What are the views considered "false convictions", and why are they false?

The following quotes are extracts from the Pali Deeganikaya Brahmajāla Sutta: The All-embracing Net of Views.

Speculations about the Past (Pubbantakappika)

"There are, bhikkhus, other dhammas, deep, difficult to see, difficult to understand, peaceful and sublime, beyond the sphere of reasoning, subtle, comprehensible only to the wise, which the Tathāgata, having realized for himself with direct knowledge, propounds to others; and it is concerning these that those who would rightly praise the Tathāgata in accordance with reality would speak. And what are these dhammas?

"There are, bhikkhus, some recluses and brahmins who are speculators about the past, who hold settled views about the past, and who on eighteen grounds assert various conceptual theorems referring to the past. And owing to what, with reference to what, do these honorable recluses and brahmins frame their speculations?

1. Eternalism (Sassatavāda): Views 1–4
2. Partial-Eternalism (Ekaccasassatavāda): Views 5–8
3. Doctrines of the Finitude and Infinity of the World (Antānantavāda): Views 9–12
4. Doctrines of Endless Equivocation (Amarāvikkhepavāda): Views 13–16

"In the fourth case, owing to what, with reference to what, are some honorable recluses and brahmins endless equivocators, resorting to evasive statements and to endless equivocation?

"Herein, bhikkhus, a certain recluse or a brahmin is dull and stupid. Due to his dullness and stupidity, when he is questioned about this or that point, he resorts to evasive statements and to endless equivocation: 'If you ask me whether there is a world beyond — if I thought there is another world, I would declare that there is. But I do not take it thus, nor do I take it in that way, nor do I take it in some other way. I do not say that it is not, nor do I say that is neither this nor that.'

"Similarly, when asked any of the following questions, he resorts to the same evasive statements and to endless equivocation:

A.
• 2. Is there no world beyond?
• 3. Is it that there both is and is not a world beyond?
• 4. Is it that there neither is nor is not a world beyond?
B.
• 1. Are there beings spontaneously reborn?
• 2. Are there no beings spontaneously reborn?
• 3. Is it that there both are and are not beings spontaneously reborn?
• 4. Is it that there neither are nor are not beings spontaneously reborn?
C.
• 1. Is there fruit and result of good and bad action?
• 2. Is there no fruit and result of good and bad action?
• 3. Is it that there both is and is not fruit and result of good and bad action?
• 4. Is it that there neither is nor is not fruit and result of good and bad action?
D.
• 1.Does the Tathāgata exist after death?
• 2.Does the Tathāgata not exist after death?
• 3.Does the Tathāgata both exist and not exist after death?
• 4.Does the Tathāgata neither exist nor not exist after death?

"This bhikkhus, is the fourth case.

"It is on these four grounds, bhikkhus, that those recluses and brahmins who are endless equivocators resort to evasive statements and to endless equivocation when questioned about this or that point. Whatever recluses or brahmins there may be who resort to evasive statements and to endless equivocation, all of them do so on these four grounds or on a certain one of them. Outside of these there is none.

"This, bhikkhus, the Tathāgata understands... and it is concerning these that those who would rightly praise the Tathāgata in accordance with reality would speak.

5. Doctrines of Fortuitous Origination (Adhiccasamuppannavāda): Views 17–18

Speculations about the Future (Aparantakappika)

"There are, bhikkhus, some recluses and brahmins who are speculators about the future, who hold settled views about the future, and who on forty-four grounds assert various conceptual theorems referring to the future. And owing to what, with reference to what, do these honorable recluses and brahmins frame their speculations?

1. Doctrines of Percipient Immortality (Saññīvāda): Views 19–34

"There are, bhikkhus, some recluses and brahmins who maintain a doctrine of percipient immortality[10] and who on sixteen grounds proclaim the self to survive percipient after death. And owing to what, with reference to what, do these honorable recluses and brahmins proclaim their views?

"They proclaim: 'The self is immutable after death, percipient, and:

A.
• 1. material
• 2. immaterial
• 3. both material and immaterial
• 4. neither material nor immaterial
B.
• 1. finite
• 2. infinite
• 3. both finite and infinite
• 4. neither finite nor infinite
C.
• 1. of uniform perception
• 2. of diversified perception
• 3. of limited perception
• 4. of boundless perception
D.
• 1. exclusively happy
• 2. exclusively miserable
• 3. both happy and miserable
• 4. neither happy nor miserable.'

"It is on these sixteen grounds, bhikkhus, that those recluses and brahmins who maintain a doctrine of percipient immortality proclaim the self to survive percipient after death. Whatever recluses or brahmins maintain a doctrine of percipient immortality, all of them do so on these sixteen grounds or on a certain one of them. Outside of these there is none.
"This, bhikkhus, the Tathāgata understand... and it is concerning these that those who would rightly praise the Tathāgata in accordance with reality would speak.

2. Doctrines of Non-percipient Immortality (Asaññīvāda): Views 35–42
3. Doctrines of Neither Percipient Nor Non-Percipient Immortality (N'evasaññī-nāsaññīvāda): Views 43–50
4. Annihilationism (Ucchedavāda): Views 51–57
5. Doctrines of Nibbāna Here and Now (Diṭṭhadhammanibbānavāda): Views 58–62

This teaching on the 62 (false) convictions is from the Brahmajala Sutta (in the Pali Digha Nikaya -- adapted herein from Walshe).

At the end of this Sutta the Buddha declares that this teaching may be known by the following names:

• The Net of Advantage (Attha = Artha)
• The Net of Dhamma
• The Supreme Net
• The Net of Views
• The Incomparable Victory in Battle

In his glossary entry on the “sixty-two convictions” in the Vimalakirti Sutra, Thurman states:

These ... consist of all views other than the "right view" of selflessness. All sixty-two fall into either one of the two categories known as the "two extremisms": "eternalism" (sashvatavada) and "nihilism" (ucchedavada).

[However,] for Vimalakirti’s take on this subject, see his exchange with Manjushri below.

Vimalakirti’s Take on the 62 Convictions (From p. 44 of Thurman’s translation):

Mañjushri: Householder, where should emptiness be sought?

Vimalakirti: Mañjushri, emptiness should be sought among the sixty-two convictions.

Mañjushri: Where should the sixty-two convictions be sought?
Vimalakirti: They should be sought in the liberation of the Tathagatas. Mañjushri: Where should the liberation of the Tathagatas be sought? Vimalakirti: It should be sought in the prime mental activity of all living beings.

Mañjushri, you ask me why I am without servants, but all Maras and opponents are my servants. Why? The Maras advocate this life of birth and death, and the bodhisattva does not avoid life. The heterodox opponents advocate convictions, and the bodhisattva is not troubled by convictions. Therefore, all Maras and opponents are my servants.

Buddha's conclusion (From Wikipedia)

"The Tathagata knows these sixty-two views. He also knows the dhamma which surpasses them. Knowing that dhamma, he does not view it in the wrong way. Since he does not view it in the wrong way, he realizes by himself the extinction of defilements (i.e., greed, anger, and ignorance of the Four Ariya Truths).

Buddha finally concludes the exposition of these 'wrong' beliefs by stating that these (62) beliefs, if they are believed, will certainly cause agitations and cravings. It implies that the beliefs come to conclusion due to the inability to see the truth, as they are seized by craving (clinging), agitated by longing (feeling).

The Buddha further explains that the beliefs are originated from Contact (Phassa) as the cause. The contact is a phenomenon when the perception recognised an object beyond our Self. Then, from this brief (like lightning in the sky, Nagasena analogued in Milinda Panha) event, rise up feelings.

Buddha states that there are no possibilities of feeling without contact. Thus, according to the law of Twelve Related Chain of Cause and Effects (Pratitya-samutpada), the people who believe in one of many of these sixty-two beliefs, will end up in round cycle of sufferings; as they have not found the truth on the cease of sufferings.

Due to their faith, they will experience feelings as a result of repeated contact through the six sense bases. In them feeling gives rise to craving; craving gives rise to clinging; clinging gives rise to current existence (upapatti bhava) and the kammic causal process (kamma bhava); the kammic causal process gives rise to rebirth; and rebirth gives rise to ageing, death, grief, lamentation, pain, distress and despair.

The Buddha states that Monks who have realized and understood the origin of contact of the six senses, and escaped the round of sufferings, would see Dhamma (Truth) of Precepts (Śīla), Concentration (Samadhi) and Wisdom (Pańńa) which surpassed all the wrong beliefs.

The Buddha then makes an analogy of a fisherman using a fine-meshed net to catch the fish in the pond. The fish represent the ascetics who cling to their beliefs. They will rise and sink in the pond, but in the end will unavoidably be caught in the net. Whereas the Buddha, who stand outside the net has found the truth and has transcended the cycle of suffering.

The Brahmajala Sutta ends with this quotation:

"When the Bhagava had delivered this discourse, the Venerable Ananda addressed him thus: "Marvellous indeed, Venerable Sir! Extraordinary indeed, Venerable Sir! What is the name of this exposition of the dhamma?"

"Ananda!" said the Bhagava, "Bear in mind that this exposition of the dhamma is called Atthajala, the Net of Essence, as well as Dhammajala, the Net of the Dhamma, as well as Brahmajala, the Net of Perfect Wisdom, as well as Ditthijala, the Net of Views, as well as Anuttarasangama Vijaya, the Incomparable Victory in Battle."

Thus said the Bhagava.