Assumptions Vs Facts: 3 most common logical fallacies


Irrespective of how serious we feel we are, we commit numerous logical fallacies throughout our daily life. A logical fallacy is an assumption which is made as the base of an argument and is asserted strongly as being a fact. All it does it waste your time & energy and bring down the level of the debate or inquiry. Following are the most common of them.

  • Appeal to purity: “Too pure to commit any wrong” is a small illustration of this logical fallacy. It could apply to a person, a group or even an ideology, which ‘you assume’ to be the epitome of purity, ethics or morals. Here it is ‘your assumption’ which at first has to be proved to be true.


  • Appeal to authority: This is just another shade of the aforesaid fallacy. This takes into consideration the professional status or general social status of the person being discussed or the person speaking. “He is a scientist, so whatever he says about science or nature, has to be true in all cases” is an illustration. Second illustration could be “I am a lawyer, how can I be wrong about the interpretation of this legal provision”. In both the cases, it is the ideas being produced by the scientist & the lawyer which are to be examined, irrespective of the good or bad record of professional performance of both of them.


  • Fallacy of proportion/constitution: “Out of numerous parts of something, if one part of it is of a particular nature, so all parts of it must be of that very particular nature” is an illustration. The assumption is that all parts are equal in all respects. This illustration can also apply for proving something or someone as being wholly good or wholly bad.


If you value your time and energy, if you value your own self, if you respect your own self, then you must guard your intellectual integrity and must not present your assumptions as facts, that simply means you must not lie.

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My ideal world

Everyone has his or her ideal world, differing on one’s emphasis about what is the most essential element to one’s life. The thing on which I put the greatest emphasis is abstract, yet rational and is probably the real centre of our existence and growth.

My ideal world is a world where ideas are put at the centre of the whole view, irrespective of who produces them and how weird they may sound at that point. In that world, there wouldn’t be any fanclubs. There would be no allegiance to any person, group or ideology. There would be a true seeking of what is true, irrespective of how adverse would it be to one’s own agreed-upon opinions.

In that world, people wouldn’t be in a hurry to judge ideas, let alone judging people & situations. There would be an agreement on considering it a sin to jump to conclusions, and it would be the highest virtue to closely observe and analyse ideas without biases. No one would be rebuked for questioning the agreed-upon ideas some day. Where the lust for great ideas would never die, that is my ideal world.

Why hope is logical?


No matter how mindful are you of your present, the future is always a mystery. You never know what is going to happen in the next moment. The reason for this could be that for every one event, there are many influencing factors, some of which aren’t known to us. So it’s all about uncertainty. Some people could take it to the negative side & find even ‘life’ to be just on the edge of the tip of a mountain facing a deadly trench. This point of view could lead to mental disasters. One could lose much interest in life itself.

But there is another side of this uncertainty, that is the question of ‘what if something good happens?’. When it is true that we do not know what is going to happen in the next moment, why not think about there being a chance of something good happening? Both the views, the negative & this positive, are based on uncertainty. But there is a difference of effect.

When we feel to be on the edge of the tip of a mountain facing a deadly trench, life starts seeming as ‘not worth investing effort’. One becomes way too passive. Even though some bad doesn’t happen to him, his mind would make it appear as one. His creativity would drop down, and he being devoid of any good ideas, would eventually lead a miserable life.

On the other hand, with hope, he wouldn’t find life so worthless. This would consequently keep his mind open to new ideas & new opportunities, eventually making his life better than what it was previously. This is how our minds, brains, whatever you call them, are known to work. Negativity blocks our mind, blocking the probability of a better life. Whereas, positivism opens it. This is the logic behind hope.

We all utterly lack in the knowledge of the future, so better not assert about what’s going to happen, just await a surprise, a positive surprise. Do it because it is logical.

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Aryabhatta Vs. Pingala: Who was the first in knowing zero as a separate number?

Aryabhatta is usually credited to have invented the number zero, at the least in India. One of the arguments for it is that he knew the place value system of the 10s, 100s, 1000s, etc. But this argument takes the use of zero back to 1500-1200 BCE. In the white Yajurveda (17.2), this very system is mentioned upto 12 zeros. It is Brahmagupta’s book on math, Brahmasphutasiddhanta (kuttukadhyaya, 30), where we see an obvious mention of zero (shunya) being used as a number to describe the difference between, for example, +2 & -2. This is back in 7th century CE.

I wanted to find a similar text where zero or shunya had been used as a specific number or digit. I then found one book, dated around 200-100 BCE, called the Chhanda-Sutra or Chhanda-Shastra, written by Pingala. It is a book on sanskrit prosody. It describes various precise calculations regarding precise poetic meters. In its sutra numbers 28 & 29 of chapter 8, Pingala mentions a certain calculation for which he uses two numbers as place markers. The numbers he uses are two (dvi) & zero (shunya). His formula is based on halving a number. For example, if you have to halve number 6, you should write ‘2’ next to it signifying that it has been divided into ‘two’ parts. Then minus 3 from 6 (its half), and you get 3. As 3 is an odd number, and as the author suggests to subtract 1 from it to make it even, it is not halved yet. Hence ‘o’ is written next to it signifying that number 3 has been divided into zero parts (no parts). The next calculation is not related to this discussion.

I first had a doubt about the usage of the word ‘shunya’ in the sutras. But the single most point that it has been used along with the number ‘two’, signifying into how many parts is a number divided (2 for two parts, 0 for no parts), I am pretty sure that zero has been regarded as a separate number by Pingala back in the 2nd or 1st century BCE. It might not be necessarily true that Pingala invented the number ‘shunya’. But it is possible that he knew it as a separate number.

My conversation with Mr. Dinanath Batra, the man who got Wendy Doniger’s book banned in India

Mr. Dinanath Batra is the man who got indologist Wendy Doniger’s book ‘The Hindus- An Alternative History’ banned in India on the accusation of it projecting hinduism as being filled with sexual elements. Last year I got a chance to see him live in Chandigarh. After his speech, he was to answer questions from the public. As was asked, I also wrote my question on a paper. Two other men sitting next to Mr. Batra filtered out my letter (probably due to consequent embarrassment), and it never reached Mr. Batra. So I sent him the same question as a letter by post. Following is the letter.

“Respected Batra ji

I am Satyan, a post grad student of Sanskrit at the Panjab University, Chandigarh. I was there at your seminar at the Law Bhavan, Chandigarh on January 17. It was the first time I saw you speaking live. After you spoke, there was a question-answer session. I too sent my question written on a slip. It did not reach you as it was filtered out by Mr. Kuthiala and Mr. K.S. Arya. The question is important as it relates to your social audit of books. Here is the question (originally in Hindi):

You got Wendy Doniger’s book banned due to the presence of sexually explicit content in it. In the Vamana Purana(chapter 6) Shiva has been depicted as a lustful person and his ‘linga’ has been depicted as phallus quite clearly. In the Bhagawata Purana (canto 8, chapter 12) the story of Shiva running lustfully after Mohini and his consequent ejaculation is mentioned. Also there (canto 10, chapter 29, verses 45-46) is the story of Krishna’s rasa-leela in which he is depicted as doing something which is sexual in nature. In the Garuda Purana (chapter 109, verses 27 onward) there is a very sexually explicit and disrespectful mention of women. What do you think about such Hindu scriptures?

I had seen your full interview with Abhinandan Sekhri on youtube. You had mentioned your aversion to the mention of Shiva linga as Shiva’s phallus. Also you had mentioned that the cover of Wendy Doniger’s book has a picture of Krishna’s feet on Gopis’ breasts (mentioned as a wish of Gopis in Bhagawata Purana, canto 10, chapter 31 which is fulfilled in chapter 32). I was wondering that the things you mentioned as being bad, have been mentioned in the Hindu scriptures alone.

I request you to throw light on this issue. I was deprived of your views on my question at the Law Bhavan. I hope I receive your views duly this time.”

And I got his reply. He did not at all talk about the scripture references I had given. The crux of his reply was that we should forget those images (in the scriptures) that move us into sensuality/sexuality & remember those parts which make us introverts.

Anyone can verify those scripture references. All I want to show is the bias he holds for the Hindu scriptures. Even though some Hindu scriptures do contain some sexual element, he does not want to give the same reaction (getting banned) towards them.

Original reply by Mr. Batra:

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How to deal with sacrilege?


To a religious person, not only god but also anything that acts as god’s symbol or command is sacred. He makes sure that every such symbol and scripture is protected against any disrespect. This is the point where any religious person would lose his cool. And so, this is the point which is of the utmost utility to the political groups. These political groups or parties use multiple ways and means to divert people’s attention from the core issues, for example poverty, education, health, etc. They know that as long as these issues survive, they’ll survive, and as soon as these issues are solved, they’ll lose their existence.

So in order to keep these issues alive, they can either stop addressing it, or they can turn a blind eye towards the common man, or else they may use the best tool possible, that is religion. Religion is a life-saver for these groups. They take any incident or issue and try to find even an atom of religious-discrimination or sacrilege in it. If they cannot find one, they may create one, a bigger one, a more painful one. The guaranteed consequence of a sacrilege is that people get carried away very easily. Every one of them becomes the guardian of their religion, its symbols and scriptures.

How religious people react to such an event decides how successful the miscreants have been. The miscreants want people to be carried away, so that their attention could be diverted from the core issues. This time in Punjab, some religious protests led to traffic jams. What does it mean? It means people walked hand-in-hand with the miscreants as they helped them achieve their goal, that is unrest and diversion of attention from the most important issues. So it’s no use separating those protestors from the miscreants.

So how to deal with sacrilege in a smart way? Do not give a damn. Yes, that’s it. Next time such a thing happens anywhere, do not give your precious time & effort to it. Let the miscreants know that they have failed in creating any form of unrest and any diversion of attention. Let everything run smooth as if nothing of such nature has happened. Remember, it is the responsibility of the religious people to free their religion from political usage.

Going a bit into philosophy, ask yourselves, are you really a steadfast believer in your religion or not? Ask yourselves that is your religion so weak that it could be disturbed by such meagre incidents like those of sacrilege? Remember that you appear as a practical result of your religion and the god you believe in. The weaker you behave, the weaker your religion and your god appears. Stop adding fuel to the fire created for political purposes. Once the political groups know for sure that you cannot be carried away by such means, they’ll stop using religion for their narrow purposes.

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The big bang of the Rigveda


We’ve all heard about the Big Bang Theory, not the comedy show, but the other one which is about the beginning of this universe. Scientists estimate a primordial explosion to have taken place inside a bubble, and they call that explosion as the Big Bang. It is said that the Belgian priest Georges Lemaître is the founder of the Big Bang Theory. So this theory has its origin in the 19-20th century AD.

The Rigveda is till now the oldest literature of the Indian civilisation. It dates back to more than 1800 BCE. Rigveda has many hymns describing how the universe came into being. I happened to read the most unpopular one, a hymn composed by Laukya Bṛhaspati and/or Aditi Dākṣāyaṇī. It is the 72nd hymn in the 10th book of the Rigveda.

To my surprise, in its second verse, it clearly speaks of a bang like happening. Here is my translation of it:

“Like a blacksmith (karmāra iva), the protector of expansion (brahmaṇaspatiḥ), completely blew/blasted the births (/birthplaces) of the natural forces [into flames] (etā samadhamat). In the ancient era (pūrvye yuge) of the natural forces (devānāṃ), manifest was born (sadajāyata) from unmanifest (asataḥ).” 

(brahmaṇaspatiretā saṃ karmāra ivādhamat. devānāṃ pūrvye yuge asataḥ sadajāyata.)

I chose to translate the word ‘deva’ as ‘natural force’ because in the Rigveda ‘deva’ doesn’t always seem to translate as ‘god’. The Rigvedic people worshipped air, fire, earth, rain, the force behind rain, etc. 

Look at the imagination, the poet describes the ‘force’ behind the big bang as being like a blacksmith, the surface is kind of heated and then he blows/blasts it. And then he/she says that in the ancient era of the natural forces, manifest was born from unmanifest. There is heat & there is a blast and that too in the births or as I think  the poet means, in the birthplaces of the natural forces.

Another interesting part is that the force to which the big bang is attributed is brahmaṇaspati or the protector of ‘expansion’. Brahma means that which expands (brahmaṇaḥ = of brahma), pati means protector. A force of expansion has been said to have done the blast like act.

So near about 1800 BCE, or even earlier, there was a poet, who imagined that the beginning of this universe happened in a bang like manner. The confidence of the poet’s imagination reflects in the first verse which I’ve translated as:

“In detail do we speak about the origin of the natural forces, so that in the future, in the praises being sung, one could see them.”

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Criminalisation Of Shurpanakha – Was she really that bad? Was Ram so wise?


Being born in a Hindu family, it is not uncommon to be influenced by the Hindu mythology. Even though not most of us read the actual scriptures talking of those myths originally, we have made conclusions regarding who is the hero and who is the villain. Throughout my childhood, I was told that Ram and Lakshman were heroes. I trusted the readily available opinions because it doesn’t take much of one’s energy doing that.

Talking of Ram, we are told that he was at the top of the ‘best men list’, why so? Ramayan says so. Now I didn’t enquire about the verse or the chapter which said so. I simply took it as it is “Ram is Maryada Purushottam”. The Shurpanakha incident, as everybody knows is very popular ‘cause it is from there that Ravan, the villain enters into the story.

I happened to read the original Ramayan composed by Valmiki. In the Aranya Kand (the forest book), I read the whole incident on Shurpanakha. One shocking information I got was that not only the nose, even the ears of Shurpanakha were chopped off by Lakshman. As far as I remember and know, nobody has ever talked about the ears.

Now why did Lakshman do this? Shurpanakha enters the forest, sees Ram and asks him to marry her as she suits him more than Sita does. Ram tells her that he can’t marry her, but the ‘unmarried’ Lakshman can. Now wait! Lakshman is single? Didn’t he marry Urmila? Then in the next shlok, Ram again says that Lakshman is unmarried. Shurpanakha asks Lakshman to marry her, to which he says “as I’m just a servant to Ram and Sita, how would you feel if you’re called a servant’s wife?” So he tells her to go to Ram again as he’s the most suitable groom for her. Shurpanakha gets frustrated and zeroes in on Sita as her single enemy because both Ram and Lakshman are saying her ‘no’ indirectly due to the presence of Sita. Shurpanakha declares to eat up Sita and then moves towards her just when Lakshman chops off her ears and nose.

Obviously Shurpanakha had insulted Sita to get more scores, but tossing her here and there doesn’t seem a noble behaviour. Why did Ram tell her to ask Lakshman to marry her? Why didn’t he say a simple ‘no’? Also why did Lakshman again toss her back toward Ram? Is saying a simple ‘no’ too difficult? Couldn’t Lakshman just push her some other side while she walked toward Sita? Haven’t we all heard about how powerful their arms were? Was chopping her ears and nose off so inevitable? Which brother would sit back easy while his sister faces such humiliation for such a reason?

While giving orders to Lakshman to move toward Shurpanakha, Ram specifically tells him to ‘disfigure’ her. The order could have been about protecting Sita and not about disfiguring a potentially threatening being. Let me make it clear that I am not making all this up. All that I am talking about is written in the Valmiki Ramayan which is taken to be the source of the actual story of Ram. It is much more important to note that even though the author Valmiki is sure to make Ram a hero & Ravan a villain, he writes down such an incident which would cast doubts on Ram’s wit.

The author’s bias clearly appears when, after Khar & Dushan try in vain to avenge Shurpanakha’s humiliation, she goes up to Ravan & praises Ram of letting her go alive. Shurpanakha also calls Lakshman an intelligent man. Then Shurpanakha is shown to praise Sita and ask Ravan to marry her. Such a saint would she have been, that after such an adverse incident, Shurpanakha is praising not just Ram and Lakshman, but also Sita.

Talking of Sita’s abduction, Valmiki Ramayan shows Ravan and Sita having a full debate. Ravan insists on the incompetence of Ram who had put such a graceful & worthy lady as Sita in a forest. After the debate is over, Ravan ‘forcefully’ takes Sita to Lanka. In Lanka, Ravan keeps Sita in his renowned garden Ashok-Vatika & is all polite with Sita. In the chapter where he asks her to marry him, he is even shown saying that he would massage Sita’s two feet with his heads and that he is her obedient servant.

In the following chapters, Ravan keeps trying to convince Sita to marry him. Ravan is shown to be within good limits during his correspondence with Sita. Even after Sita replies him with harsh words, he says that even though she is worth slaying, he won’t kill her. He gives a two-month deadline at the completion of which Sita should either marry Ravan or be killed.

The story, though revered throughout the Hindu community, shows the bias of the author. Why would Shurpanakha praise Ram, Lakshman and Sita after bearing such humiliation? Couldn’t she simply ask Ravan to avenge her humiliation? She is instead shown asking Ravan to marry Sita. If Shurpanakha had asked Ravan to avenge her humiliation, he could have attacked Ram and Lakshman in the forest alone, at a time when the brothers had no army of theirs at all.

The loophole of the story, as it seems, is twofold. First is that Ram has to be projected as a hero and Ravan as a villain. So no matter what each of them does, the story shall be tilted in such a way. The second loophole is putting a silent blame on women. First it was Kaikeyi who asked Dashrath to order Ram to be sent to the forest. After that Shurpanakha asked Ravan to marry Sita, and he starts the procedures to do so. Then Ravan comes as a disguised saint at Ram’s house in the forest and even though he praises Sita in an explicit manner (praising her breasts and hips), Sita doesn’t suspect his sainthood at all and asks him to come and be seated (there is no mention of Lakshman-Rekha in Valmiki Ramayan), which then leads to her abduction.

None of us knows about what the original story was. But reading the renowned ‘original’ account of Valmiki Ramayan, it seems that the story has been tilted on one side. It is the Shurpanakha’s incident of disfiguring, after which Ravan enters the scene. Just imagine if Ram could have said a simple ‘no’ to Shurpanakha and not toss her here and there, the story could have been different. It seems that for justifying Shurpanakha’s incident, the following story has been tilted.

It seems quite logical that the abduction of Sita was to bring Ram to his knees to avenge the humiliation Shurpanakha had faced. The thought of marrying Sita may have come later in Ravan’s mind. If lust was on his mind, he could have done anything with Sita, as she was at his mercy. Why did he give her a deadline of two months then? Even though Valmiki has tried his best to make Ravan look a villain, he too couldn’t help giving some hints about his decency.

The questions then arise: was Shurpanakha really so criminal? Was Lakshman’s act to disfigure her so wise? Couldn’t a simple ‘no’ avoid the whole rivalry between Ram and Ravan and save a few more lives at the least? I would call this incident and the stand people usually take regarding Shurpanakha, as her criminalisation to justify the direction of Ram and the action of Lakshman.

If any doubt regarding Shurpanakha’s story arises in your mind while reading this, kindly read the 17th and 18th chapters of Valmiki Ramayan’s Aranya Kand. What better if you could read the whole of Aranya Kand & Sundar Kand.

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What does Rigveda say on its origin? Divine or human?


There is a lot of debate about whether the Vedas are a divine or human creation. One school of thought opines that the Vedas came into existence with the creation of this universe (god-made), while the others say that Vedas are man-made. To enquire better into the subject, I decided to look into the Vedas, specifically Ṛgveda (the foremost Veda) to see what does it have to say about the creation of the Vedic hymns. I found certain hymns directly pointing to the human creation of the Ṛgvedic hymns. The hymns are:

1. navaṃ nu stomaṃ agnaye divaḥ śyenāya jījanaṃ. vasvaḥ kuvid vanāti yaḥ. (ṛṣi vasiṣṭhaḥ) [Ṛgveda 7.15.4] Here it is said that ‘I create a new hymn’. The verb used to denote ‘creation’ is ‘jījanaṃ’ which is translated by Sāyaṇa as ‘janayāmi’ meaning ‘I create’. Here a new hymn has been created for Agni. The composer of this mantra is Sage Vasiṣṭha.

2. athā somasya prayatī yuvābhyāṃ indrāgnī stomaṃ janayāmi navyam. (ṛṣi kutsaḥ) [Ṛgveda 1.109.2] Here it is clearly said that ‘I am creating a new hymn for indrāgnī’. And here the verb ‘janayāmi’ (I make or I create) has been directly used. The composer of this mantra is Sage Kutsa.

3. imā hi tvā matayaḥ stomataṣṭā indra havante sakhyaṃ juṣāṇāḥ. (ṛṣi viśvāmitraḥ) [Ṛgveda 3.43.2] In this hymn, Sāyaṇa has translated ‘matayaḥ’ as ‘hymns’ and the word ‘stomataṣṭā’ straightforwardly means the ‘hymns created by the creators of hymns’. The composer of this mantra is Sage Viśvāmitra.

4. ete dyumnebhir viśvamātiranta mantraṃ ye vāraṃ naryā atakṣan. (ṛṣi vasiṣṭhaḥ)  [Ṛgveda 7.7.6] In this hymn the verb used in relation to hymns is ‘atakṣan’ which means ‘created or perfected or carved’ (3rd person plural). Sāyaṇa translates ‘naryā’ as ‘manuṣyāḥ’. The composer of this mantra is Sage Vasiṣṭha.

5. ṛṣe mantrakṛtāṃ stomaiḥ kaśyapodvardhyangiraḥ. (ṛṣi kaśyapaḥ mārīcaḥ) [Ṛgveda 9.114.2] This hymn breaks the base of the divine-creation myth of the Vedic hymns. Here an adjective has been used for the Ṛṣis or sages that is ‘mantrakṛt’ which directly means ‘makers of the mantra’. Although in the explanation of this hymn Sāyaṇa translates the word ‘ṛṣi’ as ‘seer of the mantra’ (sūktadraṣṭā). But here’s the point, even if we keep in mind the poetic meter used here, if the poet really meant ‘seer of the hymns’ then he could have used the word ‘mantradṛṣ’ (dṛṣ = seer, mantra=hymn). So any deviation is unnecessary. The composer of this mantra is Sage Kaśyapa Mārīca.

Sāyaṇa or Sāyaṇācārya as he is regarded, is one of the main authorities in the field of the explanation of the Vedic hymns (bhāṣya). These hymns are directly from the Ṛgveda. The words are clear. Still the protagonists of the divinity of the Vedas might use the last card that Vedic words have many many meanings. This proposition can be refuted by just one fact that there is solid linguistic evidence that the Vedic language was a spoken language of a wide area, so such a highly ambiguous language couldn’t have served the purpose of communication. Also that all natural languages have some element of ambiguity, but that doesn’t so much hinder the process of successful communication.

Last but not the least, let us give our Ṛṣis or poets their due credit for composing such beautiful rhythmic hymns. If we take God or a supreme being to be the creator of Vedic hymns, then it would seem that the creator of the whole world is begging from the Vedic gods for a full ripe age, for gifts, for success, etc. For me it is enough for pride that back in the day, our ancestors had made this huge compilation of various hymns of various poets (including a few female poets). As it is the Vedic hymns that themselves refute the theory of divine origin of the Vedas, so no further third party ideas need to be entertained.

Why I am now an agnostic: A response to irrational certainties of atheism & theism

Though they may not like it, but I am putting the theist X and atheist Y in one box. I find them similar, asserting their opinions with unparalleled certainty. One says ‘god made this universe’ while Y says ‘god did not’. They are so sure about their conclusions as if they had massive amounts of data to start with. To attribute the origin of the universe to a supernatural being, X must’ve studied this universe precisely and massively. The atheist Y dismissed the idea of a supernatural being because of what? Because he actually knew how the universe is and how it works, so that he could ascertain its origin being whatsoever. But did both X and Y really know what the fundamental reality is? Do they even ‘know’ how this perceived reality works?

Both X and Y think they know stuff and so they are in a position to go far into the past, pierce through the layers of the perceived reality and take a stand on their conclusions. But what about the limits of human perception? The people studying neurology and biology have come across the fact that to say ‘my senses give me the true picture of reality’ is dubious. We don’t even know if the image being constructed by our brains is really a true reflection of the outside reality, let alone the fundamental reality and that too about the origin of the universe.

To say that ‘I perceive reality’ and provide as a proof the testimonies of masses is actually an ‘appeal to popularity’ logical fallacy (which can also prove that god exists). The long list of cognitive biases we unconsciously use is a proof that we are fallible. To accept or reject a supernatural entity, is going way too far. We’ve not even known completely about the natural world and the forces of nature yet, what to say of the supernatural. That ego, that I can know everything no matter what, may lead one to cook stories up.

To me, this fallibility has made me a bit humble. There is a limit to my knowledge of truth. The fact is that even after forsaking belief in a god, I’ve not put myself into any kind of a jeopardy. But I am not an atheist anymore, I am not at the extremes of certainty, certainty about the fundamental reality, in front of which we’re probably not even subatomic particles. I am an agnostic. I don’t even ‘know’ by myself about what actually happens in my phone when I click a picture from it, let alone ascertaining the happenings of the fundamental reality, taking my umwelt as the fundamental reality and say ‘no supernatural entity exists’. I suspend my judgement as a rational response to such a puzzle and my limits against solving it.