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Contemporary logical theory is marked by an apparent paradox. There is general agreement as to its proximate subject-matter. With respect to this proximate subject-matter no period shows a more confident advance. Its ultimate subject-matter, on the other hand, is involved in controversies which show little sign of abating. Proximate subject-matter is the domain of the relations of propositions to one another, such as affirmation-negation, inclusion -exclusion, particular-general, etc. No one doubts that the relations expressed by such words as is) is-not, if-then, only (none but), and, Of, some-all, belong to the subject-matter of logic in a way so distinctive as to mark off a special field. When, however, it is asked how and why the matters designated by these terms form the subject-matter of logic, dissension takes the place of consensus. Do they stand for pure forms, forms that have independent subsistence , or are the forms in question forms of subject-matter? If the latter, what is that of which they are forms, and what happens when subject-matter takes on logical form? How and why? These are questions of what I called the ultimate subject-matter oflogic; and about this subject-matter controversy is rife. Uncertainty about this question does not prevent valuable work in the field of proximate subject-matter. But the more developed this field becomes, the more pressing is the question as to what it is all about. Moreover, it is not true that there is complete agreement in the more limited field. On the contrary, in some important matters, there is conflict even here; and there is a possibility (which will be shown in the sequel to be actualized) that the uncertainty and diversity that exists in the limited field is a reflection of the unsettled state of opinion about ultimate subject-matter. To illustrate the existing uncertainty as to ultimate subject-matter, it is only necessary to enumerate some of the diverse conceptions about the nature of logic that now stand over against one another. It is said, for example, that logic is the science of necessary laws of thought, and that it is the theory of ordered relations-relations which are wholly independent of thought. There are at least three views The Problem of Logical Subject-Matter From Logic: The Theory of Inquiry (1938) 157 held as to the nature of these latter relations: They are held (1) to constitute a realm of pure possibilities as such, where pure means independent of actuality; (2) to be ultimate invariant relations forming the order of nature; and (3) to constitute the rational structure of the universe. In the latter status, while independent of human thought, they are said to embody the rational structure of the universe which is reproduced in part by human reason. There is also the view that logic is concerned with processes of inference by which knowledge , especially scientific knowledge, is attained . Of late, another conception of its subjectmatter has appeared upon the scene. Logic is said to be concerned with the formal structure of language as a system of symbols. And even here there is division. Upon one view, logic is the theory of transformation of linguistic expressions , the criterion of transformation being identity of syntactical forms. According to another view, the symbolic system, which is the subject-matter of logic, is a universal algebra of existence. In any case, as regards ultimate subjectmatter , logic is a branch of philosophic theory; so that different views of its subject-matter are expressions of different ultimate philosophies, while logical conclusions are used in turn to support the underlying philosophies. In view of the fact that philosophizing must satisfy logical requirements there is something in this fact that should at least provoke curiosity; conceivably it affects unfavorably the autonomy of logical theory On the face of the matter, it does not seem fitting that logical theory should be determined by philosophical realism or idealism , rationalism or empiricism, dualism or monism, atomistic or organic metaphysics. Yet even when writers on logic do not express their philosophic prepossessions, analysis discloses a connection. In some cases conceptions borrowed from one or another philosophic system are openly laid down as foundations of logic and even of mathematics. This list of diverse views given above is put down by way of illustration. It is not exhaustive , but it suffices to justify one more endeavor to deal with proximate subject-matter in terms of a theory concerning the ulti158...

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