Mathematical biophysics of abstraction and logical thinking

Developing further a recent suggestion of H. D. Landahl, equations are derived which give the probability for an individual to judge two stimulus patterns as similar or dissimilar. The possibility of experimental verification of those equations is discussed. Next, a mechanism is described which provided for abstraction by responding only to “essential” components of a stimulus pattern. Equations, verifiable in principle experimentally, are derived. Finally, a mechanism is suggested for logical inferences, and equations are derived which give the probability of making an error in a reasoning consisting of a chain of syllogisms, as well as the probability of being unable to complete the chain of reasoning at all.