Peano Russell notation

The Peano-Russell notation is a notation for logical formulas that was developed by Giuseppe Peano in his Formulio Mathematico (5th ed. 1908) on the one hand and by Bertrand Russell and Alfred North Whitehead in their Principia Mathematica (1910-1913) on the other. In contrast to Gottlob Frege's conceptual writing (1879), it is linear (one-dimensional), more closely based on the spelling of algebra and, with minor changes, is mostly used to this day. Russell and Whitehead write in the first chapter of the Principia :

“The notation we use in this book follows that of Peanos, and the following explanations are based in part on the ones he prefixes his Formulio Mathematico . We adopt his use of dots instead of brackets and many of his symbols. "

The main logical symbols in Peano Russell notation are:

{\ displaystyle \ sim p}

for the negation

{\ displaystyle p \ lor q}

for the disjunction

{\ displaystyle p \ cdot q}

for the conjunction

{\ displaystyle p \ supset q}

for the implication

{\ displaystyle p \ equiv q}

for equivalence

{\ displaystyle \ exists x. \ phi (x)}

for the existential quantifier

{\ displaystyle (x). \ phi (x)}

for the universal quantifier

{\ displaystyle \ vdash .p}

as an assertion mark

Periods and colons act as auxiliary characters for grouping, like brackets in modern spelling.

Individual evidence

^ Bertrand Russell / Alfred North Whitehead: Principia Mathematica , Vol. I, Cambridge 1910, chap. 1, p. 4. [Original: "The notation adopted in the present work is based upon that of Peano, and the following explanations are to some extent modeled on those which he prefixes to his Formulio Mathematico . His use of dots as brackets is adopted, and so are many of his symbols. "]

Web links

Bernard Linsky: The Notation in Principia Mathematica . In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .
List of definitions at the end of Volume I of the Principia
The Principia Mathematica online (University of Michigan Historical Math Collection):

[1] Bertrand Russell / Alfred North Whitehead: Principia Mathematica , Vol. I, Cambridge 1910, chap. 1, p. 4. [Original: "The notation adopted in the present work is based upon that of Peano, and the following explanations are to some extent modeled on those which he prefixes to his Formulio Mathematico . His use of dots as brackets is adopted, and so are many of his symbols. "]