Limited understanding is apparent in mathematics

It is difficult to imagine a world in which no truths exist, which is perhaps why we are eager to accept some things as absolutely true. As our understanding of the world is limited, it is debatable whether truths which we perceive in our reality can ever be considered absolute. For example, it could be claimed that in mathematics and the natural sciences, absolute truths, such as the existence of gravity or the fact that potassium is more reactive than sodium, subsist. However, the existence of these ‘absolute truths’ could be partially accounted for by humans’ limited capacity and ability to understand and perceive things.

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An example of our limited understanding is apparent in mathematics. Most high school students learn Euclidean geometry in school, which, for example, teaches us, as an absolute truth, that two parallel lines never meet. Euclidean geometry serves our reality well in the sense that we can use it and perceive it and conduct lives which do not contradict it. However, it is not the only geometric theory, and other schools of mathematical thought, such as Elliptic and Hyperbolic geometry also exist.

They differ from the Euclidean theory mainly in their concepts of parallel lines as, for example, in Elliptic geometry parallel lines always meet. It is incredibly difficult for us to comprehend this if we have been brought up to think in Euclidean terms, because we have a hard time imagining something that we cannot connect with the world we live in. Thus an example of Elliptic geometry, which relates to our reality, has been constructed: the lines of longitude on a globe are parallel, but as they exist in a spherical space, they curve and intersect at the ‘poles’ of the globe.

Thus parallel lines do meet. 1 Because some concepts are beyond our capacity to imagine, it is easy to accept those notions which we can imagine, as absolute truths. These absolute truths, however are only true in certain paradigms, such as Euclidean geometry, and are relative in a larger context. Ethics is an area of knowledge in which truth is often considered to be relative, as what is right or wrong does not correspond to facts like it does in mathematics and sciences.

In these areas of knowledge, things can be proven right or wrong empirically, but morale decisions are different, as whether something is right or wrong depends mostly on one’s opinions, which are often culturally dependent. For example I would argue that capital punishment is always morally wrong largely due to the environment in which I have been raised. Someone, like the governor of Texas, might argue that the capital punishment is morally right, because of the environment in which they have been raised. This shows that in ethics truth is rather relative, though some people argue that there are absolute truths in ethics.

Perhaps this is true, and some things such as rape or murder, can never be justified and are thus always wrong. In this case the relativity would come into play in the decision between the lesser of two or more evils; for example in deciding whether one person’s pain and suffering is acceptable if it leads to the happiness of another. But if everything is relative and thus context is, in fact, all, can truth exist? At this point it is perhaps important to differentiate truth from The Truth, a state in which everything is absolute and context is irrelevant.

As we have already said, if truth is a set of beliefs which correspond to the reality which we perceive, then it only exists in that paradigm and is relative in a larger context. This is a limited, although pragmatic, truth, which enables us to function in our own reality. It exists even when context is all, as it is an individual truth; what is true in my perception of reality, is perhaps not true in yours. It is vital to establish that individual truth and belief are not synonyms and so even if I believe in unicorns, this does not mean that it is true that they exist in my reality.