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.
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.
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 ∀/𝚺 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 that it would be better measured by the logarithm of what he calls chance, which is closely related to probability but has more intuitive properties.
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 - unstarted
Peirce derives induction, deduction, and abduction (his invention/coinage) from the classical syllogism and distinguishes between them. These three form the logic of science and, underpin whatever we might call “the scientific method.”