user11063: First of all, I'd like to say I'm a scientist. This means fact will always come before faith, even if it hurts. In general, one's opinion doesn't mean much if the question itself has no meaning, but when the question is well phrased and has a quantitative background, then experiment is the ultimate - and decisive - destination. 
Secondly, I'm afraid this will be a rather long question.
According to Walpola Rahula in his book What the Buddha Taught, Buddhism denies the existence of a soul or spirit:

Buddhism stands unique in the history of human thought in denying the existence of such a Soul, Self, or Atman. According to the teaching of the Buddha, the idea of self is an imaginary, false belief which has no corresponding reality, and it produces harmful thoughts of 'me' and 'mine', selfish desire, craving, attachment, hatred, ill-will, conceit, pride, egoism, and other defilements, impurities and problems. It is the source of all the troubles in the world from personal conflicts to wars between
  nations. In short, to this false view can be traced all the evil in the world.

This pleases me very much. As a scientist, I cannot conceive the existence of something we cannot observe or measure that lives on after I die. Everything Buddhism talks about pleases me very much: everything is dukkha, there's a way out of dukkha, we are unhappy because we cling to everything, and the path outside this unhappiness is to understand nothing has intrinsic value or meaning. In resume: I think Buddhism, unlike the other religions I've been exposed to, is beautiful and makes sense. But then I have a problem - and it's a big one, because it's in the eye of the tornado. 
According to Walpola Rahula (same book), 

Will, volition, desire, thirst to exist, to continue, to become more and more, is a tremendous force that moves whole lives, whole existences, that even moves the whole world. This is the greatest force, the greatest energy in the world. According to Buddhism, this force does not stop with the non-functioning of the body, which is death; but it continues manifesting itself in another form, producing re-existence which is called rebirth.

Now we have a problem. I've seen people discussing the differences between mind, brain, consciousness, etc. Well, science is pretty clear: the evidence is now overwhelming that every aspect of the mind is produced by the brain. I'm pretty familiar with NMR scanning and did read some hundreds of articles about the subject, and we have a huge, massive consensus that nothing survives our death. Not a force, not a will... Nothing. We can't see nothing. It doesn't exist.
Now, I have come to a more traditional (non-westernized) version of rebirth by reading this wonderful, majestically written article by an evolutionary biologist (and aspiring Buddhist): even though people like to talk about rebirth as a deterministic process, it is not. It appears Buddha himself (see article) has said that rebirth is like lighting a candle with another's fire: everything is lost and there cannot be a causal process that links you to "former lives". Actually, the only part of rebirth that doesn't violate scientific laws is to say that my atoms will be reborn in other creatures and objects. And that pleases me very much.
Now, a famous quote says that:

If science proves some belief of Buddhism is wrong, then Buddhism will have to change.

It is attributed to Dalai Lama (probably wrongly), and is found in this great article by Tenzin Gyatso, where many scientifically proved benefits of meditation are discussed. If this sentence makes sense to Buddhists, why do they keep insisting in the concept of rebirth? Science is clear: there's no support of any evidence in its favour, at least not in the way I see people treating the subject. Buddha's metaphor about "lighting candles" is much better to have as an example, since it doesn't contradict facts, even though it doesn't make a lot of sense either. 
I'd therefore like to know passages from suttas where Buddha affirms that knowledge of past lives is unattainable, or at least where He elucidates reincarnation is not something causal. If there aren't any, why do people still believing in this concept? Only because they feel safer? 
Edit: This question is turning into a chimaera of weird unwanted lessons: people telling me I'm not ready for knowledge, or that articles that elucidate their misconceptions are not valid, or that I don't know the meaning of truth, or people trying to teach me concepts my PhD is about, and even people saying their own views are perfect. Until now, the most useful references where given by Dhammadhatu, and the best answers by ChrisW and Tenzin Dorje. Please refrain from counselling and preaching.

user6994: 
Everything is dukkha

Not everything is dukkha. Otherwise, there would be no way out.

Nothing has intrinsic value or meaning. 

It is not so much that phenomena lack intrinsic value or meaning, it is that they lack intrinsic existence. The object of negation is a mode of existence, it is not just value or meaning.
As to your question, consciousness is that which is clear and knowing. It is in the nature of clarity and has the function of knowing. Since a consciousness is always a consciousness of something, we usually speak in terms of instances. For instance, we speak of "an eye consciousness apprehending a cup", "an ear consciousness apprehending a birdsong", "a memory consciousness remembering a person" and so forth. There is no consciousness that does not depend on a basis that is its apprehended object. This is one of the various reasons we say there is no soul (if by soul we mean something immaterial that does not depend on an apprehended object).
Furthermore, we would probably agree with the scientific claim that "Consciousness depends on the brain." The whole question is: In what way does consciousness depend on the brain? What is the nature of that dependence?
A consciousness also depends on its apprehended object, since there is no independent consciousness. A consciousness also depends on its function, since there is no consciousness that does not accomplish a function. A consciousness also depends on the previous moment of consciousness, and so forth. Thus, a consciousness depends on various factors, but that does not mean that these factors are necessary conditions.
I doubt His Holiness (whom you quote) would be convinced that the brain and consciousness (that is, the mind stream) are one entity. I doubt he would be convinced one is a necessary condition of the other. In fact, there is no proof that the brain is a necessary condition, merely that consciousness depends on it. In short, we do not know the nature of this dependence.
All in all, His Holiness's school posits that the substantial cause of consciousness is a preceding moment of consciousness. It means that a consciousness is like a seed to a tree. A seed causes the tree, it becomes the tree, it no longer exists at the time of the tree (unlike your parents who caused your birth and still exist after that), and is a necessary condition. It is the main reason why we say that, since a consciousness can not turn into anything but a next moment of consciousness, the continuum does not end. So-called Hinayana tenets might hold a different view.

user254: why do people still believing in this concept? Only because they feel safer?
That sounds like a question which ought to have been answered by this earlier question: What's the value or harm of a literal belief in rebirth?
The most on-topic answer to that question seems to me to be Ven. Yuttadhammo's, and the second article of Bhikkhu Bodhi's which he quotes.
I summarize these answers as:

It's what the Buddha taught, according to the suttas
It encourages moral behaviour (even virtuous deaths)
It encourages us to be, not only heedful of the now, but to also wisely review our past
It makes us examine cause-and-effect, and conditionality (as you are doing, in this topic)
It makes us consider what (and when) conciousness is (e.g. it's not the same thing as the body)

I'd therefore like to know passages from suttas where Buddha affirms that knowledge of past lives is unattainable, or at least where He elucidates reincarnation is not something causal.
There are passages in the suttas where, I think, the Buddha affirms that he has seen his own past lives. It's described in Maha-Saccaka Sutta MN 36 in which he describes his becoming enlightened:

When the mind was thus concentrated, purified, bright, unblemished, rid of defilement, pliant, malleable, steady, & attained to imperturbability, I directed it to the knowledge of recollecting my past lives. I recollected my manifold past lives, i.e., one birth, two...five, ten...fifty, a hundred, a thousand, a hundred thousand, many eons of cosmic contraction, many eons of cosmic expansion, many eons of cosmic contraction & expansion: 'There I had such a name, belonged to such a clan, had such an appearance. Such was my food, such my experience of pleasure & pain, such the end of my life. Passing away from that state, I re-arose there. There too I had such a name, belonged to such a clan, had such an appearance. Such was my food, such my experience of pleasure & pain, such the end of my life. Passing away from that state, I re-arose here.' Thus I remembered my manifold past lives in their modes & details.
This was the first knowledge I attained in the first watch of the night. Ignorance was destroyed; knowledge arose; darkness was destroyed; light arose — as happens in one who is heedful, ardent, & resolute. But the pleasant feeling that arose in this way did not invade my mind or remain.

In other suttas the Buddha sometimes also described what someone's current (new) abode was, after they died.
But apart from that, to try to answer your question, there are other suttas too, where I think he does suggest that knowledge of past lives is unattainable or, at least, not a useful goal at this stage.
The Sabbasava Sutta warns that there are questions:

Was I in the past? Was I not in the past? What was I in the past? How was I in the past? Having been what, what was I in the past? Shall I be in the future? etc. etc.

... and views:

The view I have a self arises in him as true & established, or the view I have no self... or the view It is precisely by means of self that I perceive self... or the view It is precisely by means of self that I perceive not-self etc. etc.

... and warns that these kinds of thinking do not lead to freedom:

This is called a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views. Bound by a fetter of views, the uninstructed run-of-the-mill person is not freed from birth, aging, & death, from sorrow, lamentation, pain, distress, & despair. He is not freed, I tell you, from suffering & stress.

I take that as a warning that thinking about (having views about) a "self" will produce a "thicket of views".
Another part of Buddhism Dharma is anatta which you may need to integrate or reconcile with the theory-or-doctrine of rebirth.
Some (many) people distinguish "reincarnation" from "rebirth": in that "reincarnation" implies that something, the same thing (e.g. a "soul"), is being reincarnated (which is contrary to the Buddhist doctrine of Anatta); whereas "rebirth" just implies another birth (of a different "being").
And some people say that "past life" is a mistranslation of "past abode" ... and that successive lives should be understand as successive moments of being or of identity-view (i.e. of believing that the self exists), within this (body's) life ... I think this is as opposed to a so-called "literal belief in rebirth".
Actually, the only part of rebirth that doesn't violate scientific laws is to say that my atoms will be reborn in other creatures and objects.
If my mum and I look at some apple, do we see the same thing? Are we both conscious of seeing it? Do we both have apple-seeing-consciousness? Do we share apple-seeing-consciousness? And without "she" and "me" as personal identities, does apple-seeing-consciousness exist in two bodies?
It may be a mistake to see them as "my" atoms (or my apple-seeing-consciousness). The first sutta of the Anatta doctrine teaches, "this is not me, this is not mine, this is not my self".
the evidence is now overwhelming that every aspect of the mind is produced by the brain
Taking Isaac Newton as a famous example, isn't it more obvious that (moment of) consciousness was produced by an apple, falling on his head?
I think I understand what you're saying, though, which is that "mind is conditioned by the brain". I think that translations of Buddhism into English uses the verb condition, to mean, "a brain is a necessary condition for a mind to exist, so if brain ceases then mind ceases (or, mind doesn't arise) too".
But rebirth: a new brain, the whole apparatus (ignoring, for the sake of argument, possibility of rebirth in one of the formless realms).

11063: <p>First of all, I'd like to say I'm a scientist. This means fact will always come before faith, even if it hurts. In general, one's opinion doesn't mean much if the question itself has no meaning, but when the question is well phrased and has a quantitative background, then experiment is the ultimate - and decisive - destination. </p>

<p>Secondly, I'm afraid this will be a rather long question.</p>

<p>According to Walpola Rahula in his book <a href="https://rads.stackoverflow.com/amzn/click/0802130313" rel="nofollow noreferrer">What the Buddha Taught</a>, Buddhism denies the existence of a soul or spirit:</p>

<blockquote>
  <p>Buddhism stands unique in the history of human thought in denying the existence of such a Soul, Self, or Atman. According to the teaching of the Buddha, the idea of self is an imaginary, false belief which has no corresponding reality, and it produces harmful thoughts of 'me' and 'mine', selfish desire, craving, attachment, hatred, ill-will, conceit, pride, egoism, and other defilements, impurities and problems. It is the source of all the troubles in the world from personal conflicts to wars between
  nations. In short, to this false view can be traced all the evil in the world.</p>
</blockquote>

<p>This pleases me very much. As a scientist, I cannot conceive the existence of something we cannot observe or measure that lives on after I die. Everything Buddhism talks about pleases me very much: everything is dukkha, there's a way out of dukkha, we are unhappy because we cling to everything, and the path outside this unhappiness is to understand nothing has intrinsic value or meaning. In resume: I think Buddhism, unlike the other religions I've been exposed to, is beautiful and makes sense. But then I have a problem - and it's a big one, because it's in the eye of the tornado. </p>

<p>According to Walpola Rahula (same book), </p>

<blockquote>
  <p>Will, volition, desire, thirst to exist, to continue, to become more and more, is a tremendous force that moves whole lives, whole existences, that even moves the whole world. This is the greatest force, the greatest energy in the world. According to Buddhism, this force does not stop with the non-functioning of the body, which is death; but it continues manifesting itself in another form, producing re-existence which is called rebirth.</p>
</blockquote>

<p>Now we have a problem. I've seen people discussing the differences between mind, brain, consciousness, etc. Well, science is pretty clear: <a href="http://www.huffingtonpost.com/michael-graziano/the-spirit-dies-when-the-brain-dies_b_983852.html" rel="nofollow noreferrer">the evidence is now overwhelming that every aspect of the mind is produced by the brain.</a> I'm pretty familiar with NMR scanning and did read some hundreds of articles about the subject, and we have a huge, massive consensus that nothing survives our death. Not a <em>force</em>, not a <em>will</em>... Nothing. We can't see nothing. It doesn't exist.</p>

<p>Now, I have come to a more traditional (non-westernized) version of rebirth by reading <a href="https://www.psychologytoday.com/blog/pura-vida/201312/buddhist-reincarnation-and-the-silliness-about-souls" rel="nofollow noreferrer">this wonderful, majestically written article</a> by an evolutionary biologist (and aspiring Buddhist): even though people like to talk about rebirth as a deterministic process, it is not. It appears Buddha himself (see article) has said that rebirth is like lighting a candle with another's fire: everything is lost and there cannot be a causal process that links you to "former lives". Actually, the only part of rebirth that doesn't violate scientific laws is to say that my atoms will be reborn in other creatures and objects. And that pleases me very much.</p>

<p>Now, a famous quote says that:</p>

<blockquote>
  <p>If science proves some belief of Buddhism is wrong, then Buddhism will have to change.</p>
</blockquote>

<p>It is attributed to Dalai Lama (probably wrongly), and is found <a href="http://www.nytimes.com/2005/11/12/opinion/our-faith-in-science.html" rel="nofollow noreferrer">in this great article by Tenzin Gyatso</a>, where many scientifically proved benefits of meditation are discussed. If this sentence makes sense to Buddhists, why do they keep insisting in the concept of rebirth? Science is clear: there's no support of any evidence in its favour, at least not in the way I see people treating the subject. Buddha's metaphor about "lighting candles" is much better to have as an example, since it doesn't contradict facts, even though it doesn't make a lot of sense either. </p>

<p><strong>I'd therefore like to know passages from suttas where Buddha affirms that knowledge of past lives is unattainable, or at least where He elucidates reincarnation is not something causal. If there aren't any, why do people still believing in this concept? Only because they feel safer?</strong> </p>

<p><strong>Edit:</strong> This question is turning into a chimaera of weird unwanted lessons: people telling me I'm not ready for knowledge, or that articles that elucidate their misconceptions are not valid, or that I don't know the meaning of truth, or people trying to teach me concepts my PhD is about, and even people saying their own views are perfect. Until now, the most useful references where given by Dhammadhatu, and the best answers by ChrisW and Tenzin Dorje. Please refrain from counselling and preaching.</p>
 6994: <blockquote>
  <p>Everything is dukkha</p>
</blockquote>

<p>Not everything is dukkha. Otherwise, there would be no way out.</p>

<blockquote>
  <p>Nothing has intrinsic value or meaning. </p>
</blockquote>

<p>It is not so much that phenomena lack intrinsic value or meaning, it is that they lack intrinsic existence. The object of negation is a mode of existence, it is not just value or meaning.</p>

<p>As to your question, consciousness is <em>that which is clear and knowing</em>. It is in the nature of clarity and has the function of knowing. Since a consciousness is always a consciousness of something, we usually speak in terms of instances. For instance, we speak of "an eye consciousness apprehending a cup", "an ear consciousness apprehending a birdsong", "a memory consciousness remembering a person" and so forth. There is no consciousness that does not depend on a basis that is its apprehended object. This is one of the various reasons we say there is no soul (if by soul we mean something immaterial that does not depend on an apprehended object).</p>

<p>Furthermore, we would probably agree with the scientific claim that "Consciousness depends on the brain." The whole question is: In what way does consciousness depend on the brain? What is the nature of that dependence?</p>

<p>A consciousness also depends on its apprehended object, since there is no independent consciousness. A consciousness also depends on its function, since there is no consciousness that does not accomplish a function. A consciousness also depends on the previous moment of consciousness, and so forth. Thus, a consciousness depends on various factors, but that does not mean that these factors are necessary conditions.</p>

<p>I doubt His Holiness (whom you quote) would be convinced that the brain and consciousness (that is, the mind stream) are one entity. I doubt he would be convinced one is a necessary condition of the other. In fact, there is no proof that the brain is a necessary condition, merely that consciousness depends on it. In short, we do not know the nature of this dependence.</p>

<p>All in all, His Holiness's school posits that the substantial cause of consciousness is a preceding moment of consciousness. It means that a consciousness is like a seed to a tree. A seed causes the tree, it becomes the tree, it no longer exists at the time of the tree (unlike your parents who caused your birth and still exist after that), and is a necessary condition. It is the main reason why we say that, since a consciousness can not turn into anything but a next moment of consciousness, the continuum does not end. So-called Hinayana tenets might hold a different view.</p>
 254: <p><strong>why do people still believing in this concept? Only because they feel safer?</strong></p>
<p>That sounds like a question which ought to have been answered by this earlier question: <a href="https://buddhism.stackexchange.com/q/51/254">What's the value or harm of a literal belief in rebirth?</a></p>
<p>The most on-topic answer to that question seems to me to be Ven. Yuttadhammo's, and the second article of Bhikkhu Bodhi's which he quotes.</p>
<p>I summarize these answers as:</p>
<ul>
<li>It's what the Buddha taught, according to the suttas</li>
<li>It encourages moral behaviour (even virtuous deaths)</li>
<li>It encourages us to be, not only heedful of the now, but to also wisely review our past</li>
<li>It makes us examine cause-and-effect, and conditionality (as you are doing, in this topic)</li>
<li>It makes us consider what (and when) conciousness is (e.g. it's not the same thing as the body)</li>
</ul>
<p><strong>I'd therefore like to know passages from suttas where Buddha affirms that knowledge of past lives is unattainable, or at least where He elucidates reincarnation is not something causal.</strong></p>
<p>There are passages in the suttas where, I think, the Buddha affirms that he has seen his own past lives. It's described in <a href="http://www.accesstoinsight.org/tipitaka/mn/mn.036.than.html" rel="nofollow noreferrer">Maha-Saccaka Sutta MN 36</a> in which he describes his becoming enlightened:</p>
<blockquote>
<p>When the mind was thus concentrated, purified, bright, unblemished, rid of defilement, pliant, malleable, steady, &amp; attained to imperturbability, I directed it to the knowledge of recollecting my past lives. I recollected my manifold past lives, i.e., one birth, two...five, ten...fifty, a hundred, a thousand, a hundred thousand, many eons of cosmic contraction, many eons of cosmic expansion, many eons of cosmic contraction &amp; expansion: 'There I had such a name, belonged to such a clan, had such an appearance. Such was my food, such my experience of pleasure &amp; pain, such the end of my life. Passing away from that state, I re-arose there. There too I had such a name, belonged to such a clan, had such an appearance. Such was my food, such my experience of pleasure &amp; pain, such the end of my life. Passing away from that state, I re-arose here.' Thus I remembered my manifold past lives in their modes &amp; details.</p>
<p>This was the first knowledge I attained in the first watch of the night. Ignorance was destroyed; knowledge arose; darkness was destroyed; light arose — as happens in one who is heedful, ardent, &amp; resolute. But the pleasant feeling that arose in this way did not invade my mind or remain.</p>
</blockquote>
<p>In other suttas the Buddha sometimes also described what someone's current (new) abode was, after they died.</p>
<p>But apart from that, to try to answer your question, there are other suttas too, where I think he does suggest that knowledge of past lives is unattainable or, at least, not a useful goal at this stage.</p>
<p>The <a href="http://www.accesstoinsight.org/tipitaka/mn/mn.002.than.html" rel="nofollow noreferrer">Sabbasava Sutta</a> warns that there are questions:</p>
<blockquote>
<p>Was I in the past? Was I not in the past? What was I in the past? How was I in the past? Having been what, what was I in the past? Shall I be in the future? etc. etc.</p>
</blockquote>
<p>... and views:</p>
<blockquote>
<p>The view I have a self arises in him as true &amp; established, or the view I have no self... or the view It is precisely by means of self that I perceive self... or the view It is precisely by means of self that I perceive not-self etc. etc.</p>
</blockquote>
<p>... and warns that these kinds of thinking do not lead to freedom:</p>
<blockquote>
<p>This is called a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views. Bound by a fetter of views, the uninstructed run-of-the-mill person is not freed from birth, aging, &amp; death, from sorrow, lamentation, pain, distress, &amp; despair. He is not freed, I tell you, from suffering &amp; stress.</p>
</blockquote>
<p>I take that as a warning that thinking about (having views about) a &quot;self&quot; will produce a &quot;thicket of views&quot;.</p>
<p>Another part of Buddhism Dharma is <a href="/questions/tagged/anatta" class="post-tag" title="show questions tagged &#39;anatta&#39;" rel="tag">anatta</a> which you may need to integrate or reconcile with the theory-or-doctrine of rebirth.</p>
<p>Some (many) people distinguish &quot;reincarnation&quot; from &quot;rebirth&quot;: in that &quot;reincarnation&quot; implies that something, the same thing (e.g. a &quot;soul&quot;), is being reincarnated (which is contrary to the Buddhist doctrine of Anatta); whereas &quot;rebirth&quot; just implies another birth (of a different &quot;being&quot;).</p>
<p>And <a href="https://buddhism.stackexchange.com/a/18103/254">some people say</a> that &quot;past life&quot; is a mistranslation of &quot;past abode&quot; ... and that successive lives should be understand as successive moments of being or of identity-view (i.e. of believing that the self exists), within this (body's) life ... I think this is as opposed to a so-called &quot;literal belief in rebirth&quot;.</p>
<p><strong>Actually, the only part of rebirth that doesn't violate scientific laws is to say that my atoms will be reborn in other creatures and objects.</strong></p>
<p>If my mum and I look at some apple, do we see the same thing? Are we both conscious of seeing it? Do we both have apple-seeing-consciousness? Do we share apple-seeing-consciousness? And without &quot;she&quot; and &quot;me&quot; as personal identities, does apple-seeing-consciousness exist in two bodies?</p>
<p>It may be a mistake to see them as &quot;my&quot; atoms (or my apple-seeing-consciousness). The first sutta of the Anatta doctrine teaches, &quot;this is not me, this is not mine, this is not my self&quot;.</p>
<p><strong>the evidence is now overwhelming that every aspect of the mind is produced by the brain</strong></p>
<p>Taking Isaac Newton as a famous example, isn't it more obvious that (moment of) consciousness was produced by an apple, falling on his head?</p>
<p>I think I understand what you're saying, though, which is that &quot;mind is conditioned by the brain&quot;. I think that translations of Buddhism into English uses the verb <em>condition</em>, to mean, &quot;a brain is a necessary condition for a mind to exist, so if brain ceases then mind ceases (or, mind doesn't arise) too&quot;.</p>
<p>But rebirth: a new brain, the whole apparatus (ignoring, for the sake of argument, possibility of rebirth in one of the formless realms).</p>
