§ 1. Provisional Definitions
Mill opens the first section of the introduction by reporting that there is a wide variety of proposed definitions of logic (as well as for ethics and jurisprudence). He then observes:
This diversity is no so much an evil to be complained of, as an inevitable and in some degree a proper result of the imperfect state of those sciences. It is not expected that there should be agreement about the definition of anything, until there is agreement about the thing itself. (p. 3)This means that definitions laid out at the outset have to be provisional:
[I]n the case of so complex an aggregation of particulars as are comprehended in anything which can be called a science, the definition we set out with is seldom that which a more extensive knowledge of the subject show to be the most appropriate. Until we know the particulars themselves, we cannot fix upon the most compact mode of circumscribing them by a general definition. (p. 4)The provisional definitions Mill has in mind are intended, then, to indicate "the scope of our inquiries", and so, the goal of the introduction would appear to be laying out the boundaries of what falls under the scope of logic in particular.
§ 2. The Art and Science of Reasoning?
Mill approvingly cites Archbishop Whately's definition of logic as "the Science, as well as the Art, of reasoning; meaning by the former term, the analysis of the mental process which takes place whenever we reason, and by the latter, the rules, grounded on that analysis, for conducting the process correctly" (p. 4). In the remainder of the section, Mill goes on to say that while that some people limit the application of "Reasoning" to syllogizing, there is a broader use, which he will follow, on which reasoning has to do with any sort of inferring whatsoever (which means that induction is included, as well as geometric demonstrations). Perhaps the most interesting aspect of the discussion of this definition of logic is Mill's tangential claim about the relationship of knowledge to action:
Art necessarily presupposes knowledge; art, in any but its infant state, presupposes a scientific knowledge: and if every art does not bear the name of a science, it is only because several sciences are often necessary to form the groundwork of a single art. So complicated are the conditions which govern our practical agency, that to enable one thing to be done, it is often requisite to know the nature and properties of many things. (p. 4, my emphasis)The view that knowledge is prerequisite to action is hardly unorthodox. I take it that this outlook clashes with elements of pragmatism, or with, for instance, some background assumptions of Alva Nöe's enactive account of perception. That Mill has this view, then, isn't the interesting part, so much as the fact that it is stated so straightforwardly in this passage. At any rate, Mill next turns to the worry that this definition of logic is too narrow.
§ 3. The Art and Science of Pursuing Truth?
It seems that one point of section 3 is to establish that the scope of logic includes, beyond the science and rules of inference, some treatment of terms and propositions. Mill observes that scholastic treatments of logic typically treat terms and propositions, not simply arguments, and then goes on to note:
[A] man is is often called a great logician, or a man of powerful logic, not for the accuracy of his deductions, but for the extent of his command over the premises; because the the general propositions required for explaining a difficulty or refuting a sophism, copiously and promptly occur to him: because, in short, his knowledge, besides being ample, is well under his command for argumentative use. (p. 5-6)This leads him to consider the expanded definition of logic as "the science which treats of of the operations of the human understanding in the pursuit of truth." The definition would, Mill says, take logic to include naming, classification, definition, etc.
Mill also makes sure to address the worry that this definition of logic is going to subsume all treatment of language, given the expansive definition which includes definition, naming, and so on. He responds to the worry by observing that those operations, besides being used in the pursuit of truth, serve other purposes as well:
For instance, that of imparting our knowledge to others. But viewed with regard to this purpose, they have never been considered as within the province of the logician. The sole object of logic is the guidance of one's own thoughts: the communication of those thoughts to others fals under the consideration of Rhetoric, in the large sense in which that art was conceived by the ancient; or of the still more extensive art of Education. (p. 6)
There is a remaining worry, which we will begin with next time: the worry that our definition is still too liberal because it includes sense-perception and intuition, which are not to be included in logic proper.