Book Review: Square One

Square One: The Foundations of Knowledge by Steve Patterson

The first of a series of planned philosophy books by Steve Patterson, who runs the Patterson in Pursuit podcast that I listen to, Square One is about the ultimate grounding of human knowledge in necessary logic.

In the first chapter, Patterson lays out a tree analogy for one’s worldview, where the leaves are conclusions, the branches are premises, and the roots are the foundations. People spend most of their time on the leaves, when it’s the roots that matter most (if you get the foundations wrong, all your conclusions are in serious doubt). This is contrasted with the “web of knowledge” way of thinking where there are no foundations but instead all your beliefs consist of one interconnected layer. He argues that the roots of knowledge are the laws of logic, which are necessary and can be known for certain.

In the second chapter, Patterson addresses implausibility arguments against humans attaining such certain knowledge. Examples include the skeptical injunction to always be humble about what we can know, the evolutionary origins of the brain which emphasizes what works rather than what is necessarily true, and the implausibility of the universe needing to be sensible to humans. While these arguments have some persuasive power, they cannot establish that certain truths are unknowable. Impossibility arguments are addressed in chapter five.

Chapter 3 is the core of the book, where the laws of logic are laid down: the law of identity, the law of non-contradiction, and the law of excluded middle. Patterson hammers home that these are necessarily true and cannot be denied, for the denial of them assumes their truth. Chapter 4 extends these basic laws to some necessary consequences, such as how theory is prior to data and how we can be certain there exists the phenomena of awareness by a mind. This is not a textbook on logic, though, so he doesn’t demonstrate the formalization of propositional logic and how it can be used and manipulated (perhaps that could have made a short appendix? For people who want to explore this topic more and in particular how logical operations can be mechanized, try The Logician and the Engineer).

The final fifth chapter addresses “impossibility argument” counters to the claim that we can be certain about the laws of logic. Some major arguments that he addresses are the liar’s paradox (a misuse of language), quantum indeterminacy (whatever else, logic is prior to physics), and the “mere tautology” reply (mathematics can be thought of as a series of “mere tautologies”, but we sure as hell learn something new).

Short and readable, this makes for a good primer on logic and the rationalist worldview and I wouldn’t hesitate to recommend it to a logic neophyte or to somebody who claims that “we can never really know anything”. I look forward to Patterson’s subsequent books.

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