Transcript: Podcast with Professor of Mathematics James Franklin

Date of recording: January 21, 2026, The Savvy Street Show

Hosts: Vinay Kolhatkar and Roger Bissell Guest: James Franklin

 

For those who prefer to watch the video, it is here.

Editor’s Note: The Savvy Street Show’s AI-generated transcripts are edited for removal of repetitions and pause terms, and for grammar and clarity. Explanatory references are added in parentheses. Material edits are advised to the reader as edits [in square brackets].

 

Vinay Kolhatkar

Hello and good evening. Welcome to 2026 and to The Savvy Street Show’s first recording of the year. A very good and Happy New Year to all our viewers and listeners. As often before, we have a special guest tonight, and my co-host is the same old Roger Bissell, musician and part philosopher, and needs no more introduction. But our special guest tonight is Professor James Franklin, who is an expert in the philosophy of mathematics and the foundations of ethics. Sounds like two different animals, but it’s perhaps a match made in heaven instead of an odd couple. James got his PhD in algebra from the University of Warwick in 1982, and he has taught for nearly 40 years at the University of New South Wales in Sydney, Australia. He’s the author of at least nine books, including three that we may talk about today, An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure, then a book on ethics called The Worth of Persons: The Foundations of Ethics, and his latest release very recently is The Necessities Underlying Reality: Connecting Philosophy of Mathematics, Ethics and Probability.

Welcome to The Savvy Street Show, Dr. Franklin.

 

James Franklin

Thanks for the invitation. Glad to be here.

 

Vinay Kolhatkar

And over to Roger.

 

Roger Bissell

Thank you, Vinay, and welcome, Dr. Franklin. In the epilogue of your book on philosophy of mathematics, you refer to mathematics as “the last bastion of reason.” Even hard sciences like physics and chemistry have been corrupted, and so it’s up to the philosophers to defend the ability of mathematics to give us objective knowledge about the real world, and only an Aristotelian philosophy of mathematics can help us meet that challenge. I happen to agree with this, but I would like to hear your thoughts, your explanation of why this is true. More generally, how does Aristotle’s philosophy or perhaps an adaptation of his philosophy succeed in defending reason and objectivity while other approaches have simply fallen short?

 

James Franklin

Nearly everyone except a few postmodernists thinks that 2 plus 2 is 4, that it’s objectively and absolutely true. But unfortunately, there are many philosophies of mathematics, explicit and implicit, that say even if that’s true, it’s explained away because mathematics is not somehow a real science about the real world. So many people’s experience of mathematics at school has been perhaps unfortunate as if it’s a method of moving around symbols or just a language of science or something like that. Physicists and engineers, for example, think it’s just methods and that’s not actually about anything. Well, that undermines mathematics as a bastion of reason because it says it’s kind of trivial. On the other extreme, there are Platonists who think that mathematics is absolutely true, not of this world, but of some other abstract world, nonphysical world of numbers, sets, groups, and so on. Again, that underplays what mathematics is really like as a science of the real world.

An Aristotelian realist philosophy of mathematics says that it’s about aspects of the real world, for example, ratio and symmetry.

But in between those two, an Aristotelian realist philosophy of mathematics says that it’s about aspects of the real world, for example, ratio and symmetry. They are absolutely and certainly true facts about those that you can understand by reason, and therefore we have necessary truths known with certainty about the real world, and that’s why it’s a bastion of reason. Physics and chemistry do tell you about objective facts about the real world, sure, but they are facts that could have been otherwise, maybe if the laws of nature were different. But the laws of mathematics can’t be different. They’re true in all possible worlds. So again, you’re getting in touch with a level of reality that is more basic than anything else.

 

Vinay Kolhatkar

Just on that issue, this corruption in the objectivity of mathematics by postmodernists, is it a matter of them attacking on the basis that it’s an outgrowth of white supremacy that tramples on the truth?

 

James Franklin

There are some, yes, there is that part of the humanities world especially. That kind of view is not found in mathematics faculties, but it is found in education faculties, which have become quite corrupted by that kind of political ideology that replaces truth.

 

Vinay Kolhatkar

What’s the best way of dealing with these education faculties who try to turn people away from reason?

 

James Franklin

Decrees have been issued by the legislators on behalf of the taxpayers to remove gender and race ideology from philosophy courses.

My expertise is not in politics, I have to say. I can only argue against them. I notice that in Texas and certain other places, there is some actual action about those, and decrees have been issued by the legislators on behalf of the taxpayers to remove gender and race ideology from philosophy courses. Whether that’ll work, I don’t know, but it’s one way of doing it, playing politics very hard. It’s not going to happen in my country, Australia. But of course, we don’t have the same kind of president as you—which we needn’t go into whether that’s a good or bad thing, but it’s certainly making a difference to how these things play out politically.

 

Roger Bissell

In your mathematics book, I like the distinction that you drew between elementary and advanced mathematics. Every one of the topics in elementary math are ones that I was quite good at and enjoyed a lot, starting with arithmetic, algebra, geometry, trigonometry, calculus, applied math, even measurement theory. Then on the upper level is advanced math, and you said that was more structural, and there are topics like topology or abstract algebra. I wanted to ask you a question that relates to my own personal experience, my own frustrations. I’m just curious to understand what was happening to me. In high school, I was a whiz. I got everything fine. Even my first year in calculus in college, that was fine. But in my second year, I hit a brick wall. I took abstract algebra, and I crashed and burned. I had to drop my math major and switched over to music, but I never lost my love for math. I love structures and patterns just as much as I love thinking about numbers and quantities. But how could advanced math be so different that I couldn’t get it in my brain? It didn’t compute. I mean, maybe I was just too busy playing in bands and singing in choruses, but is there a different way that a person’s brain works in advanced math than in all those other [elementary] subjects?

 

James Franklin

I’m sorry to hear you had that experience, but it is, I have to say, a common one. People are great with mathematics of quantity, including calculus, but then they get to abstract algebra and topology, and they don’t get it. So, why don’t we start again and try to give you a very simple example of abstract algebra that I think you and all your listeners can understand.

Suppose I take a page and turn it over, so I see the other side of the page. If I turn it over again, I get back to where I started. In a sense, the operation of turning it over cancels itself out. Do it twice, and it’s the identity, as we say in algebra, it cancels out. It’s a toggle, as you say in computer science, like “caps lock.” Press it, press it again, and you’re back where you started. Now, suppose I ask you, if I turn it over 128 times, which side am I on? I think you can easily answer that, that it’s back to the same side, the original side, because it’s an even number. And that if it were an odd number, you’d be seeing the other side. Well, in that case, you know everything there is to know about the abstract group of order 2, which has two things in it. Toggle, do something and the repeat of it, the square of it, is back, it cancels out, and any even power of that is the same as the identity, and the odd power is the same as itself. That’s it.

So, there’s no quantity, measurement, or anything. It’s just some kind of abstract structure of operations. But it’s not hard. You need to get that, then you need to get the more complicated groups, for example the group of all the rotations of a cube. It’s abstract, but you can imagine it if you’re good at mental visualization and you rotate it 90 degrees this way, then 90 degrees that way. What is the combination? You’re dealing with something that is abstract, but at the same time is perfectly well realized in the physical world, like toggles are. Well, there you are. Take those examples, think about them, and you’re about halfway into abstract algebra. But you can see it’s a different kind of thinking to anything about quantity.

 

Vinay Kolhatkar

Interesting. Now that we’re moving on to real life applications, maybe we can jump to a big one. This is relevant to your Worth of Persons book. For instance, all Iranians are human beings, therefore as human beings, they have human worth. Very recently, Ayatollah Khamenei, the 86-year-old chief, admitted that their army had to kill thousands in the streets, which is an outrageous violation. These were peaceful protestors, and the army or even worse, some other nation’s mercenaries, were ordered to kill them. Can you say any human being on this earth has the moral right to kill that Ayatollah, at least to partially restore respect for human worth and dignity? Are there some easier illustrations of the ethics of the worth of persons in, say, parenting, schools, universities, business, and government?

 

James Franklin

The main idea of my book, The Worth of Persons: The Foundations of Ethics, is that the worth or dignity of persons is the main foundational concept in ethics, at least of interpersonal ethics. Now, it’s quite a way from that foundation to the frontier of what you actually should do. It’s clear that because people are of worth, killing them is bad. But where there’s a conflict between the worth of different persons, for example, in self-defense or what you should do if political leaders are killing their people, it’s hard to say what exactly the conclusion for action is. But you can certainly say that it’s an extremely bad thing that the ayatollahs are killing their own people. It suggests that you might be justified in killing them the same way you’re justified sometimes in killing in self-defense because that means that you would be preventing, hopefully, worse from happening. Of course, we have to think about side effects, as apparently President Trump is thinking, about whether you can actually make it work. But in principle, the worth of persons says it is something that you could try, and the reason is the worth or dignity of the people being killed in Iran.

But for some other things that are not quite as urgent as that, well, let’s say if you go to the doctor’s waiting room and speak to the receptionist, you should treat the receptionist politely and vice versa, just because you two human beings are interacting and should respect each other’s dignity. Though it’s not very exciting or controversial even, that is the reason. It’s the same kind of reason that means that the worth of Iranian protesters is something to be taken into account. Again, why is it a good thing to educate people in the right, in objective truth, as opposed to, let’s say, postmodernism? Well, because part of what gives human beings worth is their rationality. So, to develop that by teaching well is something that respects their worth and is something suggested by the theory of the worth of persons.

 

Roger Bissell

In your newest book, The Necessities Underlying Reality, you say that there are structures in the world and these are necessary. They actually, necessarily exist, and they are the foundation for both mathematics and ethics. They, plus our ability to know, are the reason that we can know absolute truths and we can have certainty in mathematics and in ethics. Also, those structures connect mathematics and ethics. Now I’m interested to hear from you: What are these structures? I think our listeners, our viewers would be interested to know what you see as being these underlying structures and how do they connect these two fields. Is human nature part of the answer to that question?

 

James Franklin

Yes, it is part of the answer but let me take a couple of examples in each field, mathematics and ethics, that are not specially connected with each other, so that we see what sort of things we’re talking about. Ratio and symmetry, I think, are excellent examples of mathematical properties of reality. If we were all three in the same room, the person looking at us could immediately perceive the approximate ratio of our heights. I’m of medium height, let’s say you’re tall, and the ratio of your height to mine is maybe about 1.1. That’s immediately perceptible, but the theory of ratios—and you said you studied the theory of measurement, that’s much the same thing—tells you a great number of things about those. Different kinds of things can have ratios, heights can have ratios, time intervals, volumes, and so on. The theory of ratios itself is pure mathematics, and it’s something you can have necessary truths about, for example, the transitivity of “greater than” between ratios. If A is greater than B and B is greater than C, then A is greater than C. That’s locked in and can’t be otherwise. The same, with symmetry.

But let’s not go into too much about that, and let’s move to ethics. I think perceiving the worth of persons or—perhaps perceiving is not the right word—understanding the worth of persons is essential to ethics. The seven-year-old understands that if someone else gets an ice cream, “It’s not fair. I should be getting the same ice cream,” they have some kind of understanding that there is worth of different persons, not just all about me.

The Iranian protester being killed is worth just as much as the Ayatollahs or yourselves.

Now, what about the connection between mathematics and ethics? Well, one connection is just that all of those things that I’ve mentioned, you can understand by reason, and they’re not like laws of nature that could be otherwise. But there is a bridge between the two, namely, the notion of equality. There’s a reason why mathematics is full of equations. You find things are equal. In the example I took, turning over the page 128 times is equal to, in some sense, doing nothing. In the quantitative, when you’re doing calculus full of equations, things are found to be equal. Now, in ethics as well, the equality of persons is a very crucial thing. You think that the Iranian protester being killed is worth just as much as the Ayatollahs or yourselves, and you think of putting yourself in their position, “What would it be like for me?” and you appreciate that they have an equality of worth, and that the equality of worth accounts for a very great deal of the facts of ethics.

 

Vinay Kolhatkar

You were speaking about a bridge, and we also, Roger and I, spoke about a bridge from the field of “is” to the field of “should” and “wants” or “oughts.” And there’s the famous Hume’s paradox in the field of ethics where he says you can’t jump from “is” to “ought,” and I think he’s absolutely right. But what we did in our book was to say, okay, this is the field of the “is.” But do you want to construct a meaningful life? If your answer is, “yes,” that is an “ought,” and now we are into the field of “oughts.” So, your human worth, that they are intrinsically worth something, does that fit in the field of the “is,” the state of nature? And then how would you then build a bridge to the field of “oughts”?

 

James Franklin

Yes, so is the worth of persons an “is” or an “ought”? Well, it’s kind of in between, because it’s not an “ought” in the sense of telling you ought to do something. It’s not about action at all. It’s said to be about a property of human beings. On the other hand, it’s not a natural, scientific property. It’s not something you can measure or observe through a microscope. My idea is that the “is” to “ought” bridge is done in two steps. There’s a steppingstone in the middle that is an “is,” but an ethical “is.” Now, how does it work? In my view, the way to get from the scientific “is” to moral worth is the philosophers’ notion of supervenience, that humans have certain properties that you can in a sense observe or understand like rationality, emotional structure, individuality, free will that are different than stones, and it’s the possession of those that causes necessarily them to have worth, so that if anything had those properties, whether human or not, it would make them superior in some sense to stones and lifeless galaxies. Now then, if you accept that much, then you have to get from the moral worth of persons to “oughts.” Well, there is a close connection, but it’s not the same sort of gap as trying to get from natural properties to “oughts.” So, if something is worthy, you can understand why deleting it is bad or wrong, because something important has gone out of existence. So, why is killing wrong? It’s not, in the first instance, a command of God or the greatest happiness of the greatest number or something. It’s because you’ve destroyed something that inherently has worth. I think we can understand that there is a gap, but a gap that we can perhaps feel comfortable with and understand how there’s a bridge there. So, yes, I think it’s a two-step process, natural properties like rationality to moral worth as a property of humans, and then a step from there to how you ought to treat those things of worth.

 

Vinay Kolhatkar

Yes, I believe our next step—as you’re saying, the bridge—might be a bridge of justice. If you want a just world, then you’ve got to start at the foundation, which is the moral worth of all human beings.

 

James Franklin

That’s right. A lot of what you will actually be doing in bridging from the worth of persons to “oughts” involves justice. But then the point is: Who is owed justice? It has to be something that is itself of worth. I mean, stones aren’t owned justice because they’re not the right kinds of thing.

 

Roger Bissell

A large part for me of philosophy is trying to connect ideas and trying to get across these gaps, to connect them, to make a larger structure of ideas that hold together and that help us understand the world and figure out what to do. One of the gaps that we run into is: how do you get certainty if you’re starting with probability? You kind of think you know, you have some evidence, but how do you get certainty out of that? There’s a big gap or chasm to jump there. And probability is really important. If somebody says, “Well, you said that it’s probable that this is going to happen. Are you certain that it’s probable, or is it just probably probable?” You can see you’ll be chasing your tail and eventually even your probable knowledge will evaporate unless you have something that’s solid to put the probability on top of. So, how does that all work in your opinion?

 

James Franklin

Good question. The answer is, as you put it, it’s certainly probable, which might seem a contradiction in terms, but really it isn’t. It’s important that the relation between evidence and hypothesis itself is a necessary one. To take one of the most basic examples, if you have a theory, scientific theory, it predicts some experimental result, and you go out and observe that experimental result, then that is good news for the theory. It makes it more probable. Now, that itself, the principle that the theory is confirmed by its consequences, is a necessary principle. It’s a matter of logic, the same way as modus ponens or something like that is. It’s just a matter of the necessary connections between propositions, but the necessary connection that is, is only probabilistic. It’s the same if you’re in a jury in court. Your job is to evaluate if the evidence shows beyond reasonable doubt that the defendant is guilty. Whether it does or not is a matter of necessary connections between evidence and conclusion, the conclusion being that the person is guilty, and you have to evaluate that, and it doesn’t depend on any scientific facts. It’s just logic, and you’ve got to get that straight—the fact that the probabilistic relation between evidence and conclusion is itself a necessary matter of logic. Once you’ve got that straight, you can be happy, perhaps, in some cases you only get probability. Okay, you’re not going to prove that the person is guilty. You have to accept that it’s just proof beyond reasonable doubt, but that itself is a solid result.

 

Vinay Kolhatkar

Okay, last question of the day perhaps. You mentioned in an email that you found the approach we took in Modernizing Aristotle’s Ethics to be interesting. Could you possibly elaborate on what your specific agreements and disagreements are with the approach we took?

 

James Franklin

Yes, well there’s a lot to like about that book, there certainly is. It is a genuine updating in the spirit of Aristotle’s ethics and brings in some developments by Ayn Rand, which I think are definitely in the spirit of Aristotle. What is good about it, from my position, is that it does connect ethics back to metaphysics. You had a chapter on the nature of humans, which is the right place to start exactly on ethics. You’ve to get straight what the nature of humans is before you can decide what they ought to do as a life course. You foregrounded the self-actualization or self-realization of the potentialities of humans, and I agree with all that, and I agree that it’s in the spirit of Aristotle.

What I was not totally happy with is that Jesus and the Bible are not in the index, and I think they have something to add to Aristotle and ancient Greek ethics generally. There’s a reason why the ancient Greek virtues like justice, courage, temperance, and prudence don’t include the Christian virtues, especially charity or love. I realize that in your book you did say something about benevolence and said something positive about that. But what it seems to me [that] Aristotle and Ayn Rand don’t have is a correct symmetry argument about the equal worth of persons and what it implies. So, if self-realization or self-actualization is good for me, it’s equally and for the same reason good for everyone else, and that might imply that I need to self-sacrifice or something like that. As Jesus says, love your neighbor as yourself. Well, it’s a big call, and it might be bad news for your own self-actualization, but I think it’s required by understanding properly the equality of persons.

 

Roger Bissell

I wanted to point out that, in just regard to what you said, we talk about the four orders of humaneness, and these are toward others and toward ourselves, very similarly to what you were saying, to love your neighbor as yourself. We were arguing for being humane toward others as toward yourself. Many people don’t even think of themselves in that regard, while other people do but don’t think of others. So, it’s kind of a 360-degree ethics. To us, that’s a bedrock principle, just as the equal worth of persons. You’re one of those persons, so you should think of yourself as the equal of others, just as you would think of others as the equal of yourself in terms of human worth.

 

James Franklin

It’s good that you have moved your ethics in that direction from Aristotle’s concentration on the megalopsychos [great-souled man.

Yes, I think in fact it’s good that you have moved your ethics in that direction from Aristotle’s concentration on the megalopsychos [great-souled man; see Aristotle’s Nicomachean Ethics], who seems to be always well and always in charge of the city-state. I would hope that an ethic that suits everyone is an ethic that [also] suits vulnerable and sick people. It’s not all that easy to move the position of Aristotle and Ayn Rand in that direction, but I agree that you’ve done something about that and, yes, that’s great that you’re moving there.

 

Vinay Kolhatkar

Would you say that Christianity does move much further on that notion about looking after the vulnerable and the sick?

 

James Franklin

Yes, I think that’s the historical record—that Catholic and other Christian bodies have done a lot with hospitals over the last 2,000 years, for example, hospitals and leprosariums and that kind of thing. They’ve certainly been motivated to do that in a way that I think not many other ideologies have been found to do. It’s said that Indian ones are a little bit inclined to think you shouldn’t catch other people’s karma by being too charitable to them. I don’t know if that’s exactly right, but yes, I think many, many Christian heroes have gone out there and looked after the worst off just because they were people and in the image of God as the Old Testament says and then deserving of charity and doing the best for them.

 

Roger Bissell

Before we have to go: this was not on our list of questions we’d like to talk about, but you mentioned India and, many years ago, I found out about a mathematician named Srinivasa Ramanujan, and he had an untimely death. I mean, he wasn’t that old, but he was some kind of incredible genius—in number theory, correct? [James: In number theory, yes.] And he’d have notebooks full of formulas that just sort of came to him, and he wrote them out, and there was no indication of how he got them. It’s almost become a college industry for graduate students to try to prove these formulas. Are they correct? Or did he just write some stuff that seemed to look good? So, my question to you is, do you have any faint notion of how in the world somebody like that comes about and can produce that much material without just really cranking out line after line of proofs? He just said, here’s a formula. Here you go. It’s like, here’s a cake. I’m not going to tell you how I made it. Here’s the cake.

 

James Franklin

Yes, he just knew it. It’s hard to talk sensibly about inspiration. He said himself that the goddess [Namagiri] dictated them to him. They’re nearly all true. He made a few mistakes, but they’re nearly all true. Whenever you get some kind of inspiration, even if you have been in a mathematics exam, and the question is not exactly anything you came across before, but you had to get from A to B, and suddenly there it was. How is this possible? We don’t know how that’s possible. Our AI appears to do it, but it does it by, so to speak, harvesting what everyone else has done by their inspiration. So, it doesn’t do genuine understanding itself. We don’t know how to make it do it, and we don’t know how we do it either.

 

Vinay Kolhatkar

I wish we could replicate genius. Then we could do that for ourselves and many, many other people. It’s been a great pleasure talking to you, Dr. Franklin, and thank you also to Roger for his penetrative questions.

 

James Franklin

Yes. Many thanks. Very pleasurable. Thank you.

 

Roger Bissell

It was a pleasure.

 

Vinay Kolhatkar

And to the listeners, keep tuning in to keep yourselves savvy and to make yourselves more savvy. Good night and good luck.