Nice quotations/passages:
"We all have extraordinary finesse at ordinary language" (28).
I like his use of the word "vacuous" here: "Grouping may also be indicated in ordinary language by inserting a vacuous phrase such as 'it is the case that', balanced with another 'that' to show cooridination of clauses" (28).
"Parentheses show groupings unfailingly, and are simple to use. They have the further virute of allowing complex clauses to be dropped mechanically into place without distortion of clause or context. This particular virtue has been of incalculable importance; without it mathematics could never have developed beyond a rudimentary stage.
Even so, parentheses can be a nuisance. Unless conventions are adopted for omitting some of them, our longer formulas tend to bristle with them and we find ourselves having to count them in order to pair them off" (29).
Funny: "Students are tempted to tinker with the dot conventions with a view to economy" (31).
Comment:
I like Lukasiewicz's notation.
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