How We Know #10: Logic

Chapters 6 and 7 are about logic -- theory and practice, respectively.

The three laws of logic are the law of identity, the law of non-contradiction, and the law of excluded middle. His more economical formulations of these in the same order are: Everything is something. A thing can’t be everything. A thing can’t be nothing.

The nature of man’s consciousness include two facts central to logic: (1) Perception is the base of all conceptual cognition. (2) Only a few distinguishable units can be held in one frame of awareness.

Context is important. “The contextual nature of knowledge reflects a metaphysical fact and as epistemological one.” Metaphysical: reality is an interconnected whole. Epistemological: human consciousness works by detecting similarities and differences (198).

Hierarchy pertains to a number of ways in which things exist in an order of dependency. There is a hierarchy of learning and one of inference. Regarding the latter, Quine is sharply criticized for his flippant dismissal of hierarchy.

The section The Spiral Process of Knowledge echoes Leonard Peikoff.

Logic is not concerned only with inference or the manipulation of symbols as often presented. It is the means of keeping conceptual cognition connected to reality. On to logical practice, it is often assumed that logic is only about inference, but logic exists for all conceptual functions subject to volitional control (213).

About logic and concepts, he gives rules for definitions, reformulating traditional negative ones in positive terms. The traditional one of stating the essential attributes of the concept’s referents becomes the rule of fundamentality.

He addresses several things to avoid such as misclassifying. “Carving nature at the joints – i.e. on the basis of fundamentals – provides the most unit-economical system of classification.”  As an example of misclassifying would be to divide all living organisms between "stripes" and "solids." Besides excluding organisms that are neither, it is non-essential and explains nothing else. He comments on Rand's Razor: concepts are not to be multiplied beyond necessity or integrated in disregard of necessity (230- 232). 

A proposition is “a grammatically structured combination of concepts to identify a subject by a process of measurement-inclusion.” Concepts are not properly described as true or false, but as valid or invalid. (239). 

Venturing beyond Ayn Rand he addresses non-referential propositions and the “fallacy of pure self-reference” (248-51).