On the influence of signs in mathematical reasoning / by Charles Babbage.

  • Babbage, Charles, 1791-1871.
Date:
1826
Catalogue details

Licence: Public Domain Mark

Credit: On the influence of signs in mathematical reasoning / by Charles Babbage. Source: Wellcome Collection.

Provider: This material has been provided by The Royal College of Surgeons of England. The original may be consulted at The Royal College of Surgeons of England.

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    must be regulated by definition; and here arises one of the great differences which characterise this science, the definitions themselves being exceedingly simple, comprising but few ideas, whilst in other sciences they are usually much more complicated. In Geometry, definition is the beginning of any enquiry; in meta- physical science, it is frequently the result of one : thus that a triangle is a figure formed by three sides, is a convention on which many of Euclid’s propositions rest, and from this, as a point of departure, numerous deductions are made: on the other hand, our idea, and consequently our definition of beauty, is only the result of considerable thought and enquiry. In the language of analysis, it is very rare that any symbol possesses more than one meaning; in ordinary language, it is as rare to find a word having but one signification: nor is this the only difference; when an algebraical symbol has more than one mean- ing, they are always well defined and distinct, and should there exist several signs for the same operation, the only difference is in their external form, not the slightest in their meaning; whilst in common language, the meanings of words shade away into each other, and it is frequently difficult, even on mature consideration, to assign the precise limits of the signification of words which are nearly synonymous. Now if this be the case when the words themselves are the especial objects of our thoughts, how open must all reasoning be to inadvertencies when the mind is compelled to occupy itself at once on the various meanings of the signs it uses and on the train of consequences which it endeavours to deduce by them. The multitude of significations which attach to many of the words that compose our ordinary language, is a disadvantage which is completely removed from that of analysis. In our rea- soning concerning any objects even of a moderately complicated nature, we are obliged to make use of the words attached to those a2