Foundations Of Cognitive Science

All-Or-None Law

A crucial property of the action potential is that it is an all-or-none phenomenon, representing a nonlinear transformation of the summed graded potentials.  The neuron converts continuously varying inputs into a response that is either on (action potential generated) or off (action potential not generated).  This has been called the all-or-none law (Levitan & Kaczmarek, 1991).  “The all-or-none law guarantees that once an action potential is generated it is always full size, minimizing the possibility that information will be lost along the way” (Levitan & Kaczmarek, 1991, p. 43).  The all-or-none output of neurons is a nonlinear transformation of summed, continuously varying input, and is the reason that the brain can be described as digital in nature (von Neumann, 1958).

The all-or-none behavior of a neuron makes it logically equivalent to relays or switches.  This logical interpretation was exploited in an early mathematical account of the neural information processing (McCulloch & Pitts, 1943).  McCulloch and Pitts used the all-or-none law to justify describing neurons very abstractly as devices that made true or false logical assertions about input information.  "The all-or-none law of nervous activity is sufficient to ensure that the activity of any neuron may be represented as a proposition.  Physiological relations existing among nervous activities correspond, of course, to relations among the propositions; and the utility of the representation depends upon the identity of these relations with those of the logical propositions.  To each reaction of any neuron there is a corresponding assertion of a simple proposition." (McCulloch & Pitts, 1943).


  1. Levitan, I. B., & Kaczmarek, L. K. (1991). The Neuron: Cell And Molecular Biology. New York: Oxford University Press.
  2. McCulloch, W. S., & Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5, 115-133.
  3. von Neumann, J. (1958). The Computer And The Brain. New Haven, CN: Yale University Press.

(Added October 2010)