Will Science Become Obsolete?
Will a point come where society moves past science? After all, there should come a point in dialogue (or monologue) where one questions the longevity of a pursuit. If that pursuit is a job, the questioning most likely comes from analyzing oneâs self (acknowledgment of potential, dissatisfaction with a current situation, etc.). With an idea, its lasting power comes from its perception among that particular society; ideas that donât have a following or are disagreed upon are often countered by other, more agreeable ideas.
If we define science as one of these pursuits, then we can break down the question of society moving past science into a more basic question: Will there come a point when the pursuit of science is pointless?
Many â myself included â would say ânoâ. But regardless, I think thereâs an interesting discussion to be had here.
An axiom is a statement which we know to be true without any further proof. In math, we know that, if a = b and b = c, then a = c; no proof needed. In science, empirical observations are axioms. For example, the fact that the universe has order and follows predictable rules which we could make conclusions about. Often, these axioms are building blocks that form the basis for questions that scientists and mathematicians then dig into to create mathematical systems or scientific systems, which are composed of theorems.
If these theorems can prove every unknown question, then a system exhibits completeness. In other words, the system has all the necessary theorems to tackle any question. That already sounds like a tall order.
Lastly, any supposedly complete system should have an answer that proves the truth of only one thing, not its opposite. For example, if a lawyer were to prove their client guilty of a specific crime, they should also not be able to prove them not guilty of that crime. If they could, then one of those proofs - guilty or not guilty - is false, yet proven, which would throw the entirety of a system into question, including the theorems and, by extension, the axioms that make up those theorems. Systems that donât contradict themselves are known as consistent.
GĂśdelâs Incompleteness Theorem
In the early 1900s, Kurt GĂśdel, a logician and mathematician, created two theorems to demonstrate the limits of any axiomatic system, or any system built on axioms.
But the consensus for GĂśdelâs theorems is that they only work for mathematics. Why is that, when science also contains axioms? To find out, we have to dig deeper.
The first theorem states that a system can only be complete or consistent, but never both. This is true. There are no systems that exist that can answer every single question and have provable answers without some of those proofs contradicting each other. For example, if my system was inconsistent, then I would be able to prove that, for example, humans are both warm-blooded and cold-blooded. If I can prove that âhumans are warm-bloodedâ and âhumans are cold-bloodedâ, then my system is complete, even if one or both of those statements are wrong. This is, obviously, catastrophic. We donât want that inconsistency; itâs disturbing and unwelcome for our curious minds.
But what about the opposite? Would a system thatâs consistent, but incomplete be just as catastrophic? Actually, no. In fact, we would prefer if it was a system that couldnât answer every question, so long as it doesnât contradict itselfâŚWait, that sounds familiarâŚI canât put my finger on itâŚwhat does that sound like?
Oh! Right! The answer is ârealityâ. No system can answer every truth; hence âincompletenessâ.
But, thereâs one problem. How do you prove consistency? Say that you only had one system to work with. How does that system prove itself to be consistent? Can you use theorems within a system to prove that system? The answer is ânoâ. We donât say that gravity exists because of the theorem of gravity. We say it exists because of the force that it creates, which dips into a second system: physics, or, more specifically, the Second Law of Motion. Simply put, you canât prove that your system is consistent because, within that system, you canât prove that there are no contradictions. No consistent system can prove its own consistency; this is GĂśdelâs second incompleteness theorem.
The Difference Between Science and Mathematics
If math is a system that science dips into to explain its observed phenomena, then why would science not also be subject to GĂśdelâs Incompleteness Theorems? The answer is found within those axioms, the very building blocks of systems. The axioms of mathematics and the âaxiomsâ of science are not as alike as one might initially think.
A mathematical axiom is something that is true, no matter the situation. That is because we created math as a tool to explain something observed. For us to be able to accurately translate an observed phenomenon into a mathematical model, the math has to be axiomatic. Would a shovel with a pole chewed out by termites be able to perform the job of scooping up heavy dirt well? Probably not. Likewise, math that is hollow and easily disproven cannot be used to explain anything.
Scientific axioms are a bit different. While axioms in math are common and play a foundational role in more complex math, axioms in science are either limited or even nonexistent. Why? Science is not rigid. While mathematics is bound, science is limitless. Axioms only work in certain contexts, but science constantly redefines its context. I could say that one day that a scientific axiom is that the universeâs center is the Earth, but, upon the revelation of new observations, that axiom changesâŚand thatâs one thing an axiom doesnât do.
So, to correct and clarify, science uses postulates, which are similar to axioms, but more flexible. They function as âpresumptionsâ, which may or may not be correct. Postulates provide science with enough of a stable ground to explore through the scientific method. When it comes to math, postulates are axioms, but science operates on logical presumptions.
So, what happens to the GĂśdelâs Incompleteness Theorem if there are no true axioms, like in science? Yes, my curious readers, it does not apply.
The longest-lasting pursuits are those that are ingrained in the longest-lasting aspects of humanity. In other words, the pursuits that are closest to us as humans will survive as long as humans do.
Science is such a pursuit. From agriculture to agricultural engineering, science and the pursuit of knowledge has been with us forever. In fact, knowledge is among the essential human conditions.
If you ask if there will ever be a point that science will become pointless, I would have to say ânoâ. Not because science is equivalent to fact and facts are valuable. As weâve seen, âscientific factsâ change the more we explore. Science will never become pointless because we continue to explore! Until there is nothing more to learn; until humans decide that knowledge itself is worthless, science will continue to stand the test of time.