When, therefore, we emerge from the domains of Mathematics, Astronomy, and Physics, we are leaving the field of _positive assurance_, of _undeniable_ truth, and entering the realms where opinion, conjecture, and variable degrees of certainty prevail. _The Facts of Observation may be, indeed, as plain here as elsewhere and as firmly established. But the conclusions drawn from them, the Scientific Principles assumed to be established, may be erroneous or defective, and the power of prevision, the great test of Scientific accuracy, is proportionally wanting._ Derived, as we have hitherto seen these conclusions to be, from Phenomena, on the supposition that a given range of Observation will secure all the essential Principles which appertain to the _whole_ of the Phenomena included in the range, we can never be _entirely sure_ that our basis of Facts is sufficient for our purpose, and hence the _possibility_ of error always exists.
It is not to be understood, therefore, that first or observational _Facts_ are not rightly to be known in other departments of investigation than Mathematics, Astronomy, and Physics; but that Laws, Principles, or Generalizations which _relate_ Facts and serve as instruments for penetrating into the deeper arcana of Nature, cannot be precisely, accurately, and certainly _known_, in their relations and belongings, until we are able to establish their connection with the lowest, most fundamental, and self-evident truths, and in this manner become competent to advance step by step from undeniable first truths to those equally undeniable. In Mathematics, in Astronomy, and in Physics, we are able to do this. We _know_ the Laws or Principles of these Sciences, therefore, so far as we have developed the Sciences themselves. We know the relations of the various Laws within the range of each Science, and the relations of the different Sciences with each other. We can advance, within their boundaries, from the simplest and most positive verities, such as the whole is equal to all its parts--a self-evident truth, which it is impossible to conceive as being otherwise than as here stated--up to the most intricate ulterior Facts of the universe, by Inferences which are as irresistible to the mind as the axioms with which we started. In no other domains of Thought can this be done by any methods now in vogue. In no other realms, therefore, are complete precision and infallibility attainable. It is this which constitutes the peculiar character of these three Sciences, and distinguishes them radically from all others.