The Idea of Freedom in the Modern World

By Simon Thomas

Soul Freedom Chained, by Khalil Gibran

Freedom is a magnificent idea, yet it is much misunderstood. Some claim freedom in the idea that you should be able to express yourself as you wish, without restraint (which is positive freedom).  It is the idea of mind over matter, reality over unreality, which has its roots in René Descartes.

Descartes takes it further, noting that there is a materialistic type of freedom where you have the means to meet all your material needs (which is negative freedom). Maslow’s hierarchy gives us an idea of the needs concerned. If a person feels that their need for security, food, shelter, and some creature comforts are met, then they can live a satisfactory and contented life. It is true, therefore, that the fulfillment of such needs is a type of freedom.

However, that is only half the story. Jean Jacques Rousseau put it aptly when he said, ‘Man is born free, but everywhere he is in chains.’ Rousseau‘s starting point is that man is inherently good, and therefore freedom is possible – provided he is not unduly restrained by unjust laws to protect the wealthy. Yet common sense, and experience of the modern world, seem to indicate the opposite of Rousseau's Utopian idea. It seems a fallacy that people are inherently good. If they were inherently good, they would not enforce their will on others, and thereby enslave them – in Rousseau’s terms, put them in chains.

Now there is another type of freedom, which is more a matter of the mind. Philosopher Richard Rorty said that what you put in your mind – which is, the way you interpret the world – that’s what there is. Therefore if you have a subservient mind-set, you cannot be free – regardless of the kind of liberty your accumulated wealth brings you. He continues by saying that the only true freedom we can enjoy is metaphysical in nature, because humanity cannot find lasting meaning purely in material needs being met.

This is exactly the mind-set we are contending with in society today – and does not to resound with previous generations. I have recently been talking to people who were children during World War 2. The mind-set out of that era was by and large, work hard, fight for liberty and justice, and accumulate wealth, no matter the personal cost to home and family. We have seen the effects of this unfold since the 1960s till the present time: rebellion against authority by younger generations, and ever increasing hostility against law and order.

Breaking free from law and order in society has never been a workable idea. Anarchy has never produced freedom. Instead, it has produced tyrants and addicts. Neil Postman, in his novel 'Entertaining ourselves to death', makes the point that our society has produced people with a mind-set which needs to be entertained all the time. Yet this produces addiction to visual media, harmful cravings for the next high, or more recently, cyber addiction.  Again, there is no freedom in that.

Related to this, the notion has become epidemic that having what you cannot normally afford will bring lasting satisfaction. Thus people get themselves into inordinate amounts of debt – and often, instead of freedom, it brings financial ruin. Having said this, however, it is not just a problem of the individual, but of nations. There is a huge debt bubble – which, while it caused the demise of some leading banks in 2008, was just cosmetically treated.

On point with these examples is that freedom in the Western world is a fallacy, because it is built on an idea that we are entitled to have whatever we want, regardless of how we get it – and regardless of those who are injured along the way.

Freedom, as Rorty said, is metaphysical in nature. A person can be in dire circumstances, yet still be free. The martyr Polycarp, of distant memory, said this to his persecutors when they demanded his freedom of religion: ‘You can take my life if you wish, my property if you want, but you cannot make me deny the faith that saved me.’

That is freedom. It is the grand idea that freedom is only attainable when you let go of the idea of materialistic happiness, and learn to be content in whatever circumstance you find yourself. As the sages of old often said, ‘Bloom where you are planted.’ In this is freedom: to be at peace with yourself.

Are ‘Designer Offspring’ Our Destiny?

The promise of gene editing and designer offspring may prove irresistible

Posted by Keith Tidman

It’s an axiom that parents aspire to the best for their children — from good health to the best of admired traits. Yet our primary recourse is to roll the dice in picking a spouse or partner, hoping that the resulting blend of chromosomes will lead to offspring who are healthy, smart, happy, attractive, fit, and a lot else. Gene editing, now concentrated on medical applications, will offer ways to significantly raise the probability of human offspring manifesting the traits parents seek: ‘designer offspring’. What, then, are the philosophical and sociological implications of using gene editing to influence the health-related wellbeing of offspring, as well as to intervene into the complex traits that define those offspring under the broader rubric of human enhancement and what we can and ought to do?

‘All the interests of my reason, speculative as well as practical, combine in the three following questions: What can I know? What ought I to do? What may I hope?’

— Immanuel Kant

The idea is to alter genes for particular outcomes, guided by previous mapping of every gene in the human body. To date, these selected outcomes have targeted averting or curing disorders, like cystic fibrosis, Huntington’s, and sickle-cell disease, stemming from gene mutations. As such, one of the central bioethical issues is for parents to freely decide which disorders are ‘unacceptable’ and thus to prevent or fix through gene editing. The public, and the medical field, already make similar medical decisions all the time in the course of treatments: stem cells to grow transplantable organs, AI-controlled robotic surgery, and vaccinations, among innumerable others. The aim is to avoid or cure health disorders, or minimally to mitigate symptoms.

As a matter of societal norms, these decisions reflect people’s basic notions about the purpose of health science. Yet, if informed parents knowingly choose to give birth to, say, an infant with Down syndrome, believing philosophically and sociologically that such children can live happy, productive lives and are a ‘blessing’, then as a matter of ethics, humanitarianism, and sovereign agency they retain that right. A potential wrinkle in the reasoning is that such a child itself has no say in the decision. Which might deny the child her ‘natural right’ not to go through a lifetime with the quality-of-life conditions the disorder hands her. The child is denied freely choosing her own destiny: the absence of consent traditionally associated with medical intervention. As a corollary, the aim is not to deprive society of heterogeneity; sameness is not an ideal. That is not equivalent, however, to contending that a particular disorder must remain a forever variation of the human species.

‘We are going from being able to read our genetic code to the ability to write it. This gives us the … ability to do things never contemplated before’

— Craig Venter, writing in ‘Heraclitean Fire: Sketches from a Life Before Nature’.

Longer term, people won’t be satisfied limited to health-related measures. They will turn increasingly to more-complex traits: cognition (intelligence, memory, comprehension, talent, etc.), body type (eye and hair colour, height, weight, mesomorphism, etc.), athleticism (fast, strong, agile, endurance, etc.), attractiveness, gender, lifespan, and personality. The ‘designer offspring’, that is, mentioned above. Nontrivially, some changes may be inheritable, passed from one generation to the next. This will add to the burden of getting each intervention right, in a science that’s briskly evolving. Thus, gene editing will not only give parents offspring that conform to their ideals; also, it may alter the foundational features of our very species. These transhumanist choices will give rise to philosophical and sociological issues with which society will grapple. Claims that society is skating close to eugenics —a practice rightly discredited as immoral — as well as specious charges of ‘playing God’ and assertions of dominion may lead to select public backlash, but not incurably so to human-enhancing programs.

Debates will confront thorny issues: risk–reward balance in using gene editing to design offspring; comparative value among alternative human traits; potential inequality in access to procedures, exacerbating classism; tipping point between experimentation and informed implementation; which embryos to carry to term and childhood; cultural norms and values that emerge from designer offspring; individual versus societal rights; society’s intent in adopting what one might call genetic engineering, and the basis of family choice; acceleration and possible redirection of the otherwise-natural evolution of the human species; consequences of genetic changes for humanity’s future; the need for ongoing programmes to monitor children born as a result of gene editing; and possible irreversibility of some adverse effects. It won't be easy.

‘It is an important point to realize that the genetic programming of our lives is not fully deterministic. It is statistical … not deterministic’ 

— Richard Dawkins

The promise of gene editing and designer offspring (and by extension, human enhancement writ large) may prove irresistible and irreversible — our destiny. To light the way, nations and supranational institutions should arrange ongoing collaboration among philosophers, scientists, the humanities, medical professionals, theologians, policymakers, and the public. Self-regulation is not enough. Oversight is key, where malleable guidelines take account of improved knowledge and procedures. What society accepts (or rejects) today in human gene editing and human enhancements may well change dramatically from decade to decade. Importantly, introducing gene editing into selecting the complex traits of offspring must be informed and unrushed. Overarching moral imperatives must be clear. Yet, as parents have always felt a compelling urge and responsibility to advantage their children in any manner possible, eventually they may muse whether genetic enhancements are a ‘moral obligation’, not just a ‘moral right’.

Picture Post 44: The Lifeboats

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'Because things don’t appear to be the known thing; they aren’t what they seemed to be neither will they become what they might appear to become.'

Posted by Martin Cohen

      

‘Life Is a Shipwreck, But We Must Not Forget To Sing in the Lifeboats’.

It’s a great thought, and can be found on the internet attributed to Voltaire, but it doesn’t sound quite like the great French philosopher, and indeed Garson O’Toole is probably right to point at a later book editor commenting on the world view behind Voltaire’s bitterly witty story, Candide.

Here in these images surely, the passengers do not sing, but seem instead curiously withdrawn, as if trying to shut their eyes to an awful sight. And indeed that might be just what they were doing, as these plucky little lifeboats were chugging away from a Titanic, sinking and still packed with thousands of desperate passengers. Second and Third Class ones, that is. For the real scandal of the Titanic was not that it sank, not even that its Captain was so dilatory in asking for assistance (or the boats around in offering any) but that the social conventions of the era implied that most of the lifeboats were for First Class passengers only, with no mixing. Though to be sure, the small number of officers and  richer passengers left on the boat did mix with the other passangers later... in the cold grey waters of the Atlantic.

Facts-wise, then, the fact is that the first six lifeboats were at less than one third loaded capacity, and the passengers were only First Class passengers or… Ship’s Officers. Six underloaded boats like the ones in the picture, which had a capacity for 40 persons meant 150 passangers drowned to defend the niceties  of wealth.

That said, Captain Edward Smith was on the bridge at 2.13am, seven minutes before the Titanic disappeared beneath the waves, and went down with the ship.

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Read more…

http://www.icyousee.org/titanic.html#life

Doublethink 27 - Eugenics

 

Pi is pleased to present another bonus episode of

 Youngjin Kang's Doublethink

What Truly Exists?

Posted by Thomas Scarborough

Magritte’s iconic painting of a man looking in a mirror,
reminds us that the world we perceive is not real,
but rather constructed

A core question of ontology, or theories about the nature of being and existence—and perhaps its most pressing question from a practical point of view—is which individuals or 'things' are really real. What truly exists? It seems that there are three broad possibilities:

• material entities alone (which is materialism),
• mental entities alone (which is idealism),
• or both (which is dualism).

However it is very difficult, as the cognitive scientist Aaron Sloman has put it, to distinguish between ‘real existents’ and ‘useful fictions’—or for that matter, useless ones. As philosophy professor Simon Blackburn notes:

‘Everything you can think of has at some time or another been declared to be a fiction by philosophers bent on keeping a firm check on reality—among them matter, force, energy, causes, physical laws, space, time, possibilities, numbers, infinity, selves, freedom of the will, the will itself, desires, beliefs, identity, things, properties, society, language, and money.’

Intuitively, we feel that what we see, hear, smell, taste, and touch—or perceive in any way with our senses—is real. Yet what are we to make of things we do not perceive—either because, momentarily, we find that they lie beyond our senses, or because they are what we call ‘constructs'—compound ideas which may lack empirical evidence?

The problem strikes close to home. Take the one hundred most commonly used nouns in English. The first on the list is ‘time’. You cannot see it or touch it or anything like that. The second is ‘year’. The same applies. The third on the list is ‘people’. Now here is something we can see and touch—at least when those people happen to be around. The fourth term, though, ‘way’, is both real and unreal. And so, depending on how we categorise these nouns, fully half of them may not be ‘real’ at all.

It would be helpful to start with the simplest distinction—namely that which we make between real things we experience directly, and real things we do not.

Imagine that I am cycling down a narrow cycle track under some coconut palms. I see the world in front of me as I go—but do not see the world behind me. I saw it a moment ago—a thicket of breadfruit trees, and children playing. But I know that they are there. I saw them, heard them, smelled them. Besides, I could easily stop my bicycle now and look back to confirm it.

In what sense, then, are those things there, which are now behind me? After all, I do not directly perceive them.

We may conduct a simple thought experiment.

Imagine that, as I ride my bicycle under the coconut trees, we switch off my senses and freeze this moment in time. Without my senses, the perceived and the unperceived look largely the same in my brain—namely, arrangements of synapses in a vast network of neurons.

In my brain, then, there is little difference between the seen and the unseen (or the heard and the unheard, and so on). Both exist in the vast neural network which is or contains the mind. Everything, whether real or imaginary, ends up there. The question now is not so much whether my mind contains things perceived or unperceived. In the first case, my senses are activated; in the second, they are not—but in both cases, they are as real to me as anything possibly can be.

This becomes important now for the more vexing question as to how we are to understand constructs. There is more to riding my bicycle than what I see, hear, smell, taste, and touch. If there were not, I would be wobbling on my bicycle without anything left to orientate me:

Does this outing fit my purpose? Did I steal this bicycle? Do I need a passport here? Should I turn around now? And so on. None of these ‘surplus’ things—purpose, ownership, citizenship, and so on—is immediately real to me, yet all of them are vital. My mind is filled, not only with the things that I see, or saw a moment ago—but with many things which are in a sense unreal. One could say, things which are lacking empirical evidence, although in every case, they can be tested in some way.

Are these constructs real? In fact they are real—at least, as real as the coconut trees before me, and the breadfruit trees and the children behind me, given the fact that I arrange them, too, in my mind—each as a distinct concept with a unique label. As such, they do not fundamentally differ from those things which ‘exist’.

It would be wise for us to pause for a moment. We know well that we are capable, as human beings, of thinking of fictions which are not so. On the one hand, fictitious concepts—say magic spells, or the quintessence—on the other hand, fictitious entities—say the planet Vulcan, or fairies and gnomes. Sometimes, too, we believe that our fictions exist—or that they will exist at some time in the future.

Yet the separation of the real and the fictitious would seem to be fairly straightforward. ‘Real’ things correspond with the reality we perceive, while pure fictions do not. Does time therefore exist—or identity or society or any one of hundreds of thousands of constructs there are? Given that they correspond with the reality we perceive, we can only say yes.

The ultimate question is, does God exist? Given the right conditions, the answer to this, too, could be yes. The ‘right conditions’ for God’s existence would be threefold:

• that he is not purely ideational
• that the concept ‘God’ corresponds with the reality we perceive
• and that this concept is not invoked arbitrarily.

Or put it this way—for God to exist, there needs to be something permanent in our experience which necessitates him.

Lessons of the “Prisoner's Dilemma” for Real Life

Posted by Keith Tidman

The ‘prisoner’s dilemma’ is a classic example of game theory and a tool for decision-making, where two rational, independent players must choose between cooperation and conflict to arrive at what’s perceived as the best outcome. Central to the interactive nature of the game is that the payoff (optimal or otherwise) for any single player deliberating his or her decisions and the consequences of those decisions hinges on the strategies that the other player chooses to implement according to assumptions and rules.

The prisoner’s dilemma was the product of modeling work performed in 1950; however, it was the mathematician Albert Tucker who ultimately structured and named the thought experiment as we know it today. The standard description of the prisoner’s dilemma runs along these lines:

Two prisoners are being interrogated apart from one another for crimes they are believed to have committed jointly. Although officials have enough evidence to convict both suspects on the lesser of the two charges, they have insufficient evidence for a conviction on the more severe crime they’re suspected of. The prosecutor, therefore, simultaneously but separately offers each prisoner a plea deal. The deal offered is either to provide information adequate to convict the other suspect in an act of betrayal, or to remain silent and refuse to testify, this being in effect a form of continued cooperation with their fellow prisoner.

There are three ways the preceding situation may play out:

• If both prisoners refuse to talk about their involvement in the main crime — that is, they cooperate with each other — they will both serve only one year (for the lesser crime). 

• If one prisoner refuses to talk, but his partner chooses to betray (implicate) the other regarding the main crime, the silent prisoner will be sentenced to three years while the testifying prisoner will be set free. 

• If, instead, both suspects implicate each other, both will fetch a sentence of two years.

The thought experiment is supposed to illustrate that neither prisoner has faith that his accomplice will stay tight-lipped, so both prisoners cannot resist testifying, with the tantalising hope of going free. These supposedly rational prisoners therefore pursue their self-interest, implicating each other. But the result is that both prisoners end up serving two years instead of one year if both had remained mum.

The lessons of the prisoner’s dilemma have been applied to many real-life, non-zero-sum situations. In such situations, cooperation results in better outcomes for all parties than if each party single-mindedly chases his or her own interests (rather than mutual interest) in order misguidedly to gain advantage over the other. So, for example, individually self-interested decisions can lead to injurious consequences for all. There are many everyday instances of the dilemma playing out, cutting across diverse behavioural arenas, such as economics, politics, biology, psychology, sports, academia, business, commerce, the workplace, and more. I'll briefly describe one particular instance.

In international strategic positioning, one theory assumes that all states ultimately compete rather than cooperate, their decisions reflecting rational self-interest to acquire advantage. For example, during the seventy-year Cold War, the phalanxes of NATO and the Warsaw Pact faced three options:

• Both sides endlessly scramble to deploy ever-more-advanced nuclear and conventional weapons to protect themselves and menace others, this being a policy with enormous, hard-to-sustain economic cost;

• One side greatly expands and enhances its forces while the other side doesn’t, the latter fearing betrayal and placing itself in peril while, on the upside, conserving its economic resources;

• Or both sides agree to disarm, thus reducing the probability of war while both avoid the massive expense of highly robust militaries.

It seems that the last of these choices, cooperation, would have led to the most desirable shared outcome; however, the delusion of ‘rational self-interest’ — doggedly pursuing individual reward — led both alliances to arm to the teeth, escalating the chance of conflict while hugely taxing both economies. Eventual arms-control agreements, though shaky and often tested, attempted to showcase cooperation, albeit fed by acute wariness: to keep a first-strike advantage out of the opposition’s hands.

The fragility of such agreements has been evident recently, in the fraught pursuit of arms control between the West and North Korea (with an already-existing nuclear arsenal) and the West and Iran (with an incipient capability, along with a presumably quick breakout to deployed nuclear weapons). In prisoner’s dilemma fashion, the resultant policies have reflected rational self-interest more so than cooperation, goaded by various motivators: 

• Distrust over intent and betrayal, such as ‘regime change’; 

• Anxiety over cheating and existential threats;

• Incendiary rhetoric threatening obliteration; 

• The honest-to-goodness objectives that skulk below the public pronouncements;

• Risk of later repudiation of agreements; 

• Bristling at the opposition’s negotiation tactics, where cultural differences intrude. 

Thus far, outcomes, such as they are, have mirrored these dynamics of distrust and antagonism, stemming from what is sometimes referred to as the Hobbesian trap, where parties default to tit-for-tat parrying over non-cooperative prisoner’s dilemma strategies.

Few circumstances, however, quite rise to the level of conforming to the idealism captured by John Rawls’s assertion that:

‘The hazards of the generalized prisoner’s dilemma are removed by the match between the right and the good.’

Yet, the prisoner’s dilemma thought experiment does bear upon many real-life situations that decision-makers around the world tackle daily. Scenarios that reflect how the push–pull between cooperation and conflict, as well as outcomes and payoffs, become complex — the more so with multiple parties in play, as in the example of strategic defence just described.

Another case involves the environment and global measures to mitigate serious threats emanating from climate change, as well as from the dilated timeline for halting or slowing the trajectory of that change. The key goal being to yield benefits shared across national borders. The self-serving interests so often associated with prisoner’s dilemma thinking — and the assumption that other countries will shoulder the burden of changing policies that harm the environment — might result in even developed nations keeping performance targets easy. 

The purpose would be to protect themselves from social and economic disruption, as well as not to be taken advantage of in, say, lowering pollutants. Meanwhile, yet other countries may silently breach the Paris climate accord and the agreements reached recently in Katowice, Poland — neither of which arguably provides adequate confidence in the ‘fair play’ of others, provides sufficient metrics and accountability, proves demonstrably enforceable, or meaningfully disincentivises cheating.

Despite, therefore, the apparent win–win payoff that can stem from cooperation, from focus on mutual interests, and from trust-building, the strategic application of the prisoner’s dilemma in seeking maximum payoffs may still lead to parties succumbing to the myopic illusion of advantaged self-interest, and the delusion of being able to avoid incurring costs as a consequence.

Picture Post #43: The Signpost

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'Because things don’t appear to be the known thing; they aren’t what they seemed to be neither will they become what they might appear to become.'

Posted by Thomas Scarborough

    

A signpost on a public road in South Africa’s remote Suurveld. What stood out for me immediately was the letter ‘O’. The signmaker, a long time ago, clearly made a better job of the ‘O’s than the other letters. Some day, I thought, one may make out little more than the ‘O’s.

Great men and women of the past left our civilisation with vital signposts: the rule of law, universal suffrage, equal rights, and more. Some of their signposts are no longer clearly seen, nor are the reasons why they put them there. How well are our signposts made today, for tomorrow?

 

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Picture Post #43: The Signpost

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'Because things don’t appear to be the known thing; they aren’t what they seemed to be neither will they become what they might appear to become.'

Posted by Thomas Scarborough

    

A  signpost on a public road in South Africa’s remote Suurveld. What stood out for me immediately was the letter ‘O’. The signmaker, a long time ago, clearly made a better job of the ‘O’s than the other letters. Some day, I thought, one may make out little more than the ‘O’s.

Great men and women of the past left our civilisation with vital signposts: the rule of law, universal suffrage, equal rights, and more. Some of their signposts are no longer clearly seen, nor are the reasons why they put them there. How well are our signposts made today, for tomorrow?

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Is Mathematics Invented or Discovered?

Posted by Keith Tidman

I’m a Platonist. Well, at least insofar as how mathematics is presumed ‘discovered’ and, in its being so, serves as the basis of reality. Mathematics, as the mother tongue of the sciences, is about how, on one important epistemological level, humankind seeks to understand the universe. To put this into context, the American physicist Eugene Wigner published a paper in 1960 whose title even referred to the ‘unreasonable effectiveness’ of mathematics, before trying to explain why it might be so. His English contemporary, Paul Dirac, dared to go a step farther, declaring, in a phrase with a theological and celestial ring, that ‘God used beautiful mathematics in creating the world’. All of which leads us to this consequential question: Is mathematics invented or discovered, and does mathematics underpin universal reality?

‘In every department of physical science, there is only so much science … as there is mathematics’ — Immanuel Kant

If mathematics is simply a tool of humanity that happens to align with and helps to describe the natural laws and organisation of the universe, then one might say that mathematics is invented. As such, math is an abstraction that reduces to mental constructs, expressed through globally agreed-upon symbols, serving (in the complex realm of human cognition and imagination) as an expression of our reasoning and logic, in order to better grasp the natural world. According to this ‘anti-realist’ school of thought, it is through our probing that we observe the universe and that we then build mathematical formulae in order to describe what we see. Isaac Newton, for example, developed calculus to explain such things as the acceleration of objects and planetary orbits. Mathematicians sometimes refine their formulae later, to increasingly conform to what scientists learn about the universe over time. Another way to put it is that anti-realist theory is saying that without humankind around, mathematics would not exist, either. Yet, the flaw in this scientific paradigm is that it leaves the foundation of reality unstated. It doesn’t meet Galileo’s incisive and ponderable observation that:

‘The book of nature is written in the language of mathematics.’

If, however, mathematics is regarded as the unshakably fundamental basis of the universe — whereby it acts, so to speak, as the native language of everything (embodying universal truths) — then humainity’s role becomes to discover the underlying numbers, equations, and axioms. According to this view, mathematics is intrinsic to nature and provides the building blocks — both proximate and ultimate — of the entire universe. An example consists of that part of the mathematics of Einstein’s theory of general relativity predicting the existence of ‘gravitational waves’, the presence of which would not be proven empirically until this century, through advanced technology and techniques. Per this kind of ‘Platonic’ school of thought, the numbers and relationships associated with mathematics would nonetheless still exist, describing phenomena and governing how they interrelate and in so doing bring a semblance of order to the universe — a universe that would exist even absent humankind. After all, this underlying mathematics existed before humans arrived upon the scene — merely awaiting our discovery — and this mathematics will persist long after us.

If this Platonic theory is the correct way to look at reality, as I believe it is, then it’s worth taking the issue to the next level, which is the unique role of mathematics in formulating truth and serving as the underlying reality of the universe — both quantitative and qualitative. As Aristotle summed it up,  the ‘principles of mathematics are the principles of all things’ — thus foreshadowing the possibility of what later became known in the mathematical and science world as a ‘theory of everything’, unifying all forces, including the still-defiant unification of quantum mechanics and relativity. 

As the Swedish-American cosmologist Max Tegmark provocatively put it, ‘There is only mathematics; that is all that exists’ — an unmistakably monist perspective. He colorfully goes on:

‘We all live in a gigantic mathematical object — one that’s more elaborate than a dodecahedron, and probably also more complex than objects with intimidating names such as Calabi-Yau manifolds, tensor bundles and Hilbert spaces, which appear in today’s most advanced physics theories. Everything in our world is purely mathematical— including you.’

The point is that mathematics doesn’t just provide ‘models’ of physical, qualitative, and relational reality; as Descartes suspected centuries ago, mathematics is reality.

Mathematics thus doesn’t care, if you will, what one might ‘believe’; it dispassionately performs its substratum role, regardless. The more we discover the universe’s mathematical basis, the more we build on an increasingly robust, accurate understanding of universal truths and, even, get ever nearer to an uncannily precise, clear window onto all reality — foundational to the universe. 

In this role, mathematics has enormous predictive capabilities that pave the way to its inexhaustibly revealing reality. An example is the mathematical hypothesis stating that a particular fundamental particle exists whose field is responsible for the existence of mass. The particle was theoretically predicted, in mathematical form, in the 1960s by British physicist Peter Higgs. Existence of the particle — named the Higgs boson — was confirmed by tests some fifty-plus years later. Likewise, Fermat’s famous last theorem, conjectured in 1637, was not proven mathematically until some 360 years later, in 1994 — yet the ‘truth value’ of the theorem nonetheless existed all along.

Underlying this discussion is the unsurprising observation by the early-20th-century philosopher Edmund Husserl, who noted, in understated fashion, that ‘Experience by itself is not science’ — while elsewhere referring to ‘the profusion of insights’ that could be obtained from mathematical research. That process is one of discovery. Discovery, that is, of things that are true, even if we had not hitherto known them to be so. The ‘profusion of insights’ obtained in that mathematical manner renders a method that is complete and consistent enough to direct us to a category of understanding whereby all reality is mathematical reality.

Is Mathematics Invented or Discovered?

Posted by Keith Tidman

I’m a Platonist. Well, at least insofar as how mathematics is presumed ‘discovered’ and, in its being so, serves as the basis of reality. Mathematics, as the mother tongue of the sciences, is about how, on one important epistemological level, humankind seeks to understand the universe. To put this into context, the American physicist Eugene Wigner published a paper in 1960 whose title even referred to the ‘unreasonable effectiveness’ of mathematics, before trying to explain why it might be so. His English contemporary, Paul Dirac, dared to go a step farther, declaring, in a phrase with a theological and celestial ring, that ‘God used beautiful mathematics in creating the world’. All of which leads us to this consequential question: Is mathematics invented or discovered, and does mathematics underpin universal reality?

‘In every department of physical science, there is only so much science … as there is mathematics’ — Immanuel Kant

If mathematics is simply a tool of humanity that happens to align with and helps to describe the natural laws and organisation of the universe, then one might say that mathematics is invented. As such, math is an abstraction that reduces to mental constructs, expressed through globally agreed-upon symbols. In this capacity, these constructs serve — in the complex realm of human cognition and imagination — as a convenient expression of our reasoning and logic, to better grasp the natural world. According to this ‘anti-realist’ school of thought, it is through our probing that we observe the universe and that we then build mathematical formulae in order to describe what we see. Isaac Newton, for example, developed calculus to explain such things as the acceleration of objects and planetary orbits. Mathematicians sometimes refine their formulae later, to increasingly conform to what scientists learn about the universe over time. Another way to put it is that anti-realist theory is saying that without humankind around, mathematics would not exist, either. Yet, the flaw in this paradigm is that it leaves the foundation of reality unstated. It doesn’t meet Galileo’s incisive and ponderable observation that:

‘The book of nature is written in the language of mathematics.’

If, however, mathematics is regarded as the unshakably fundamental basis of the universe — whereby it acts as the native language of everything (embodying universal truths) — then humanity’s role becomes to discover the underlying numbers, equations, and axioms. According to this view, mathematics is intrinsic to nature and provides the building blocks — both proximate and ultimate — of the entire universe. An example consists of that part of the mathematics of Einstein’s theory of general relativity predicting the existence of ‘gravitational waves’; the presence of these waves would not be proven empirically until this century, through advanced technology and techniques. Per this ‘Platonic’ school of thought, the numbers and relationships associated with mathematics would nonetheless still exist, describing phenomena and governing how they interrelate, bringing a semblance of order to the universe — a math-based universe that would exist even absent humankind. After all, this underlying mathematics existed before humans arrived upon the scene — awaiting our discovery — and this mathematics will persist long after us.

If this Platonic theory is the correct way to look at reality, as I believe it is, then it’s worth taking the issue to the next level: the unique role of mathematics in formulating truth and serving as the underlying reality of the universe — both quantitative and qualitative. As Aristotle summed it up, the ‘principles of mathematics are the principles of all things’. Aristotle’s broad stroke foreshadowed the possibility of what millennia later became known in the mathematical and science world as a ‘theory of everything’, unifying all forces, including the still-defiant unification of quantum mechanics and relativity. 

As the Swedish-American cosmologist Max Tegmark provocatively put it, ‘There is only mathematics; that is all that exists’ — an unmistakably monist perspective. He colorfully goes on:

‘We all live in a gigantic mathematical object — one that’s more elaborate than a dodecahedron, and probably also more complex than objects with intimidating names such as Calabi-Yau manifolds, tensor bundles and Hilbert spaces, which appear in today’s most advanced physics theories. Everything in our world is purely mathematical— including you.’

The point is that mathematics doesn’t just provide ‘models’ of physical, qualitative, and relational reality; as Descartes suspected centuries ago, mathematics is reality.

Mathematics thus doesn’t care, if you will, what one might ‘believe’; it dispassionately performs its substratum role, regardless. The more we discover the universe’s mathematical basis, the more we build on an increasingly robust, accurate understanding of universal truths, and get ever nearer to an uncannily precise, clear window onto all reality — foundational to the universe. 

In this role, mathematics has enormous predictive capabilities that pave the way to its inexhaustibly revealing reality. An example is the mathematical hypothesis stating that a particular fundamental particle exists whose field is responsible for the existence of mass. The particle was theoretically predicted, in mathematical form, in the 1960s by British physicist Peter Higgs. Existence of the particle — named the Higgs boson — was confirmed by tests some fifty-plus years later. Likewise, Fermat’s famous last theorem, conjectured in 1637, was not proven mathematically until some 360 years later, in 1994 — yet the ‘truth value’ of the theorem nonetheless existed all along.

Underlying this discussion is the unsurprising observation by the early-20th-century philosopher Edmund Husserl, who noted, in understated fashion, that ‘Experience by itself is not science’ — while elsewhere his referring to ‘the profusion of insights’ that could be obtained from mathematical research. That process is one of discovery. Discovery, that is, of things that are true, even if we had not hitherto known them to be so. The ‘profusion of insights’ obtained in that mathematical manner renders a method that is complete and consistent enough to direct us to a category of understanding whereby all reality is mathematical reality.