This repetition of that which has been substantially stated before, brings us to the final consideration of the distinctive nature of different departments of Thought, as indicated by the Methods of Proof which respectively prevail in them; and hence as embodying either exact and definite _Knowledge_, or only varying degrees of _Probability_. We have already seen that in at least one sphere of intellectual activity we are able to start from the most basic and fundamental conceptions, from axiomatic truths so patent and universal that they cannot even be conceived of as being otherwise than as they are, and to proceed from them, by equally irresistible Inferences, to conclusions which are, from the nature of the human mind, inevitable. It is in the Mathematics, in which the Deductive Method is rightly operative, that this kind of Proof--Demonstration in the strict sense of the term--prevails. The various branches of Mathematics have therefore been appropriately denominated the _Exact_ Sciences, in contradistinction from those domains of Thought whose Laws or Principles are liable to be somewhat indefinite or uncertain; hence, called the _Inexact_ Sciences. Exact Science--in its largest sense, that which extends to all domains in which the proper Deductive Method has been or may hereafter be rightly employed--is therefore a _system or series of truths relating to the whole Universe, or to some department of it, consecutively and necessarily resulting from, and dependent upon, each other, in a definite chain or series; and resting primarily upon some fundamental truth or truths so simple and self-evident, that, when clearly stated, all men must, by the natural constitution of the human mind, perceive them and recognize them as true. Demonstration is the pointing out of the definite links in the chain or series by which we go from fundamental truths, clearly perceived and irresistible, up to the particular truth in question_. Thus far in the history of Science, Mathematics, as a whole, has ranked as the only Exact Science; being the only department of intellectual activity, all of whose Laws or Principles are established on a basis of _undeniable certainty_. If, however, theories of Cosmogony and considerations of Cosmography be excluded from the field of Astronomy, this Science consists almost wholly of the application of the Laws of Mathematics to the movements of the celestial bodies. Restricting Astronomy proper to this domain, where, as a _Science_, it strictly belongs, and setting aside its merely descriptive and conjectural features, as hardly an integral part of the Science itself, we have another Exact Science in addition to Mathematics.