Natural Logic

ISSN 2567-6458, 19.August 2022 – 19 August 2022
Author: Gerd Doeben-Henisch


This text is part of the subject COMMON SCIENCE as Sustainable Applied Empirical Theory, besides ENGINEERING, in a SOCIETY. It is a preliminary version, which is intended to become part of a book.

Natural Logic

The foregoing comparison of derivations in a ‘boolean logic setting’ and in an ‘everyday language setting’ shows a remarkable difference: while the inventors of boolean logic focused on formal expressions only by cutting of all ‘natural meaning’, the ‘inventor’ of natural language — the whole biosphere! — created ‘normal language’ to be a ‘medium’ to encode the ‘internal states’of the sending brain into expressions which can be transmitted to other brains which as ‘receivers’ should be able to ‘decode’ these expressions into the internal states of the receiving brains. Thus ‘expressions as such’ are of nearly no help for the survival of brains. Survival needs cooperation between different brains and the only chance to enable such cooperation is communication of internal states by ‘encoded expressions’.

From this follows that ‘natural logic’ has to follow completely different patterns than ‘boolean logic’. Let us look to the example again.

We continue using the before introduced abbreviations A := ‘Die Ampel zeigt rot’ etc.

In figure 3 a simple ‘sequence of states’ has been outlined where the usual sequence of showing ‘red’, ‘orange’, and green is assumed. In certain types of cultures this is a typical everyday situation.

Thus we can assume a ‘state S1’ where the traffic light is showing ‘red’. This can be represented by the expression:


All participants know, that this expressions describes a real situation where the ‘learned meaning of this expression’ is in accordance with the actual ‘perceptions’ which are assumed to be in ‘accordance’ with some ‘real situation outside the brain and outside the body’. In that case the ‘speaker’ and ‘hearer’ of expression ‘A’ agree – under normal circumstances — that the ‘meaning’ associated with the expression ‘A’ is ‘true’. If the perception would provide ‘another concrete construct’ triggered by a traffic light showing ‘orange’ instead of ‘red’ then the learned meaning of expression ‘A’ would not match. In that mismatch situation speaker and hearer would agree – under normal circumstances — that the ‘meaning’ associated with the expression ‘A’ is ‘not true’, and this is a case of being classified as ‘false’.

Now, what could in such a situation be a ‘derivation’ in the context of a ‘natural logic’?

As has been mentioned before the ‘abstract structures’ of the meaning space are ‘dynamic constructions’ allocating many different properties of the perceived real world into ‘internal (neural = cognitive) clusters’ representing these properties within these structures. Thus, the abstract structure ‘traffic light’ is a structure possessing the typical collection of three different lights with their typical pattern of sequential activations.[19] A brain which has built up such abstract structures can use these to produce ‘forecasts’ by ‘reading its learned structures’!

Assume that the perceived situation is that state called S1 which can be described with the expression ‘A’:

S1 = {A}

From the learned abstract structure ‘traffic light’ the brain could ‘derive the rule’


IF there is a situation S which has a property described by an expressions ‘A’, THEN it can happen in a follow up state S’, that the expression ‘A’ does not any more match’, but expression ‘B’.

If we make the set of derivation rules X equal to the set comprising rule R1 with X = {R1} then we can built the following natural logic derivation:

S  X S’

with S ={A} and S’={B}.

This kind of derivation is radically different to a boolean logic derivation:

(i) While boolean logic can only derive something which is ‘already true’, natural logic can derive something which ‘could become true in the future’ by assuming, that the ‘learned meaning’ is ‘true’.

(ii) While boolean logic can only use derivation rules based on operations with expressions only, natural logic can exploit the vast amount of ‘learned meaning structures’ owned by an individual brain and which is partially ‘shared’ with other brains.

Based on (ii) a brain is always capable to ‘construct its own derivation rules’ simply by ‘exploiting’ its learned abstract (dynamical) structures. Thus every brain can ‘invent’ new types of logic only by using its ‘learned experience’.

From this follows directly that human actors which want to ‘think explicitly about some possible future’ should abandon boolean logic and instead should exercise to exploit their learned knowledge.

In a historical perspective it is very strange that the most advanced complex system of the whole known universe — the biosphere, and as part of it the homo sapiens population — decided to use as logic a system, which abandons all this fantastic inventions of more than 3.5 billion (10^9) years to select a system of sign operations, which is more than pure and of not too much help for survival. The construction of programmable machines (usually called computers) by using boolean logic has enabled an interesting tool, but only if we use this as ‘part of biological intelligence’.

— draft version —