Ever since the establishment of new logic (to be distinguished from the old fashion of Aristotelian Syllogism) in the late nineteenth century (thanks to Frege, Cantor, Boole and some others), and its development in the first half of the twentieth century (thanks to Peano, Russell, Zermelo, Hilbert, Tarski, Gödel, Turing, Church, etc.), logic has had a strong and significant impact on the investigation of contemporary philosophy, in particular the so-called Anglo-American philosophy or analytic philosophy. In the heyday of logical positivism (from the late 1920 to1950), it was widely taken for granted that philosophical investigation should take logic as the guiding principle, or even the tribunal for the philosophical debates. This is partly because one of the primary concerns of Frege’s establishment of new logic is to establish a much more solid foundation of mathematics in that all mathematical propositions can be reformulated in a language suitable for logic and all mathematical truths can be proved in such a logical system. (This is why, sometimes, the alleged new logic is sometimes referred to as symbolic logic or mathematical logic.) Another main reason can be also traced back to Frege, which has something to do with the so-called linguistic turn. Frege’s original idea is to deal with the meaning of a singular term such as the numeral ‘0’ (for the number 0) by asking the sense of a sentence/proposition in which the very term occurs, rather than simply asking what it is to which the term refers. To generalize this approach, it is claimed that all philosophical issues/problems can be and should be dealt with by analysing the construction of the related sentences and their meanings. Perhaps it is this approach which paved a way to the flourishing movement of analytic philosophy in the 20th century. As a result, the so-called contemporary philosophy has almost dominated by the philosophy of language, together with a general scope of the study of logic.
After the 1950’s, the impact of logic on the investigation of philosophy becomes more and more prominent, thanks to Wittgenstein, Carnap, Quine, and Kripke. More and more distinguished logicians have devoted themselves to a large number of philosophical issues. It has then become a natural inclination for philosophers and logicians of this type to pay their attention not only to the construction of formal logical systems (including the language in use, the establishment of appropriate semantics and the formalization of deductive systems), but also to its philosophical significance and impact on traditional philosophical issues.
Yet, no sharp boundary could be drawn between the scopes of these two aspects of logical study. Surprisingly, with the profound and ramified interaction amongst logic and some notable philosophical issues, it is realized that perhaps we need to re-examine the nature of logic and its scope, including the well-known, and perhaps widely accepted, logical concepts, such as propositions, logical consequence, truth, the meaning of logical constants, modality, etc. A serious study of the philosophical aspect of logic is nowadays entitled the philosophy of logic.
In a strict sense, the primary concern of philosophy of logic is with a more rigorous investigation into the nature of logical concepts, their philosophical implication and the application of logic to philosophical questions/problems. An introductory course for such study thus focuses on a variety of logical concepts (including syntactic and semantic), and related philosophical presuppositions/significance, both metaphysically and epistemologic- ally. It should be noted that the main concern of philosophy of logic is not a study of logic on its own, nor a study about logic. Rather, the title ‘the philosophy of logic’ is used merely to serve as a unifying label to signify a field of philosophical investigation, which at the core involves a family of logical concepts, and a variety of topics related to certain logical concepts, which have been the centre of traditional philosophical disputes, especially in metaphysics and epistemology, such as the notion of a proposition, truths, modality, vagueness, propositional attitudes, . . . , etc.
Interestingly, these topics are closely interdependent and interrelated in that brief discussions on issues concerning any one of these topics require understanding, to a certain level, of some others. Moreover, with respect to each topic, there are always a great number of different views; and none has ever enjoyed a dominant role. As a consequence, it has been a really tough job for students to grasp what these concepts are supposed to mean and what the genuine problems surrounding these topics are.
It is noteworthy that sometimes the aforementioned concepts and topics can be found in the scope of another branch of logical/philosophical study, known as philosophical logic. Although the boundary line between philosophy of logic and philosophical logic is to a certain extent not always clear. However, the following contrast seems to be widely accepted:
• Philosophy of logic is devoted to examining the scope and nature of logic, and the investigation with conceptual analysis with regard to the philosophical issues arising in logic, such as the notion of proposition, the meaning of logical connectives, logical consequence, quantification, to mention a few.
• Philosophical logic is concerned with the application of formal logical techniques, especially the so-called non-classical logic, to metaphysical/epistemological issues/problems, such as reference, identity, predication, existence, modality, and vagueness, etc.
[Still, one may find some topics in common such as truth, modality, vagueness, etc.]
An introductory course, wherein related topics are briefly mentioned, discussed, and dealt with, would be helpful. Of course, no such a course could exhaust all topics involved, let alone the depth of such an enquiry. In this course we shall only examine a variety of logical concepts, as shown in the contents, which are involved in the construction of logic at the elementary level, and their philosophical implications.