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The Unknown Science: Understanding the Epistemology of Logic through Practice

Periodic Reporting for period 1 - EpiLog (The Unknown Science: Understanding the Epistemology of Logic through Practice)

Reporting period: 2018-09-01 to 2020-08-31

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.
EpiLog’s research was broken down into three work packages, which were implemented sequentially.

The aim of work package 1 was to extract from actual logical debates the methodological principles appealed to by logicians in arguing for their own logics and against competing logics. The majority of the work package was spent looking at the particular debate over whether inconsistent theories are true. Using this debate, I have shown that logicians appeal to a range of methodological principles in order to justify their logics, including that: (i) logics should solve semantic and mathematical puzzles, including the liar paradox; (ii) logics should accommodate other well-evidenced commitments, such as our best scientific theories and mathematical results; (iii) logics should be able to accommodate the majority of our judgements about whether natural-language arguments are correct and not. These results were published in “Searching for Deep Disagreement in Logic” and “Identifying Logical Evidence”.

Work package 2 aimed to use the methodological principles identified in work package 1 to justify a nuanced account of logic’s epistemology, as well as to specify how logic’s methodology differs from the sciences’ based upon this account. Using the results from work package 1, a novel account of logic’s epistemology called Logical Predictivism was proposed, according to which logics are supported on the basis of their ability to: (i) successfully predict which arguments are correct or incorrect, (ii) provide insightful explanations of why particular arguments are (in)valid, and (iii) fit with other well-evidenced commitments, such as our best scientific theories. These results are published in “Logical Predictivism”.

Work package 3 defends the practice-based approach which EpiLog uses, by showing that logicians’ actual practice is a reliable guide to the epistemology of the field. This defense has taken two forms. Firstly, it’s been argued that the methodology used by EpiLog is similar to kind to that used by philosophers of science and mathematics to provide accounts of the epistemology of these fields. Secondly, it’s been argued that as logicians are experts in their respective field, they are reliable guides to what constitutes suitable evidence for a theory in the field. These defenses have been published in “Identifying Logical Evidence”.
EpiLog makes three contributions that go beyond the state of the art:

1) It provides the first detailed case studies of the types of evidence appealed to by logicians in supporting their theories, and the methodological principles these logicians rely upon.

2) Based upon logicians’ practice, it provides the most detailed account yet of how logics are ultimately justified, through successful predictions and insightful explanations of arguments’ validity (a proposal known as Logical Predictivism).

3) EpiLog shows how logicians’ actual practice can be used to inform our theories of logic’s epistemology, and that this practice is a reliable guide to logic’s epistemology.

These contributions to the state of the art hold the potential for two significant impacts on the field:

1) EpiLog has provided the field with a new reliable method to investigate logic’s epistemology—the practice-based approach. By demonstrating that a “bottom-up” practice-based approach is a robust and reliable method for developing and testing epistemologies of logic, EpiLog has provided the blueprints for how future work in the area should methodologically proceed.

2) EpiLog’s logical predictivism can be used to inform current and future theory choices in logic. By providing a detailed and practice-informed account of theory choice, logical predictivism has the advantage that it can be fed back into logicians’ practice to inform that practice. When following a methodology blindly, we can make mistakes and miss important factors. By highlighting features of the logical method to practitioners, they can follow the community’s rules more thoroughly, improving practice. Thus, predictivism can provide logicians with a useful tool to evaluate the relative success of competing logics, helping to adjudicate future theoretical disputes.
Logical Disagreements