How Could Mathematics Appear Without a Creator?

Mathematics, like electricity, is something we discover rather than invent. This concept is central to understanding how mathematical truths can emerge without the need for a creator. Let's delve into various philosophical and mathematical perspectives that support this idea.

Mathematics as a Discovery, Not an Invention

Mathematics is not a creation but a discovery. The principles of mathematics are inherent and have been uncovered by humans, much like how we discover electrical phenomena. We understand and define mathematical structures, but these structures already exist, waiting to be discovered.

Just as the laws of electricity were waiting for us to discover, mathematical principles were waiting for humans to uncover. These principles are often likened to ripe fruit hanging on a tree, ready to be picked. They are not brought into existence but are parsed and defined by human minds.

Theoretical Perspectives on Mathematics

Platonic Realism

Platonic realism is a philosophical stance that believes mathematical abstractions are real and exist in a Platonic realm. For Platonists, mathematical entities are eternal and unchanging, existing independently of human thought and creation. This means that these entities do not need a creator; they simply are.

Plato himself believed that the creator of our universe, who is eternal and unchanging, modeled the mutable physical world after the perfect, eternal world of mathematical forms. This idea was widely accepted in both Christian and Muslim thought for millennia, with figures like Plotinus and Thomas Aquinas offering similar perspectives.

Formalism

Another perspective on mathematics is formalism. Formalists argue that mathematics arises from the rules and axioms we choose for our symbolic systems. With these rules, we can manipulate symbols mindlessly, producing truths that are inherently true by virtue of the rules we have chosen. Physics, in this view, is a search for the axioms that best describe our universe, with all else following as a matter of course.

For those with infinite intelligence, mathematics would be immediately obvious, encompassing all possible systems and their truths. However, for humans with finite intelligence, finding interesting axiom systems and deducing their consequences is a process of discovery rather than creation.

Godel's Incompleteness Theorems

The works of Kurt Godel further challenge the idea that mathematics is trivial and tautological. Godel's incompleteness theorems demonstrate that mathematical truth is not limited to what can be derived from a set of axioms. This introduces a layer of creativity and unpredictability, suggesting that mathematics is not just a set of mechanical truths but can lead to unexpected results.

Despite these challenges, some still see Godel's theorems as reinforcing the idea that mathematics is creative and dynamic, rather than static and unchanging. This aligns with the idea that God might create the universe by choosing specific axioms and letting them unfolded, much like a writer might create a story by choosing certain characters and letting the narrative develop.

Mathematics as a Human Construction

Mathematics as Fiction

A different perspective suggests that mathematical objects are human inventions, akin to stories or fictional narratives. In this view, mathematics is a creation of the human mind, built and evolved over time by a vast community of mathematicians. This community, like the Doctor Who franchise, shares a collective vision and evolution of mathematical ideas.

Just as the Doctor Who series has a creator, the mathematical community has a creator in the sense that the mathematical structures we discover and develop are the result of collective human effort and intelligence.

Philosophical and Theological Implications

If you posit that God created mathematics, the question of whether mathematics could exist without God becomes trivial, as it would be true by definition. However, this answer is not particularly meaningful in the broader context of mathematical philosophy and discovery.

Ultimately, the way we understand mathematics is through philosophical inquiry and scientific exploration. We work out compelling philosophies, argue for them, and then see what follows. The notion that mathematics needs a creator may arise from a need to explain the existence of mathematical truths, but it is just one of many possible philosophical viewpoints on the nature of mathematics.

In conclusion, the idea that mathematics could appear without a creator aligns closely with the views of discovery and exploration in mathematics. Whether through Platonism, formalism, or as a human construction, mathematics emerges as a natural and inevitable product of human inquiry and intellect.