The Practicality of Logic: From Symbols to Everyday Use
If you look at logic, it’s full of symbols. How does that material relate to everyday reasoning?
I think of logic as being the guardian of coherence. To guard coherence is to focus on patterns of reasoning, on how beliefs or opinions interact together, on how theories hold with the various assumptions they make and how they make predictions or prove theorems. Coherence is a vague term, and it can be measured with different standards. In mathematics, coherence means consistency, the avoidance of contradiction. The adopted standards for mathematical reasoning are those of validity. Validity is very strict, if not austere. In the court of law, we adopt less demanding standards, encapsulated by the idea of “reasonable doubt.” We wouldn’t be able to prosecute anyone if we adopted the standards of validity, and everyone would end up in jail if our logical standards made us gullible. In some scientific contexts, we work with explanation, based on partial evidence from the past or traces of events, and we try to work out what happens from this limited information. In other branches, we try to make predictions under uncertainty, so we adopt standards that align with probabilistic reasoning.
This brings us to the heart of the matter: logic and its symbols. In the twentieth century, as mathematics grew increasingly complex and weird, mathematicians revamped logic research to provide a solid foundation, leading to the development of formal languages and symbolic logical theories. So philosophers and mathematicians began asking how we could fortify the standards of mathematical reasoning, and how we could make sure that it never leads to contradiction, no matter how intricate it got. Developing formal languages became a necessity for this endeavour. The result was the development of symbolic logical theories that have been refined and simplified, and that we can now teach at a relatively basic level to students. We get from the symbolism the kind of clarity of what ideal reasoning might look like.
How does that then relate to everyday reasoning? I’m not too sure. I have a friend who learned quite advanced mathematics when they went to university to study engineering, and they are now working on research and development of airplane engines, and they apply very little of the maths they learned at university. I doubt they could still perform the maths they had to learn for their core examination in their first year. The same thing with other people I know who have learned a great amount of mathematical economics and are now working in investments; they don’t get to apply the mathematics that they learned directly and probably forgot most of it. Similarly, learning the symbolism of logic subtly trains the mind, providing tools that, while not always directly applied, enhance our cognitive processes and decision-making in everyday life.
What I think is lacking, however, is a more mundane discussion of logical reasoning in society. Analytic philosophers write papers with the rigidity of validity for their logical standards, but I don’t know that many others explicitly try to seek logical guidance. Regrettably, logicians have not yet succeeded in making discussions of everyday logical reasoning accessible and beneficial to a broader audience. I’m trying to bridge that gap.
