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Abstract: A life spent in the world of abstract ideas – mathematics, philosophy, the history of ideas – gives a unique perspective on more practical matters. A focus on principles gives different insights from those of the “practical man” based solely on experience. Euclid brought clarity and certainty to the very practical world of geometry by organising it as a logical structure of theorems provable from self-evident first principles. Surely complex matters of policy, law, ethics and culture would be much simplified if we could understand the applicable basic principles? The lecture lays out how to think in terms of abstract principles, some of the mistakes so identified (such as thinking in terms of collectivities of people instead of individuals), and the deep positive results that result (such as the foundation of ethics in the worth of persons).
You’ll remember the story of Rip Van Winkle. Rip is a villager in the old Dutch regions of the Hudson Valley in the late eighteenth century, with “an insuperable aversion to all kinds of profitable labour”. One day he goes hunting in the Catskill Mountains and meets a group of mysterious men in old Dutch colonial dress. He joins them drinking and falls asleep. When he awakes next morning and returns to his village he finds that twenty years have passed. Great changes have taken place and Rip himself is barely remembered.
That happened to me too.
I arrived as a first-year undergraduate at Sydney University in 1971 – just as the full force of the Sixties hit, with its libertarian and anti-establishment thought forms. I had a brief period of radical youth (brief as in “blink and you’ll miss it”) – I demonstrated against the Springbok tour of 1971, when South Africa sent a football team with only white players. “No ray-shist too-ers”, we chanted; “Paint ‘em black and send ‘em back”.
I found the world of debate about political, economic, ethical and policy ideas completely confusing. People seemed to take positions very quickly and passionately. On left and right they advanced opposite ideas very confidently, irrespective of how much they knew about the topic. What they said had a certain initial plausibility. But I couldn’t see what their principles were, or whether their positions were coherent, or how they were replying seriously to opposing ideas. It was all too complicated, I concluded, for a simple philosophy and mathematics student like myself. In any case, I realised I had no political, organisational or persuasive skills whatsoever, so it would be a waste of time for me to try to do anything political. That saved a lot of trouble.
Like Rip, I went off somewhere else for a few decades. Not with the ghosts of Dutch settlers in the Catskills, but into a world equally foreign to most people, the realm of abstract ideas. I did a PhD in pure mathematics, in algebra (entitled ‘Homomorphisms between Verma modules and Weyl modules in characteristic p’). I wrote a book on ancient and medieval ideas of probability and evidence, another on Australian philosophy, one on philosophy of mathematics, one on the foundations of ethics. Fascinating topics, but there is no pretending they are any immediate use. Like Rip, I had an aversion to all kinds of profitable labour – if “profitable” means useful or lucrative.
Now I’m back. The world of profitable labour, of policy, law, politics and economics still looks to me unutterably strange, and more so than in 1971. But this time, I’ve concluded it’s not just me that’s confused, it’s them. I’m ready to pick apart some concepts and excoriate a few trends. And for doing that, a background in the abstract world is not a bug, it’s a feature.
Useful or not, living in the world of abstract ideas does attune one to certain aspects of reality, aspects that can be lost if one starts empirically from the ground up and just takes on the received ideas of the surrounding culture. Aspects like the reach of very general principles, and necessities.
Mathematicians would like to do things in a certain way. Take geometry, undoubtedly a subject with its uses. Euclid laid out geometry by stating definitions and axioms at the beginning, then proving all the later theorems from the axioms by strict logic. Thus, a circle is defined as a curve “such that all the straight lines falling upon it from one point among those lying within the figure equal one another” and one of the axioms is “it is possible to draw a circle with any centre and any radius”. Then the theorems proceed logically in order: Book I proposition 47 is Pythagoras’ theorem, “The square on the hypotenuse of a right-angled triangle is the sum of the squares on the other two sides”, and by that stage the results are well beyond what is intuitively obvious. So geometry rests on solid foundations; the foundations can be seen and it is clear exactly what they are, and how the more complex truths follow from them.
Practical people might say that Euclid is not much use for working out how far it is to the shops. As Aristotle reports, just before Euclid’s time, people were already complaining that geometry is all very well for perfect circles, but what about real and imperfect wheels and coins? But geometry does apply to those “imperfect” shapes too. If baking paper is cut to fit around the cake tin, and made three times the diameter, it will not fit right around. Pythagoras’s theorem does measure, approximately, how much distance will be saved by cutting a corner. The first four governors of New South Wales were naval officers and hence highly trained in spherical trigonometry, which is how Euclidean geometry adapts to the round shape of the earth; just as well, because despite its size Australia is easy to miss if you head east from the Cape of Good Hope. If you drove here and asked google maps to plan the route, or you came by Uber, a mathematical spatial algorithm plotted your shortest route.
It is true that real-world information is needed for the principles to work on, but the principles explain what to do with the data.
A further advantage of geometry in the style of Euclid is that it attunes those who learn it to the difference between practical matters and the abstract principles behind them. As Plato says, it would be ludicrous to interpret mathematicians’ talk of actions like adding numbers, constructing circles and extracting square roots as implying that mathematics is really about action. No, it is pure knowledge, he says, “the knowledge of that which always is, and not of a something which at some time comes into being and passes away.” One thing that becomes evident in the rarefied air up there in the world of abstractions is the force of necessities. Truths like 2 + 2 = 4 do not “come to be and pass away” because they have to be that way. The necessity can be easily seen in this example:
The six crosses form both two rows of 3, and three columns of 2. So it is possible to see (literally see) not only that 2 × 3 = 3 × 2, but that it must be so. Pure necessity is made visible.
I would like to see necessities like that recognised more widely; including in debate about policy, law etc. Will abstractions, necessities and attention to principles help there?
As I was saying, after forty years or so in the abstract world, I came back and cast my eye over what was doing in what is sometimes laughingly called the “real world”. It looked strange, even stranger than in 1971.
The younger generation inhabited something called “social media” which caused them to have the attention span of a mayfly and the thought diversity of a bee colony.
There was a whole industry of leaders of institutions tearfully apologising for things other people had done decades earlier.
Various philosophical mistakes apparently finished off in the fifth century BC had been resuscitated under the name of postmodernism and were all the rage in literary studies.
On the plus side, people didn’t blow smoke in your face in restaurants any more, and there was a solid consensus that we baby boomers were doing such a good job of running everything that we should be paid a lot of money to keep doing it.
One thing hadn’t changed. Debate about political, economic, legal and ethical issues proceeded with the same heat and the same lack of attention to principles as ever. Important questions like abortion and euthanasia were fought out with competing slogans like pro-life and pro-choice, without the principles behind those slogans being laid out and examined. The way debates proceeded was the anti-principled one perfected, if that is the right word, in the law of English-speaking countries: hired champions with expensive training in rhetorical skills battle it out in court with reference to a lot of cases, and a jury of twelve people randomly dragged off the street votes the result – without being allowed to do their own research.
Mathematics could be done that way, though I would not advise it. Classical Chinese mathematics was something like that. Matteo Ricci, the first Jesuit missionary in China around 1600, reported:
Nothing pleased the Chinese as much as the volume on the Elements of Euclid. This perhaps was due to the fact that no people esteem mathematics as highly as the Chinese, despite their method of teaching, in which they propose all kinds of propositions but without demonstrations … The result of such a system is that anyone is free to exercise his wildest imagination relative to mathematics, without offering a definite proof of anything. In Euclid, on the contrary, they recognized something different, namely, propositions presented in order and so definitely proven that even the most obstinate could not deny them.”1
So Ricci and his Chinese collaborator Xu Guangqi translated Euclid into Chinese.
This time, when I saw debate on practical matters proceeding as ever, with everyone “free to exercise their wildest imagination” about ethical and policy questions, “without offering a definite proof of anything,” I decided I wasn’t going to take it lying down anymore.
By way of explaining how a more principled approach to policy matters would work, I will look at one way to go wrong with abstractions, one widespread wrong principle, and one right principle that has not been got into focus.
Political argument is still given to clashes of free-floating one-sided ideological packages that do not gel with reality or engage with alternatives. Around 2000 I became disturbed by the mismatch between the well-known extreme levels of violence and poor health in remote Australian indigenous communities, and the obfuscatory Latinate discourse of city “progressives” about “reconciliation”, “colonialism”, “disadvantage”, “sovereignty not ceded”, “intergenerational trauma” and “self-determination”. This is a real example:
“the consequences of colonisation, intergenerational trauma, and systemic racism continue to cause enduring physical and mental harm and perpetuate inequities relating to the social determinants of health.”2
Those abstractions are devices for not thinking. If Anglo-Saxon words were used instead, like “people are hitting one another every night”, the picture would be clearer.
The 250,000 people who walked across the Sydney Harbour Bridge in 2000 “for reconciliation” had no wish, it seemed to me, to know about Skull, Walker and Ruben’s 1997 article on ‘Malnutrition and microcephaly in Australian Aboriginal children’.3 I resolved to be on the lookout for better-grounded thinking on indigenous affairs.
What sort of principled thinking might be better? You could do worse than to start with Thomas Hobbes, the political philosopher of the seventeenth century. He says that the first condition of civilisation is the control of interpersonal violence. In a famous passage, he writes,
it is manifest that during the time men live without a common power to keep them all in awe, they are in that condition which is called war; and such a war is of every man against every man … In such condition there are … no arts; no letters; no society; and which is worst of all, continual fear, and danger of violent death; and the life of man, solitary, poor, nasty, brutish, and short.4
He is right. With the levels of interpersonal violence in remote communities, there is little chance of making progress by supplying resources for education and health. We will just keep scratching our heads as to why “Closing the gap” is not happening.
It could be useful to add to that principles taken from human rights. Article 3 of the Universal Declaration of Human Rights is:
“Everyone has the right to life, liberty and security of person.”
We will walk out of this building in half an hour confidently expecting life, liberty and security on the way home. There is a system that protects us. People in remote communities deserve the same rights.
Then I looked for someone – someone better informed than myself – who was saying those sort of things in indigenous affairs already. In 2009 I attended a speech by the Warlpiri leader Bess Price,5 which did say that. I supported her as she became a minister in the Northern Territory government, and later I supported her daughter Jacinta Price, now a Senator, who has the same message. You’ll hear more from her.
In cases like these, a principled approach will not always deliver exact policy prescriptions, since that involves some experience of the situation on the ground and what policies have been found to work. (That is the same as google maps’ algorithm needing information about roads.) How exactly to make remote communities safer needs thinking about in the light of many facts, for example about cultural differences. However, a principled approach will explain what counts as success, so we know which direction is forward and can do honest evaluation and accountability. Money spent is not a criterion of success. Lower rates of hospital admission for head trauma are.
Next, one wrong principle.
As I said, when I came back to the real world from the realm of abstractions, I found a pile of confusions which I concluded were not just my confusions. One that I kept seeing, time and again, is what I would call the collectivist error. It means praising and blaming collectivities or groups of people, when praise and blame can only attach to agents with intentions, that is, individuals.
We can learn a lot from looking at one of the worst examples, the anti-semitism that has disfigured many centuries of Christian history. It affected even as smart a person as Thomas Aquinas. He was once asked by the Countess of Flanders whether she could confiscate money from Jewish moneylenders. His reply is even-handed and says that the same conditions apply to Christian moneylenders, but he does start with this principle as if it is agreed by everyone: “as the laws say, the Jews by reason of their fault are sentenced to perpetual servitude.” 6 The “fault” he means is the crucifixion of Jesus. The idea that Jews were collectively responsible for the death of Jesus has been a long-running thread in Christian anti-semitism over many centuries and was used to motivate and justify pogroms. Besides being morally revolting, it is conceptually incoherent to blame a people for what certain individuals did in 33AD. Guilt cannot be collective, it cannot apply to people other than those who did whatever it is that was wrong or at least acted in support of those who did. It cannot be inherited. Someone as smart as Thomas Aquinas should have understood that.
Unfortunately, the idea of collective guilt has not disappeared with medieval antisemites. We have seen plenty of collective blaming since last October 7th.
A similar mistake of collectivist thinking is “affirmative action” policies that mechanically apply membership of a disadvantaged group to give an individual in that group an advantage. A year ago the US Supreme Court rightly struck down US college race-based affirmative action admissions policies. It makes no sense either statistically or morally to give possibly privileged members of some collectivity an advantage solely on the basis that the average or majority of that collectivity is disadvantaged. Australian practice, I am glad to say, has been better. Australian universities typically have Access schemes where any applicant for entry can tell their story of disadvantage. Their membership of a generally disadvantaged group might be some evidence of that, but it has to bear on their individual case. That is as it should be.
To take a final example, some people believe very passionately that “Taiwan is an integral part of the People’s Republic of China.” That claim is not just false but meaningless – as physicists say about really confused theories, “not even wrong”. Taiwan and the People’s Republic of China are de facto separate and functioning states, and there is no collectivity that they could be an integral part of.
Now, it is quite true that humans are social beings and organise themselves into groups, like families, companies, churches and nations, to get things done. There is a reason why a company or a school can own property and can sue and be sued. Loyalty to a group is natural, up to a point. But it still makes no sense to blame a company. The company’s policies are decided and implemented by certain individuals with certain knowledge, who are to blame or praise for what the company does, in various degrees according to their influence on decisions.
It is also true that some people are born with disadvantages which they share with a group of other people, such as fetal alcohol syndrome. It is appropriate to act on that and to examine the historical and present-day causes why some groups are especially affected. But that is still to analyse the problem based on causes affecting individuals, which is very different from blaming or compensating collectivities.
Now let us turn to something more positive – determining what the principles of ethics are.
Ethics is a topic particularly full of positions talking past one another and failing to get a grip on principles. Books on business or medical ethics typically start with a quick run-through of different views on the nature of ethics – utilitarianism, deontology, divine command theory, natural law, virtue theory and others – and conclude that it is hard to decide but it doesn’t matter in practice.
Of those standard positions, utilitarianism is interesting because it does derive ethics from a clear principle. It says that an action is right when it increases the stock of happiness – in a catchphrase, it is for the “greatest happiness of the greatest number”. That sounds good – who isn’t in favour of more happiness? Unfortunately it is the wrong principle: which is clear from its consequences. For example, it says that you should sacrifice one person unjustly for the sake of the good of all, because that increases the total happiness – in a classic example, a sheriff in a racist southern US town should execute an innocent black to prevent a riot that would create havoc (“one man should die for the people,” as the Sanhedrin put it in deciding to get rid of Jesus). But worse than that, in such a case, utilitarianism gives no weight to justice at all – justice itself is not about the greatest happiness of the greatest number. So justice doesn’t count unless it happens to have good consequences in a particular case.
Who, then, has better principles for ethics? Jesus answered that question, or almost. In Matthew 22 Jesus is asked:
“Teacher, which is the greatest commandment in the Law?” Jesus replied: “‘Love the Lord your God with all your heart and with all your soul and with all your mind.’ This is the first and greatest commandment. And the second is like it: ‘Love your neighbour as yourself.’”
And note especially what comes next:
“All the Law and the Prophets hang on these two commandments.”
What does “hang on” mean? It can only mean one thing, the same as in Euclid: deducibility from. This is Jesus’s “Euclidean moment”, where he lays down axioms and invites the derivation of theorems. And plainly a lot does follow from loving one’s neighbour – once Jesus has laid down, as in the Parable of the Good Samaritan, that everyone counts as neighbour. Any kind of deliberate harm is ruled out, for a start, which covers a great deal of ethics.
Jesus talks about “the Law”, but from a modern ethical perspective we can ask: why should we love one another? What is it about people that makes that worth doing, that gives it some point?
Jesus had something to say about that too: something that modern readers of the Bible tend to skip over as a platitude, but which is unique to the Jewish tradition. Matthew 10:31 says “you are more valuable than many sparrows”.
What is it, then, about you that makes you valuable – that makes your survival, and what happens to you, matter absolutely? Why is the death of a human a tragedy, while the explosion of a lifeless galaxy is just a firework?
It must be something about the special properties that humans have, which lifeless galaxies do not have. A traditional answer is that one main feature distinguishes humans – rationality. “Humans’ excellence,” says Saint Augustine, “consists in the fact that God made them to His own image by giving them an intellectual soul which raises them above the beasts of the field.”7 It is a good start – rationality really is exceptional in the universe and very special – but as an answer it is too simple. Shakespeare has a quick sketch that suggests some complexity: “What a piece of work is man,” says Hamlet. “How noble in reason, how infinite in faculty, In form and moving how express and admirable, In action how like an Angel, In apprehension how like a god … ” Hamlet is right that possession of such properties as reason, apprehension, the capacity to act freely, emotional structure and individuality confer on humans a moral weight, a nobility, dignity, or inherent worth that makes what happens to humans important in an absolute sense.8
Notice though that these concepts are far from ethics in the sense of what to do: moral action, dilemmas, rights and duties, virtues. The worth of persons is not itself about actions, it is about the nature of humans.
But it does have implications for action, in something the same way as Jesus’s “Love your neighbour” is not about action but has implications for action. It explains why murder is wrong – murder involves the deliberate destruction of an infinitely valuable person. Murder is wrong because of that, not because it subtracts from the greatest happiness of the greatest number or violates a command of God or society. Killing in self-defence: – we may have to consider it because it involves a conflict between the survival of two persons. To take a completely different kind of example, a right to education follows from the role of rationality in giving persons worth. Rationality is, in Aristotle’s language, a perfection of humans, so they ought to be given the means to exercise their rationality, which is what education is.
And so on. Any ethical matter involving actions towards people, which is most of ethics, will be seen to involve essentially the worth of persons.
Plato advised that the guardians of the state, those who would be rulers of society and, as we now say, “set strategic directions”, ought to start with a long training in mathematics. That would ensure that they understood principles, necessity and the connections of ideas. They would look behind plausible flights of rhetoric to evaluate genuine reasons. He was right.
At this late stage we may have to let off humanist scholars with a minimal amount of school mathematics and look to something else as a training in proof and necessity. Perhaps logic. But in debating policy, there is no substitute for a return to principles and necessities.
My advice to anyone who wants to maintain the practice of policy discussion via rhetoric based on cherry-picked cases is the same as Lucy’s in the comic strip Peanuts whenever she’s asked for psychiatric advice: Snap out of it.
1 China in the Sixteenth Century: The Journals of Matteo Ricci, 1583-1610, trans. L.J. Gallagher (Random House, New York, 1953), pp. 235, 476.
2 https://www.snaicc.org.au/wp-content/uploads/2023/11/Family-Matters-Report-2023.pdf, p 46.
3 Susan A. Skull, Alan C. Walker and Alan R. Ruben, Malnutrition and microcephaly in Australian Aboriginal children, Medical Journal of Australia 166 (1997), 412–4.
4 Thomas Hobbes, Leviathan, bk 1 ch. 13.
5 Bess Nungarrayi Price, Inaugural Peter Howson lecture, 3 Dec 2009, https://web.archive.org/web/20120204195843/http://www.bennelong.com.au/conferences/lecture2009/howson-lecture-2009.php
6 Thomas Aquinas, Letter to Margaret of Flanders, https://thomistica.net/letter-to-margaret-of-flanders
7 Augustine, De Genesi ad litteram, bk 6 ch 12.
8 More fully in James Franklin, The Worth of Persons: The Foundation of Ethics (Encounter Books, New York, 2022), ch 6.
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