Realism: Truth Doesn’t Care About Your Feelings

I wrote this for my philosophy class. I thought it was nice, and so should you.

This question is trying to trigger the realist vs anti-realist debate, so to begin, let’s define those two with help from Tennant’s Introducing Philosophy on p.28.

Realism vs. Anti-Realism

Realism: Scientific and mathematical truth exists independent of our perception of it. Everything in the mathematics and sciences is either a true or a false, regardless of what we currently, or ever will, know. If the Goldbach conjecture is true, there is a possibility we may never create a proof for it. This is the humble position to take, because the position admits the limited, fallible cognitive capacity of the human mind. This essentially opens the possibility for hard ‘epistemic agnosticism’ to exist. Hard agnosticism is the belief that the nature of God’s existence can never be known, so hard epistemic agnosticism is the belief that some truths can never be known. Note, realism is not hard epistemic agnosticism per se, but just confirms its possibility.

Anti-realism: Scientific and mathematical truth is dependent on our perception of it; if something in the mathematics and sciences is true, then we must be able to confirm it eventually. If Goldbach conjecture is true, then a proof must exist, but we may not know it at this point! This assumes that the human mind was designed to understand the universe in which it is put in. This view is incredibly solipsistic and arrogant. This view negates the possibility that hard ‘epistemic agnosticism’ will ever exist.

Keeping this in mind, let’s address the philosophical problem.

If a mathematical conjecture is provably unprovable from our current axioms, and also provably irrefutable on the basis of those axioms, does it follow that the conjecture must be false if those axioms are true?

A realist would assert, definitely not! Just because we cannot prove truth with axioms doesn’t mean that it is false. Again, this is because the realist says truth exists independent of our perception of it. The realist would be more comfortable assuming the Goldbach conjecture to be true, because they accept that there may never be a proof for the truth of it. Thus, they would be more open to a pragmatic perspective of truth. If the Goldbach conjecture is useful in cryptography, and it hasn’t been proven to be false, then it could be considered true in spite of the absence of proof.

An anti-realist would hesitate a bit more. An anti-realist would suggest that because we cannot prove the conjecture’s truth (as we have proved that it is unprovable), we cannot say it to be true. At the same time, since that we proved that it is irrefutable, we cannot prove the conjecture to be false either. Since the anti-realist cannot adopt a hard ‘epistemic agnostic’ perspective to this issue, i.e. that we will never be able to prove it true or false, the anti-realist would be persuaded to, at worst, accept a soft epistemic agnostic position, that we don’t know its truth yet. They will assume that there was some systematic error in the positive proof for or the negative proof of the Goldbach conjecture: for example, that there are axioms that we haven’t discovered yet, that there are methods of proof that we haven’t invented yet, or that there are mistakes in the proofs that we haven’t realized yet.

My Perspective

I take the position of realism. Truth exists whether we experience it or not. Let us consider for a second that our cognitive capacities were so limited that we could not formulate mathematical proofs for the Pythagorean theorem. Imagine, that we were shielded from the truth of his existence from all angles. The truth of the Pythagorean theorem does not care about our perpetual ignorance.

From the Islamic perspective that I assume upon myself, all knowledge is possessed by God and he reveals knowledge to whom he wills. Mathematical and scientific truth exists, it is up to him whether God reveals it to us or not.

I prefer to take a pragmatic perspective of truth. If the Goldbach conjecture works in cryptography without flaw, then I can comfortably say the Goldbach conjecture is true for all intents and purposes. From this perspective, the proof does not serve any purpose!

In realism, mathematical and scientific truth exist and they don’t care about your feelings.