From: Jos Lehmann (University of Amsterdam)

Subject: Counterfactual notation in Chapter 7

**Question to author:**

Jos Lehmann noticed potential ambiguity in
the notation used for counterfactual propositions.
Capital letters, like *"A"* or *"B,"* are sometimes used to
denote propositional variables, and sometimes to denote
propositions. For example, in the function *A = C*
(Model M, page 209) *"A"* stands for the variable
"whether rifleman*-A* shoots", and takes on
values in {true, false}, while in statements S1-S5 (page 208),
*A* stands for a proposition (e.g., "Fireman-*A* shot").

**Author answer**

The use of capital letters for both variables and
propositions is an effective abbreviation that might admittedly
lead to some ambiguity. However, the ambiguity can be resolved
(or minimized) through the following
syntactic distinction: When *A* appears in an equation it denotes
a name of a variable, and when it appears
alone, or in a propositional formula (i.e., without the structural
equality sign), it stands for the proposition "*A* is true".
I believe that the benefits of abbreviating "*A* is true"
with "*A*" outweighs the risks of potential ambiguity.

Next discussion (Lindley: *On functional models for predicting the effect of actions*)