text:
What *is* intrinsically real? Is the "unconditioned", "absolute", or "ultimate" intrinsically real?
To better see the relative, insubstantial nature of phenomena, maybe it is helpful to think about this another way, that is, seeing what is not relative, not conditioned, not empty.
It has been said that all phenomena are conditioned, not intrinsically real, empty of independent, self-existence.
What is intrinsically real?  Is nibbāna intrinsically real?

O bhikkhus, what is the Absolute (Asaṃkhata, Unconditioned)? It is, O
  bhikkhus, the extinction of desire (rāgakkhayo) the extinction of
  hatred (dosakkhayo), the extinction of illusion (mohakkhayo). This, O
  bhikkhus, is called the Absolute

When the terms unconditioned, absolute, and ultimate are used, as in the above and below quotes, do they not mean the same as intrinsically real? Does un-conditioned not mean "independent of conditions" and hence self-existing?

Bodhicitta literally means “awakened heart.” On the relative level it
  is compassion, expressed in the bodhisattva vow to save all beings; it
  is the aspiration to awaken from ignorance in order to live one’s life
  for the benefit of all. On the ultimate level, bodhicitta goes beyond
  the concepts of self and other. It is the empty, aware nature of the
  mind itself.

The first draft of this question was partly motivated by the question, "is compassion real?", however, from reading One Dharma: The Emerging Western Buddhism (Joseph Goldstein), my understanding is now that compassion is relative (not intrinsically real), i.e. as Joseph Goldstein puts it:

I realized that the relative level is the expression of the ultimate:
  compassion is the activity of emptiness.

Since that part of my question has been answered, it has now been revised.

When mental afflictions arise in me, I remind myself "it's insubstantial, not intrinsically real.". Maybe the antidote to this suffering is to see what is real.

I see you’ve edited the question, but to my mind the answer is the same: nothing whatsoever is intrinsically real. But emptiness can be said to be real when “real” is defined as something appearing in an unmistaken manner to a reliable cognizant. Still, emptiness is not intrinsically real.

You can't walk under a rainbow - in this sense it is an illusion. And yet rainbow is a meteorological phenomenon that actually occurs - in this sense it is not an illusion.
In Mahayana Buddhism we say that the rainbow is "empty". Meaning, if we disassemble it, there is nothing inside, no core, no secret ingredient. If we examine it closely, we will see the water droplets, the sunlight, the reflection, refraction, dispersion, and the observer looking at it from a certain angle - all these things combined lead to appearance of an arch in the sky - but in actuality there is no arch.
When you see a homeless person, and out of pity give him money for food - on one hand that's real metta-karuna operating in you. On the other hand, giving him money won't really change anything. Perhaps it actually makes it worse, by enabling him to buy alcohol. Perhaps if you took him home by force and taught Dharma - that would be actual help, but you don't do that. So maybe it's not metta, maybe it's ignorance operating in you. Or perhaps, who knows - may be the homeless person should feel pity for you, because he can wander unfettered and you have to go to work every day. In that sense, maybe it's not metta, maybe it's conceit operating in you. In that sense, our metta is not real. Who can judge whether our kindness is real kindness or fake kindness? It depends on the judge. And yet we try to be as kind as we can, and as wise as we can. So metta is like rainbow - depends on the object, the situation, and the position of the observer.
According to Mahayana (specifically the part called Madhyamaka - "the meaning of the middle way"), everything is like that: on one hand it's real - and on the other hand it's not; on one hand it exists - and on the other hand it's an illusion; it looks solid from afar - but falls apart under careful examination. Nothing is real - and yet everything is real.
They say even this ^^^ understanding above is not "real", because it is only a conceptual map - and map is never exactly the same as the territory.
In this sense nothing is intrinsically real. All our experiences are like "rainbows" in some sense. All our concepts are like "maps". Even Nirvana is just a word that gives a label but does not really explain anything. Entire Dharma is a map or a guidebook that only approximately explains what happens in real life.
In Mahayana we say that going beyond these rainbows and maps (="Realizing Emptiness"), is a big step towards Enlightenment.
Now, depending on a particular school we either say that the actual "ground reality" beyond the rainbows and maps (=ontological reality behind experiences and descriptions) is intrinsically real. OR we say that there is no such absolute ground and everything is completely relative. If you belong to Nyingma or Kagyu - then you say that the ground reality is real, just indescribable and not accessible to direct experience, but we actually are living it. And if you belong to Gelug, then you say that this ground is only an abstraction in our mind, leaving us with nothing to stand on. This is known as
the Rangtong-Shentong distinction.

Do you know of any active Tibetan teachers who espouse Shentong like Dolpopa?

Anyone in the lineage of Jamgon Kongtrul, so definitely Thrangu Rinpoche and Khenpo Tsultrim Gyamtso Rinpoche; the new Karmapa and therefore all Karma Kagyu teachers under him. I bet that most of Nyingma teachers are Shentong as well whether they admit it or not.

All phenomena(Dhamma) are real. Metta is real. Anger is real. There's nothing relative about it.
All phenomena are grouped into 4 categories

Rupa - form
Citta - consciousness
Cetasika - concomitants of consciousness
Nibbana

Metta(kindness), anger(Dosa), ignorance(Moha) etc. come under Cetasika.
They are all real.
Emptiness in Buddhism does not mean "not real". It just means empty of satisfaction, empty of permanence, empty of a self. Here's a related video.

Nothing whatsoever is intrinsically real. Metta is not intrinsically real. The Tathagata is not intrinsically real. Nirvana is not intrinsically real. Emptiness is not intrinsically real. To be very clear, I'm not saying "nothing" taken as subject is intrinsically real either. If you could point to even one intrinsically real thing, then all this ^^^^^ would be refuted.
The word "intrinsically" in the phrase "intrinsically real" signifies that it is being used synonymously or mutually inclusively with inherent existence. This is not always the case.
Sometimes the word "real" is not used synonymously with inherent existence, but rather it is used to signify things that appear in concordance with how they actually exist. Under this definition, there is only one real thing: emptiness or the lack of inherent existence. That is to say, the only real thing - in that it appears the way it actually exists - is emptiness. All other things are false in the sense that they appear discordant with how they actually exist. They appear to us as having inherent existence, but they actually do not have inherent existence even in the slightest; thus they are unreal or false.
To ordinary beings who don't understand the unreality of things, phenomena like a face in a mirror [or a mirage of water, dreams, a snake imputed on a rope etc.,] are considered unreal in contradistinction to so-called real things. It is easy for ordinary beings to see that a face in the mirror is unreal ie., that it does not exist in concordance with how it appears. However, it is very hard for us to see that other phenomena that we regard as "real" ... are actually completely unreal.
The Prasangika Madhyamaka tenet system as elucidated by Je Tsongkhapa is considered by some the definitive and most subtle understanding of the doctrine emptiness. Under this system:

Only in relation to the world - ie., ignorance - it is said that some phenomena are real and some are unreal.
However, all things - save emptiness - are actually unreal ie., they do not exist in concordance with how they appear.
All things lack inherent existence including emptiness itself.

So how do the Four Noble Truths actually exist for instance? They exist utterly empty of inherent existence. They exist in dependence on conditions. It is easy to see how the First Noble Truth is dependent. The Buddha has taught that suffering is not permanent. If suffering is not dependently arisen, then it could not be impermanent.
What about "The Four Noble Truths" as an abstract concept? I hope it goes without saying that abstract concepts are not intrinsically real. One might say they exist, but of course they are dependent upon conditions including the mind that conceives them or communicates them.
Generally speaking, there are different forms of dependence. Dependence on causes and conditions, dependence on parts, dependence on name and form, dependence on a basis of designation and labels, etc. All existing and non-existing things (like the son of a barren woman) are included in the selfless. Even permanent things like uncompounded space are included in the selfless.
Objection! If they do not exist inherently, then they must not exist at all like the son of a barren woman!
Nagarjuna gives voice to this objection and then refutes it in the Fundamental Treatise on the Middle Way:

If all this is empty,
There would be neither arising nor ceasing,
And for you, it follows that
The Four Noble Truths do not exist.

Nagarjuna then goes on to give 5 more verses of objections in Chapter 24 before he responds with:

Here we say that you do not understand
Emptiness, or the purpose of emptiness,
Or the meaning of emptiness.
As a consequence you are harmed by it.

The Buddha’s teaching of the Dharma
Is based on two truths:
A truth of worldly convention,
And an ultimate truth.

Je Tsongkhapa in his Ocean of Reasoning commentary on Nagarjuna's Fundamental Treatise gives extensive explanation of the refutation. I will invite you to read it along with Nagarjuna's Treatise and here only repeat Nagarjuna:

If all this were nonempty, as in your view,
Then there would be no arising and ceasing.
It would follow that the
Four Noble Truths Would not exist.

Warning:
If you take anything I've said above as indicating that nothing exists or that this line of thought refutes the Four Noble Truths, Karma, Rebirth, the Dharma, the Buddha, the Path and the Fruits, etc., then I've miscommunicated and I apologize. Nothing could be further than the truth! Consider this warning a handrail to lean on if you take the above to indicate nihilism:

By a misperception of emptiness
A person of little intelligence is destroyed:
Like a snake incorrectly seized,
Or like a spell incorrectly cast.

In summary, I think you're saying that, for example, the Four Noble Truths "are not refuted" -- and, you're saying that they "are not intrinsically real": in other words that they "have no inherent existence" -- which, isn't meant to be a statement about whether their "appearance concords with how they actually exist".

Logically, I guess "actually exist" and "intrinsically exist" aren't the same -- e.g. something might be "actually a chair" without being "intrinsically a chair"? And what's the reason for saying that the 4NTs don't intrinsically exist? Is it that they're compound or conditioned (if so, what are their components or conditions)? And/or is it (e.g. per Navneet Nair's answer) that they are mind-made, or "exist in the mind only"?

@ChrisW I've updated to hopefully clarify your questions. Let me know if I can clarify further.

You wrote that "the Four Noble Truths actually ... exist in dependence on conditions" (and, without wanting to muddy the water, I'd also guess you might say this about Nibbana too, given that it too is "empty"). What (for example) are the "conditions, in dependence on which the Four Noble truths actually exist"?

I've added a bit about how the first truth of suffering is dependent as well as the abstract concept of the four truths and a bit about the different types of dependence. I'll leave nirvana to the other thread. That deserves a different treatment and more can be said. @Tenzin Dorje please check for errors or perhaps your own answer :)

That's really pretty clear now, thank you. Doubtless there's more can be said, but is said already in the references, and needn't be added to your answer, which is clearer now for including an example (of the Four Noble Truths). I was guessing that "being named as such" might be one of the conditions -- I wasn't sure though, because naming a snake as a garden hose isn't sufficient to make it actually so.

@YesheTenley - It may take me more time to understand all of this answer, but one question comes to mind from the start, where you say Nirvana is not intrinsically real. I have read other Buddhist writers say that nibbana is unconditioned. Is nibbana then not conditioned, not dependent, and therefore inherently and objectively real?

No, Nirvana is not inherently and objectively real. The best way to understand this is to read Nagarjuna's Fundamental Treatise chapter 24 - the chapter on Nirvana and how Nirvana is also empty of inherent existence - along with Je Tsongkhapa's commentary. If you have questions that come up feel free to post them. @avatar Korra I just don't want to overload this OP/answer...

It really depends upon the level of the disciple. The Buddha taught different stages of understanding of reality and each progressively works on adding subtlety to the understanding of reality.
In the First Turning of the Wheel of Dhrama, the Buddha taught about the five aggregates and how they are impermanent and the self itself is impermanent. He went on to explore the self and how it cannot be found as one with the aggregates or separate from the aggregates thus expounding the concept of selflessness. Then in the Second Turning of the Wheel of Dharma, the Buddha taught the perfection of wisdom where he refuted the existence of even the five aggregates. However since these were two rather extreme views, the Buddha taught in the Third Turning of the Wheel of Dharma about the view that things exist in the mind-only.
The above is a rather simplistic essence, but what the Buddha was doing during the three turnings was introducing the nature of reality from the less subtle to the most subtle understanding.
We have to realize, that we may not be ready for the most subtle understanding of reality just yet and have to work our ways up the levels of subtlety.
Sometimes it does help to look at metta as truly existing. At times it helps to look at a basal consciousness and karmic imprints as existing. It can also help by looking at conventional and ultimate reality as two modes. Or you may be better of looking at the Madhayamika Prasangika view of the absence of inherent existence and the reality that is solely based on dependant origination.
So to answer your question if metta is real, the best way to look at it would be from understanding your own understanding and how it corresponds to the four schools of tenets and working the way up.
https://studybuddhism.com/en/advanced-studies/abhidharma-tenet-systems/the-indian-tenet-systems/the-four-buddhist-tenet-systems-regarding-the-self

It has been said that all phenomena are conditioned, not intrinsically real
When you asked that, you were quoting an answer of Yeshe Tenley's.
I think the Pali doesn't say "all phenomena are conditioned", but it does talk about "conditioned phenomena" (sankhara) ... and refers to Nibbana as "the Unconditioned" (and other epiphets) ...
see also What are conditioned as opposed to unconditioned phenomena?
I think that the doctrine which Yeshe Tenley was explaining says that Nibbana too is "not intrinsically real". There's an example of that in this answer and its comments; and maybe this comment is a reference to detailed explanations:

You said, "I don't know how to reconcile that with the doctrine that "nibanna isn't conditioned" (or "is unconditioned")." I'd suggest that a careful study of Chapter 25 of Nagarjuna's Fundamental Treatise of the Middle Way along with the excellent commentary by Je Tsongkhapa in Ocean of Reasoning might help to understand this.

So what is intrinsically real?
I don't know how other people understand the term "intrinsically real".
I think (in classic English) that the word "real" meant "thing-like": maybe substantial or tangible. An opposite of "real" might be "ideal", i.e. an idea as opposed to a thing.
According to that classification, the body might be "real" but a feeling might not be (a feeling is more "ideal", i.e. idea-like rather than thing-like). I wouldn't necessarily mean that a feeling is imaginary or non-existent, but it's not substantial nor exactly tangible.
Related to that is the idea of reifying ideas, i.e. the process of treating ideas as if they were real. As you can see from that Wikipedia link (which isn't even Buddhism-specific) that's a complex topic or a set of related topics: different topics include "linguistics" (talking about ideas as if they're real), psychology (perceiving ideas as if they're real), and as a type of fallacy (a type of logical mistake, e.g. mistaking an idea for reality when it's really only an idea, and maybe not even a 'true' one).
I say this to illustrate that the English language or meaning (of the word "real") is complicated, and if you assume you know what it means that might be misleading.
I might add that that emphasis on what's "real", in the sense I described it, might be missing the whole point, from a Buddhist point of view: because Buddhists might dismiss that as mere "materialism".
I'm not sure what "intrinsically" means, either. I think it's used to argue that all composite things, at least, aren't intrinsically real in the sense that, for example, "a chair isn't intrinsically a chair: because if you disassemble it, take it apart, then it isn't a chair anymore".
And I'm not sure what "relative" means. I assume it means that a property exists as a result of comparing one thing relative to another: for example a mountain is high because a valley is low, or shadow is cold because sunshine is warm, and so on -- which I think is central to the Taoist doctrine of Yin and Yang. I'm not sure (I doubt) whether that (relativism) is so prevalent in the Pali. The Pali is very dualistic, IMO, e.g. it consists of doctrine about whether an action is "skilful" versus "not skilful" ... I'm pretty sure it wouldn't say that these aren't real just because they're relative. Another meaning of "relative" I guess might be that it's an artefact of a relationship with the observer: e.g. what I perceive as a "tree" isn't real, that's just an artefact of contact between the tree-as-sense-object with the sense-organs (e.g. the eye), and memories and linguistic associations ("that collection of sense-impressions may be called 'a tree'"), and changes (or vanishes) e.g. when the observer moves.
There's a Pali sutta called the Tatha Sutta ("Real": SN 56.20):

Tatha Sutta: Real
Monks, these four things are real, not unreal, not otherwise. Which four?
"'This is stress,' is real, not unreal, not otherwise. 'This is the origination of stress,' is real, not unreal, not otherwise. 'This is the cessation of stress,' is real, not unreal, not otherwise. 'This is the path of practice leading to the cessation of stress,' is real, not unreal, not otherwise.
"These are the four things that are real, not unreal, not otherwise.
"Therefore your duty is the contemplation, 'This is stress... This is the origination of stress... This is the cessation of stress... This is the path of practice leading to the cessation of stress.'"

The Pali word that's translated as "real" is tatha. Tatha is used in the word tathagatta and also (as well as "real") means "true" ... or "so" (in the phrase, "that is so") or "such".
Anyway that illustrates another meaning of "real": i.e. it means "true". Even in (non-Buddhist) English, something (especially a story) that's "fabricated" implies it might be untrue, or at least (if it's a consumer product) unreliable, disposable, transient.

The Buddha did teach emptiness in the Pali Suttas, but it is restricted to the nature of the self i.e. all phenomena is empty of a self (see Shunya Sutta). The Buddha did not comment on the nature of all non-sentient things like the universe, besides noting them as being conditioned, compounded and impermanent.
The Buddha was not interested in commenting on the nature or origin of the universe, because he considered it to be unimportant to the path to liberation from suffering - see the Parable of the Poisoned Arrow (from MN63). The Buddha was not interested in metaphysical speculations (also see Simsapa Sutta). This is also the stand of Theravada Buddhism today.
While the Buddha (of the Pali Suttas) stopped at describing the "middle way" (between eternalism and annihilationism) and emptiness with respect to the nature of the self, Mahayana philosopher Nagarjuna expanded these concepts to cover the nature of the universe and all reality.
Rather than the annihilationism that nothing exists or the eternalism that something exists eternally, Nagarjuna taught the "middle way" that all phenomena is empty of its own "inherent existence" or "substance" or "essence" (what he called svabhāva).
If nothing has inherent substance, then nothing can depend on something else for substance, so there is no other inherent substance (para-bhāva).
A key concept of Madhyamaka is that even this emptiness is empty i.e. this emptiness does not have its own inherent substance. This means that there is no transcendental reality beyond phenomenal reality. This is what is implied by ultimate reality not being absolute reality.
A very nice and simplified explanation of the Madhyamaka emptiness can be found in Zen master Thich Nhat Hanh's writing, "The Fullness of Emptiness". I quote some parts of it below:

If you are a poet, you will see clearly that there is a cloud floating
  in this sheet of paper. Without a cloud, there will be no rain;
  without rain, the trees cannot grow; and without trees, we cannot make
  paper. The cloud is essential for the paper to exist. If the cloud is
  not here, the sheet of paper cannot be here either. We can say that
  the cloud and the paper inter-are. “Interbeing” is a word that is not
  in the dictionary yet, but if we combine the prefix “inter-” with the
  verb “to be,” we have a new verb, “inter-be.”
If we look into this sheet of paper even more deeply, we can see the
  sunshine in it. If the sunshine is not there, the forest cannot grow.
  In fact, nothing can grow. Even we cannot grow without sunshine. So we
  know that the sunshine is also in this sheet of paper. The paper and
  the sunshine inter-are. And if we continue to look, we can see the
  logger who cut the tree and brought it to the mill to be transformed
  into paper. And we see the wheat. We know that the logger cannot exist
  without his daily bread, and therefore the wheat that became his bread
  is also in this sheet of paper. And the logger’s father and mother are
  in it too. When we look in this way, we see that without all of these
  things, this sheet of paper cannot exist. .....
When Avalokita says that our sheet of paper is empty, he means it is
  empty of a separate, independent existence. It cannot just be by
  itself. It has to inter-be with the sunshine, the cloud, the forest,
  the logger, the mind, and everything else. It is empty of a separate
  self. But, empty of a separate self means full of everything. So it
  seems that our observation and that of Avalokita do not contradict
  each other after all. Avalokita looked deeply into the five skandhas
  of form, feelings, perceptions, mental formations, and consciousness,
  and he discovered that none of them can be by itself alone. Each can
  only inter-be with all the others. So he tells us that form is empty.
  Form is empty of a separate self, but it is full of everything in the
  cosmos. The same is true with feelings, perceptions, mental
  formations, and consciousness.
Form is the wave and emptiness is the water. To understand this, we
  have to think differently than many of us who were raised in the West
  were trained to think. In the West, when we draw a circle, we consider
  it to be zero, nothingness. But in India and many other Asian
  countries, a circle means totality, wholeness. The meaning is the
  opposite. So “form is emptiness, and emptiness is form” is like wave
  is water, water is wave. “Form is not other than emptiness, emptiness
  is not other than form. The same is true with feelings, perceptions,
  mental formations, and consciousness,” because these contain each
  other. Because one exists, everything exists.

So, to answer your question, something that's intrinsically real, is something that has separate, independent existence. Since the sheet of paper does not have separate, independent existence, so it's not intrinsically real. According to this concept, you cannot find a true boundary where the paper ends and the rest of the universe begins. They all depend on each other.

Does the sheet of paper depend upon the awareness perceiving it? Or would the sheet of paper exist without depending upon the awareness perceiving it? @ruben2020


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What does 'loke' mean, in 'Sabba Loke Anabhirata Saññā' (not taking delight in 'worlds')?
I'm referring to Girimananda Sutta (AN 10.60), where the Buddha introduces 9 perceptions + mindfulness with breathing:

The perceptions of impermanence, not-self, ugliness, drawbacks, giving up, fading away, cessation, dissatisfaction with the whole world, non-desire for all conditions, and mindfulness of breathing.
  Aniccasaññā, anattasaññā, asubhasaññā, ādīnavasaññā, pahānasaññā, virāgasaññā, nirodhasaññā, sabbaloke anabhiratasaññā, sabbasaṅkhāresu anicchāsaññā, ānāpānassati.

How is this perception to be understood? Is 'Loke' here translated as our 'world' (5 aggregates) or is it the external world and the intrinsic dukkha in it?
Thanks

This is a very good question because the word "world" ("loka") appears to have many meanings; such as the "world of suffering" (SN 12.44; AN 4.45); the mundane world of defilements & samsara (Lokavagga; AN 8.6; SN 35.82) the world or realms of mental states (MN 79) and the world of people (AN 2.9; AN 3.23). One of the definitions of Nibbana is: "not this world; not the other world".
Personally, I don't know Pali and I have a natural retardedness for grammar however my Dhamma intuition doubts the translation because of what I regard a mistranslation of "sabba" as "whole" instead of "all".
I can't imagine each of the Western translators is wrong here however I tried to examine the term "sabbaloke anabhiratasaññā" and think (possibly wrongly) the noun (loka) is in the "accusative case", which makes "loke" a plural and makes the translation: "dissatisfaction with all worlds".
The "worlds" are any type of conditioned & impermanent mental state, such as the jhana "world of only pleasant feelings (ekantasukhassa lokassa)" described in MN 79. Therefore, "dissatisfaction with all worlds" includes dissatisfaction with every "world", such as the "human world" (manussaloka), "deva world" (devaloka), "brahma world", "jhana world" (sukhassa lokassa), "hungry ghost world" (pettivisaya), world of change and distress (lokavipatti; AN 8.6) etc.

Note: I provided the above answer without reading the sutta. The answer appears to be in the sutta.

Idhānanda, bhikkhu ye loke upādānā cetaso adhiṭṭhānābhinivesānusayā, te pajahanto viharati anupādiyanto. Ayaṃ  vuccatānanda, sabbaloke
  anabhiratasaññā.
And what is the perception of distaste for every world? There is the case where a monk abandoning any attachments, clingings, fixations of
  awareness, biases or obsessions with regard to any world, refrains
  from them and does not get involved. This is called the perception of
  distaste for every world. (Thanissaro)
It’s when a mendicant lives giving up and not grasping on to the attraction and grasping to the world, the mental resolve, insistence,
  and underlying tendencies. This is called the perception of
  dissatisfaction with the whole world. (Sujato)
And what, Ānanda, is the perception of non-delight in the entire world? Here, a bhikkhu refrains from any engagement and clinging,
  mental standpoints, adherences and underlying tendencies in regard to
  the world, abandoning them without clinging to them. This is called
  the perception of non-delight in the entire world. (Bodhi)

Note: Thanissaro has translated similar to myself, using the translation "every world", which is similar to "all worlds".

Nice answer: thank you. I guess translators assume loka is declined there as a singular locative -- not "taking-no-delight-in .. all-the-worlds" but "taking-no-delight .. in-all-the-world".

Sometimes e.g. here the translation is "for every world".

Please comment more on the grammar. Why is it not the "accusative" ? Thanks

Well I think that the grammar could be either (i.e. singular locative or plural accusative). Either of these (so far as I know ... I too don't know Pali) would seem to me to make sense -- accusative (where "all the worlds" are the object of the dissatisfaction); or, locative (where "the whole world" is the location of the dissatisfaction). I think that (grammatically) sabba can be used with a singular or plural (e.g. "all the world" or "all the worlds"), so one couldn't tell from that, either. I don't see it makes a huge difference to the overall meaning.

I was commenting about why a translator might have construed it singular: i.e. "world" seems to me to be a noun that could plausibly be declined in the locative.

Hi Chris. Note Thanissaro's translation above.

Yes I referenced that in my second comment to this answer.

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Why did Tsongkhapa list guru devotion first in his Lamrim while Atisha did not?
Lama Atisha famously brought the teachings of Nalanda back to Tibet and authored his famous, A Lamp for the Path to Enlightenment upon which the new translation schools were founded. This seminal text is the foundational document of the lamrim upon which all subsequent lamrims are based.
Atisha did not seem to mention guru devotion in his lamrim. Spiritual teachers are mentioned only in the course of explaining how to properly receive the Bodhisattva vows and to receive Tantric initiations. Nowhere can I find the idea that guru devotion is the root of the path to enlightenment.
Je Tsongkhapa on the other hand listed guru devotion towards the very beginning of his lamrim and it is widely taught in new translation schools that guru devotion is the root of the path to enlightenment. Why is this? Why would something so important and fundamental be left out entirely by Lama Atisha from his seminal text?
Also, this is what His Holiness the Dalai Lama has said about guru devotion in Questioning the Advice of the Guru:

It is frequently said that the essence of the training in guru yoga is
  to cultivate the art of seeing everything the guru does as perfect.
  Personally I myself do not like this to be taken too far. Often we see
  written in the scriptures, “Every action seen as perfect.” However,
  this phrase must be seen in the light of Buddha Shakyamuni’s own
  words: “Accept my teachings only after examining them as an analyst
  buys gold. Accept nothing out of mere faith in me.” The problem with
  the practice of seeing everything the guru does as perfect is that it
  very easily turns to poison for both the guru and the disciple.
  Therefore, whenever I teach this practice, I always advocate that the
  tradition of “every action seen as perfect” not be stressed. Should
  the guru manifest unDharmic qualities or give teachings contradicting
  Dharma, the instruction on seeing the spiritual master as perfect must
  give way to reason and Dharma wisdom.
Perhaps you will think: “The Dalai Lama has not read the Lam Rim
  scriptures. He does not know that there is no practice of Dharma
  without the guru.” I am not being disrespectful of the Lam Rim
  teachings. A student of the spiritual path should rely upon a teacher
  and should meditate on that teacher’s kindness and good qualities; but
  the teaching on seeing his or her actions as perfect can only be
  applied within the context of the Dharma as a whole and the rational
  approach to knowledge that it advocates. As the teachings on seeing
  the guru’s actions as perfect is borrowed from Highest Tantra and
  appears in the Lam Rim mainly to prepare the trainee for tantric
  practice, beginners must treat it with caution. As for spiritual
  teachers, if they misrepresent this precept of guru yoga in order to
  take advantage of naive disciples, their actions are like pouring
  the liquid fires of hell directly into their stomachs.

Emphasis mine. If preparing the trainee for Tantric practice is the reason for adding it to the Lamrim, then is it true that guru devotion is not of such importance for those studying sutra only? In other words, can it be said that for those practicing sutrayana only that guru devotion is not the root of the path?

Very good question. This is a quote by Lama Zopa Rinpoche that seems to cover this point.

Lama Tsongkhapa asked Manjushri, “What is the way to achieve quick
  realizations of the path to enlightenment?” Manjushri answered, “To
  purify the mind of the obstacles to realizations and to collect the
  necessary conditions, the merit, to collect extensive merit, that’s
  one thing. The other one is one-pointedly making requests to the
  guru,” that means with devotion. The third one is meditating on the
  path.

Thus it may have been under Manjushri's guidance that Je Tsongkhapa adopted this order.
You are of course right about the order in which the Lamrim points are presented is different in the various Lamrims. While Jowo Je Atisha used Bodhichitta as the first step on the path, Gampopa in his "Jewel Ornament of Liberation" begins with Buddha Nature. While Patrul Rinpoche begins "The Words of My Perfect Teacher" with the precious human life.
Atisha begins his Lamrim after explaining the three scopes with the following verse:
For these excellent beings
Who aspire to supreme enlightenment,
I shall explain the perfect method
Taught by my spiritual masters.
Thus the Lamp on the Path to Enlightenment is primarily addressed to Mahayana practitioners and thus generating the Spirit of Enlightenment is the first step he presents.
Gampopa has a very interesting presentation in "Jewel Ornament of Liberation". Buddha Nature is the primary cause, the precious human life is the working basis while reliance on a spiritual master is the contributory cause.
Patrul Rinpoche's combines 'Reliance on a Spiritual Master' together with generating the spirit of enlightenment and development of Bodhichitta. One of my teachers has explained that the above are three levels of refuge and Patrul Rinpoche uses it as the preliminaries before the introduction of Mahamudra, Chod and Transference teachings.
Since the Lamrim Chenmo is a sutric text it does not go into the tantra except towards the end where Je Tsongkhapa mentions that the disciple has to practice the teachings of the Vajrayana before undertaking the four methods of gathering disciples. However the Vajrayana is a part of the entire path and thus from Je Tsongkhapa's point of view the preliminaries should include guru devotion.
This is explained further in Panchen Chyoki Gyaltsen's 'Easy Path' where each section is divided into the preliminary, the actual meditation session and time in between sessions. This format is adopted by Kyabje Pabonka Rinpoche as well in 'Liberation in you Hands'. In the preliminary, is the primary practice of Guru Yoga and supplication which helps you understand the meditation topic better.
Thus in the Gelug Lamrims following Tsongkhapa the importance on the Reliance on the Spiritual Master being the root of the path is emphasised. This can be best explained by the benefits of relying upon a spiritual master as found in the Precious Master's Instructions Outline to the Lamrim.
The eight benefits of relying on spiritual masters:
* Coming closer to achieving Buddhahood
* Pleasing all conquerors
* Being invulnerable to demons and misleading friends
* The automatic reduction of disturbing mental factors and incorrect behaviour
* The increase of all grounds, paths and realisations
* Never being deprived of a teacher in all future lives
* Not falling into lower rebirths
* Effortlessly achieving all temporary and ultimate goals

In the same answer LZR says that Tsongkhapa is Manjushri himself which is confusing to me. I've heard the tales of Tsongkhapa talking to Manjushri in a dream (think it was either a Thurman book or Hopkins?), but never heard that this was the impetus for placing guru devotion first in the lamrim.
Also, I appreciate your answer, but can you specifically answer this: "In other words, can it be said that for those practicing sutrayana only that guru devotion is not the root of the path?"

If you follow the Gelug lineage of Tsongkhapa, Guru Devotion is the root. For every topic of the Lamrim one visualizes a merit field in front of them. Then one supplicates the guru to come and reside on the crown of your head. When you withdraw the merit field, the guru on the crown of your head becomes one with the Buddha (Lama Losing Tuwab Dorje Chang). This visualisation is part of the sutra and you can find it in liberation in your hands by Pabonka Rinpoche. Hence in the Gelug tradition especially if you follow the Quick Path or Easy Path (Nyur-lam/De-lam).

But my precious teacher has also given an oral instruction that if you wish to make progress in the path you need to gain realisations in one of the three topics of Guru Devotion, Precious Human Rebirth or Death and Impermanence. So in some way all of them are important preliminaries. I spent about a year on each topic and there was a significant improvement in understanding. No realisations, but still...

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text:
Why does Lama Atisha say those "observing pure conduct" shouldn't take (some) Tantric initiations?
In Lama Atisha's, A Lamp for the Path to Enlightenment he ends the teaching this way:

Because the Great Tantra of the Primordial Buddha
  Forbids it emphatically,
  Those observing pure conduct should not
  Take the secret and wisdom initiations.
If those observing the austere practice of pure conduct
  Were to hold these initiations,
  Their vow of austerity would be impaired
  Through doing that which is proscribed.
This creates transgressions that are a defeat
  For those observing discipline.
  Since they are certain to fall to a bad rebirth,
  They will never gain accomplishments.
There is no fault if one who has received
  The preceptor initiation and has knowledge
  Of suchness listens to or explains the tantras
  And performs burnt offering rituals,
  Or makes offering of gifts and so forth.

I interpret this to mean that people holding vows of conduct that are in contradiction to what is required in some Tantra (so-called taboo practices of sex, alcohol or other illicit activities) should emphatically not take those Tantric initiations.
In Louisville, Kentucky in 2013 I heard His Holiness the Dalai Lama explain that monks should not be engaging in sexual tantric practices and that to do so is a defeat that will lead to bad rebirth. Was I misunderstanding something or is it not the case that Tantric practices that involve activities in contradiction to pure conduct should be avoided by those who hold vows of pure conduct?
Do any schools of Tibetan Buddhism disagree with Lama Atisha's seeming prohibition? How about any schools of Vajrayana outside of Tibet?

Verse 64 mentions the secret and wisdom initiations.
These two initiations are taken only in the context of highest yoga tantra. Therefore, the three lower tantras are not concerned here.
From the point of view of highest yoga tantra, there are two ways of achieving enlightenment:

With an actual consort
In the bardo, after death

It is said that lama Je Tsonkhapa could have achieved enlightenment with an actual consort, but he would have to disrobe (or to ensue a defeat). Instead, he chose to achieve enlightenment in the intermediate state.
So, there are these two ways of actualizing the completion stage and upholding the secret and wisdom initiations. One them would be a defeat.
Other practices, such as the consumption of infinitesimally small dosage of alcohol, is not considered as a transgression of the pratimoksha. During Lama Chöpa Tsok, for instance, we dip our finger into alcohol and lick it. There is no practice where you consume more alcohol than that. In addition, we say that if you refuse to do it while you actually took a highest yoga tantra initiation, it is breaking your tantric commitments.

Hi, are there any places where tbey teach such tantra without becoming a monk?

@BodhiWalker yes, tantra isn't just for monks. At Nalanda monastery (France) and Istituto Lama Tsongkhapa (Italy), for instance, there are teachings on tantra. However, if you don't have highest yoga tantra initiation, you might not be able to study. Or at least have studied lam rim, etc. and ask the teacher if he will allow you.


text:
Difference between Buddhist and materialist views of no self?
This question follows from a discussion on the materialist, scientific reductionist understanding of no self, and was posted in a comment:

In what way does the materialist view differ from Buddhism on the
  discussion of self?

Similarities
Both Buddhist and materialist/scientific-reductionist schools refute the notion of a self, an atman, an eternal, unchanging soul. Both schools understand the most obvious meaning of anatta:

the lack of a permanent, unitary, and independent person.

Furhermore, Buddhism asserts that the body is constituted by way of material elements, and that a person is made up of the five aggregates. And similarly, a materialist, scientific reductionist understanding posits (quote):

That people can be viewed as a composite of sub-atomic particles
  governed by the laws of chemistry and physics. We learn in elementary
  and middle school about caloric intake, cellular division (mitosis and
  meiosis), evolution, genetics and epigenetics which all make it
  trivial to ascertain that the person is thoroughly non-permanent,
  non-unitary, and dependent.

Differences?
It appears Wikipedia tells us that the difference between Buddhist and materialist views on no self lies in karma and rebirth:

Buddha criticized the materialistic annihilationism view that denied
  rebirth and karma, states Damien Keown.[46] Such beliefs are
  inappropriate and dangerous, stated Buddha, because they encourage
  moral irresponsibility and material hedonism.[46] Anatta does not mean
  there is no afterlife, no rebirth or no fruition of karma, and
  Buddhism contrasts itself to annihilationist schools.

But I'm not sure whether this quote is accurate, or a misunderstanding
If Buddhist and materialist schools share the same view on the most obvious meaning of anatta (quoted above),
then what distinguishes the Buddhist view from the materialist view on no self?
Is there a not-so-obvious meaning of anatta which materialist/scientific reductionist schools fail to understand?

I get the impression that a materialist might say, "I exist because I have (or am) a body." And might say, "I will die (and not be reborn) when my body dies..." And might add, "... therefore I have no incentive to behave morally in this life."
Conversely I think that the Buddhist definition of "self" has approximately four meanings:

Definitions for atta

the self, the soul, as a permanent, unchangeable, autonomous entity (always rejected by the Pāḷi Buddhist texts as not corresponding to any reality).
the self, one’s own self (the abstract individual); the image in a looking-glass; especially.
oneself, himself, yourself, (used (in the sg.) as reflexive pronoun for all three persons and genders); instr. attanā, by oneself; in oneself, as for oneself, often used in the sense of a nom.

It seems to me that the Pali texts:

Assert that there's no such thing as "soul" (first meaning): by saying "look at everything -- everything (each thing) is impermanent, therefore it's not (fit to be viewed as) permanent soul/self"
Say that "self-view" (second meaning) is a wrong view: by saying "any form of self-view, including views like I exist or I don't exist or I existed in the past or I won't exist in the future, are a cause of suffering and are best avoided and are a result of attending inappropriately."
Use pronouns (like "oneself") in an ordinary way, without comment, in conversation

I think there's a 4th meaning of "self", which may have roots in the Pali text but which is explained as a more detailed doctrine in the Second Turning: which says that not only "Nothing is me" or "I don't have self", but also "Nothing else has a 'self' either" or "everything has no self of its own".
I think the 2nd meaning above is related to the 1st -- i.e. self view is wrong view because:

It's a view conducive to suffering
Anything which might be considered self, including any self-view itself, is subject to cessation.

is a belief in rebirth and karma what distinguishes the Buddhist from the materialist view on no self?
The definitions or differences that I gave above don't mention karma or rebirth.
So I (personally) don't usually regard the doctrines of karma and rebirth as essential -- or at least as not essential for explaining the difference between Buddhism and materialism, although the doctrine of karma is useful for other reasons.
But they are part of the Buddhist doctrine.
I don't disbelieve what you quoted from Wikipedia, i.e. that annihilationism is considered wrong view because it's conducive to immorality (i.e. annihilationism gives no argument against immorality, which the doctrines of karma and rebirth do) ... but I haven't found the reference to that argument (against annihilationism) in the suttas.
Instead I think that annihilationism is wrong view because it's a self-view (a view about self).

Your answer is a bit confusing. You say that karma is not essential, so if this is the case, a Buddhist who doesn't believe in karma has no incentive to behave morally either, just like a materialist. Similarly, a Buddhist who doesn't believe in rebirth might say "I will die (and not be reborn) when my body dies...".

Apart from that, it seems to me that there is nothing wrong for a Buddhist to say "I exist because I have (or am) a body.", as long as he/she understands that he/she is speaking about the conventional truth, not the ultimate truth.

IMO karma is (although important for other reasons) not essential for explaining the difference -- IMO a more essential difference is that materialism is a (type of) self-view, whereas Buddhism categorises any and every type of self-view (including, but not limited to, annihilationism and eternalism) as wrong view.

That makes sense, I think the answer would be clearer if you replaced the first paragraph by what you've written in the comment. The difference doesn't lie in what Buddhists and materialists might say, but in how they view themselves.

@ChrisW Thanks for this answer, and I think you may have answered this question, in its now edited form, i.e. that there is a salvation meaning of no self which materialists fail to understand, here.

I think that "salvation" bit which you quoted was about karma -- e.g. skilful or unskillful, and consequences. I think this is important in Buddhism -- and, if materialists are immoral because they don't believe in karma, that's antagonistic to the Buddhist doctrine of the Pali canon. But you were asking about "the view of no-self", and IMO that's a different topic: the materialist view is something like, "a person is a composite of four primary elements" -- but according to Buddhism, "I exist because I have (or am) a body" is IMO a self-view, from attachment to the clinging-aggregate of form.

I don't buy that dis-belief in rebirth and karma is necessarily conducive to immorality (or in otherwords, that morality requires belief in rebirth and karma). Why would one need belief in karma and rebirth simply to see that sila assists in ending craving and hence suffering?

@avatarKorra I don't buy it either, so I said "if materialists are immoral because etc.", in case maybe not all materialists are immoral. I've heard this same about other religions, e.g. "Is it possible to be moral if you don't believe in God and heaven and hell?" I suppose the sutta was describing a particular type of materialist, i.e. a "nihilist" of some kind.

IMO this answers the question, as the materialist, even with a coarse undersanding, still holds on to the 2nd, wrong view, and is ignorant of the 4th view, related to emptiness.

Apart from what you have mentioned,  materialists usually think that the mind is a byproduct of the brain. In other words, electrical traces stored in neurons. This is not the case in Buddhism. Brain is a concept according to Buddhism. The reality is fundamentally grouped into 2 categories: the mental(Nama) and the physical(Rupa).
The four noble truths hold true at all times regardless of what one believes. But one is not able to attain enlightenment, if one holds to the view that all mental activities end at death. This belief is called Saggawarana & Maggawarana:  conceals the path to heavens and conceals the path to enlightenment.
Here's a related answer by ven.Yuttadhammo.

I marked this answer down because its ideas about "the brain" has no source in the Pali suttas. It is just papanca or imaginations of non-Buddhist egoistic eternalist ideas.

@Dhammadhatu hence the idea of a brain is a concept according to Buddhism. You seem to have a talent for misinterpreting my answers :)

This question has many facets, but I will answer in as straightforward a manner as I'm capable. You ask:
Still, I want to ask here and verify that this quote is accurate, and not a misunderstanding. i.e. is a belief in rebirth and karma what distinguishes the Buddhist from the materiast[sic] view on no self?
I'm not sure your paraphrase of the meaning of this quote is accurate insofar as it seems to imply that a belief in rebirth and karma is the only distinguishing factor between a materialist view and what the Buddha taught. If that paraphrase of the meaning is accurate, then the answer is a decided No! to my mind. There are many differences including the truth of rebirth between what materialists think and what the Buddha taught. Still, we should be careful to distinguish between different views that can be lumped together under the designation "materialist" yet may have subtle differences. For instance, there is the ancient Indian materialist school of Charvaka or Lokāyata which although seemingly has many similarities with modern materialists or scientific reductionists, may have material differences. Yes, the pun was intended :)
Anyway, did the Buddha distinguish his views from the ancient Indian materialists? Yes! And he did so in the Pali canon as well as in Mahayana Sutras. For instance, in the Samaññaphala Sutta: The Fruits of the Contemplative Life this account is given of an encounter with the ancient Indian materialist Ajita Kesakambalin who was a contemporary of Buddha Shakyamuni:

"Another time I approached Ajita Kesakambalin and, on arrival,
  exchanged courteous greetings with him. After an exchange of friendly
  greetings and courtesies, I sat to one side. As I was sitting there I
  asked him: 'Venerable Ajita, there are these common craftsmen... They
  live off the fruits of their crafts, visible in the here and now... Is
  it possible, venerable sir, to point out a similar fruit of the
  contemplative life, visible in the here and now?'
"When this was said, Ajita Kesakambalin said to me, 'Great king, there
  is nothing given, nothing offered, nothing sacrificed. There is no
  fruit or result of good or bad actions. There is no this world, no
  next world, no mother, no father, no spontaneously reborn beings; no
  brahmans or contemplatives who, faring rightly and practicing rightly,
  proclaim this world and the next after having directly known and
  realized it for themselves. A person is a composite of four primary
  elements. At death, the earth (in the body) returns to and merges with
  the (external) earth-substance. The fire returns to and merges with
  the external fire-substance. The liquid returns to and merges with the
  external liquid-substance. The wind returns to and merges with the
  external wind-substance. The sense-faculties scatter into space. Four
  men, with the bier as the fifth, carry the corpse. Its eulogies are
  sounded only as far as the charnel ground. The bones turn
  pigeon-colored. The offerings end in ashes. Generosity is taught by
  idiots. The words of those who speak of existence after death are
  false, empty chatter. With the break-up of the body, the wise and the
  foolish alike are annihilated, destroyed. They do not exist after
  death.'

So on the narrow question of whether the Buddha distinguished his teaching from that of the ancient Indian materialists I think there can be no doubt so long as one accepts the validity and authenticity of this Sutra. Of course, one could quibble with the definition of "materialist" and say that this is an incorrect designation, but for the purposes of your question I think the definition is fine, right? Moreover, contemporary researchers of this school of ancient Indian thought give it this label. Please let me know if you disagree.
To go further, I think the view described above and attributed to the ancient Indian ascetic Ajita Kesakambalin is in fine concordance with many modern day scientific reductionists although they would surely replace the four elements with modern day conceptions of matter and energy. Also, "Generosity is taught by idiots" is also in concordance with many immoral or amoral scientific reductionists. At best, modern scientific reductionism is neutral on the question of ethics.
If so, then do the Buddhist teachings on no self and the Third Noble Truth only hold if one believes in rebirth, in the literal sense?
Not sure what you mean by "only hold", but I think you are asking something like, "besides moral questions and knowledge of the truth of rebirth, what other differences can be found between modern scientific reductionists and the teachings of the Buddha?"
Many! However, here I'll only list one that is very pertinent and profound to my mind: the Buddha taught that matter and energy are unreal and not inherently existent. We should regard this phenomenal world filled with matter and energy as like:

“As a star, a visual aberration, a lamp, an illusion, dew, a bubble, a
  dream, lightning, and a cloud – view all the compounded like that.”

This is decidedly not the program of the modern scientific reductionist or scientific realist which believes wholeheartedly in the objective solid physical world made of matter and energy and governed by the fundamental laws of physics. And yet, the Buddha taught that all is ephemeral like a dream without even the slightest bit of inherent or fundamental existence. Hopefully, you can see how the two views are in conflict :)
A different question, but one which I think you are pointing at is whether belief in karma, rebirth and the moral/contemplative life is necessary to achieve the soteriological goals of Buddhism. For my part, I do believe it is at least highly highly highly advantageous. I'll even go so far as to say I'm not sure how one could achieve the soteriological goals of Buddhism without belief in karma, rebirth and the moral contemplative life.
To my mind, refuting the truth of rebirth requires something akin to the materialist trap: it hypostatizes or reifies matter and energy as fundamental and explains consciousness as emerging from it. This is akin to saying that the phenomenal world is intrinsically or inherently existent; but it is utterly not. How can one dispute that consciousness continues even after the breakup of the body without reifying the body and regarding it as fundamental and inherently existent in contradistinction to consciousness? I don't think it is possible.
Nevertheless, I'm convinced it is absolutely necessary to regard karma, rebirth, and the moral life as similarly ephemeral and lacking of intrinsic existence as all other phenomena including consciousness, matter and energy, in order to achieve the final soteriological goals of Buddhism.
If Buddhist and materialist schools share the same view on the most obvious meaning of anatta (quoted above), then what distinguishes the Buddhist view from the materialist view on no self?
Well, here we get into perhaps the subtle differences between "materialist" schools. I can't speak to the ancient Indian Charvaka materials school, but it is most obvious that modern scientific reductionists of the atheistic persuasion do not believe in any kind of permanent, unitary or independent self. So it is clear that someone like say Daniel Dennett (a modern day materialist) shares the belief in the most coarse meaning of anatta with Buddhists even though he does not - to my knowledge - identify himself as Buddhist; he does not take refuge in the Three Jewels and he does not share our soteriological goals nor even believe they are possible to accomplish. This is not to say that our soteriological goals themselves distinguish between the coarse and subtle meanings of emptiness! Just that if you believe it is possible to accomplish our soteriological goals, then it is manifestly evident that a meagerly coarse understanding of anatta cannot by itself accomplish them. Which brings us to...
Is there a not-so-obvious meaning of anatta which materialist/scientific reductionist schools fail to understand?
Yes!
And I believe understanding it is imperative to achieving the soteriological goals of Buddhism. Now, that isn't to say that understanding the most coarse meaning of anatta is useless. This is emphatically not the case! In fact, understanding the most coarse meaning of anatta is necessary waypoint to understanding the more subtle meanings. This is, after all, why the Buddha taught it :)
So how can one go beyond the coarse understanding to the more subtle meaning? Well, this is the question isn't it...
At this point, I want to make clear that I probably know nothing or that anything I might know is merely regurgitated (poorly) from much more qualified teachers. I'm just a lowly suffering sentient being trying to find liberation and aspiring to the motivation to achieve this for the benefit of all. In other words, take everything I say with a grain of salt and go check for yourself :)
Anyway, Je Tsongkhapa in his Great Treatise on the Stages of the Path (Volume 3, pages 204 - 215) spells out the actual object to be negated. Understanding the actual object to be negated is a key prerequisite to reasoning out the subtle meaning of emptiness and distinguishing it from the coarse meaning. This is very difficult and requires a ton of merit. Why? Because we have been blinded to this object - just assuming it a priori - since beginningless time. It is so ingrained in our thinking and taken as a given that we are just blind to it. This is our ignorance and delusion.
For lack of better terms we call this object many things: intrinsic existence, inherent existence, true existence, essential existence etc., But terms can't help us too much unless we know what they are referring to and for that we have to develop our intuition through study. To overcome our ignorance we must develop certain knowledge that nothing whatsoever has the type of existence pointed at by those inadequate terms.
If I had to pick one section of Je Tsongkhapa's Treatise that tries to directly answer the question of what the object of negation is it would be this section on page 212 and 213:

Question: How does ignorance superimpose intrinsic nature?
Reply: In general, there appear in Candrakırti’s texts many usages of verbal
  conventions such as “nature” or “essence” with regard to objects that
  exist only conventionally. However, here in the case of reification by
  ignorance, there is, with regard to objects, be they persons or other
  phenomena, a conception that those phenomena have ontological status—a
  way of existing—in and of themselves, without being posited through
  the force of an awareness. The referent object that is thus
  apprehended by that ignorant conception, the independent ontological
  status of those phenomena, is identified as a hypothetical “self” or
  “intrinsic nature.” For, Aryadeva’s Four Hundred Stanzas says:
All of this is without its own power; Therefore there is no self.
Commenting on this, Candrakirti’s Commentary on the “Four Hundred
  Stanzas” says:
It is that which exists essentially, intrinsically, autonomously, and without depending on another....
Thus, he says that
  those are synonyms. “Without depending on another” does not mean not
  depending on causes and conditions. Instead, “other” refers to a
  subject, i.e., a conventional conscious- ness, and something is said
  not to depend on another due to not being posited through the force of
  that conventional consciousness.
  Therefore, “autonomously” refers to
  the nature of an object that has its own unique ontological status or
  manner of being. It is just this that is called “essence” or
  “intrinsic nature.” Take, for example, the case of an imaginary snake that is mistakenly ascribed to a
  rope. If we leave aside how it is ascribed from the perspective that
  ap- prehends a snake and try to analyze what the snake is like in
  terms of its own nature, since a snake is simply not present in that
  object, its features cannot be analyzed. It is similar with regard to
  these phenomena. Suppose that we leave aside analysis of how they ap-
  pear—i.e., how they appear to a conventional awareness—and analyze the
  objects themselves, asking, “What is the manner of being of these
  phenomena?” We find they are not established in any way. Ignorance
  does not apprehend phenomena in this way; it apprehends each
  phenomenon as having a manner of being such that it can be understood
  in and of itself, without being posited through the force of a
  conventional consciousness. Candrakırti’s Commentary on the “Four
  Hundred Stanzas” says:
Without any doubt, what exists only through the presence of conceptual thought, and does not exist without conceptual thought, definitely does not exist essentially—as in the case of a snake that is imputed to a coiled rope.
Thus Candrakırti
  states how phenomena do not essentially exist.
Therefore, what exists
  objectively in terms of its own essence without being posited through
  the power of a subjective mind is called “self” or “intrinsic nature.”
  The absence of this quality in the person is called the
  selflessness of the person; its absence in phenomena such as eyes,
  ears, and so forth is called the selflessness of objects. Hence, one
  may implicitly understand that the conceptions of that intrinsic
  nature as present in persons and objects are the conceptions of the
  two selves. It is as Candrakırti’s Commentary on the “Four Hundred
  Stanzas” says:
“Self” is an essence of things that does not depend on others; it is an intrinsic nature. The nonexistence of that is selflessness. Because of the division into objects and persons, it is understood as twofold: a “selflessness of objects” and a “selflessness of persons.”

Now, let's say someone truly arrives at this subtle understanding... how does this help to achieve our soteriological goals? The best way I can answer that is this allegory that is given in Insight into Emptiness page 258:

“For example, a young woman may want to have a child. When she is
  asleep, she dreams she gives birth to a child and is elated. But later
  in the dream, the child dies and she is devastated. However, on
  waking, she sees that neither the exhilarating appearance of having a
  child that brought her joy nor the horrible appearance of the child’s
  death that caused her anguish is real.”

Understanding upon awakening that the dream was unreal the young woman was able to dispel the exhilaration as well as the devastation she felt. Likewise, upon truly realizing that all this phenomenal world is unreal - utterly not existing as it appears - we too can "wake up" and achieve our aims by cutting off the craving and attachment we acquire by believing in this completely ephemeral and hallucinatory "real" world.

I've made some edits to clarify my question. Namely, if Buddhist and scientific reductionist thinking share the same view on the most obvious meaning of anatta, then does the difference in thinking lie within a not-so-obvious meaning of anatta which materialist/scientific reductionist schools fail to understand?

It occurred to me while reading your answer that a difference between the two schools of thought, is that Buddhists define cessation as the cessation of craving, and not by death (therefore rebirth is possible), whereas materialists/scientific reductionists define the end as death (therefore no rebirth possible). This is my general observation, which might not say anything about the discussion on anatta, though.

@avatarKorra I've updated the answer to address your revised questions :)

Thank you, Yeshe! Please forgive me for asking for further clarification..I'm just not sure I can see the answer to my revised questions yet. For what distinguishes the Buddhist view from the materialist view on no self?, did you mean to say that, what distinguishes Buddhists from modern scientific reductionists on anatta, is that the latter does not share our soteriological goals?  For Is there a not-so-obvious meaning of anatta which materialist/scientific reductionist schools fail to understand? I was hoping to know what these subtler meanings are! These might answer my first question!

Here's an attempt to answer the remaining questions from my last comment: While the modern scientific reductionist/materialist view of anatta is similar to the Buddhist insofar as a coarse intellectual understanding, a materiallist still grasps at a sense of "I" or "mine", therefore indicating an incomplete understanding of no self, probably through failing
to understand of emptiness. @Yeshe Tenley, does any of that sound correct to you? Thanks!

@avatarKorra I'm probably just rambling at this point, but I've updated the answer. Hope it is at least somewhat helpful... getting quite long so maybe best to stop here.

So what I've now gathered is, first, that materialists are still ignorant that nothing is worth clinging to, nothing "mine", nothing that belongs to a self. Secondly, the subtler meaning of anatta which modern materialists fail to understand is emptiness. Ignorance on both these points would seem totally miss the soteriological goals of the Buddhist understanding of anatta.

@avatarKorra, I agree that materialists are still ignorant even after arriving at the coarse meaning of emptiness. I wouldn't call the subtler meaning of anatta emptiness insofar as anatta and emptiness mean the same thing... the only difference is the object they refer to; generaly speaking anatta refers to the selflessness of persons while generally speaking emptiness includes both the selflessness of persons and the selflessness of phenomena. It is ignorance on how reality actually exists that prevents us from achieving our aims of happiness.

There is no such thing as "doctrine of materialism" in the Pali suttas. Therefore, this term "materialism" should be completely ignored.
The Buddha taught all things, including Nibbana, were "elements" (MN 115) and this is a supreme enlightened view in Buddhism.
However, there are some alien doctrines the Buddha criticized that included the doctrine of elements because these these alien doctrines also included the doctrine of the inefficacy of kamma and the non-benefit of giving. These doctrines did not believe in morality, virtue & kammic inheritence, which is why the Buddha criticised them.
As for the doctrine "annihilationism" ("ucchedavāda"), in the Pali, this does not refer to disbelief in kammic inheritence & disbelief in causality (which are called "natthikavādo", "akiriyavādo" and "ahetukavādo"; per MN 60) or the disbelief in life after death. The term "annihilationism" ("ucchedavāda") refers to the view that a "self" ("atta") ends at "death". "Annihilationism" ("ucchedavāda") is a "self-view", which is why it is wrong view. Please refer to DN 1.

Annihilationism (Ucchedavāda)
There are, bhikkhus, some recluses and brahmins who are annihilationists and who on seven grounds proclaim the annihilation,
  destruction and extermination of an existent being. And owing to
  what, with reference to what, do these honorable recluses and brahmins
  proclaim their views?
Herein, bhikkhus, a certain recluse or a brahmin asserts the following doctrine and view: 'The self, good sir, has material
  form; it is composed of the four primary elements and originates from
  father and mother. Since this self, good sir, is annihilated and
  destroyed with the breakup of the body and does not exist after death,
  at this point the self is completely annihilated.' In this way
  some proclaim the annihilation, destruction, and extermination of an
  existent being.
DN 1

Please respect the Pali suttas, study Dhamma in the right way and take refuge in the Buddha rather than take refuge in teachers and worldly scholars that teach contrary to the Buddha.

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Responsibility in Buddhism
If nothing can be considered 'myself' or 'mine', if nothing is in my complete control (take volition for example), how can people be held responsible for their thoughts, words and deeds, if they are by definition not in charge?

Your question is a variation of the question, "if there is no self, then who is responsible for actions?"
The Buddha rubbished the notion that there is no self doing anything, in the Attakari Sutta:

“Venerable Gotama, I am one of such a doctrine, of such a view: ‘There
  is no self-doer, there is no other-doer.’”
  (“Natthi attakāro, natthi parakāro.”)
“I have not, brahman, seen or heard such a doctrine, such a view. How,
  indeed, could one — moving forward by himself, moving back by himself
  — say: ‘There is no self-doer, there is no other-doer’? What do you
  think, brahmin, is there an element or principle of initiating or
  beginning an action?”
“Just so, Venerable Sir.”
“When there is an element of initiating, are initiating beings clearly
  discerned?”
“Just so, Venerable Sir.”
“So, brahmin, when there is the element of initiating, initiating
  beings are clearly discerned; of such beings, this is the self-doer,
  this, the other-doer.
“What do you think, brahmin, is there an element of exertion ... is
  there an element of effort ... is there an element of steadfastness
  ... is there an element of persistence ... is there an element of
  endeavoring?”
“Just so, Venerable Sir.”
“When there is an element of endeavoring, are endeavoring beings
  clearly discerned?”
“Just so, Venerable Sir.”
“So, brahmin, when there is the element of endeavoring, endeavoring
  beings are clearly discerned; of such beings, this is the self-doer,
  this, the other-doer. I have not, brahmin, seen or heard such a
  doctrine, such a view as yours. How, indeed, could one — moving
  forward by himself, moving back by himself — say ‘There is no
  self-doer, there is no other-doer’?”

There is a self (the self-doer), but this self is impermanent, conditioned and compounded. It arises from the inter-working of the five aggregates, and ceases when the five aggregates cease. By breaking down a violin to its constituent components, you cannot find something called music. Similarly, by breaking down the five aggregates, you cannot find anything called the self. The self, like music, depends on the inter-working of other components, that are themselves dependent on other things. The self, like music, is not non-existent. Please see this answer for more details.
There is such a thing as the concept of wholesome thinking in Buddhism. Being virtuous, one reaps material benefits (see Ittha Sutta) and is also lead towards enlightenment (see Kimattha Sutta).
So, how can a lay person cultivate a wholesome way of thinking that would lead him towards becoming virtuous? AN5.57 holds the answer:

“And for the sake of what benefit should a woman or a man, a
  householder or one gone forth, often reflect thus: ‘I am the owner of
  my kamma, the heir of my kamma; I have kamma as my origin, kamma as my
  relative, kamma as my resort; I will be the heir of whatever kamma,
  good or bad, that I do’? People engage in misconduct by body, speech,
  and mind. But when one often reflects upon this theme, such misconduct
  is either completely abandoned or diminished. It is for the sake of
  this benefit that a woman or a man, a householder or one gone forth,
  should often reflect thus: ‘I am the owner of my kamma, the heir of my
  kamma; I have kamma as my origin, kamma as my relative, kamma as my
  resort; I will be the heir of whatever kamma, good or bad, that I do.’

And what about a noble disciple?

“This noble disciple reflects thus: ‘I am not the only one who is the
  owner of one’s kamma, the heir of one’s kamma; who has kamma as one’s
  origin, kamma as one’s relative, kamma as one’s resort; who will be
  the heir of whatever kamma, good or bad, that one does. All beings
  that come and go, that pass away and undergo rebirth, are owners of
  their kamma, heirs of their kamma; all have kamma as their origin,
  kamma as their relative, kamma as their resort; all will be heirs of
  whatever kamma, good or bad, that they do.’ As he often reflects on
  this theme, the path is generated. He pursues this path, develops it,
  and cultivates it. As he does so, the fetters are entirely abandoned
  and the underlying tendencies are uprooted.

By reflecting on the notion that all beings are owners of their kamma (and inherit the results), the noble disciple cultivates a wholesome thinking that results in renunciation.

When the Buddha taught about "not-self", he did so as a "realisation". This means, in the realised mind/person, selfishness ends; thus unwholesome & irresponsible actions end.
The Buddha did not teach "not-self" as expressed in the question. In other words, to laypeople living ordinary lives, the Buddha taught about "self" & "kamma" (i.e., "moral responsibility"). The suttas about "kamma & re-birth" do not teach about "not-self" ("anatta").
MN 117 describes the two sorts of Right View taught by the Buddha: (i) worldly right view for worldlings; and (ii) Noble Right view for aspirants. Kammic inheritance is worldly right view and anatta is Noble Right View. MN 117 is a crucially important sutta.

The quoted word "realisation": is that abhisambujjhati, is that the word English-speaking Buddhists mean when they write "realised"?

So noble right view refers to the 4 NT, correct? How are they experienced at best? I don't quite understand it. The Buddha talks about analysis and factors.

My primarily point is any understanding or reference to not-self (anatta) must result in unselfishness. There is no point using anatta merely as a philosophical idea that has no impact of relinquishment upon the mind. When the mind has no selfishness it will only do good. actions. A person cannot realise not-self and do immoral actions. This is impossible. Therefore evil & immoral Buddhist teachers (such as Chogram Trumpa) never ever realised not-self (even though they taught about it). Regards

If nothing can be considered 'myself' or 'mine', if nothing is in my complete control (take volition for example), how can people be held responsible for their thoughts, words and deeds, if they are by definition not in charge?
This question hints at two things to my mind: the notion of free will or agency and the notion of karma as a judge of right and wrong. Further, I think there might be confusion in the question with regards to the doctrine of anatta and the implication that persons lack agency.
Buddhism does not teach that persons lack volition... exactly the opposite! Buddhism teaches that actions are only accomplished with intent and persons manifestly do have agency. If persons did not have agency and we were all zombies forced to follow a completely deterministic path, then obviously there would be nothing to do. What could we do? Nothing. What choice would we have? None.
This is manifestly not what the Buddha taught.
Karma is also not some sort of judge of our right and wrong actions punishing us for our evil deeds and rewarding us for our righteous ones. The law of karma is simply an observation that certain actions bare certain fruits and we classify accordingly.
The doctrine of anatta and sunyata is deep and difficult to comprehend. It is famously said the Buddha despaired and hesitated before teaching it fearing that no one would be able to understand it. I think this saying is a precaution to guide us away from thinking the doctrine of anatta or emptiness somehow implies that persons lack agency or that our actions do not matter. Nothing could be further from the truth.


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What does Buddhism teach about the start and end of world?
I always wonder how all this started... How did we arrive here? What are we doing in this place?
So are there teachings in Buddhism that are clear on this point?
How did the world start? and How is it gonna end?

Here is one teaching the Buddha gave on the start of the world:

Dwelling at Savatthi. There the Blessed One addressed the monks: "I
  will teach you the origination of the world & the ending of the world.
  Listen & pay close attention. I will speak."
"As you say, lord," the monks responded to the Blessed One.
The Blessed One said: "And what is the origination of the world?
  Dependent on the eye & forms there arises eye-consciousness. The
  meeting of the three is contact. From contact as a requisite condition
  comes feeling. From feeling as a requisite condition comes craving.
  From craving as a requisite condition comes clinging/sustenance. From
  clinging/sustenance as a requisite condition comes becoming. From
  becoming as a requisite condition comes birth. From birth as a
  requisite condition, then aging & death, sorrow, lamentation, pain,
  distress, & despair come into play. This is the origination of the
  world.

And in the same teaching the Buddha gave the explanation for the end of the world:

"And what is the ending of the world? Dependent on the eye & forms
  there arises eye-consciousness. The meeting of the three is contact.
  From contact as a requisite condition comes feeling. From feeling as a
  requisite condition comes craving. Now, from the remainderless
  cessation & fading away of that very craving comes the cessation of
  clinging/sustenance. From the cessation of clinging/sustenance comes
  the cessation of becoming. From the cessation of becoming comes the
  cessation of birth. From the cessation of birth, then aging & death,
  sorrow, lamentation, pain, distress, & despair all cease. Such is the
  cessation of this entire mass of stress & suffering. This is the
  ending of the world.

To understand this I think takes familiarization with the Dharma and specifically the teachings on the Four Noble Truths and dependent origination.

how all these started?

There's no real starting point. But if you are asking the origin of earth and how it's populated, how we came here etc. you can read the Agganna sutta. We basically came from a Brahma realm called Abhassara. We were luminous beings. Not at all like monkeys. Only after a long time we changed into this monkey like form because of our behavior and what we consumed.

What are we doing in this place?

That's up to you to decide.

How it is gonna end?

Read the Satta Suriyuggamana sutta or Satta Suriya Patubava sutta. I don't have a link to a good English translation. Basically, it will end in fire this time. According to the Sutta, 7 suns will appear and burn the earth to a crisp. Some translate it as the sun expanding 7 times. But, given that the Andromeda galaxy is heading towards the Milky Way for a big clash before our sun dies, it's not unlikely that 7 suns will appear after about 4 billions years and burn us to oblivion.

To add to Yeshe Tenley's answer, the origin of the world is explained in Pali Canon's teaching on Dependent Co-arising, also known as the Twelve Nidanas. It all starts with Ignorance and proceeds to Craving (and Aversion) which leads to separation into "self" and "the world".
While Pali suttas don't go in too much details, this process of separation is further explained in the Tibetan tradition. Here is, for example, an abridged quote from Lamp of Mahamudra by Tsele Natsok Rangdrol:
Primordial "ground"

Your natural essence [...] is neither tainted nor spoiled by such designations as pleasant or unpleasant, being or not being, existent or nonexistent, permanent or annihilated, self or other, and so forth. Because it is not established as a certain kind of identity, your essence can serve as the basis for the manifestation of any form or conception to manifest. Yet, no matter how it manifests, ultimately this essence has no true existence. Thus, it is a great emptiness free from the limitations of arising, dwelling, and ceasing.

Ignorance

...Due to the ignorant aspect of this neutral all-ground, you do not cognize your own essence, and the natural state is not realized. In this way have you obscured yourself. Called "coemergent ignorance" or the "great darkness of beginningless time" since it is the basis from which all disturbing emotions and deluded thoughts arise, it is also known as the "all-ground of various tendencies." Hence it is the ground of confusion of all sentient beings.

Craving and separation

...From this coemergent ignorance arises a fixation on an ego and self-entity. On the basis of this "self" arises the fixation on "other." Not recognizing this personal manifestation for what is, a personal manifestation, one grasps at it as though it were an external object. [...] It is the cognitive act of confusing object and mind as being separate and is accompanied by the forty thought states resulting from desire, such as attachment and clinging.

The origin of the world

...Through the power of being habituated to confused fixation, your personal manifestations will appear as a world with inhabitants. [...] The various objects of gross materiality and the pure and impure parts of nadi, prana, and bindu of the inner body, as well as all the various phenomena of samsara and nirvana, the worlds and beings of the three realms, appear externally in an interdependent manner.

“Yet, no matter how it manifests, ultimately this essence has no true existence.“ thanks Andrei, I am not very familiar with Tantra so I appreciate this answer. One question... is “true existence” used here synonymously with inherent existence? On first glance it appears so to my mind...

Well, I think this text (and Kuntuzangpo's Aspiration Prayer it's based on) is an example of Shentong view. It makes a nod to Emptiness, but it is Shentong in spirit nevertheless. "True existence" must be a translation of Tibetan word for svabhava, though I don't know Tibetan so can't tell. Buddha would probably not approve of how it talks about "your essence" but the part about separation is good.

There are 10 questions that Buddha didn't answered..
About the beginning and end of world is one such question...
that subject is much far beyond from brain of human..And otherwise we don't need to know extra useless things to understand the truth what we are finding...

I take these statements to be true:

"A beginning is not evident" (a formula, describing samsara, which appears in several suttas)
"The cosmos is eternal" and "The cosmos is not eternal" have not been declared by the Blessed One (SN 44.7).

In other words, these are among The unanswered questions.
I prefer this to assuming that every conceivable question has a good answer -- see also for example Simsapa Sutta (SN 56.31).

This is a very good answer and I think it points to a difficulty here: what is the definition of the world and from which viewpoint are we speaking? For instance, in modern culture the world might be defined as the universe and the start the Big Bang... but even that has infamous and well known problems :)

I think that the word "samsara", and Buddhist dharma in general, describes a phenomenological world (I mean that loosely, not in a strict Western-philosophical sense), a perceived world as-experienced, and is all the more useful for doing so. As for "modern culture defining the world as the universe starting with the Big Bang", I dislike pointing to alleged parallels between Buddhism and Physics: especially, pointing to modern Physics to say "See? Buddhism was right all along: what Buddhism said earlier is what Physics is saying now!"

"I dislike pointing to alleged parallels between Buddhism and Physics"
You've said as much in the comment on the neuroscience question...
Can you say why? Also, why do you dislike comparisons of Buddhist doctrines to other religious/scientific doctrines or consider them off-topic? For me, I've found comparisons highly educational and useful to understanding... BTW, I was not using the Big Bang as a way of saying, "Buddhism was right all along" :)  Insofar as the Big Bang posits an absolute beginning my comment was much the opposite.

Sorry to repeat myself, then. Can you say why? I think they're misleading: Physics is (IMO) an attempt to explain what you see when launch cannon-balls, when you fire electrons at gold leaf or at a double-slit, or when you peer through a telescope, or put an airfoil in hypersonic wind flow, or any number of other experiments. And Buddhism isn't. And, I think it's a weak argument, i.e. "Buddhism is right because (a.k.a. if) it agrees with Physics", which might (wrongly) appear to leave Buddhism in second place.

@YesheTenley Also, why do you dislike comparisons of Buddhist doctrines to other religious/scientific doctrines or consider them off-topic? Part of that dislike is institutional rather than personal, i.e. it's policy of this site to dislike or distrust such questions: See Can we ban “comparative-religion” questions? for example or just for starters; also the "Broad comparisons" section of this; also Andrei's anser and comments here.

Fair enough. I've an education in Physics so for me it is much more than what you describe especially paired with the philosophy of science. I'd describe it as one of the leading zeitgeists of our time that's had profound impacts on our culture, our way of looking at the world and our place in it, and our very conception of ourselves and note that the Buddha did make explicit comparisons of his teachings with the prevailing zeitgeists of his time in order to guide people on the correct path.

Let us continue this discussion in chat.