Peirce’s 1870 “Logic of Relatives” • Comment 11.14

Let’s now look at a concrete example of a morphism say, one of the mappings of reals into reals commonly known as logarithm functions, where you get to pick your favorite base.

Here we have and and the formula becomes where ordinary multiplication and addition are indicated by a dot and a plus sign respectively.

Figure 49 shows how the multiplication, addition, and logarithm operations fit together.

In short, where the image operation is the logarithm map, the source operation is the numerical product, and the target operation is the numerical sum, we have the following rule of thumb.

The image of the product is the sum of the images.

Resources

• Peirce’s 1870 Logic of Relatives • Part 1 • Part 2 • Part 3 • References
• Logic Syllabus • Relational Concepts • Relation Theory • Relative Term

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