§ 4. Logic Concerns Inference, not Intuition
Mill had been concerned that "the art and science of Reasoning" was too narrow, and that "the art and science of the pursuit of truth" too broad. His middle route between the two is to distinguish between truths known "directly", and those known "through the medium of other truths". The suggestion is that logic is concerned with inferences from intuitive (i.e. directly known) truths, and not with the intuitive truths themselves. Importantly, this will not limit our attention to deductive inference, since it was already flagged that Mill intends to include inductive reasoning, as well as syllogistic under the scope of inquiry.
Most interesting in this section is Mill's discussion of the certainty of directly known truths, and related caveat:
Whatever is known to us by consciousness, is known beyond possibility of question. What one sees or feels, whether bodily or mentally, one cannot but be sure that one sees or feels. No science is required for the purpose of establishing such truths; no rules of art can render our knowledge of them more certain than it is in itself. There is no logic for this portion of our knowledge.
But we may fancy that we see or feel what we in reality infer. A truth, or supposed truth, which is really the result of a very rapid inference, may seem to be apprehended intuitively. It has long been agreed by thinkers of the most opposite schools, that this mistake is actually made in so familiar an instance as that of the eyesight. (p. 7)
Mill goes on to discuss our knowledge of distance through sight. Also worth noting in this section is the claim that it is "almost universally allowed that the existence of matter or of spirit, of space or of time, is in its nature unsusceptible of being proved" (p. 9). He ends the section by declaring that "logic is not the science of Belief, but the science of Proof, or Evidence."
§ 5. Logic and Other Sciences
Mill moves on to consider the "authority of logic" with regard to other sciences, concluding that, because most of our knowledge is inferred, "the greatest portion of our knowledge...is amenable to the authority of logic" (p. 9). He is careful though to distinguish logic from knowledge::
Logic, however, is not the same thing with knowledge, though the field of logic is coextensive with the field of knowledge. Logic is the common judge and arbiter of all particular investigations. It does not undertake to find evidence, but to determine whether it has been found. Logic neither observes, nor invents, nor discovers; but judges. (p. 10)
Mill's example is the appearances found to accompany a violent death. Logic, he says, isn't in the business of telling the surgeon which appearances those are (that is the business of observation and testimony). "Logic sits in judgment on the sufficiency of that observation and experience to justify his rules, and on the sufficiency of his rules to justify his conduct." It appears, then, that Mill thinks logic also bears on what we would term "practical reasoning", though this is the first mention I've noticed of anything like that.
Also important to note: Mill does not seem to think that the fact that this science is grounded on the descriptive science of our actual human mental operations of inferring stops logic from being "the science of science itself."
§ 6. Logic is Useful
The main thrust of this section is that, with the rare exception of certain savants, most people benefit from knowledge of the principles governing good inference, rather than simply following our unreflectively acquired or natural inclinations.
§ 7. Logic Defined
We are finally told (provisionally) what logic is:
Logic, then, is the science of the operations of the understanding which are subservient to the estimation of evidence: both the process itself of advancing from known truths to unknown, and all other intellectual operations in so far as auxiliary to this. (p. 12)
We are also informed of what this amounts to, in terms of a goal for the project of Mill's System:
Our object, then, will be, to attempt a correct analysis of the intellectual process called Reasoning or Inference, and of such other mental operations as are intended to facilitate this: as well as, on the foundation of this analysis, and pari passu with it, to bring together or frame a set of rules or canons for testing the sufficiency of any given evidence to prove any given proposition. (p. 12)
Also worth noting in this section, is Mill's claim that he will be treating certain operations/processes as relative primitives (i.e. as not subject to analysis for his purposes), without intending to claim that they are themselves primitive. His comparison is to "analytical chemistry", of which he says the results "are not the less valuable, though it should be discovered that all which we now call simple substances are really compounds." (p. 13). In other words, there may be more analysis left to do, but we can make progress in developing this science without entering into those analyses.
I have no doubt that I have overlooked some important and interesting elements of the discussion Mill provides in the Introduction (and might well return to some of this later), but for next week, I'll be on to the beginning of book one, "Of Names and Propositions".