Monthly Archives: June 2014

Peirce’s 1870 “Logic Of Relatives” • Intermezzo

This brings me to the end of the notes on Peirce’s 1870 Logic of Relatives I began posting to the web in various online discussion groups a dozen years ago.  Apart from that there are only scattered notes and bits … Continue reading

Peirce’s 1870 “Logic Of Relatives” • Comment 12.5

The equation can be verified by establishing the corresponding equation in matrices: If and are two 1-dimensional matrices over the same index set then if and only if for every   Thus, a routine way to check the validity of is to check … Continue reading

Peirce’s 1870 “Logic Of Relatives” • Comment 12.4

Peirce next considers a pair of compound involutions, stating an equation between them that is analogous to a law of exponents in ordinary arithmetic, namely, Then will denote whatever stands to every woman in the relation of servant of every … Continue reading

Peirce’s 1870 “Logic Of Relatives” • Comment 12.3

We now have two ways of computing a logical involution that raises a dyadic relative term to the power of a monadic absolute term, for example, for “lover of every woman”. The first method operates in the medium of set … Continue reading

Peirce’s 1870 “Logic Of Relatives” • Comment 12.2

Let us make a few preliminary observations about the operation of logical involution, as Peirce introduces it here: I shall take involution in such a sense that will denote everything which is an for every individual of   Thus will … Continue reading

Peirce’s 1870 “Logic Of Relatives” • Comment 12.1

To get a better sense of why the above formulas mean what they do, and to prepare the ground for understanding more complex relational expressions, it will help to assemble the following materials and definitions: is a set singled out … Continue reading

Peirce’s 1870 “Logic Of Relatives” • Selection 12

On to the next part of §3. Application of the Algebraic Signs to Logic. The Sign of Involution I shall take involution in such a sense that will denote everything which is an for every individual of   Thus will … Continue reading

Peirce’s 1870 “Logic Of Relatives” • Comment 11.24

We come to the end of the “number of” examples that we noted at this point in the text. NOF 4.5 It is to be observed that Boole was the first to show this connection between logic and probabilities.  He … Continue reading

Peirce’s 1870 “Logic Of Relatives” • Comment 11.23

Peirce’s description of logical conjunction and conditional probability via the logic of relatives and the mathematics of relations is critical to understanding the relationship between logic and measurement, in effect, the qualitative and quantitative aspects of inquiry. To ground this … Continue reading

Peirce’s 1870 “Logic Of Relatives” • Comment 11.22

Let’s look at that last example from a different angle. NOF 4.4 So if men are just as apt to be black as things in general, where the difference between and must not be overlooked. (Peirce, CP 3.76) In different … Continue reading