Can logic lead to unreasonable beliefs or fallacy?

(Pic credits- Bill Watterson’s Calvin Hobbes)

Can logic lead to ungrounded beliefs or fallacies? This may be an important question given that these days we base most of our scientific reasonings in logical arguments. Can logic be faulty? Isn’t logic same as truth?

Logic has naturally being associated with truth in all history. Whether one studies the Greek philosophy which tries to make sense of the world by applying logical reasoning, or advanced mathematics like Algebra, or the computational and AI algorithms of today- logic is mostly associated with truth. Rightly so? I studied Electronics Science in my undergrad in India. I clearly remember studying about “truth tables” when learning the functioning of logic gates like AND, OR, NAND etc. Below is what an AND truth table looks like. The AND function behaves like a multiplication operator where the value of the two inputs A and B is multiplied and the output C is generated. What I want to emphasise on is that these logic gates had truth tables implying, logic being naturally associated with truth.

There was another topic I learnt in high school mathematics that I clearly remember as pure logic- the topic of Mathematical induction.

Mathematical Induction

Mathematical induction is a method for proving that a statement P(n) is true for every natural number n, that is, that the infinitely many cases P(0),P(1),P(2),P(3),…  all hold. This is done by first proving a simple case, then also showing that if we assume the claim is true for a given case, then the next case is also true. A proof by induction consists of two cases. The first, the base case, proves the statement for n=0 without assuming any knowledge of other cases. The second case, the induction step, proves that if the statement holds for any given case n=k, then it must also hold for the next case n=k+1. These two steps establish that the statement holds for every natural number n. The base case with n=0, or n=1, and/or possibly with any fixed natural number n=N, establishing the truth of the statement for all natural numbers n≥N.

So if the logic is correct and astute, we are basically able to prove what is true for n=N or n=N+1, is also true for all natural numbers >N as well.

Where logic fails

Unfortunately, without understanding above in the right way, we often use logic erroneously in our day to day lives mostly “guesstimating” the outcomes and simply making assumptions. Logic should also be used in a limited way in certain fields only, especially the scientific or mathematical ones, where logic really finds its truthful applications. The concept of logic actually emanates from space and waves and applying extrapolation or assuming things in these context, does not hurt. For example, space is expandable by nature. One can observe that on a day to day basis or more deeply by practising concentration meditations (Jhanas). Hence, applying logic in the physical context makes sense. For example, we can assume that space exists in the universe and hence we are able to send our space shuttles to explore the cosmos. Similarly, waves exist in space, and if we see a sinusoidal wave moving across vacuum or air, we can extrapolate and make assumptions about its wave equation or space time trajectory. If we follow scientific principles, we wouldn’t be that wrong.

The problem happens when we start applying logic to make guesses about how others would think or act in a particular circumstance by extrapolating from before or making assumptions about how they feel etc. Mind is not a logical entity at all and does not work according to mathematical logic or induction. Or at least if it does, it adheres to very different logical principles. Most of us, take thoughts for granted and have no idea how overthinking can do enormous harm. People in scientific fields too often make the mistake of guessing or extrapolating in thought- which is often a result of habit patterns formed due to problem solving by deep thinking– very common in scientific fields. Unfortunately, mind forms a habit of logical extrapolation and starts applying that everywhere simply because such a pattern of thinking is available to us- we do this daily at work.

For example-

While at work, Sheila solves problems in molecular electronics by logical thinking. She has recently discovered that molecules can self-assemble themselves over Silicon or other semiconductor surface to form monolayers. She then  extrapolates in her mind how such monolayer can be grown to a substantial size (area). And then wonders if it can be used as an electronic insulator or diode of sorts or perform a logic gate operation. The thoughts of insulator or diode etc are thoughts of association. Her mind tries to associate the insulating quality of monolayers with insulating operations in semiconductor physics and comes up with a new idea. This idea seems valid and can now be tested in the laboratory for truth validation.

Above chain of thought is a logical chain of thought and has an element of “mental associations”. However one must know that even though such an idea came to her mind, it may be far from truth and will only become a reality if it is tested in a laboratory which will be a challenging job. Every day in the scientific field, people come up with at least a million theories, and only a few handful of them see their way into a scientific paper and even less than them are accepted as working theories. Rest of them go to the bin. It is so hard to validate a logical theory. And this is essentially the gap between logic and reality. Just because we can think, assume, extrapolate, guess or logically theorise something, it does not make it the truth. Reality has way too many factors and possibilities and has all capacity to look any logic faulty.

Applying logic in scientific fields vs applying logic to mental phenomena

So one has to be very careful of habits, especially mental. Just because we are used to logical thinking, it should not be applied to all fields. In fact, other than physical or mathematical fields, logic rarely works. For example, the same Sheila has a meeting with her boss and her boss makes a comment about her work- “Your work was fine but there were some issues, please solve these by end of day today”. Now again in her mind, using her logical and extrapolating abilities, she extrapolates, makes assumptions, guesses and interprets about what her boss meant-“He said fine. Does fine mean not good? Did he mean I am not good enough?” etc and goes on. Here, the new thoughts that are getting generated in her mind are not helpful at all and will soon dip her into a low mood. In this case also, just like above (molecular electronics expt), the thoughts need to be tested and validated for truth. The only way they can be truly validated is by seeking clarification from the boss. Only that can help her know the truth of what he really meant. Again, he may hide the truth or she may again over-interpret and this can go on. Besides, can we seek clarification over every such conversation? No, right? So, in the end, it is best to take things as they are and not add any interpretations, assumptions, extrapolations etc.

It is important to note that while thinking endlessly in any case, can cause distress to any mind;  thinking endlessly about a scientific topic may not be as harmful as thinking endlessly about what someone meant or intended. Because in such a case, there is no limit to what and how the mind can think or guess and the impact of that is only born by us. Often mind assumes a lot about others’ intentions and starts generating fear, hatred inside as a reaction to those assumptions and one can go on like this for years. Similarly, one can wrongly attribute success to oneself and not the team due to a biased view towards oneself and thus, develop delusional beliefs of personal grandeur. These kinds of mental tendencies often end up in a disorder of sorts and eventually creates a lot of suffering. Hence, it is extremely important to not think too much on day to day matters or at least not wonder about what other people mean or intend.

Buddha’s teachings on how the mind really works

Dependent Origination is the foundational teaching of the Buddha. In fact all Buddhas teach dependent origination –Paticcasamuppada. It is the knowledge of how suffering arises in us as a chain of causation (conditioned phenomena) and how the suffering can cease to arise by following the wheel of Dhamma. By understanding this, we also come to the understanding that there is actually no self in the universe (Anatta).

A Vipassana Research Institute article to understand better if you are inclined to go deeper.

According to this doctrine, twelve links form the wheel of becoming-

Forward Order

Dependent on ignorance, reaction (conditioning) arises;
Dependent on reaction (conditioning), consciousness arises;
Dependent on consciousness, mind-body arise;
Dependent on mind-body, the six senses arise;
Dependent on the six senses, contact arises;
Dependent on contact, sensation arises;
Dependent on sensation craving and aversion arise ;
Dependent on craving and aversion, clinging arises ;
Dependent on clinging, the process of becoming arises ;
Dependent on the process of becoming, birth arises;
Dependent on the base of birth, ageing and death arise,
together with sorrow, lamentation, physical and mental sufferings and tribulations.

Thus arises this entire mass of suffering.

Reverse Order

With the complete eradication and cessation of ignorance, reaction (conditioning) ceases;
with the cessation of reaction (conditioning), consciousness ceases;
with the cessation of consciousness, mind-body cease;
with the cessation of mind-body, the six senses cease;
with the cessation of the six senses, contact ceases;
with the cessation of contact, sensation ceases;
with the cessation of sensation, craving and aversion cease;
with the cessation of craving and aversion, clinging ceases;
with the cessation of clinging, the process of becoming ceases;
with the cessation of the process of becoming, birth ceases;
with the cessation of birth, ageing and death cease, together
with sorrow, lamentation, physical and mental sufferings and tribulations.

Thus this entire mass of suffering ceases.

Explanation–

The main observation of the Buddha was that there is a cycle of causation and there is a link in this chain where we can break the cycle of ignorance. In the chain, the below 3 links were important-

Phass paccaya Vedana (Contact leads to sensation)

Vedana Paccaya tanha, (Sensation leads to craving)

Tanha paccaya Upadana (Craving leads to attachment)

We keep making sensory contact with the universe through our eyes, ears, taste, smell, touch. This cannot be helped because we live in Samsaara – the sensory universe. Whenever there is sensory contact sensations are generated on the body (vibrations like light, sound, touch etc). When mind perceives sensations on the body- one generates craving (or aversion) because of a prior habit pattern of “judgment” of categorizing things into “good” or “bad”. Due to craving (or aversion), clinging happens. This cycle continues and we remain in misery.

And then Buddha understood that there was only one thing we could do in this whole chain of causation to cut from the cycle– not react to the sensations. Instead of rolling in the sensations (believing in the stories of images, thoughts, feelings etc), we could choose to not react. This could be done by developing objectivity in our minds- Anapana meditation, a practice of focusing attention on breath could achieve that. Concentration improves and so does objectivity. When objectivity increases one can switch from being a “thinker” or a “feeler”, to a “non intentional observer”. This allow nonjudgmental observation of our sensations- Vipassana meditation. Thus we are able to break through the cycle of attachment and come out of our misery. What the nonjudgmental observation leads us to is the realisation that there is actually no self within us (Anatta), just conditioned phenomena acting on their own accord- as explained in Paticcasamuppada.

This was Buddha’s principle teachings.

Link to – Vipassana Meditation

The Atomic Truth- as taught by Buddha-

In simple words, Buddha found out that it is the bodily sensations in the form of thoughts and feelings that we are reacting to. We never really react to a circumstance or a situation. When our senses contact the outside world (through forms or vibrations- people, objects, sounds, speech, touch, taste, smell) based on our awareness levels – we form a perception. The perception has judgment and immediately labels the situation or person as good or bad. If the judgment is “good”, our sensory system generates craving, if it is “bad” it generates aversion. The craving or aversion sensations flow as feelings and corresponding thoughts in our body and mind. And we inherently (by habit) react to them by wanting them more or rejecting them. So it is our perception of the sensations getting generated inside us that is really causing misery or suffering. If we are objective observers of reality, our perception would be whole- there would be no judgment or labeling. And there would be no reactive feelings of craving or aversion. And hence, no suffering. So basically we have to shift our thinking towards an objective mind that observes and does not judge. This is what would lead to a highly focused, present and tranquil mind. Such a mind is attentive and observant to the present reality and does not guess, assume, extrapolate, believe. Hence, such a mind is strongly rooted in reality and is free from all fallacy.