Muhammadul-Fareed Ajimoti & Al-Fawaz Ajimoti, Graduate, Philosophy, Nigeria & Student, Jamia Ahmadiyya International Ghana
If you’ve ever heard of Russell’s Paradox, then you already understand why this article demands your full attention. If you haven’t, let us ask you a simple yet mind-bending question: “If a set is defined as the set of all sets that do not contain themselves, is that set part of itself?”
Confused? You’re not alone. Here’s a little context to help you out. The truth is, the sentence above – short as it is – is one of the most profound paradoxes in the world of philosophy, if not the intellectual world at large. But what makes it especially significant is that it exposes the limitations of human logic – an important realisation for anyone seeking ultimate truth.
The origin of Russell’s Paradox
As the name suggests, the paradox is attributed to Bertrand Russell, a British Philosopher and Mathematician. The paradox arises from an attempt to construct a logically sound definition of sets – one that is free from contradictions and paradoxes.
A set is simply a collection of distinct elements. For example, the set of all even numbers or the set of all books in a library. In the early 20th century, Gottlob Frege, a German logician, was working on formalising mathematics. Part of his goal was to define sets in a way that avoided paradoxes and contradictions.
However, just as he neared the completion of the second volume of his work, Grundgesetze der Arithmetik (The Basic Laws of Arithmetic), Russell sent him a letter asking a simple, yet groundbreaking question. He asked: “Consider the set of all sets that do not contain themselves. Does this set contain itself?”
Recognising the severity of the problem, Frege famously acknowledged that it completely shattered the very foundations upon which he had based his entire work. He was thus forced to quickly prepare an appendix to his book, admitting to the error. Frege was, in his own words, “thunderstruck,” and he never fully recovered from the blow.
In other words, Russell’s single logical paradox had dismantled years of Frege’s philosophical research. And, although several reformative theories have been since proposed to address the issue, the paradox remains a glaring proof that reason, when left on its own, is inherently vulnerable to contradiction.
The Barber Paradox
Because Russell’s Paradox is highly abstract, many find it difficult to understand – or even realise that something is logically wrong. To make it easier to grasp, philosophers often explain it using a simpler version – the Barber Paradox.
Imagine a barber in a town where he follows one simple rule: He shaves all and only those who do not shave themselves. Now, ask yourself – should the barber shave himself?
Although at first glance, this seems like a simple yes/no question. The problem is, it is not. If the barber shaves himself, that means he belongs to the group of people who shave themselves – so he shouldn’t shave himself. And if he does not shave himself, that means he belongs to the group of people who do not shave themselves – so he should shave himself.
In both cases, an unresolvable contradiction is created – a logical dead end. This is exactly what happened to Russell’s set theory.
What this means for philosophy
While paradoxes like these may seem like mere intellectual curiosities, they expose a critical flaw in philosophy: it cannot lead to absolute certainty. No doubt, philosophy is a powerful tool for reasoning, questioning, and refining thought. In fact, it often deals with questions that cannot be directly observed or experimentally tested, and its nature also allows for a depth and breadth of inquiry that is unparalleled in other disciplines.
However, there is a fundamental problem. Philosophy, by its very nature, is limited. As the Promised Messiahas often said, reason can only take us to the realm of what should be, but it cannot establish with certainty what is. It constantly evolves, contradicts itself, and corrects its past mistakes, leaving its followers with uncertain and half-baked knowledge. (See, for example, Tafsir Hazrat Masih-e-Maud [2015], Vol. 4, pp. 159ff. and Malfuzat [English], Vol. 10, pp. 455-456)
Imagine if Russell had never pointed out this paradox, and Frege’s work had been published without question. For decades, millions would have accepted a faulty system as the ultimate truth. This highlights a key problem: if human reason alone is relied upon, it will always be vulnerable to errors and paradoxes.
The problem with mere logic
No doubt, relying solely on logic inevitably leads to problems – the greatest of which is, whose logic should we follow?
Logic is used to argue both for and against the existence of God. Some claim it proves God exists, while others “logically” argue that there’s neither a need nor evidence for God’s existence.
Similarly, logic has been used to argue that God is one. Using the same logic, some others claim that He is more than one. Even absurd claims – like the Earth being flat, the moon landing being fake are all based on some people’s logic. Now, if logic can differ this much on almost all important issues, to what extent can we rely on it to guide us to the ultimate truth – one that is meant to be eternal, objective, and unchanging?
The need for a Higher Source of Truth
If we have agreed that reason alone cannot satisfactorily lead to a point of certainty, where does that leave us then? The Promised Messiahas beautifully explains:
“I have repeatedly stated that it is absolutely impossible that reason should be able to attain the stage of perfect certainty by just piling up hypothetical needs and mere conjecture […] In short, reason cannot consistently conclude anything with certainty on its own unless it is paired with a companion. Without such a companion, it cannot remain safe and immune from mistake and error. (Barahin-e-Ahmadiyya [English], Part 4, p. 76)
He further clarifies:
“Hence, the Ever-Merciful and Noble God, who desires to lead man to the level of absolute certainty, has fulfilled this need by providing human reason with many allies. He has opened the path to certainty so that man may not be deprived of his most cherished goal of bliss and salvation, which is only possible through perfect conviction, and so that he may quickly cross the perilous bridge of ‘should be’—which his reason has built on the dangerous river of doubt and conjecture—and reach the impregnable castle of ‘is’ where he finds peace and security.” (Barahin-e-Ahmadiyya [English], Part 2, p. 93, footnote 4)
The companions of reason, as postulated by the Promised Messiahas
- If the testimony of reason relates to perceptible objects that can be seen, heard, smelled or touched, the ally that helps it to reach the stage of certainty is called observation or experience.
- If the testimony of reason relates to events that happen or have happened in various ages and places, it finds another ally in the form of historical books, writings, letters and other records. (Ibid.)
- If the testimony of reason relates to scientific truths or the hidden qualities of things, it requires the ally of experiment to attain certainty. Reason must therefore rely on experiments to verify claims about the natural world. (Barahin-e-Ahmadiyya [English], Part 4, p. 76)
He then explains that although these three companions are sure panaceas for all logical deficiencies, they are limited to matters of this world, the intricacies of which do not even reach a thousandth of those of the hereafter. Unlocking the secrets of the metaphysical world, therefore, demands a fourth companion – revelation.
Logic and revelation
Let’s be clear: everything stated above is not meant to undermine or discourage the usage of logic and reasoning altogether. In fact, unlike most religions, Islam strongly emphasises the usage of logic and reasoning, and sternly warns its followers against blind following. The Holy Quran and other Islamic sources repeatedly advocate tadabbur (deep meditation) and tafakkur (intellectual contemplation).
Over the centuries, countless Islamic scholars have employed philosophy to understand and explain Quranic teachings. However, there is a borderline – a limit that philosophy simply cannot cross, no matter how advanced it becomes. While philosophy can address certain intellectual enquiries, it provides absolutely no solution to existential problems.
Ask a philosopher: What is the reality of the soul? How and when does it enter or leave the body? What happens after death? What is the true purpose of our existence? Despite centuries of debate, philosophy has not, nor will it be able to, provide flawless, satisfactory answers to these questions.
However, divine revelation has already provided clear, unwavering answers to them.
Philosophy versus theology
At this juncture, philosophers often counter the theological argument by pointing out that, despite having revelation as the same knowledge source, religious scholars are divided into different sects and schools of thought based on differing interpretations.
The simple answer to this is that though certainty and ultimate truth – which is delivered through revelation – may be profound and complex, it is by its very nature, eternal, unchanging, and objective – otherwise, it wouldn’t be “ultimate” at all.
Therefore, any variation in interpretation is a reflection of human limitations, and not a flaw in the divine source itself. Revelation is thus like a life-giving rain that revives the dead land of logic. While reason can help us understand and apply divine truth, it cannot replace it. And if we rely solely on philosophy, we are left to navigate an endless cycle of contradictions and uncertainties.
Conclusion
Russell’s Paradox is not just an abstract mathematical or philosophical dilemma. It is a clear demonstration of why human reason alone is never sufficient. Philosophy, no doubt, when used correctly, can refine our understanding, but it should never be the foundation of our quest for truth.
Ultimately, the truth is not something we construct through reason alone, but rather something that is revealed to us. And our job as seekers after truth is to seek the balance between reason and revelation – using the former to understand and apply the latter, but never making it the final judge of truth itself.
We conclude with a beautiful Persian poem of the Promised Messiahas:
بنگر آخر بعقل و فکر و قیاس کہ خرد را نہ محکم است اساس
تا نباشد رفیق او دگرے نایدش از رہ یقین خبرے
“See through reason, reflection, and logic, [and you will discover that] the foundation of reason is not solid. Until it is joined by a companion, it will not know the way towards certainty.” (Barahin-e-Ahmadiyya [English], Part 4, p. 134, footnote 11)