EpiLog · The Unknown Science: Understanding the Epistemology of Logic through Practice

The Unknown Science: Understanding the Epistemology of Logic through Practice

We take ourselves to know certain logical claims. For example, that Socrates is wise and just only if he’s wise, and that Canberra is either the capital of Australia or not. Yet, currently we fail to have a viable explanation of how we possess logical knowledge. This problem is caused predominantly by the fact that logical knowledge seems to be epistemically basic, in that much of our other knowledge presupposes it. We require logic to establish mathematical truths, test our scientific theories, and engage in rational debate. Consequently, our other knowledge simply presumes we possess logical knowledge, and so cannot be relied upon to either support or undermine our logical beliefs. Two explanations of logical knowledge have dominated the philosophical landscape. Firstly, that we recognise logical truths through a form of mental insight, and secondly that logical knowledge is a sheer product of linguistic proficiency, with logical truths guaranteed by the meaning of certain special logical terms. Both accounts, however, are ultimately inadequate; while logical intuition is mysterious, appeals to linguistic proficiency are unable to explain logical disagreements. Consequently, we need a new, more complete, explanation of logical knowledge. Nor is the need for a new explanation purely theoretical. We use logic to form beliefs in all areas of life, and we now have many competing logics at our disposal to do so, all of which would lead us to reasoning differently in certain situations. For example, it is currently unsettled how we ought to reason with inconsistent beliefs. While the predominant logic of the last century, classical logic, dictates that any proposition whatsoever follows from an inconsistency, paraconsistent logics allow individuals to hold inconsistent beliefs and make informative inferences from them. Thus, while for the classical logician discovering an inconsistency in one’s beliefs necessitates making no further inferences until the inconsistency can be removed, as one inference would be as good as any other, paraconsistent logicians argue such an approach is unrealistic and irrational. It is often not apparent how to remove the inconsistency, and we can only subsequently recognise our mistake and remove the inconsistency by making inferences from these beliefs to further consequences. Consequently, in order to ensure we reason correctly, both in this and other circumstances, it is paramount that we choose the right logic. Yet, in order to make these choices, we require tools that we currently fail to possess. Namely, effective criteria to adjudicate between competing logics, which can only be formulated once we have an adequate understanding of what constitutes logical evidence. EpiLog aimed to solve these important problems, with two objectives: Objective 1. Use the actual practice of logicians to motivate and support a novel theory of logic’s epistemology called ‘logical abductivism’, which shows that logic’s methodology is akin to the empirical scientific method. Objective 2. Provide clear and detailed criteria for logical theory choice.

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