Language of Ideas.
“Philosophical problems arise when language goes on holiday.” — Wittgenstein, Philosophical Investigations
Logical forms aren’t meant to be true or false, nor reflections of how we think. They’re components of a formal machine that does the thinking for us. Thus, logic has become a language that encompasses the very nature of the unseen relationships between disparate aspects of reality. This level of comprehensiveness simultaneously makes the task of thinking easier, and far more complex, because a “language machine” only suffices as a guide through the journey between abstract to concrete. To this effect, philosophical logic is the secret bootstrap to achieve the maximum level of human understanding — as it’s the only way to explain things that can’t easily be put into words.
The following is my best attempt at visualizing the “journey between abstract to concrete”, in a way that introduces some basic tenets of propositional logic.
The Notation
Properties — A - Z
Individuals — a - w
Variables — x, y, z
Quantifiers — ∀, ∃
Connectives — ¬, ∧, ∨, →, ⇔, ≡
Modal Operators — ◻, ◇
The following is a set of logical statements which aren’t easy to define. A propositional “shape” could represent anything that shares an underlying form, like a = b, for instance. Or in natural language, “Plato is an idealist”.
The above three examples use the properties I and P, standing for “Idealist” and “Platonist”. Each hue is correspondent between each expression and its natural English counterpart. Both a universal and existential quantifier are used, which are just traditional operators, specifying the referent of their bound variables. Again, propositional translations for these formulae are directly above each, with lines.
But don’t worry. You don’t need complex math to deal with the propositional logic used in philosophy.
All you need to become a logician of philosophy is contained within this article’s basic notation alone, which encompasses the entirety of the structure of natural language itself. You only need to understand where — and how — to assign predicates and propositions.
Think of it like a word puzzle.
By adding only a few additional elements, we can distill any piece of text into propositional form. The following quotes can be found in the Transcendental Doctrine of Elements, on page 397 of Kant’s Critique of Pure Reason, which I’ve notated in standard first-order predicate logic.
The above logic can be spoken as: “All sets of simple parts constitute a composite substance — and necessarily, nothing exists which isn’t a simple compositional part”.
The above logic can be spoken as: “Universally, it’s not the case that a number of simple parts constitute a composite substance — and necessarily, nothing exists which is a simple compositional part”.
The above examples of logic might seem trivial. I chose these two passages specifically because they say opposite things from each other. But I’ve found this odd method of logical deconstruction to be instrumental in any deep analysis of philosophical texts. And though it takes your favorite writers and makes them sound entirely mechanical, it enriches your understanding of their words. Henceforth, logic in general suffices as a perfect substratum for any system of ideas.
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