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I took a symbolic logic class in college about 2 years ago and really enjoyed it. However, (in my opinion) the one thing that the class didn't emphasize enough is applying symbols and operators to real arguments. Instead, we focused mainly on structure and algebra. Although I loved learning about the structure and algebra of logic, I felt like I was missing out on the real utility of symbolic logic. I want to be able to understand/analyze arguments symbolically in real time. I also want to be able to recognize interesting or faulty arguments.

I think the best way to achieve this is to practice applying symbolic logic to interesting long-form arguments. Since I'm also interested in learning more about individual philosophers, I figured I should start there. This brings me to my question - what philosopher would you recommend studying from this perspective?

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    Unfortunately, formal logic is of little use in "real arguments", as they are informal, see argumentation theory.
    – Conifold
    Dec 21, 2019 at 12:22
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    Dec 21, 2019 at 15:39

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As Conifold rightly pointed out, practical argumentation does not use formalisms, so if you enjoy logic and argumentation, and want to deepen your appreciation of logic and argumentation, you might consider the life and work of a theory of argumentation put forth by Stephen Toulmin known as the Toulmin method to get a better sense of exactly why informal argumentation does not line up nicely with formal logic. The Toulmin method has been used as a model to teach argumentation in college-level courses. Other examples include in the courses of David Zarefsky and in textbooks such as The Aims of Argument.

Stephen Toulmin was also interested in a range of topics including attacking the positions of Thomas Kuhn's The Structure of Scientific Revolutions which evaluates the nature of science from a philosophical and historical view, one area in the analytic tradition where formal systems are of interest because of the close relationship between mathematics, computation, and science.

Ultimately, in Toulmin's model, which lays out a formal model for informal argumentation involving the inference from facts to conclusion based on sufficiently backed warrants and often anticipatory rebuttals, the structure addresses the probabilistic inference as opposed to the certain inference of deduction. In his The Uses of Argument he discusses sophisticated models put forth by Carnap and others, and the idea at length in the Chapter Probability. From page 45:

[A] reader who is interested in the application of logic to actual arguments will find it unclear what, in practical terms, are the questions under discussion, and what connection [formal arguments] are supposed to have with the sorts of everyday situation in which words like 'probably', 'likely' and 'chance' are used.

Toulmin was influenced by Wittgenstein in the same sort of way ordinary language philosophers were, and that can be seen in his analysis of argumentation by examining ordinary language use in his text.

If you enjoyed logic, you'll be encouraged to know that there are seemingly no end to proposed systems some even including the inclusion of both formal and informal, and deterministic and probabilistic models, and such logics are often studied in artificial intelligence as various ways to create machine intelligence, particularly in implementations in certain and uncertain knowledge representation and reasoning and machine learning such as those presented in Russell and Norvig's Artificial Intelligence.

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