and mathematics are abstract sciences of absolute necessities, subject matter which you can understand by pure thought, but empirical sciences are not. You can't understand them completely by pure thought. You need experimental evidence and observation.
- [43:27]
Gregory McNiff
Yeah, no, you answered that really well. I was going to read you a quote that pretty much says the same Thing there. Is there a universal objective ethics founded in reality? You would clearly say yes, regardless of place or culture.
- [43:42]
James Franklin
Okay, yes, that's right. And it's for cultures to get a better understanding of the worth of persons. So in cultural history, there's been a lot of mistakes about people thinking that our tribe is real people and the people over the hill are not real people and need to be killed. Of course, only the last couple of days here in Sydney, we've had an instance of that with Jews being shot at Bondi beach just because they're. Yeah, just because they're another people.
- [44:21]
Gregory McNiff
Absolutely tragic. I want to follow up on that question there. You sort of answered this. Why do you ground ethics in the worth of persons rather than actions or rules? And then how does a culture come to understand that, that, you know, if these are universal truths? I mean, math, every culture has mathematicians, there are proofs, there's a scientific method, a scientific process. What is the equivalent for an ethical process to determine the worth of persons?
- [44:50]
James Franklin
Well, actually, not every culture has mathematics and not every culture has proof that was really a Greek invention with only a few bits and pieces elsewhere. And that culture got it right and people studied it and realized that that's how you could have an insight into mathematical necessities. Well, it has to be the same with ethical necessities. And in fact, it was mainly the Hebrew culture that did get to that. That love your neighbor as yourself because you're both people, you're worth something, your neighbor is worth something and worth the same. So we just have to keep. Just have to promote the understanding of those ethical and likewise mathematical necessities and the reasons for them towards the end. Actually, let me mention, the Universal Declaration of Human Rights was an extraordinary. From 1948, was an extraordinary publicity success, partly because it did speak to, in a way that all cultures could understand and come to grasp the inherent rights of persons.
- [46:09]
Gregory McNiff
I want to move to part six, history, the rise and fall of absolute necessities. You trace the development of scientific revolution and you conclude that Aristotelian science has returned. What do you mean by that?
- [46:24]
James Franklin
I mean that people have come to appreciate the necessities that are in science as well as the, so to speak, Baconian aspect of science that says it's about collecting the facts and summarizing them. The scientific revolution had two aspects. The Baconian one, especially big in England, that said, it's about collecting the facts and discovering that all swans are white and so on. Or as it turned out, not all swans are white. And the Mathematical aspects, especially associated with Galileo and Newton, that found that there were mathematically necessary connections between different scientific truths. And though the individual scientific truths were contingent and not necessary, the connections were. So a famous case from the scientific revolution is Newton's derivation of the elliptical orbits of planets from the inverse square law of gravitation. So the inverse square law of gravitation is not itself necessarily true, as far as we know, but the connection between that, the consequence it has, that free planets without other forces on them in ellipses, is absolutely necessary because it's mathematically proved by Newton. And so we understand that out there in the sciences that have become mathematical, which is lots of them, we understand necessary connections between the contingent truths. So again, we need to have an. We need to be aware of the reality of relations, in this case connections between different truths.
- [48:18]
Gregory McNiff
That's interesting and it sort of sets up my final question here. James, the epilogue. How contact with the world of necessities was lost. As you noted, the Greeks discovered proofs. And throughout this book you talk about the increase and the range of proof truths in pure and applied mathematics throughout time and even, you know, through the Enlightenment. So to some extent you would think the environment and the culture is getting better to discern these ethical truths. But at the same time, you know, there's almost a step back, a crisis made me agitated or fomented by non mathematicians, this foundational crisis. So I have a two part question. If the our knowledge is getting better, these understanding of proofs, these mathematical necessities, why is, why are we taking a step back in terms of discerning the ethical necessities? And then in reference to your closing example of Socrates and the oracles who might be the oracles for today.
- [49:24]
James Franklin
Here I do blame humanity's crowd to a large extent because they neglected to study mathematics and instead they went in historicist directions. So historicism in the sense that thinking that any theories are pretty much all right and accepted for political reasons rather than for there being the best explanation of the evidence. And the historical historicist and relativist tendency of the humanities has been extremely strong in the last two centuries, it was driven. The one philosopher I think I'd blame most is Hume, who's said he was empiricist, which kind of ignores the mathematical necessities in the first place. And he has a famous saying, there is no necessary connection between distinct existences and people. This has encouraged people to think of facts as disconnected without looking at the necessary connections between them. That saying and all the German historicism is Thinking of everything is up for grabs culturally. It's just a matter of political reasons and patronage that you believe things. That was also caused by the neglect of the notion of logical probability. That has been very low profile. A great book on it by Keynes before he went on to easier stuff like economics. He wrote a book about treatise on probability that gave a logical view of it, but it hasn't had enough impact. So that's who to blame. Now, who are we going to look for as people to go back and read? There's one person that we have to go and read and it's not a new person either. We have to go and read Aristotle. We have to read especially Aristotle's Posterior analytics, which lays out a view of science as a set of necessary truths derived from necessary first principles. Euclid's Elements implements that. Exactly. We're just going to have to go back and read Aristotle as programmatic and Euclid as how to do it. And recent people. Look, I can't recommend anybody recent, really. Of course there are people and as you've mentioned, followers of Aquinas and so on who get us back to the medieval scholastics who had a better sense of these necessities than we do. The historicist people in our own day. But I think we'll have to just go back to Aristotle and Euclid and start again.
- [52:17]
Gregory McNiff
Wow, that's a serious answer. Thank you very much. I think that's a great way to end our interview. Again, the book is the Necessities Underlying Connecting Philosophy of Mathematics, Ethics and Probability by James Franklin. I don't think I have to tell anyone. It is a very deep and a very thoughtful book. James, thank you very much for your time.
- [52:40]
James Franklin
Many thanks for the opportunity.