Illustrations of the Logic of Science

An Interactive  version of Peirce's 1878 paper on probability theory and scientific inference. 

Sections of text highlighted in blue can be clicked to show an interactive example of the point being made in that paragraph. 

An app for exploring Signal Detection Theory, N-P hypothesis testing, and Severity. 

In 1884, Peirce published "A Numerical Measure for the Success of Predictions".  Earlier that year, Sgt. Finley devised a method for predicting tornadoes, and scored his method favourably. He gave it a 96% as he was right 96% of the time.  

Peirce and others responded by noting that most of Finley's  success was due to the fact that tornadoes are rare.  Finely would have gotten a better score (98%) by simply always saying "No Tornado". 

Peirce offered an alternative way to assess such methods. The score, which he called "the science of the method" is now called The Peirce Skill Score, among other things. 

In 1902, writing on the nature of classification, Peirce provides a sustained discussion on the nature of final causation. A natural class is one where items are grouped according to their final cause - according to their purpose, rather than according to our purpose for classifying them. 

He argues that natural classes can effectively merge, in that individuals from different classes can be alike. He illustrates this point with an example from Egyptology. He uses the theory of errors to analyze a set of Egyptian weights (called kets). The question is: if the weights are imperfect copies of some standard weight(s), what were those standards? 

This illustrates his broader point by showing that a weight between two standards could have been produced by either one, demonstrating that different natural classes (standards) merge in that either can produce individuals that could apparently belong to the other. 

Here is a fairly limited way to explore Peirce's (second) diagrammatic approach to logic, the Existential Graphs. This page lets users learn the basics of expressing logical formulae in the graphs, shows the rules for manipulating the graphs, and lets one try their hand at a few proofs. (It also has a automated proof finder, in case you just want a demonstration.)

Currently this works for the Alpha Graphs (sentential logic) and the Beta Graphs Second-Order Predicate Logic). I hope to later include a mode for the Gamma Graphs (Peirce's go at Modal Logic). 

The tool is based on Don Roberts' helpful book <https://philpapers.org/rec/ROBTEG>, and John Sowa's walk through MS 514 <https://www.jfsowa.com/peirce/ms514.htm> . (And my time working through the graphs myself.) In addition to the above sources, see <https://www.kenketner.net/existential-graphs> for another nice walk through.