Idea of justice as an axiom

Positing justice as a fundamental principle - in life and beyond
Idea of justice as an axiom
"Mathematics puts us “in touch with immortality in the form of eternal mathematical laws” as the historian of mathematics D. E. Smith once noted. Additionally, many learned scientists have marvelled at how this interaction can even take place." [Representational Image] Special arrangement

At the outset, I must confess I’m not eminently qualified to broach a theme about which I can’t boast of more than a smattering, a nodding acquaintance as distinct from a deep understanding involving the many facets of what has always been an extremely complex issue.

In the lines that follow, an attempt has been made to put forth my thoughts surrounding the idea of justice being posited as pivotal in order to make sense of life as we confront it on a daily basis.

As a disclaimer, it’s not intended to invoke scriptures to drive home the importance of the idea of God (Deity, Supreme Divinity) or of the Day of Judgement (Resurrection, Reincarnation as per Christian/Jewish and Hindu traditions, respectively) which constitute fundamental articles of faith across religions and schools of religious thought around the world.

Nor is it intended, for the purposes of this essay, to make a case for a ‘Muslim or a Christian God’ being advocated as ‘superior’ to those being followed as such by people owing allegiance to other religions.

The idea is to make a humble attempt, without being pretentious, to lend a certain amount of credibility to these notions as fundamental pillars of religious thought on the basis of the idea of justice while making a case for accepting and according it the status of a universal epistemic virtue across castes, creeds, communities and religious persuasions.

We begin with the following passage from Francis Su’s recent fascinating piece “Can Mathematics be Spiritual?”

“In both mathematics and in most religions, one comes face-to-face with the reality of immortal objects that we cannot see. Religious people are often mocked for belief and interaction with a non-physical supernatural God. And yet, such mockers have all learned to count, to interact and reason with non-physical Platonist conceptions of whole numbers, and even to apply them to what we call (by contrast) “the real world.”

Mathematics puts us “in touch with immortality in the form of eternal mathematical laws” as the historian of mathematics D. E. Smith once noted. Additionally, many learned scientists have marvelled at how this interaction can even take place.

Einstein himself asked, “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?” In other words, it should surprise us that Platonic mathematical objects interact with the real world so constructively — but we take this marvel for granted.”

The above paragraph helps to put into perspective an oft-encountered experience of confronting those who are seen to scoff at the very thought of a non-physical ‘non-existent’ being deified as an all knowing, all powerful supernatural entity called God, even as these same sceptics are found to be perfectly at peace with such non-physical, ethereal entities as numbers, abstract structures like the Monster (group), the random matrices or exotic spheres in mathematics or quarks, quanta and strings in physics.

Unlike in the case of mathematics where, for instance, mathematicians are comfortable with the idea – and the proof - that something called the Axiom of Choice and its negation are both consistent with the standard axioms of set theory, at least many of them - and many more non-mathematician scientists - are dismissive of the idea of an omnipotent God being up there and conducting the proceedings in running the universe ‘from behind the scene’ as it were.

In the lines that follow, an attempt has been made to propose the idea of justice as an axiom – as one does in mathematics – in order to show why the idea of God or the day of resurrection has to be factored in our discussion to make whatever little sense we can of life and the world around ourselves.

Justice as a vital component of the belief system

The fine balance and the sense of proportion that pervades the natural phenomena playing themselves out in life and elsewhere show themselves up essentially as different manifestations of the idea of justice without which such a delicate balance of competing forces in nature cannot be imagined.

It should help to understand how the idea of the role of justice in life and human relations harks back to the role of prime numbers in mathematics and how they enjoy a pivotal position among the integers, or how a thorough understanding of matter essentially reduces to a deep insight into the elementary particles which constitute the basic building blocks of matter.

Come to think about it, it’s justice which raises the human life from the level of farce and gives it some form of grace and dignity without which the society is fated to perish as a civilised, egalitarian entity where people are at peace with themselves and with nature.

That makes a strong case for the institutionalisation of justice and fair play that ought to be accorded their rightful place and priority in the society.

On the other side involving real life situations, it’s the acceptance of the postulate of justice that rules out the possibility of life and the universe at large having come about merely as a result of an accident, without a design behind it, as the agnosts or naysayers would have us believe.

Whereas it ought to be conceded that the laws of science do not necessarily rule out the possibility of such a cosmic accident having come about prior to the creation of the universe and life on earth, it makes sense to argue that a system where justice stands denied or dispensed selectively would result in the idea of a life where individual might would reign supreme, and the strong and the powerful would ride roughshod over the weak and the dispossessed and get away with it without having to pay for such transgressions.

In real, practical terms, it’s only in the presence of a robust system where the idea of justice has been accorded its well-deserved primacy would it be reasonable to hope for the weak and the dispossessed to claim their rightful place in the system while ensuring that those are held to account who had feted themselves on the toil and blood of the weak and the underprivileged during their life on earth.

In fact, it’s the idea of creation of life and the underlying design of the cosmos, marked as these processes are by a breath-taking sense of proportion and a grand design, that necessitate the postulate of justice being weighed in without which the presence of such proportion and design would have been incomprehensible.

Rational thinking fosters justice, honesty and humility

Search for truth – that necessitates rational thinking – predisposes the heart to the virtues of justice, honesty and humility.

Once it’s argued, as we have done above, that mathematics seeks to restore order and design from the vortex of utter chaos and commotion in the world of ideas within and in the world around ourselves without, it becomes clear that the endeavor of mathematics bears uncanny similarity with the idea of justice which is sought to achieve precisely that order in the society.

Justice, equality and equity are to order, design and a sense of proportion in exactly the same way as injustice, inequality and inequity are to chaos, clutter and disorder.

A further instance of commonality of our experiences in mathematics and religion may be sought in the realisation how such epistemic values as the dignity of human beings, the corrupting nature of sin, the importance of justice, and the power of forgiveness are all truths that can be felt profoundly in a religious experience as much as the beauty of symmetry or a deep connection between disparate ideas in mathematics are felt and experienced in the world of mathematics that often elicit profound awe and astonishment.

Conclusion

Application of logic in mathematics is premised on the acceptance of a set of certain ‘self-evident’ truths called axioms. In the same vein, an attempt to apply logical reasoning in social situations can’t be undertaken in vacuum, unless that effort is bolstered by a set of principles that derive from a certain belief system of the individual. By definition, being illogical means doing things that, by definition, go against logic, or cause logical contradictions.

Here, it’s important to note that what counts as a logical contradiction is in fact an assertion that is seen to contravene the established principles within a given system of beliefs or axioms. This is a crucial point because otherwise, one person’s logic might look like idiocy to another person.

The point is that the idea of absolute truth is no more than a chimera unless it’s sought to be located within a given logical framework where a certain conclusion as truth has been arrived at on the strength of the axioms and foundational principles defining that system.

Here mathematics comes across as an important enabling tool to achieve that and that necessitate creating conditions where the society is exposed to a certain basic level of mathematical familiarity/ maturity and the mind trained to think rationally and thus with honesty and justice. That would make a case for promoting the culture of mathematics in the society and thus restore to reason and critical thought the rightful place that they deserve so as to foster values of justice and peace in the society.

Prof. M A Sofi, NBHM Visiting Professor, JKIMS, Srinagar.

Disclaimer: The views and opinions expressed in this article are the personal opinions of the author.

The facts, analysis, assumptions and perspective appearing in the article do not reflect the views of GK.

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