Ayn Rand once wrote that no mind is better than the precision of its concepts. If that is the case, then Square One is the sharpening block for the concepts of the mind.
Patterson’s short little book is exactly what it claims to be, the *foundations* of knowledge. Useful to the philosopher and the novice alike, Square One provides a handy guide for reexamining our conceptions of the world through the clear, crisp lens of logic. I would highly recommend it to anybody interested in developing a better understanding of the concepts that shape reality. The book might seem a bit basic or slow at first to those familiar with the rules of logic, but it is well-worth sticking through to the end.
The core claim presented by Patterson is that objective truth exists and is discoverable. At first glance, that such a claim could be defended in a mere 125 pages might seem haughty but Patterson proves to do so masterfully by cutting away the superfluous and going to the core tool in his philosophical utility belt: logic.
Foundations of Logic
The foundational analogies from which Patterson opens the book are those of a castle and of a tree. Both of these represent beliefs and concepts (and the systems from which they spring) of the world.
A castle that is built on a swamp, no matter how beautiful, complex, or impressive its heights might be, is not a good castle. It is at risk of collapsing at any time and its complex, admirable heights are structurally compromised. This is how many existing belief systems in the modern era exist. We work from what we want to see in the castle and find the section towards the top that justifies our ways of thinking. But finding a room in the castle at the top would be useless if that castle is going to collapse at the slightest disturbance.
Most adherents of beliefs and concepts don’t realize the castle is built on a swamp, though. They aren’t actively ignorant of its compromised status because the foundation of the castle is obfuscated in a cloud of fog.
Logic is the tool by which we clear away this fog and discover whether or not the castle is built upon stone or upon a swamp. Patterson does not conjecture as to why so much of the world’s castles are surrounded by fog but it doesn’t take one much work to understand that, given the realities of the academic nature of modern philosophy and the politics involved in supporting and perpetuating such a system, the incentives are set up in such a way to focus on the heights of the castle rather than its foundation. Patterson’s own rejection of this system is a refreshing approach to how philosophy ought to be done.
The confused understanding of the world is one in which knowledge and reality has no foundations. We exist merely in a web of interconnected concepts and beliefs playing off of each other — a struggle between powers and subjective half-truths. There is no hierarchy of truth in this confused world. This is the postmodern ideal against which Patterson’s book implicitly argues.
Rather than reality existing as a web of concepts (in which one may find logic, confusingly implying that there exist elements of the web where logic does not exist), Patterson’s analogy for truth, concepts, and beliefs is that of a tree. Every leaf is attached to a twig attached to a branch, attached to a trunk, attached to the roots. Without these roots, the trunk cannot support the branches upon which the leaves sit.
Logic is the roots of reality.
Introductions to Logic
“Logic can be understood as the rules of existence.” (32)
“Existence without logic would be existence without existence — i.e., non-existent.” (41)
The meat of Square One focuses on lessons in logic. Patterson makes a case for the necessity of logic & the reality of objective truth and quickly turns to what the three basic rules of logic must, by necessity, be. These are the laws of identity (“A is A”), non-contradiction (“It is not the case that A is not-A”), and the excluded middle (“Either P or not-P”).
Having established the core laws of logic, Patterson then moves to run through exactly why deductive reasoning, axiomatic argumentation, and propositional logic carry the weight they do. This might seem out of place in the book at the time it is read but couched in Patterson’s core thesis and desire to defend the objectivity of truth, he needs to set the stage that there exist tool kits (i.e., deduction, axiomatic argumentation, and propositional logic) that can be employed against the core counterexamples of objective truth: paradoxes.
Paradoxes
Having equipped the reader with a proper understanding of the basic laws of logic and out to prove his main thesis that objective truth exists and is discoverable, the last section of the book focuses on the most obvious counterexamples to the objectivity of truth. Patterson swiftly shows that most paradoxes are mere linguistic errors and do not violate the laws of identity, non-contradiction, or the excluded middle. Here he addresses classic paradoxes like the Liar’s Paradox and the Bittersweet Paradox, showing them to be linguistic errors that show the imprecision of language more than any flaws in logic, and addresses the Copenhagen Interpretation’s understanding of particle physics.
Applications to Other Fields
“Ideas do not need to be walled off from each other.” (81)
Although only briefly addressed in Chapter 4, the most damning and far-reaching implications of the rescue of logic is the affect it has on other fields. In a time when it is considered heresy against the Grand Poobahs of Science to argue that theory must precede data, Patterson makes such a claim and goes forward to demonstrate the necessity of theory (with some understanding that it must be clear that both parties are playing the same game). Just as logic is the roots of philosophy, philosophy is the roots of all other disciplines. Science without theories to inform hypotheses is merely the collection of data; economics without theories to inform studies is just counting dollars and cents; English literature without theories of human action and struggle is just the recounting of stories. At the root of all of these is the need for theories that make sense and are discernible to the mind.
This is where the real power of Square One comes out. If the reader has a moment of clarity (and hope) when understanding just how important it is for other disciplines to be informed by crisp, clear philosophy — and how dangerous it is for them to reject logic for obfuscation or reject philosophy entirely — and gets nothing out of Square One, they’ll have gained more than most students gain in four years at a university.
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Ultimately, Square One is just the corner piece to the puzzle of Patterson’s pursuit to clear the fog from around the castles of our minds. I look forward to the next piece in the puzzle.
You can purchase a copy of Square One here.
You can follow Steve Patterson’s work here.
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