Rehabilitating Joad

Posted by Thomas Scarborough

“Poor Joad,” said the journalist John Guest, summing up the life of the late British philosopher on the BBC. The hapless C.E.M. Joad, who gained immense popularity on radio and TV, fell finally into disrepute and obscurity.

The Times of London, in its obituary, seemed to seal his final fate: “He had no interesting contribution to make as a philosopher.” Today, the dictionaries of philosophy would seem to confirm it. It is a rare dictionary in which we find his name.

Personally, I think that Joad was badly overlooked – perhaps because his very popularity detracted from his reputation as a serious thinker. Popularity was indeed, in a sense, what he wanted – not merely for popularity’s sake, but because his interest was to reach the “common man”.

Cyril Edwin Mitchinson Joad had two great and timely insights, writing at a time where philosophy was parting ways with ethics through the creeping effects of Hume's fact-value distinction, and above all, through logical positivism. The recession of religion provided fertile ground for the same.

Firstly, he recognised that the problem of the time was the loss of ethics. Above all, he saw that philosophy had lost ethics, and would be impotent until it reclaimed it. In The Plight of Civilisation *, written in 1941, Joad set out the problem like this:

“To an age governed by the stomach-and-pocket view of life and accustomed to demand of every activity proffered for its approval that it shall deliver the goods, understanding seems no doubt an inadequate object of pursuit. Yet something is, it is obvious, grievously wrong with our civilisation, and it is high time we set about the business of trying to understand what it is. Science has won for us powers fit for the gods, yet we bring to their use the mentality of schoolboys or savages.”

In his verdict, society was “grievously wrong”.  In spite of “powers fit for the gods”, men and women had lost their moral compass. Many people agreed with him then, and many surely still would today. Because, in every major area where it matters, it seems that we are in serious crisis: personal, political, social, and environmental.

With this in mind, Joad developed a unique approach to ethics – but it seems to have all but disappeared today. I needed to search far on the Internet to find what I had once read in books. Eventually, I found some of his texts in the Delhi University Library, but they were fragmented through erratic optical character recognition.

A widespread view of moral epistemology is that morality cannot be rationally grounded. Not only is it impossible to proceed from an “is” to an “ought” as Hume originally said. If we ask after the reasons why we do things – and the reasons which lie behind those reasons – ultimately we find that there is nothing there at all.

Not so, said Joad. Rather than finding nothing, we find everything. Joad innovatively turned the argument on its head. I read this first in his Guide To The Philosophy Of Morals And Politics of 1938 – however it runs through various of his works. Supposing, he said, that I take quinine for a fever:

“Quinine helps, in other words, to reduce fever; but why reduce fever? Because fever is a disease. But why not be diseased? Because health is better than disease. Why is health better than disease? At this point we may refuse to answer; we just see, we may say, that health is better than disease, and that is all there is to say about it. But in saying ‘we just see’ health to be better than disease, we are absolving ourselves from the necessity of saying why we see it to be so.”

It is at this point, he writes, that “we cease to give reasons and fall back upon the assertion ‘we just see’.” That is, when we ask after our motives, we may keep on pushing back the question, yet inevitably we reach a point where we throw up our hands and laugh. But now, he says, we are passing a judgment of “absolute, ultimate, and unique value.”

Yet we do not discover a void. Rather we discover the true axioms of ethics. On condition, that is, that we sift ultimate from penultimate axioms – over which Joad himself took great care.

This view seems to me to be unique. It seems to me to meld reason and value, scepticism and realism. It differs from ethical intuitionism, empiricism, rationalism, pragmatism, and various other views – and for its perspicacity would seem to make Joad deserving of a place on the philosophical map. I believe that he identified and addressed the most profound philosophical issues of his and our day, and did so originally and creditably.

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* Correction: this quote is taken from Philosophy For Our Times. The author mistakenly cited the section heading, and not the title of the book.

For further reading:
Return to Philosophy (1935)
Guide to the Philosophy of Morals and Politics (1938)

Disabling Self-Service

Posted by Sifiso Mkhonto

The idea that gaining power, maintaining power, maximizing power, and wielding power are central to restructuring the functions of a democratic society is a dangerous one to swallow. It does not cure the disease of oppressive and unjust government, but endorses it. With this in mind, I survey both the ideal and the reality of political power.

The ideal of political power is deliberately misconstrued. It is not the ability to control people, but the ability to instill in them the practice of altruism. By altruism I refer to the person who is motivated by the power of putting the needs of others ahead of their own happiness—I shall call this their moral purpose. Ironically, as they do, people seek to differentiate themselves from others—thus the same moral purpose is uncommon to all, and selfishness becomes common.

The reality of political power, in most nations, is that politicians are self-serving—not because of pressure from a corrupt populace within, or corrupt governments without, but by their own, false moral purpose. Tragically, the world over, as political power promotes the practice of selfishness—and thereby favours the selfish—it becomes a vehicle to deliver the product of despondency, as many in society are cast aside by the selfishness of others. While there are some who have a more altruistic view of power, they tend to be the exception rather than the rule.

The reality of political power attracts corruption as a flame attracts moths. This bears evidence to the famous words of Niccolò Machiavelli, ‘Politics have no relation to morals’. Yet not only does political power instill in people the practice of selfishness. Political power is itself selfish, to a point that the moral purpose of many politicians has resulted in patronage and corruption as the norm. A preeminent example is the South African ‘State’ which is deemed to have been captured for the benefit of a wealthy family for the personal enrichment of all involved.

In such an unbalanced society, is it possible then to overcome a self-serving tendency—as people, and as politicians? Yes, it is, through a different moral purpose, and through excellence. The moral purpose I speak of is, in philosophical terms, moral realism and moral motivation—a moral purpose which is grounded in the nature of things. The excellence I speak of is service to the people with no exceptions to venality and patronage. In other words, we have a wellspring of virtue within us, but we may permit it to be poisoned by external influence.

People easily fall to the weakness of taking care of themselves before the other, yet through altruism, which is the ideal of political power, that tendency can change. One can disable the intent to self-serve—which is the tendency to take care of oneself first—and one can change those false values instilled in society by politicians, which only serve the interest of those who identify with that political ideology. Certainly, it would be a miracle for the whole world to reach this point, yet many people believe that the miracle is possible—if not through philosophy, then through their religious conviction, which deeply believes not in human nature, but in the unseen.

If morality and excellence had triumphed in the ‘State’ of my birth country, South Africa, the State would not have been ‘captured’. We would have had leaders with integrity—leaders who could reflect on the nature of human community and government, and the relations between the collective and the individual, and could cast off the habits of exploitation and colonialism. It is hard to be in power and to act with a different moral purpose to that of selfishness, but it is possible.

What is needed is that politicians act only from benevolence and a sense of obligation. The reason to overcome the tendency to self-serve is simple. Doing what is right for the right reasons brings positive progress in society. The definition of political power, I said, is deliberately misconstrued. It is not the ability to control people. It is the ability to instill in them the practice of altruism. I now conclude that the reality of political power which is self-serving, when it is transformed and renewed, becomes the ability to instill right values in society, through the right values it holds itself.

Picture Post #34: Watching the Tide

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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 Tessa den Uyl and Martin Cohen

Photo credit: students of  A Mundzuku Ka Hina, communications workshop. Mozambique

From the plastic on the lower right corner, moving to the left, arise a man and woman, both with one hand touching their face and each with one arm posing on their leg, the diagonal movement flows into the blankets behind them out of the picture. This ‘line’ creates a certain ‘zone’ in which we seem to stand in front of a threshold.

Our eyes may enter ‘the gate’ ‘guarded’ between the two seated persons and the boy standing on the right, to look into a ‘dark’ space where people gather in a circle and diagonally expand to the left into another lateral diagonal line. The composition is as if we are introduced carefully in a gathering, ‘a zone’ we cannot truly enter, we glance at something that is far from us, almost secret.

The picture invites us to regard it from a distant point of view where, at first sight, a kind of picnic, a déjeuner sur l’herbe, slowly changes into something that is far more remote. And yet, this is how some people survive, these rubbish dumps are their home and their daily reality -- along with intoxication and poverty and helplessness as the other side of the coin.

And yet, there is something inspiring about the picture in the posture of the two person’s in the foreground and the boy: the impression is that of creating a ‘gate’ in which the ambiguity of contraries, that in ancient times was certainly seen as an essential element in speaking truth, yields to a logic of the inevitable raising problems that come with more recent social, industrial and political conditions, one in which words have to search for an adaption between truth and oblivion.

Thus as with many such terrible events that happen in the world, we hear about them, we see images, but it is not our skin. The observer, the spectator has a very protected stance

Last week in il Bairro di Hulene, which is the neighborhood of shanty homes raised around the lixeira (dump), seventeen people died under a mass of refuse that detached itself and slid down from the dump pile. Six houses and seven shacks were destroyed including a small ‘press’ that was there to crush the plastic and cans.

About The Shootings

With acknowledgement to the Chuck Gallery.

By Thomas Scarborough

About the tragic shootings in the USA, a few things are clear. Firstly, they have been possible because the weapons were accessible. Secondly, they have happened, by and large, in educational institutions. Thirdly, the shooters have targeted institutions, not individuals.

I have had the privilege of studying theology in the USA. I have studied, too, in other parts of the world. Yet what I experienced in the USA seemed unlike anything else. There was a rising feeling within me of being violated. Thankfully I never had any thoughts of harming anyone—yet the thought crossed my mind: could there be any relation to the massacres?

Beyond that sense of violation, in many cases, students may struggle to know what they are experiencing. In my own case, the situation was unusually transparent. It was not difficult to connect my feelings with the ideology which aroused them.

In theology, there has been a growing tide in the USA, which has its origins in the philosophy of Europe in the mid 20th century—more exactly, in the philosophy of Ludwig Wittgenstein. The theologian R.L. Sturch describes it like this, in the New Dictionary of Theology: ‘In terms derived from Wittgenstein, religion may be seen as a ‘form of life’ or ‘language-game’. Debate within the ‘form of life’ is legitimate, but about the form itself there can be none; either it is adopted or it is not.’ Without so much as entering into theological niceties, we may note some strong language: a form of life ‘is adopted, or it is not’, while debate is ‘legitimate’ only within a given life form. 

Take an instance of such theology, which calls itself a Theology of Communal Practice. Theologians Nancey Murphy and Brad Kallenburg state, ‘What has to be accepted, the given, is—so one could say—forms of life ... The viability of a historical community depends on the ongoing felicity of its communications. Thus, for the society to be viable, most of this communication has to be ‘true’ most of the time.’ Again, without so much as doing any theological analysis, we may simply note the strong language: forms of life ‘have to be accepted’, they are ‘given’, and they ‘have to be true’.

While this hardly serves to prove a point, such ‘compulsive’ thinking is all-pervasive in theological seminaries in the USA—while it is its application that creates the stress.

How should one guarantee ‘felicity of communications’? How should one preserve ‘legitimate' debate? How should one press ‘acceptance’? It need not be through open confrontation—in fact it may more often than not be through the violence of silence. ‘Illegitimate’ debate is greeted with silent stares—or it is channeled, rerouted, deflected. It stacks reading lists, it sustains and manages felicitous communications, it promotes methodological exercises which skirt around the content. In short, it defeats the student. This is the violation.

Is this felt in other educational institutions in the USA? While I do not have direct experience of it, the answer is yes. The psychologist Peter Gray, in Psychology Today, surveyed the ‘seven sins’ of US education. One of the items on his list was ‘Inhibition of critical thinking.’ There is a ‘powerful force’, he wrote, ‘against honest debate’. Yet the force is not merely theoretical. There are students who feel it. Forensic psychologist Stephen Diamond puts the violence down to this: ‘We are prone to feeling hurt’—and in some cases, pathologically.

Seung Hui Cho was a killer who issued a manifesto. On page one, he wrote, ‘Ask yourself what you did to me.’ His entire manifesto, while on the one hand an inscrutable rant, on the other hand reveals a sense of being violated. ‘For every action, there is an equal and opposite reaction,’ he wrote. Is this the reaction to the ‘powerful force against honest debate’?

A brief post such as this cannot hope to answer this question—yet it is surely a question which needs to be asked, and answered. As much as one needs to control access to weapons, one may equally need to overhaul the educational system—and its philosophy.

Huston Smith, a popular writer on religion, considered, ‘Our humanness flourishes to the extent that we steep ourselves in [ultimate] questions—ponder them, circle them, obsess over them, and in the end allow the obsession to consume us.’ There is little humanness in excluding or marginalising issues—in speaking the language of the ‘given’, the ‘legitimate’, and so on—whether it be in seminaries or elsewhere. One needs the marketplace of ideas—together with the freedom, transparency, bravery, and skill that its negotiation requires.

Fermi's Paradox . . . But What If?

Posted by Keith Tidman

Seven decades ago, the physicist-of-atomic-bomb-fame, Enrico Fermi, pondered with his lunchtime companions at Los Alamos whether other intelligent life forms populate planets around the Milky Way, and if so, why we have no evidence of them? He purportedly asked, “Where are they?”, meaning, of course, the alien beings. Because if other complex, intelligent, technology-clever life forms have even a fraction of humankind’s proclivity toward curiosity and, let’s say, colonization, then why is there no evidence of them having acted on these instincts throughout our galaxy? From that conundrum, Fermi’s Paradox emerged.

The American astrophysicist, Frank Drake, later thought about which factors might be necessary to address Fermi’s question and, in particular, how many technological civilizations, emitting electromagnetic signals, might exist among the stars of just our galaxy alone. These became known as Drake’s Equation, and offer a way to calculate the number of civilizations in the Milky Way based on seven variables.* Although scientists can’t yet insert firm numbers for the variables, I think Drake’s effort remains a worthy first attempt at eventually quantifying an answer to Fermi’s question. Especially given that the physical laws of evolution could well differ among far-flung, unfamiliarly diverse chemical, biological, and physical conditions and constraints, yielding singularly different intelligent species.

Many ‘what if’ hypotheses exist by way of possible answers to Fermi’s deceptively simple question. For example, perhaps technology-based civilizations and species with sophisticated intelligence are too far separated by space and time, measured even in thousands of light-years to reveal any presence. Or perhaps, because of the finely grained conditions necessary for life with high intelligence to evolve (the ‘anthropic principle’), civilizations are so rare and scattered that it’s difficult to find each other. Certainly it seems that our own sending-receiving (and space-faring) technologies are too primitive to matter much yet in the sophisticated game of cosmic outreach. Or just perhaps other civilizations have potted us, but rregard humankind as too biologically and intellectually primitive a species to bother with whom to show their hand. Or perhaps they regard humankind as a prototypically warring species, never-endingly engaged in small-minded, lethal belligerence over territory, resources, and power. Perhaps all intelligent species tend toward self-isolating wariness that outweighs curiosity about ‘the other’. Perhaps Thucydides’ theis that established and rising powers are compelled to go to war applies even on the interplanetary scale.

All that said, should there eventually be confirmation of alien intelligent species that are endowed with far higher levels of consciousness and intelligence than humankind — qualities having evolved over histories hundreds of thousands or millions of years older than ours — then the consequence would be culturally tectonic shifting. As a species, perhaps lulled by so easily triumphing over so many of our Earthly competitors, we’re prone to indulging in flights of ‘exceptionalism’. We’re predisposed to looking at our reflection in life’s mirror and — more often looking down, not up — seeing only reasons to preen over our capacity for rationality, creativity, and imagination. To be unseated, with a thud, by an alien species’ cognitive prowess — and the benefits to its civilization — could prove unsettling for humankind’s indulgences in unchallenged exceptionalism.

At the very least, discovery of our sudden non-uniqueness might compel re-examination of basic principles. It might lead to fundamentally questioning religious texts, customs, tenets, rituals, codes of morality, ‘spirituality’, and dicta. If so, the result may be to rethink and rewrite the underlying explanations and descriptions, widening out the aperture of religious philosophy and theology to take into account the new realities of not being alone in the galaxy and in larger cosmos. At the heart of such teleological investigation and reinvention might be questions, which never go away, about humankind’s purpose: about why we are here.

The stunning space-time topography of this universe isn’t hubristically ours alone. I venture it’s a matter of when, not whether, the ‘code’ to Fermi’s Paradox will be cracked.

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*Drake’s equation, as in our image, is typically shown as follows:

N = R* fp ne fl fi fc L,

Here N is the number of civilizations in the Milky Way whose electromagnetic emissions are detectable; R* is the rate of formation of stars suitable for the development of intelligent life; fp is the fraction of those stars with planetary systems; ne is the number of planets, per solar system, with an environment suitable for life (the habitable, ‘Goldilocks’ zones around their suns); fl is the fraction of suitable planets on which life actually appears; fi is the fraction of life-bearing planets on which intelligent life emerges; fc is the fraction of civilizations that develop a technology that releases detectable signs of their existence into space; and L is the length of time such civilizations release detectable signals into space.

Fermi's Paradox . . . But What If?

Posted by Keith Tidman

Seven decades ago, the physicist-of-atomic-bomb-fame, Enrico Fermi, pondered with his lunchtime companions at Los Alamos whether other intelligent life forms populate planets around the Milky Way, and if so, why we have no evidence of them? He purportedly asked, “Where are they?”, meaning, of course, the alien beings. Because if other complex, intelligent, technology-clever life forms have even a fraction of humankind’s proclivity toward curiosity and, let’s say, colonization, then why is there no evidence of them having acted on these instincts throughout our galaxy? From that conundrum, Fermi’s Paradox emerged.

The American astrophysicist, Frank Drake, later thought about which factors might be necessary to address Fermi’s question and, in particular, how many technological civilizations, emitting electromagnetic signals, might exist among the stars of just our galaxy alone. These became known as Drake’s Equation, and offer a way to calculate the number of civilizations in the Milky Way based on seven variables.* Although scientists can’t yet insert firm numbers for the variables, I think Drake’s effort remains a worthy first attempt at eventually quantifying an answer to Fermi’s question. Especially given that the physical laws of evolution could well differ among far-flung, unfamiliarly diverse chemical, biological, and physical conditions and constraints, yielding singularly different intelligent species.

Many ‘what if’ hypotheses exist by way of possible answers to Fermi’s deceptively simple question. For example, perhaps technology-based civilizations and species with sophisticated intelligence are too far separated by space and time, measured even in thousands of light-years to reveal any presence. Or perhaps, because of the finely grained conditions necessary for life with high intelligence to evolve (the ‘anthropic principle’), civilizations are so rare and scattered that it’s difficult to find each other. Certainly it seems that our own sending-receiving (and space-faring) technologies are too primitive to matter much yet in the sophisticated game of cosmic outreach. Or just perhaps other civilizations have spotted us, but regard humankind as too biologically and intellectually primitive a species to bother with whom to show their hand. Or perhaps they regard humankind as a prototypically warring species, never-endingly engaged in small-minded, lethal belligerence over territory, resources, and power. Perhaps all intelligent species tend toward self-isolating wariness that outweighs curiosity about ‘the other’. Perhaps Thucydides’ thesis that established and rising powers are compelled to go to war applies even on the interplanetary scale.

All that said, should there eventually be confirmation of alien intelligent species that are endowed with far higher levels of consciousness and intelligence than humankind — qualities having evolved over histories hundreds of thousands or millions of years older than ours — then the consequence would be culturally tectonic shifting. As a species, perhaps lulled by so easily triumphing over so many of our Earthly competitors, we’re prone to indulging in flights of ‘exceptionalism’. We’re predisposed to looking at our reflection in life’s mirror and — more often looking down, not up — seeing only reasons to preen over our capacity for rationality, creativity, and imagination. To be unseated, with a thud, by an alien species’ cognitive prowess — and the benefits to its civilization — could prove unsettling for humankind’s indulgences in unchallenged exceptionalism.

At the very least, discovery of our sudden non-uniqueness might compel reexamination of basic principles. It might lead to fundamentally questioning religious texts, customs, tenets, rituals, codes of morality, ‘spirituality’, and dicta. If so, the result may be to rethink and rewrite the underlying explanations and descriptions, widening out the aperture of religious philosophy and theology to take into account the new realities of not being alone in the galaxy and in larger cosmos. At the heart of such teleological investigation and reinvention might be questions, which never go away, about humankind’s purpose: about why we are here.

The stunning space-time topography of this universe isn’t hubristically ours alone. I venture it’s a matter of when, not whether, the ‘code’ to Fermi’s Paradox will be cracked.

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*Drake’s equation, as in our image, is typically shown as follows:

N = R* fp ne fl fi fc L,

Here N is the number of civilizations in the Milky Way whose electromagnetic emissions are detectable; R* is the rate of formation of stars suitable for the development of intelligent life; fp is the fraction of those stars with planetary systems; ne is the number of planets, per solar system, with an environment suitable for life (the habitable, ‘Goldilocks’ zones around their suns); fl is the fraction of suitable planets on which life actually appears; fi is the fraction of life-bearing planets on which intelligent life emerges; fc is the fraction of civilizations that develop a technology that releases detectable signs of their existence into space; and L is the length of time such civilizations release detectable signals into space.

Impoverished

By Tioti Timon *

In January 2018, in Kiribati, nearly 100 people, of whom 22 school children, tragically went missing on the high seas between Nonouti and Tarawa when a ferry sank. A comparable tragedy in the United States would have seen ¼-million people lost at sea. After four days, a New Zealand Defence Force Orion aircraft found seven survivors.

The Australian Broadcasting Network (ABC) reported on the tragedy—setting it in context by describing Kiribati as “a remote, impoverished nation of thirty-three atolls that is home to about 108,000 people”. Pi approached Tioti Timon of Kiribati for comment on the word “impoverished”.  He replied with free verse:

Impoverished

Impoverished
the word as presented globally
is a discriminatory term
rooted in colonial language
that has treated our people
inhumanly

Australia is a rich country
but there are poor people
begging in the street.
They are rich
but they are poor
in their culture.

Kiribati is a poor country
but we don’t have people
begging in the street.
We are poor
but we are rich
in reciprocity and family support.

What is the meaning
of impoverished,
when we have
the vast ocean around us
and our lives are not dependent
on money.

What is the meaning
of impoverished,
when we have
a material culture
of delightful sophistication
of thousands of years.

All Kiribati people
have their lands
and live subsistently
on their islands
enjoying life,
feasting, dancing, and singing.

We are living in a paradise
that we cannot experience
in an individualistic Australia.

Impoverished
I don't understand this word
applied to our country
especially
in this sad situation
where the lives of our people are lost.

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* Tioti Timon has been at the forefront of raising awareness of the effects of globalisation on his people, and their precarious position in view of climate change.  He extends his sincere condolences to the families and friends of those who were lost. The ABC news report is here.

Picture Post #33: Bourgeois Reminiscence

'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 Tessa den Uyl and Martin Cohen

Mercato di Sant'Ambrogio . Florence . Italy

 Picture credit: Antonio Borrani, 2017

  

Fragments of appearance are offered in the form of leftovers, sold at a market stall by the ounce. Not by the weight per square metre, as used by some manufactures, or by the linear yard. In any case, most likely these surplus fabrics, extras left over after use, could not reach those required measurements.

So instead here we find the evidence of what is left. Fragments not big enough to decorate an entire sofa, but maybe for a cushion it will do. Limited quantities for limited decoration.

The leftover fabric is a measured out merchandise until complete exhaustion. An excess to be sold anew. But this is not the defence of the poor, but rather of a poverty that, solely by its unoffending presence (when permitted) constitutes a critique of possession -- respects the form of private property.

Making such sense of self through this projection into an external referent is a form of psychosis, or to use a Lacanian term, foreclosure. The relation of the subject to the Other is one of dialectic exclusion. Is aspiring to images that offer a make-believe form of prestige a way to enhance an illusion, or to add to alienation?

For sure, we do not find cushions cut from this cloth in the iconic depiction of The Potato Eaters by Van Gogh…

Poetry: On Name-dropping

Posted by Chengde Chen *

On Name-dropping

Don’t keep dropping those great names
Showing off is self-abasing
Being tall may look remarkable, but
Not by lengthening your shadow in the setting sun

If you happen to be associated with a great name
You only 'happen to be' associated with it
Beethoven’s siblings didn’t necessarily compose
Nor must Einstein’s descendants understand physics

To drink liquor you can’t rely on others’ capacity
To sign a cheque you have to use your own name
The more borrowed jewellery you wear
The more should you feel like a beggar!

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* Chengde Chen is the author of Five Themes of Today, Open Gate Press, London. chengde@sipgroup.com

The Deceptions of Mathematics

by Thomas Scarborough

Galileo Galilei, a man of formidable scientific ability, once wrote that ‘the universe cannot be read until we have learned the (mathematical) language.’  Mathematics, he suggested, would reveal the secrets of the entire cosmos.  It is a common view – yet it is deceptive.  In fact, it may reveal little more than hubris.

On the surface of it, mathematics – even more than science – would seem to be thoroughly objective.  Here there are no failed experiments, no false interpretations, no paradigm shifts.  In mathematics – so it is frequently assumed – there is perfect certainty.

1 + 1 = 2
the logarithm of 1 = 0
the square root of 1 = 1
and so on.

Yet we overlook something, which would seem as simple as one-two-three.  We apply mathematics, by and large, to things in the real world (pure mathematics being the exception to the rule) – and in order so to apply it, we identify units of quantity.  This identification of units of quantity begins with ‘quantification’ – we map our human sense observations into units of quantity, or simply, quantity. 

On first impressions, it might seem to us then that units of quantity come ready made.  Apples come in ones, oranges come in ones – so do people, animals, days, nights, doors, windows, and a great deal more.  And if they do not come in ones, then we may make them into ones: one kilogram, one litre, one block, and so on.  On this basis, we quantify things and perform various mathematical operations on them. 

However, it is not this simple – and even a child might know it.  Our ‘ones’ may really be anything at all – say, clouds with noses (‘I saw three of them today’), ants which fall off the wall (dozens), or dogs which wag their tails, and so on to infinity.  In each case we are dealing with the mathematical unit ‘one’.

The theoretical physicist Albert Einstein would surely have agreed.  He considered that a unit ‘singles out a complex from nature’.  This surely seems a contradiction in terms.  A complex consists of many different and connected parts – parts (plural) which get ‘singled’, out.  That is, one takes a bundle of things or properties, and one defines them as one.  Therefore, various things and various properties may all at once hide inside one and the same single mathematical unit. 

Now this opens up an obvious question.  Who then is to say that our mathematical units – those complexes which we have ‘singled’, out – are precisely the complexes we need for the purpose of our calculations?  Supposing that we really ought to have added something to a complex which we call ‘one’ – or that we really should have taken something out – before we began to make use of it? 

Besides, does one really find such a thing as a complex which is self-contained and closed?  Is not every singled out complex-cum-unit criss-crossed by associations and influences without number?

When we think on it, this is true even of the simplest things in this world.  For instance, we might temporarily assume that the complex ‘hamster’ does not include food or water – it merely refers to a rodent, of which there are so and so many millions in the world.  Yet this complex breaks down at a certain point, as some children can tragically relate, who forgot the food or water.

Consider a thought experiment – as if it had never been conducted before.  Supposing it is true that our complexes might leave things out – or squeeze things in that really ought to be left out.  What then would the logical consequences be?  Of course, high on the list would be that our mathematics may not fit reality, because our mathematical units are ‘not quite right’.  Not only that, but we should easily find examples of this in the world. 

And so it is.  The mathematics of circular orbits and epicycles had to be replaced with the mathematics of elliptical orbits – the mathematics of scalars, then vectors, had to be replaced by the mathematics of tensors.  The mathematics of classical thermodynamics had to be replaced by the mathematics of generalised thermodynamics – and so on.  In fact our complexes may contain an entire world-view which needs to be overhauled – for example, Newtonian physics.  Yet even with the new, we would do well to remember that we have now carved up our world into four mathematical models.

The nineteenth century American philosopher Charles Sanders Peirce saw that ‘every new concept first comes to the mind in a judgment.’  He was saying, apparently, that our ‘ones’ are simply creations of the mind.

On this basis, we may assume that even the simplest of mathematics is not as straightforward as it seems.  In fact mathematics, writes the pioneering statistician William Briggs, requires ‘slow, maturing thought’.  It is not just about numbers, but about wisdom and expansive thinking.

The deceptions are, therefore, that mathematics is objective – and that being objective, it makes an excellent fit with our world – perhaps a perfect fit with the cosmos, as Galileo suggested.   No.  On the contrary, we should see mathematics as a very flawed and very subjective tool – always too simplistic, always in some way violating the totality of the reality in which we live. Mathematics, at the least, should be handled with great humility.