# Maths: Theories of Truths

Read the TOK essay and suggest how the student could have used the concepts of coherence and correspondence

The Correspondence Theory of Truth refers to a proposition that is true only if it reflects or corresponds to reality. For example, the proposition that ‘it is raining’ is only true if it is actually raining outside, also known as reality. A limitation to this method of assessing the validity of a truth is that we know our sense can be misleading, so how do we know that reality is in fact reality? However, I will not be exploring this area, instead, in this case, we will assume that something like reality does exist and is not simply a product or construct of our mind. The Coherence Theory of Truth states that a proposition is true if it is consistent with other things or systems that are considered to be true. For example, I hear a book falling/hitting the ground. Person B in the rooms also hears it, and the book I saw a moment ago is now gone/displaced. Together, the three observations are consistent with one another,  fitting into a ‘system’, and hence, is the truth. However, similar to the correspondence theory of truth, we could question whether or not the book really fell to the ground? Or can something else explain these observations?

The essay focuses on ‘rigorous mathematical proof’. The first idea that comes to mind is that these proofs undergo the coherence theory of truth, because some may argue that we do not or in some cases, are not able to see the reality of mathematics. Instead, they are constructs of the human mind, and hence, can be seen as a language that we put meaning into. This implies that the human mind is responsible for creating boundaries or ‘rules’ in mathematics, as if we have created a game and hence creating logic. Therefore, instead of having to witness ‘reality’ that the mathematical proofs reflects, the ‘proofs’ can be seen as an evidence that fits into the wider paradigm or rules created in mathematics. The speaker also uses axioms as a means to ‘support the rigorous mathematical proof’, the use of axioms is a perfect example of drawing conclusions within the system in order to prove an idea. The speaker also claims that the use of axioms will provide complete certainty. The example given was that 3x + 5 = x + 15 , and thus x=5. however, as mentioned previously, there are limitations to the coherence theory of truth. In this case, the proof will only be true if the axiom is universally accepted. In order to further the certainty, one may think of reflecting this proof in reality or in nature. In this case, like the writer mentioned, it is questionable to what extent x=5 can be seen in reality(correspondence theory of truth).

When assessing the certainty of a specific proposition in any scenario, the correspondence theory of truth can be applied. This is seen in the mentioned example of a calculated chance of 80% for his horse to win, but instead, during the actual race, his horse took a fall due to uneven ground. Though the mathematician was certain of his maths used within the mathematical system (as he used the Coherence Theory of Truth in order to draw conclusions), reality was unable to reflect the same result (meaning that the correspondence theory of truth failed to validify and certify his proposition).

Overall, the essay discussed with the idea that a scenario that resonates with one theory may not be proved or verified by another. This is clearly seen in the horse racing example where the coherence theory was used, however, the results failed to align with the correspondence theory. Therefore, this essay ultimately comments on the bigger picture: the significance of evaluating different perspectives in a given proposition, as evidence bias will lead one to draw misleading conclusions.