17 Example of usage (Ad)

Introduction

Most of us would argue that if it is true that "No cat is sleeping in the kitchen", then it is also true that "No black cat is sleeping in the kitchen". Adding the extra qualifier "black" does not change the truth-value of the statement. But how do we prove this?

Using one of Peirce's rules

With Peirce's rules, we can. Consider the following graph:

[Proposition:
  [Kitchen: #]<-(Loc)<-[Cat]<-(Expr)<-[Sleep]
 ]
"No cat is sleeping in the kitchen".

Recall that one of the rules is:

Insertion:
Any graph may be inserted in any oddly enclosed context.

Since we have a graph (the Cat graph) that is oddly enclosed (in the negative Proposition context), we are entitled to add any graph. The new graph could look like this:

[Proposition:
  [Kitchen: #]<-(Loc)<-[Cat]<-(Expr)<-[Sleep]

  [Cat: #]->(Attr)->[Black]
 ]
"No cat is sleeping in the kitchen.  The cat that is not in the
 kitchen is black.".
"No black cat is sleeping in the kitchen."

Next

Next, we give another example.


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