## Logic

CHAPTER 2

WHAT IS LOGIC?

2.1 THE STUDY OF LOGIC

2.2 THE CONCEPTS OF TRUTH AND INFERENCE

2.3 THE PROCESS OF INQUIRY

2.4 EXERCISES

2.5 ARGUMENT AS INQUIRY

2.6 EXERCISES

2.1 THE STUDY OF LOGIC

The story of "Modern" logic can start in a variety of places. Some hold that the best place to begin is in the work of Immanuel Kant, whose Critique of Pure Reason challenged philosophers to reconsider the place of logic in human understanding and whose theory of logic gave rise to competing approaches. In his Introduction to Logic (notes he used in teaching his regular logic class) Kant writes: "This science of the necessary laws of the understanding and reason in general, or - which is the same - of the mere form of thinking, we call logic " (Kant, 1974, 15 - 6).

For Kant, logic was the study of the process of thought in its ideal sense, not as it is practiced. "Some logicians," he says, "presuppose psychological principles in logic. But to bring such principles into logic is as absurd as taking morality from life" (1974, 16). The comparison with morality is important. For Kant, logic is not about how people happen to think, but rather what is necessary in order to think well. From this angle, logicians are therefore concerned in equal measure with finding necessary truths and providing a standard according to which the actual practice of people can be evaluated.

Kant's notion of logic as " the science of thought " historically led to a division in logic: one branch treating logic as the study of the operations of mind in the process of knowing and the other having to do with the conditions of knowledge independent of thought, that is, logic as concerned with truth. The former approach considered the process of thought as a matter of the ways in which ideas relate to one another. To come to the conclusion that an apple is on the table, one would first need to have certain ideas about apples and tables. Logic is concerned with the ways in which some of these ideas are related to certain other ideas so that, given ideas about tables and apples, the idea of an apple on the table follows. Further, according to this view, since humans only have access to ideas about the world (i.e., we never grasp apples and tables themselves but only ideas of them), logic is finally only about ideas - only about thought. Such a view of thinking could reveal (according to its advocates) general patterns of relations among ideas such that they could guarantee certain beliefs, but it also necessarily became a process of theorizing about how the mind, rather than the world, worked.

By the end of the 19th century, many argued that the concept that logic was strictly about the "laws of thought" was really a form of psychology. Since Kant rejected the consideration of logic in relation to particular experience, it was a form of psychology that had little to do with knowledge and truth as it was found in the rapidly developing fields of the physical sciences. To understand scientific knowledge, many logicians decided they should stop treating beliefs as a matter of mental relations and begin to understand thought in terms of the relations that made them true. Rather than being concerned with the laws of thought, logic should consider the laws of truth as they emerge in mathematics, geometry, and physics. Rather than analyzing the interaction of ideas in consciousness, these theorists wanted to understand the relation of claims independent of consciousness so that, given certain claims about the world, certain other claims correctly follow. In geometry or arithmetic, when given the truth of certain axioms, certain theorems follow by