“The map is not the territory.” —Alfred Korzybski

Ordinary human language is based on concepts derived from perception that are, by necessity of neuronal activation logic, fuzzy-edged and equivocal. Formal language is grounded only in idealized imaginings and can therefore be hard-edged and univocal.

In Philosophical Investigations, Wittgenstein rejected the idea of precise, univocal, necessary and sufficient definitions of concepts in favor of Familienähnlichkeit (“family resemblances”).

Embodied cognition is the reason this is the case, specifically the neuronal basis of the concept. Human understanding is based on concepts which are instantiated in the brain in neural networks in which the activation of a neuron corresponding to an individual concept occurs through the activation of some critical threshold of its synapses. The combinations of synaptic inputs that may cause firing are not some simple AND/OR/NOT logic network which reproduces a univocal response and so do not rigidly map onto clear and distinct ideas. There are at least the following mismatches that generate the fuzziness of Familienähnlichkeit:

  • Multitude of synaptic firings which may activate a “conceptual” neuron within an individual human
  • Neurons rewire over time to shift the activation criteria within an individual human
  • “Conceptual” neurons must also be mapped to activate “linguistic” neurons to generate related words needed for communication
  • Different humans will have slightly different neuronal wiring for both “conceptual” and “linguistic” neurons

This is why the philosopher’s dream (since at least Leibniz, if not earlier) of an ideal language that avoids all ambiguity fails.

Formal language, like mathematics and logic, on the other hand, does not seem to share this fuzziness. Certainly, mathematical and logical concepts must also be instantiated in the same neural network, so why are they not subject to the same ambiguity? There must be a simplicity to their activation patterns that is so consistent within and among individuals that they are rigidly transferable from object to object and subject to subject.

Given that fundamental difference between ordinary and formal language, we must be careful to treat them distinctly, lest we be led astray be the clarity and certainty of the latter when making assertions about the former. This is one of the reasons “‘is’ applies only to the a priori“.

“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” —Albert Einstein, Sidelights on Relativity, 1922.