Epigraph:

بَدِيعُ السَّمَاوَاتِ وَالْأَرْضِ ۖ وَإِذَا قَضَىٰ أَمْرًا فَإِنَّمَا يَقُولُ لَهُ كُن فَيَكُونُ

He is the Originator of the heavens and the earth, and when He decrees something, He says only, ‘Be,’ and it is. (Al Quran 2:117)

Have they been created from nothing, or are they their own creators? Have they created the heavens and the earth? In truth they put no faith in anything. (Al Quran 52:35-36)

Written and collected by Zia H Shah MD

Metaphysical Necessity vs. Contingency in Philosophy

In philosophical terms, something is metaphysically necessary if it could not have been otherwise – in other words, it’s true in all possible worlds plato.stanford.edu. A contingent thing, by contrast, exists or is true but could have been different. Classic examples of metaphysical necessities are often logical or mathematical truths (e.g. 2+2=4), which many philosophers consider true in every conceivable world 1000wordphilosophy.com. By contrast, facts like “the sky is blue” or “humans exist” are contingent – we can imagine scenarios (worlds) in which they were false.

Understanding this distinction is key to our question of what is “truly necessary.” Are the foundations of reality – mathematical truths, physical laws, time itself, or a divine Creator – necessary in this strong sense? Or are they contingent features that might have been otherwise? Below, we explore each candidate in turn, integrating insights from science, philosophy, and theology.

The Status of Mathematical Truths

Mathematical truths are typically seen as necessarily true once their axioms are accepted. For example, given the standard axioms of arithmetic, it is impossible for 2+2 not to equal 4 – not just in our universe, but in any logically possible universe 1000wordphilosophy.com. This has led many philosophers and mathematicians to regard math as a realm of necessary truths, independent of the physical world. Indeed, the necessity of math is often taken for granted in modal logic and philosophy of mathematics. Some argue these truths are analytic (true by definition) or grounded in the very essence of concepts like numbers, making them true in all possible contexts 1000wordphilosophy.com.

Yet an intriguing debate remains: are mathematical entities (numbers, sets, etc.) themselves real and necessary, or are they human inventions? Mathematical Platonists hold that numbers and mathematical structures have real existence (perhaps in a non-physical realm of forms) and would exist necessarily even if no physical universe did. Others, like nominalists, counter that mathematics is a creation of the human mind, useful for describing observations but not an independent necessary reality. Regardless of one’s stance, there is a profound mystery in how well mathematics describes the contingent physical world. Physicist Eugene Wigner famously marveled at “the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics,” calling it “a wonderful gift, which we neither understand nor deserve.” mathshistory.st-andrews.ac.uk This “unreasonable effectiveness” of math in nature suggests to some that mathematics might underpin reality in a deep way.

One speculative idea inspired by this effectiveness is the Mathematical Universe Hypothesis (championed by physicist Max Tegmark), which posits that the physical universe is fundamentally a mathematical structure. In such a view, the existence of our world would be a necessary consequence of mathematics itself – essentially, all possible mathematical structures exist, and we happen to inhabit one of them. This is an extreme view, but it highlights the sense in which mathematics feels timeless and necessary. Even without adopting Tegmark’s hypothesis, many agree that if anything is a contender for “ultimate necessity,” the abstract truths of mathematics seem to fit the bill. After all, as one philosophy source puts it, mathematical and analytic truths “must be true, but not because of logic or the physical world” 1000wordphilosophy.com – their truth transcends any particular reality.

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