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In a mathematical definition, although the words in which it is expressed may vary, the meaning which it is intended to convey is always the same. Whether a straight line be defined to be a line which lies evenly between its extreme points, or the shortest line which can be drawn between two points, there never can be a difference of opinion as to the lines which are comprehended, and those which are not comprehended, in the definition.
The case is not the same with the definitions in the less strict sciences. The classifications in natural history, notwithstanding all the pains which have been taken with them, are still such, that it is sometimes difficult to say to which of two adjoining classes the individuals on the confines of each ought to belong. It is still more difficult, in the sciences of morals and politics, to use terms which may not be understood differently by different persons, according to their different habits and opinions. The terms virtue, morality, equity, charity, are in every-day use; yet it is by no means universally agreed what are the particular acts which ought to be classed under these different heads.
The terms liberty, civil liberty, political liberty, constitutional government, &c. &c., are frequently understood in a different sense by different persons.
It has sometimes been said of political economy, that it approaches to the strict science of mathematics. But I fear it must be acknowledged, particularly since the great deviations which have lately taken place from the definitions and doctrines of Adam Smith, that it approaches more nearly to the sciences of morals and politics.