In Could John Stuart Mill Have Saved Our Schools?, Siegfried Engelmann and Douglas Carnine discuss the philosophical foundations of their acclaimed Direct Instruction programme (see Part 1). They write of their serendipitous rediscovery of Mill’s work and that they
came across Mill’s work and were shocked to discover that they had independently identified all the major patterns that Mill had articulated.Theory of Instruction  even had parallel principles to the methods in [Mill’s] A System of Logic [published in 1843].
— location 543 Kindle edition
I think it’s worth looking in detail at the five principles of inference proposed by Mill, and how Engelmann and Carnine adapted them for use in educational contexts.
The five principles put forward by Mill are:
- The Direct Method of Agreement
- The Method of Difference
- The Joint Method of Agreement and Difference
- The Method of Residues
- The Method of Concomitant Variations
In this post, I will focus on the first three.
“Non-canonical” statements and inferences are highlighted with an asterisk. These are my own suppositions and, although I believe they are supported by my reading of Mill’s and Engelmann’s and Carnine’s work, I cannot claim that they have direct textual support.
To further explain the simplified “symbolic form” I have developed to highlight what I think are the salient features in the argument:
- A= “blue”
- a = is blue
- b = has beak
- c = has wings
- d = extends above the horizon
- e = has clouds
- f = has windscreen
- g = has four wheels
Please note that the “symbolic form” is currently only a shorthand system, and any resemblance to the notation of formal symbolic logic is merely coincidental.
Links to Part 5 and the other parts of the series can be found here.