How Paradoxes Result from a Bi-valued System of Logic

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How Paradoxes Result from a Bi-valued System of Logic

In this third installment of the series on differences between bi-valued logic and multi-valued logic, Aniruddha Singhal in this piece describes how all the paradoxes of science today, like the paradox of Shroedinger’s cat, can be resolved if they are seen in the framework of multi-valued system of logic, rather than the bi-valued system of logic. The author forcefully argues that the paradoxes do not represent a fault in reality, but a fault in human understanding. That is what we have to correct.

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Read the previous parts of the series here:

While in multi-valued logic systems, due to the shades of grey in truth value system, the probability of an argument to be true or false becomes zero. This lack of certainty makes people tolerant and less violent because they are not totally sure about the correctness of the premise they are told to fight for, like endless crusades and Jihads. The excluded middle enhances violence while inclusion of middle mitigates violence. That is why non-violence is cardinal principal of eastern religions.

Similar difficulties in scientific thinking are created by bivalued logic. Thus endless debates and confusion follow. For example, in quantum mechanics, the famous Schroedinger’s cat paradox illustrates such a problem which startled many great minds and confusion about it still exists.

The Schroedinger’s cat is an imaginary cat which is put inside a closed black box through which no information can pass. Along with the cat, the box contains a radioactive material whose probability of decay at the next time instant is 0.5. A Geiger counter is placed along with a phial of poison in the box. If the radioactive decay happens, the Geiger counter gets stimulated and the poison phial breaks which in turn kills the cat.

At this moment there is no information available to the experimenter who is looking at the box from outside. For this person, the cat is in an unexplainable state i.e. both dead and alive at a given instant before opening the box. This is a paradox for observer because the frame-work of yes-no logic does not provide him any answer. The state of such an imaginary cat cannot be described by binary logic. The cat is both dead and alive at the same time. The wave function of the cat collapse only when the box is opened and experimenter observes the cat to be either dead or alive.

It is surprising that quantum mechanics, which is at the bottom of the present day electronic technology works successfully, but we don’t understand what it is. This is because we want to understand it within our bi-valued mental framework. The idea of reducing the state of the cat into dead or alive is like fitting a shoe of size nine on a foot of size ten which will certainly make us uncomfortable.

To resolve such a confusing situation the great physicist Neil’s Bohr (1885-1962) had an intuition that there is a state between real and unreal and he expressed this in the following quote.

“Everything we call real is made of things that cannot be regarded as real”

Bohr implied that there are things which are not real but also cannot be called unreal. Unfortunately, no formal mathematical representation was available to him at that time to technically express such an intermediate state between real and unreal. That is why his ideas did not have much impact.

Even though the mathematics of complex numbers provides a way in disguise to deal with such an ambiguous situation, but it has never been interpreted in a trivalued way by mathematicians and philosophers. The great mathematician, philosopher and visionary Gottfried Wilhelm Leibniz (1646-1716) was able to see this trivalued connection of complex numbers with reality.

“Imaginary numbers are a fine and wonderful refuge of the divine spirit almost an amphibian between being and non-being.”

Interpretation of Reality without an amphibian state between being and non-being is bound to produce paradoxes. A paradox means that there is a mismatch between reality out there and our understanding of it inside our mind. Reality does not work to confirm our understanding of it. On the contrary, our understanding must be in tune with the mechanisms of Nature. Paradoxes exist in human mind, not in Nature. Thus, the only way to resolve a paradox is to correct our understanding in accordance with Reality. This is the essence of scientific method of experimentation.

Our understanding of Reality must be empirically validated by demonstrable and repeatable experiments in nature. If our understanding contradicts Reality then we must re-examine our own understanding of it, instead of labeling the incident as a paradox. By introducing a third logical state in the thought process it is possible to get rid of these paradoxes but if we insist on bivalued obsessions of our mind we are stuck with these unresolvable paradoxes.