ON THE USE OF DOTS IN PRINCIPIA MATHEMATICA

The distinctive squared dots in Principia Mathematica have two uses, to replace parentheses or brackets to indicate the scope of connectives and operators as well as to symbolize the sentential connective "and". The explanation of the use of dots in the Introduction shows that the punctuation dots express conjunction by symbolizing the juxtaposition of formulas, following Peano, and so they are always used as punctuation. This paper thus supports Turing's assertion that conjunction in Principia is expressed by juxtaposition. This analysis avoids Curry's proposal that an "auxiliary" connective for conjunction should be involved in interpreting the dot notation.