Home » I.M. Bochenski on the Concept of Formal Logic

Preliminary definition of the subject matter of the history of logic is hard to come by. For apart from ‘philosophy’ there is perhaps no name of a branch of knowledge that has been given so many meanings as ‘logic’. Sometimes the whole history of philosophy, and even knowledge in general, has been thus named, from metaphysics on the one hand, cf. Hegel, to aesthetics (‘logic of beauty’) on the other, with psychology, epistemology, mathematics etc. in between. With such a wide choice it is quite impossible to include in a history of logical problems all that has been termed ‘logic’ in the course of western thought. To do so would practically involve writing a general history of philosophy.

But it does not follow that the use of the name ‘logic’ must be quite arbitrary, for history provides several clues to guide a choice between its many meanings. This choice can be arrived at by the following stages.

1. First let us discard whatever most authors either expressly ascribe to some other discipline, or call ‘logic’ with the addition of an adjective, as for example epistemology, transcendental logic, ontology etc.

2. When we examine what remains, we find that there is one thinker who so distinctly marked out the basic problems of this residual domain that all later western inquirers trace their descent from him: Aristotle. Admittedly, in the course of centuries very many of these inquirers – among them even his principal pupil and successor Theophrastus – have altered Aristotelian positions and replaced them with others. But the essential problematic of their work was, so far as we know, in constant dependence in one way or another on that of Aristotle’s Organon. Consequently we shall denote as ‘logic’ primarily those problems which have developed from that problematic.

3. When we come to the post-Aristotelian history of logic, we can easily see that one part of the Organon has exercised the most decisive influence, namely the Prior Analytics. At some periods other parts too, such as the Topics or the Posterior Analytics, have indeed been keenly investigated and developed. But it is generally true of all periods marked by an active interest in the Organon that the problems mainly discussed are of the kind already to hand in the Prior Analytics. So the third step brings us to the point of describing as ‘logic’ in the stricture sense that kind of problematic presented in the Prior Analytics.

4. The Prior Analytics treats of the so-called syllogism, this being defined as a λογος in which if something is posited, something else necessarily follows. Moreover such λογοι are there treated as formulas which exhibit variables in place of words with constant meaning; an example is ‘B belongs to all A‘. The problem evidently, though not explicitly, presented by Aristotle in this epoch-making work, could be formulated as follows. What formulas of the prescribed type, when their variables are replaced by constants, yield conditional statements such that when the antecedent is accepted, the consequent must be admitted? Such formulas are called ‘logical sentences’. We shall accordingly treat sentences of this kind as a principal subject of logic.

5. Some logicians have limited themselves to the discovery, examination, and systematic ordering of logical theorems, e.g. many scholastic and mathematical logicians, as also Aristotle himself in the Prior Analytics. But logic so understood seems too narrowly conceived. For two kinds of problem naturally arise out of the theorems. First those about their nature – are they linguistic expressions, word-structures, psychical forms or functions, objective complexes? What does a logical law mean, what does a statement mean? These are problems which nowadays are dealt with in semiotics. Second, problems relevant to the question how logical laws can be correctly applied to practical scientific thought. These were dealt with by Aristotle himself, principally in the Posterior Analytics, and nowadays are the concern of general methodology. So semiotic and methodological problems are closely connected with logic; in practice they are always based on semiotics and completed in methodology. What remains over and above these two disciplines we shall call formal logic.

6. A complete history of the problems of logic must then have formal logic at its centre, but treat also of the development of problems of semiotics and methodology. Before all else it must put the question: what problems were in the past posited with reference to the formulation, assessment, and systematization of the laws of formal logic? Beyond that it must look for the sense in which these problems were understood by the various logicians of the past, and also attempt to answer the question of the application of these laws in scientific practice. We have now delimited our subject, and done so, as we think, in accordance with historical evidence.

But such a program has proved to be beyond accomplishment. Not only is our present knowledge of semiotic and methodological questions in the most important periods too fragmentary, but even where the material is sufficiently available, a thorough treatment would lead too far afield. Accordingly we have resolved to limit ourselves in the main to matters of purely formal logic, giving only incidental consideration to points from the other domains.

Thus the subject of this work is constituted by those problems which are relevant to the structure, interconnection and truth of sentences of formal logic (similar to the Aristotelian syllogism). Does it or does it not follow? And, why? How can one prove the validity of this or that sentence of formal logic? How define one or another logical constant, e.g. ‘or’, ‘and’, ‘if—then’, ‘every’ etc. Those are the questions of which the history will here be considered.

Ioseph Maria Bochenski, A History of Formal Logic

I.M. Bochenski’s History of Formal Logic presents a clear and systematic discussion of the major figures in the history of logic who have attended to problems in the above consideration, from antiquity to the early twentieth century, as well as a contrast between Western and Indian logic. We will use this text as a supplement in our upcoming Trivium: Art of Logic course (beginning May) which is available to all enrolled members.

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