Reason, as the term itself shows, implies _ratio_, estimate, proportion, or admeasurement; and in all the instances of reasoning that can be adduced, this interpretation will apply in the strictest sense. But _ratio_, estimate, &c. involve numbers, by which they can alone be characterised or defined. Thus, by way of illustration, the estimate for a building implies the number of the different materials, with their _cost_, which is the number of pounds, shillings, and pence; also the number of requisite workmen to be employed for such time, or number of weeks, days, &c. at a certain stipend: admeasurement also consists of numbers, whether it be employed on solids, fluids, or designate the succession of our perceptions, called time[17]: and ratio or proportion is equally the creature of numbers. In a preceding part of these contributions, the importance of numbers has been considered, and a confident belief expressed that no animal is capable of numeration; and that the comprehension of addition and subtraction, the basis of all calculation is exclusively the province of the human intellect. This subject, however, requires a more extended investigation; and the research would doubtless reward the toil of the inquirer. It is generally acknowledged, that arithmetic, or the combination and separation of numbers, is the purest and most certain system of reasoning, and liable, when properly conducted, to no difference of opinion; because the meaning of number is definite and universally agreed on, there being no nation that affixes a different value to the units, which are the elements of all ulterior numerative progression; and although, in different languages, they are called by different names, as [Greek: Deka], _decem_, _dieci_, _dix_,--_taihun_, _tyn_, _zehn_, _tien_, _ten_, yet they have an identical meaning, and denominate the same thing; and notwithstanding the Roman and Arabic symbols are of different character, they represent the same number, whether we employ X or 10. It is owing to this identity of meaning, that the reasoning in numbers is subject to no diversity of opinion. The names of those things which have an actual existence, and can be submitted to the inquisition of our senses, or are capable of being analysed, are subject to comparatively little error, when we reason concerning them, because their character is defined by observation and experiment: but we have terms to designate that which cannot immediately be submitted to the analytic operations of our senses, and which has no palpable existence; and from the undefined nature of these, the greatest discord and confusion have prevailed when we reason concerning them; as the terms, humanity, charity, benevolence, living principle, organisation, materialism, political expediency, taste, liberty, legitimacy, and a thousand besides.