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. The whole body of our authoritative and irrevocably determinate intellectual acquisitions lies, therefore, at the present time, so far as is commonly known, within the range of Mathematics, Astronomy, and Physics. These are in strictness the only _Sciences_ which we possess; and the only domains in which _knowledge_, in the proper sense of the term, is attainable. In passing their boundaries, we leave the regions of positive _certitude_, and come into the domain where Conjecture, varying from the strongest presumption to mere plausibility, is the highest proof. Laws or Principles are yet undiscovered there, and in their place we find Generalizations--Suppositive or Proximate Laws--which are in process of proof, or already established by such evidence as the Inductive Method can array, and which carry the conviction of their correctness with varying degrees of force, to larger or smaller classes of investigators.