Here, whether a given conclusion is deducible from or a consequence of given premises, or whether the argument from premises to conclusions is valid, is taken to depend only on their forms.
First, (deductive) logic has always had at its core a question equally relevant to philosophical dialectic and mathematical demonstration: What follows from what? Second, (formal) logic answers by pointing to and only to argument forms. But let us begin with the basics and note two points.
In the early 21st century, once one gets beyond the introductory level, it is customary to divide the field between mathematical and philosophical logic, each with subdivisions. Our concern is with what may be called, to distinguish it from other conceptions, formal, deductive logic. Historically there has been considerable variation in the understanding of the scope of the field of logic.
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