Reading notes: An Introduction to the Logic of Marxism by George Novack

An Introduction to the Logic of Marxism by George Novack

Lecture

II. The Limitations of Formal Logic

....In this second lecture we propose to uncover the limitations of formal logic and indicate how dialectics necessarily emerges from a critical examination of its fundamental ideas

....find out what the laws of formal logic are not: what features of reality they neglect and distort, and where their usefulness ends and their uselessness begins.

....acts of criticism and creation, negation and affirmation, go hand in hand as two sides of the same process.

....dual movement of destruction and creation occurs not only in the evolution of logic but in all processes. Every leap forward, every creative act, involves the destruction of outgrown and intolerably restrictive conditions.

law of identity

....A equals A? We discover that nothing in reality corresponds perfectly to the content of this proposition. On the contrary, we find that the opposite of this axiom is far closer to the truth. Wherever we encounter some really existing thing and examine its character, we find that A is never equal to A.

"....a more delicate scale always discloses a difference. "

....If, as they contend, the law of identity remains wholly true only so long as it is not applied, then it follows that the moment it is applied to any real thing, it becomes the source of error.

....the law of identity has a two-sided character. It is in itself both true and false. It holds true of things insofar as they can be regarded as fixed and immutable, or insofar as the amount of change in them can be disregarded or discounted as negligible. That is to say: the law of identity gives correct results only within certain limits. 

.... law of identity continually exceeds dialectical tolerance by becoming either more or less valid

....law of identity holds good for most of the ordinary acts of everyday life and thinking, but it must be replaced by more deep-going and complex laws where more complicated and long-drawn-out processes are involved.

....Thinking is essentially a process of intellectual production- and the limitations of the tools of thought can be overcome in the same manner. Whenever we strike a snag with the law of identity, we either have to resort to a different logical law or else we have to combine old laws in new ways in order to get at the truth. Here is where dialectical logic comes in. Just as we bring in a more developed machine or set of machines in industrial production, so, when we want more correct and exact results in intellectual production, we apply the more developed ideas of dialectics.

quantitative changes destroy the old and bring about a new quality

A becomes -A.

....We arrive then at this conclusion. While the law of identity correctly reflects certain features of reality, it either distorts or fails to reflect others. Moreover, the aspects which it falsifies and cannot express are far more pervasive and fundamental than those it more faithfully depicts.