user5801: The Theory of "Emptiness" is the concept that all phenomenon are empty of inherent existence. Something has the illusion of existence when the right causes and conditions arise. Example: there is no inherently existing chicken soup. You only get chicken soup when you put together a dead chicken, hot water. Veggies etc. in this theory, you illusory sense of self comes from the right causes and conditions, parents, a body, a brain etc. following this logic, upon death, the self should simply cease to exist because that which made you a self has dissolved and since you do not inherently exist you should just vanish, and yet the Buddha is clear we take rebirth. This is illogical and makes no sense. Perhaps this is why the Buddha never taught a theory of emptiness. This idea is nowhere in the entire Pali Canon. 

user13375: The question seems an objection to Mahayana concept of emptiness. I will try and give the answer to this objection from the Prasangika viewpoint:

the self should simply cease to exist because that which made you a self has dissolved and since you do not inherently exist you should just vanish

I don't think there is any reason to invoke rebirth if this is your objection to the emptiness of inherent existence. By this line of reasoning, if phenomena lacked inherent existence (ie, they are empty), then moment-to-moment in this very life, a person would vanish. However, we do not vanish. So, either the line of reasoning is based on incorrect assumptions or it is valid and leads to absurdity thus refuting emptiness of inherent existence.
I believe the line of reasoning is based upon an incorrect assumption: that things lacking inherent existence will be unable to function. 
Let's set aside the selflessness of phenomena and look only at the selflessness of the person as this is agreed upon by Theravada and the Mahayana. It is clear, the Theravada posits the selflessness of persons. That people lack inherent existence.
This line of reasoning also refutes the Theravada position: if people lack inherent existence, then they will be unable to function and thus they will vanish in this very moment! So either the line of reasoning is flawed - it assumes the incorrect assumption that lacking inherent existence renders things non-functional - or the Theravada selflessness of persons has also been refuted as well.

user5715: Rebirth
First of all the idea of emptiness doesn't really apply to chicken soup. This is a widespread misinterpretation. It principally applies to experiences. The basic idea is that there is a sense-object (arambaṇa) and a sense-faculty (indriya) and when the two come together in the presence of sense-cognition (vijñāna) then this produces an experience (vedanā), which then gives rise to a whole range of speculative mental processes (prapañca). 
Note that vedanā comes from a verbal root √vid, meaning "to know, to discover". We have vedanā when we know we are experiencing something. So dependent arising is describing, not the arising of chicken soup, but the arising of a conscious experience. And of course experience is characterised by impermanence (anitya), disappointment (duḥkha), and lack of substance (anātman).  
In this theory, the experience of being a self happens in just the same way. The first-person perspective and the sense of being someone who is having an experience, are just more kinds of experience. The kind that happen then the arambaṇa is a mental process and the indriya is the mental faculty and there is mental cognition. 
Any arguments over whether the experience exists (asti) or does not exist (nāsti) are kind of meaningless. When you eat a peach, does the taste of peach exist? Or not? Or is the language of "being" inappropriate here? Early Buddhist texts argue that asti and nāsti don't apply to the world of experience (e.g. Kaccānagotta Sutta SN 12.15). And one of the ways of expressing this is to say that experiences are anātman - they don't have any kind of substance. 
So to say that the self exists, or that at death it ceases to exist, is simply to misunderstand the situation. The sense of being a self, like the taste of peach, only persists when the conditions are present. It ceases, for example, if one is knocked unconscious! Or if one experiences nirodhasamāpatti in meditation. What we loosely call "self" is just an experience. At death that experience stops arising in us. Buddhists argue that either immediately, or after a period of time, that the experience arises in another being, based on the condition of the last moments of the dead persons conscious experience. 
The implication here is similar to what we find in the philosophy of Kant. Everything we know comes from experience. Experience is constantly changing. Therefore we cannot know anything that is permanent. If something were permanent we'd either have to always know it or always be ignorant of it. In fact simple introspection shows that experience is constantly changing and nothing is constantly in our minds - ergo we can have no knowledge of anything permanent. If there is a permanent ātman, we could never know anything about it.
It is important for Buddhism that rebirth happens. Without it the morality of Buddhism falls apart. Buddhists are realistic enough to see that in this life the wicked frequently go unpunished and the good go unrewarded. All moral systems of thought are oriented towards a "Just World" in which everyone gets what they deserve. In most moral systems this is overseen by a supernatural agent, a god of justice (e.g. in the Vedas Mitra and Varuṇa over see different aspects of keeping things in balance). Without a supernatural agent, it is necessary that the moral agent live again so as to experience the consequences of their actions. 
In the India systems with an ātman or jīva (i.e. a permanent aspect of the psyche) that passes from life to life this is straightforward. For Buddhists it is complicated by our denial of personal continuity. An ātman would wreck our metaphysics and so we have this on going tension between morality which demands continuity to obtain a just world, and metaphysics which denies continuity because permanence would ruin dependent arising. 
When we try to apply this theory to objects that exist independently of our experience (such as in the chicken soup example) then the theory does not hold together. Buddhists who tried this ended up proposing contradictory notions such as the Two Truths, which rather than rejecting asti and nāsti, try to argue that objects are both asti and nāsti. This is because objects and experiences are of a very different nature. What is true of experience is not necessarily true of objects. It is a bad mistake to use a theory of experience as a theory of objects; and a catastrophe to use it as a theory of reality. 
Such a theory was never meant to stand up to the kind of scrutiny we now subject it to. It was an ad hoc explanation for something that was widely believed to be the case in North Indian by at least the 8th century BCE. and for centuries people all over the world found it plausible. 
Theories of Emptiness
It is quite wrong to say that the Buddha did not teach a theory of emptiness. If you look for the Pāḷi words suññā (empty) and suññatā (emptiness) you will find that they occur many times. A survey of these uses in the Pāḷi texts and their Chinese counterparts can be found in 

CHOONG, Mun-keat. (1999) The Notion of Emptiness in Early Buddhism. 2nd. Ed. Motilal Banarsidass.

Also I believe that Bhikkhu Anālayo's new book, Compassion and Emptiness in Early Buddhist Meditation, tackles some of the same themes (though I have not read it).
It is true that the doctrine of emptiness changed over the centuries, but the Buddha (if the early Buddhist texts do represent his words) did indeed teach about emptiness. The early Buddhist texts (and the Āgamas more so than the Nikāya) use the idea of emptiness in a number of ways:

An empty place (i.e. where there are no people), which is used as a metaphor for ... 
A samādhi state (Pali suññatāvihāra; Chinese 空三昧 = Skt śūnyasamādhi) in which there is no experience, i.e. a state in which there is no conscious mental activity.
The emptiness of the world (suñño loko) of self or anything belonging to self (suññaṃ attena vā attaniyena vā).
A synonym for nibbāna.

These meanings were developed over time into the various theories of emptiness we know about today. The 3rd use in Pāḷi is adapted by Nāgārjuna to give the classic early Madhyamaka interpretation of emptiness which is that dharmas are empty of svabhāva - i.e. that nothing can be a condition for it's own existence (which was an implication of later Abhidharma speculation). 

user745: The teaching that all things composed of parts are without self, but are mere names and labels designated in dependence on their parts, is something that most definitely is taught in the Pali canon, quite explicitly in the Vajira Sutta with the analogy of the analysis of the Chariot.
The reason this doesn't contradict rebirth is that when a person dies, their final consciousnesses cause the arising of a new consciousness in dependence on a new body, and this new mind and body can be conventionally called a self, and there is a causal relationship between the two.

user18: Not all forms of Buddhism define emptiness in the way you describe; in Theravada Buddhism, for example, emptiness mainly means "empty of self":

“katamā cāvuso, suññatā cetovimutti”?
“idhāvuso, bhikkhu araññagato vā rukkhamūlagato vā suññāgāragato vā iti paṭisañcikkhati — ‘suññamidaṃ attena vā attaniyena vā’ti. ayaṃ vuccatāvuso, suññatā cetovimutti”.
"And what, friend, is liberation of mind through emptiness?"
"Here, friend, a bhikkhu, gone to the forest or gone to the root of a tree or gone to an empty dwelling reflects thus: 'empty is this of self or what belongs to self.' This one calls, friend, liberation of mind through emptiness."
-- MN 43

Being empty of self is different from not existing; it simply means that, from the point of view of experience, that which comes into existence does so from non-existence, and subsequently returns to non-existence; it has no existence outside of the single moment:

“aniccā vata saṅkhārā, uppādavayadhammino.
  uppajjitvā nirujjhanti, tesaṃ vūpasamo sukho”ti.
"Impermanent indeed are formations, of a nature to arise and fall.
  Having arisen, they cease, their tranquillizing is happiness."
-- DN 16
“yaṃ kiñci samudayadhammaṃ sabbaṃ taṃ nirodhadhamman”ti.
"Whatever is of a nature to arise, all of that is of a nature to cease."
-- DN 3
yasmā ca kho, ānanda, suññaṃ attena vā attaniyena vā tasmā suñño lokoti vuccati.
Because it is, Ananda, empty by way of self or what belongs to self, therefore 'the world is empty' is said.
--SN 35.68

There is only one example in Theravada Buddhism that I know of that is cited as support for the idea of emptiness being related to non-existence - in the Patisambhidamagga:

katamaṃ vipariṇāmasuññaṃ? jātaṃ rūpaṃ sabhāvena suññaṃ.
What is emptiness due to change? Born form is empty by way of intrinsic existence.
-- Paṭis. XX.5

The commentary to this passage refutes the idea that this refers to non-existence, however:

'Void of individual essense': here sabhāva is sayaṃ bhāvo; arising of itself is the meaning. Or sabhāva is sako bhāvo; own arising. Because of existence in dependence on conditions there is in it no essence by itself or essence of its own, thus it is "void of individual essence".
...
But if someone should say: "Own essence is individual essence; it is void of that individual essence. ... Because of the non-existence of any idea whatever it is the non-existence of materiality that is expressed by the words 'born materiality is void of individual essence.'" It should be argued thus: that being so, the words 'born materiality' would be contradicted; for what is devoid of arising is not called 'born'. ... And the word 'void' for what is non-existent contradicts the Blessed One's use of it above for the 'world' and also the words of the books of logic and linguistics; and it contradicts many logical arguments.
-- Path of Discrimination, p. 362 (Ñāṇamoli, trans)

So, while to say that "the Buddha never taught a theory of emptiness. This idea is nowhere in the entire Pali Canon." is clearly false (and should really be removed from your question), there are ways of understanding emptiness that don't contradict existence.
Further, the Buddha taught non-self; he didn't precisely teach "rebirth" - he never actually used a word, that I know of, that implies such an idea. He taught dependent origination; that mental formations lead to further becoming. It is pretty clear from reading the earlier texts (e.g. those cited above) that experiences arise and cease, being replaced by new experiences. This occurs even at the moment of physical death, hence "rebirth", or more accurately "birth".
In summary, emptiness can be understood to refer to absence of self (i.e. something eternal or immutable) and rebirth isn't really a Buddhist concept. Birth comes about because of mind states in one existence leading to future mind states in another existence - the separation between existences is merely conventional.

5801: <p>The Theory of "Emptiness" is the concept that all phenomenon are empty of inherent existence. Something has the illusion of existence when the right causes and conditions arise. Example: there is no inherently existing chicken soup. You only get chicken soup when you put together a dead chicken, hot water. Veggies etc. in this theory, you illusory sense of self comes from the right causes and conditions, parents, a body, a brain etc. following this logic, upon death, the self should simply cease to exist because that which made you a self has dissolved and since you do not inherently exist you should just vanish, and yet the Buddha is clear we take rebirth. This is illogical and makes no sense. Perhaps this is why the Buddha never taught a theory of emptiness. This idea is nowhere in the entire Pali Canon. </p>
 13375: <p>The question seems an objection to Mahayana concept of emptiness. I will try and give the answer to this objection from the Prasangika viewpoint:</p>

<blockquote>
  <p>the self should simply cease to exist because that which made you a self has dissolved and since you do not inherently exist you should just vanish</p>
</blockquote>

<p>I don't think there is any reason to invoke rebirth if this is your objection to the emptiness of inherent existence. By this line of reasoning, if phenomena lacked inherent existence (ie, they are empty), then moment-to-moment <em>in this very life</em>, a person would vanish. However, we do not vanish. So, either the line of reasoning is based on incorrect assumptions or it is valid and leads to absurdity thus refuting emptiness of inherent existence.</p>

<p>I believe the line of reasoning is based upon an incorrect assumption: that things lacking inherent existence will be unable to function. </p>

<p>Let's set aside the selflessness of phenomena and look only at the <em>selflessness of the person</em> as this is agreed upon by Theravada and the Mahayana. It is clear, the Theravada posits the selflessness of persons. That people lack inherent existence.</p>

<p>This line of reasoning also refutes the Theravada position: if people lack inherent existence, then they will be unable to function and thus they will vanish in this very moment! So either the line of reasoning is flawed - it assumes the incorrect assumption that lacking inherent existence renders things non-functional - or the Theravada selflessness of persons has also been refuted as well.</p>
 5715: <p><strong>Rebirth</strong></p>

<p>First of all the idea of emptiness doesn't really apply to chicken soup. This is a widespread misinterpretation. It principally applies to experiences. The basic idea is that there is a sense-object (<em>arambaṇa</em>) and a sense-faculty (<em>indriya</em>) and when the two come together in the presence of sense-cognition (<em>vijñāna</em>) then this produces an experience (<em>vedanā</em>), which then gives rise to a whole range of speculative mental processes (<em>prapañca</em>). </p>

<p>Note that <em>vedanā</em> comes from a verbal root <em>√vid</em>, meaning "to know, to discover". We have <em>vedanā</em> when we <em>know</em> we are experiencing something. So dependent arising is describing, not the arising of chicken soup, but the arising of a conscious experience. And of course experience is characterised by impermanence (<em>anitya</em>), disappointment (<em>duḥkha</em>), and lack of substance (<em>anātman</em>).  </p>

<p>In this theory, the experience of being a self happens in just the same way. The first-person perspective and the sense of being someone who is having an experience, are just more kinds of experience. The kind that happen then the <em>arambaṇa</em> is a mental process and the <em>indriya</em> is the mental faculty and there is mental cognition. </p>

<p>Any arguments over whether the experience exists (<em>asti</em>) or does not exist (<em>nāsti</em>) are kind of meaningless. When you eat a peach, does the taste of peach exist? Or not? Or is the language of "being" inappropriate here? Early Buddhist texts argue that <em>asti</em> and <em>nāsti</em> don't apply to the world of experience (e.g. <em>Kaccānagotta Sutta</em> SN 12.15). And one of the ways of expressing this is to say that experiences are <em>anātman</em> - they don't have any kind of substance. </p>

<p>So to say that the self exists, or that at death it ceases to exist, is simply to misunderstand the situation. The sense of being a self, like the taste of peach, only persists when the conditions are present. It ceases, for example, if one is knocked unconscious! Or if one experiences <em>nirodhasamāpatti</em> in meditation. What we loosely call "self" is just an experience. At death that experience stops arising in us. Buddhists argue that either immediately, or after a period of time, that the experience arises in another being, based on the condition of the last moments of the dead persons conscious experience. </p>

<p>The implication here is similar to what we find in the philosophy of Kant. Everything we know comes from experience. Experience is constantly changing. Therefore we cannot know anything that is permanent. If something were permanent we'd either have to always know it or always be ignorant of it. In fact simple introspection shows that experience is constantly changing and nothing is constantly in our minds - ergo we can have no knowledge of anything permanent. If there is a permanent <em>ātman</em>, we could never know anything about it.</p>

<p>It is important for Buddhism that rebirth happens. Without it the morality of Buddhism falls apart. Buddhists are realistic enough to see that in this life the wicked frequently go unpunished and the good go unrewarded. All moral systems of thought are oriented towards a "Just World" in which everyone gets what they deserve. In most moral systems this is overseen by a supernatural agent, a god of justice (e.g. in the Vedas Mitra and Varuṇa over see different aspects of keeping things in balance). Without a supernatural agent, it is necessary that the moral agent live again so as to experience the consequences of their actions. </p>

<p>In the India systems with an <em>ātman</em> or <em>jīva</em> (i.e. a permanent aspect of the psyche) that passes from life to life this is straightforward. For Buddhists it is complicated by our denial of personal continuity. An <em>ātman</em> would wreck our metaphysics and so we have this on going tension between morality which demands continuity to obtain a just world, and metaphysics which denies continuity because permanence would ruin dependent arising. </p>

<p>When we try to apply this theory to objects that exist independently of our experience (such as in the chicken soup example) then the theory does not hold together. Buddhists who tried this ended up proposing contradictory notions such as the Two Truths, which rather than rejecting <em>asti</em> and <em>nāsti</em>, try to argue that objects are both <em>asti</em> and <em>nāsti</em>. This is because objects and experiences are of a very different nature. What is true of experience is not necessarily true of objects. It is a bad mistake to use a theory of experience as a theory of objects; and a catastrophe to use it as a theory of reality. </p>

<p>Such a theory was never meant to stand up to the kind of scrutiny we now subject it to. It was an ad hoc explanation for something that was widely believed to be the case in North Indian by at least the 8th century BCE. and for centuries people all over the world found it plausible. </p>

<p><strong>Theories of Emptiness</strong></p>

<p>It is quite wrong to say that the Buddha did not teach a theory of emptiness. If you look for the Pāḷi words <em>suññā</em> (empty) and <em>suññatā</em> (emptiness) you will find that they occur many times. A survey of these uses in the Pāḷi texts and their Chinese counterparts can be found in </p>

<blockquote>
  <p>CHOONG, Mun-keat. (1999) The Notion of Emptiness in Early Buddhism. 2nd. Ed. Motilal Banarsidass.</p>
</blockquote>

<p>Also I believe that Bhikkhu Anālayo's new book, <a href="http://windhorsepublications.com/compassion_and_emptiness_in_early_buddhist_meditation" rel="nofollow">Compassion and Emptiness in Early Buddhist Meditation</a>, tackles some of the same themes (though I have not read it).</p>

<p>It is true that the doctrine of emptiness changed over the centuries, but the Buddha (if the early Buddhist texts do represent his words) did indeed teach about emptiness. The early Buddhist texts (and the Āgamas more so than the Nikāya) use the idea of emptiness in a number of ways:</p>

<ol>
<li>An empty place (i.e. where there are no people), which is used as a metaphor for ... </li>
<li>A samādhi state (Pali suññatāvihāra; Chinese &#31354;&#19977;&#26151; = Skt <em>śūnyasamādhi</em>) in which there is no experience, i.e. a state in which there is no conscious mental activity.</li>
<li>The emptiness of the world (<em>suñño loko</em>) of self or anything belonging to self (<em>suññaṃ attena vā attaniyena vā</em>).</li>
<li>A synonym for <em>nibbāna</em>.</li>
</ol>

<p>These meanings were developed over time into the various theories of emptiness we know about today. The 3rd use in Pāḷi is adapted by Nāgārjuna to give the classic early Madhyamaka interpretation of emptiness which is that dharmas are empty of svabhāva - i.e. that nothing can be a condition for it's own existence (which was an implication of later Abhidharma speculation). </p>
 745: <p>The teaching that all things composed of parts are without self, but are mere names and labels designated in dependence on their parts, is something that most definitely is taught in the Pali canon, quite explicitly in the <a href="http://www.accesstoinsight.org/tipitaka/sn/sn05/sn05.010.bodh.html" rel="nofollow noreferrer">Vajira Sutta</a> with the analogy of the analysis of the Chariot.</p>
<p>The reason this doesn't contradict rebirth is that when a person dies, their final consciousnesses cause the arising of a new consciousness in dependence on a new body, and this new mind and body can be conventionally called a self, and there is a causal relationship between the two.</p>
 18: <p>Not all forms of Buddhism define emptiness in the way you describe; in Theravada Buddhism, for example, emptiness mainly means "empty of self":</p>

<blockquote>
  <p><em>“katamā cāvuso, suññatā cetovimutti”?</em></p>
  
  <p><em>“idhāvuso, bhikkhu araññagato vā rukkhamūlagato vā suññāgāragato vā iti paṭisañcikkhati — ‘suññamidaṃ attena vā attaniyena vā’ti. ayaṃ vuccatāvuso, suññatā cetovimutti”.</em></p>
  
  <p>"And what, friend, is liberation of mind through emptiness?"</p>
  
  <p>"Here, friend, a bhikkhu, gone to the forest or gone to the root of a tree or gone to an empty dwelling reflects thus: 'empty is this of self or what belongs to self.' This one calls, friend, liberation of mind through emptiness."</p>
  
  <p>-- MN 43</p>
</blockquote>

<p>Being empty of self is different from not existing; it simply means that, from the point of view of experience, that which comes into existence does so from non-existence, and subsequently returns to non-existence; it has no existence outside of the single moment:</p>

<blockquote>
  <p><em>“aniccā vata saṅkhārā, uppādavayadhammino.
  <br/>uppajjitvā nirujjhanti, tesaṃ vūpasamo sukho”ti.</em></p>
  
  <p>"Impermanent indeed are formations, of a nature to arise and fall.
  <br/>Having arisen, they cease, their tranquillizing is happiness."</p>
  
  <p>-- DN 16</p>
  
  <p><em>“yaṃ kiñci samudayadhammaṃ sabbaṃ taṃ nirodhadhamman”ti.</em></p>
  
  <p>"Whatever is of a nature to arise, all of that is of a nature to cease."</p>
  
  <p>-- DN 3</p>
  
  <p><em>yasmā ca kho, ānanda, suññaṃ attena vā attaniyena vā tasmā suñño lokoti vuccati.</em></p>
  
  <p>Because it is, Ananda, empty by way of self or what belongs to self, therefore 'the world is empty' is said.</p>
  
  <p>--SN 35.68</p>
</blockquote>

<p>There is only one example in Theravada Buddhism that I know of that is cited as support for the idea of emptiness being related to non-existence - in the Patisambhidamagga:</p>

<blockquote>
  <p>katamaṃ vipariṇāmasuññaṃ? jātaṃ rūpaṃ sabhāvena suññaṃ.</p>
  
  <p>What is emptiness due to change? Born form is empty by way of intrinsic existence.</p>
  
  <p>-- Paṭis. XX.5</p>
</blockquote>

<p>The commentary to this passage refutes the idea that this refers to non-existence, however:</p>

<blockquote>
  <p>'Void of individual essense': here <em>sabhāva</em> is <em>sayaṃ bhāvo</em>; arising of itself is the meaning. Or <em>sabhāva</em> is <em>sako bhāvo</em>; own arising. Because of existence in dependence on conditions there is in it no essence by itself or essence of its own, thus it is "void of individual essence".</p>
  
  <p>...</p>
  
  <p>But if someone should say: "Own essence is individual essence; it is void of that individual essence. ... Because of the non-existence of any idea whatever it is the non-existence of materiality that is expressed by the words 'born materiality is void of individual essence.'" It should be argued thus: that being so, the words 'born materiality' would be contradicted; for what is devoid of arising is not called 'born'. ... And the word 'void' for what is non-existent contradicts the Blessed One's use of it above for the 'world' and also the words of the books of logic and linguistics; and it contradicts many logical arguments.</p>
  
  <p>-- Path of Discrimination, p. 362 (Ñāṇamoli, trans)</p>
</blockquote>

<p>So, while to say that "the Buddha never taught a theory of emptiness. This idea is nowhere in the entire Pali Canon." is clearly false (and should really be removed from your question), there are ways of understanding emptiness that don't contradict existence.</p>

<p>Further, the Buddha taught non-self; he didn't precisely teach "rebirth" - he never actually used a word, that I know of, that implies such an idea. He taught dependent origination; that mental formations lead to further becoming. It is pretty clear from reading the earlier texts (e.g. those cited above) that experiences arise and cease, being replaced by new experiences. This occurs even at the moment of physical death, hence "rebirth", or more accurately "birth".</p>

<p>In summary, emptiness can be understood to refer to absence of self (i.e. something eternal or immutable) and rebirth isn't really a Buddhist concept. Birth comes about because of mind states in one existence leading to future mind states in another existence - the separation between existences is merely conventional.</p>
