This is a project to translate the writings of logician/experimentalist/philosopher/semiotician/all-around-polymath C.S. Peirce (1839-1914) into language more accessible to a modern audience.
The “Illustrations of the Logic of Science” series
The Journal of Speculative Philosophy cognition series
Introduction to the “Champaign Covers”
I explain what I’m doing in the series and why I’m thinking of myself as a “cover band” playing Peirce’s songs in my own style.
While I’d like my posts to be self-contained, the “music theory” posts provide some background you may find adds to your understanding.
Music Theory: Peirce and Kantian chords
Peirce is very engaged with Immanuel Kant’s philosophy. This post describes Kant’s idea of “the thing in itself” and the related idea of the “transcendental ego.” It also briefly explains something that I find a barrier to understanding Peirce: early on, he’s still working with a centuries-old but inadequate notion of the raw material of logic: the rigid <subject> <copula> <predicate> proposition.
This was a series of articles or essays that Peirce wrote for Popular Science Monthly. They were published in 1877-8. They are fairly early in Peirce’s corpus. His ideas will evolve, but the essays introduce many key themes. I’ll frequently call those out in an ending section titled “Commentary, 149 years later.”
Peirce claims that oddities provoke doubt. Doubt produces irritation. Irritation produces inquiry. Inquiry removes the doubt, either by reinforcing an earlier belief or installing a new one. Belief is intimately tied to habit: when the belief is relevant, you act without thinking.
There are various ways to create and stabilize belief:
I also cover the classical syllogism because that had been the dominant kind of formal reasoning for many centuries. That was changing toward our more familiar boolean logic and predicate calculus during Peirce’s lifetime, and he was part of that change. (He invented the ∀/∃ notation, together with less successful terminology like legisign and qualisign.)
This is certainly Peirce’s most-read text because it introduces the famous (to some) Pragmatic Maxim, though that won’t be named until considerably later. (I’ve written an example-driven introduction to it elsewhere.)
Peirce says that the meaning of a belief is entirely due to the actions (habits) it causes. If two different beliefs have the same practical consequences, they are not actually different. Reasoning clearly means focusing on those consequences.
Peirce also introduces the idea that truth is that which all inquiry, by all people (or successor species), will converge to over time. Truth requires community to “even out” individual quirks and biases.
Science advances by replacing categorization and counting with measurement, where the primary value of measurement is that it works with continuous (in the mathematical sense) quantities. We can make a better tool for inquiry by laying classical (continuous) probabilities over classical (categorical) logic. However, what we really need is not probability, which reasons forward from known values to likely outcomes, but the new field of statistics, which reasons backward from observations to likely regularities. That last is called induction (which is not, alas, what mathematicians mean with the technique of proof by induction).
“The Probability of Induction”
Peirce is groping toward what we now call confidence intervals (like the notorious p < 0.05). He gives formulae for estimating them.
Peirce is an early adopter of what we now call “frequentist” probability, which he contrasts with the more popular “subjectivist” probability. (He’ll later switch to a “propensity” interpretation.) He gives examples of how the subjectivist interpretation of probability can lead to absurd results.
In the subjectivist interpretation, probability is equated to degree of belief. Peirce argues belief would be better estimated by the logarithm of what he calls chance, which is closely related to probability but has more intuitive properties. (Nowadays, we call this the logit function.)
Peirce argues that the nature of the universe is a mixture of chance and predictability. Such a universe supports his version of induction. Moreover, we can reason inductively about the universe because our minds are strongly adapted to do so.
He contrasts his view to the more popular one of J.S. Mill.
He talks about the implications of scientific discoveries for religion.
“Deduction, Induction, and Hypothesis”
Peirce derives induction, deduction, and hypothesis (which he will later call “abduction”) from the classical syllogism and distinguishes between them. These three form the logic of science and underpin whatever we might call “the scientific method.”
The dominant Cartesian style of philosophy is outdated. Philosophy should take heed of the scientific style of truth-seeking and also the advances of modern logic.