user-1: When the Pali suttas say that it is not the "same" bundle of psycho-physical properties that is born and dies what do they mean: do they mean that conventional desginators like "I" only refer to different concrete things (a baby, an old man) but they also mean something different? 
Specifically: can we say, conventionally or otherwise, that the old man or the baby have aged, or that the baby grew up into an old man?

“Exactly so, venerable sir. As I understand the Dhamma taught by the
  Blessed One, it is the same consciousness that runs and wanders
  through the round of rebirths, not another.”
“What is that consciousness, Sāti?”
“Venerable sir, it is that which speaks and feels and experiences here
  and there the result of good and bad actions.”
“Misguided man, to whom have you ever known me to teach the Dhamma in
  that way?

Hope I haven't misread it! He then goes on to describe dependent origination.

user8157: 
When the Pali suttas say that it is not the "same" bundle of psycho-physical properties that is born and dies

The words "birth" ("jati") and "death" ("marana') are defined in SN 12.2 as producing or imputing the idea of "a being" ("satta") upon the manifestations or changing appearances of the aggregates. 
What is important to understand is not so much the aggregates but how ideas of 'self', 'persons' or 'beings' are imputed upon the aggregates. 
For example, when you see "my mother", "my father", "my wife", "my friend", "my enemy", "my favourite pop star", etc; and Arahant, in the same situation, sees only aggregates, elements and sense objects. 

Specifically: can we say, conventionally or otherwise, that the old man or the baby have aged, or that the baby grew up into an old man?

Convention is different than ultimate truth. In ultimate truth, only aggregates change & cease. This is why there are so many suttas that says an arahant is not born, does not age, does not die (example, MN 140; SN 22.85; etc). 
When there is no idea or view of a "self", "person" or "being", the ideas of birth & death do not arise. 

user43: This topic is analyzed a hundred times over in all schools. For example, in The Questions of King Milinda:

The king said: ‘He who is born, Nāgasena, does he remain the same or become another?’
[Nagasena:] ‘Neither the same nor another.’
[King:] ‘Give me an illustration.’
[N] ‘Now what do you think, O king? You were once a baby, a tender thing, and small in size, lying flat on your back. Was that the same as you who are now grown up?’
[K] ‘No. That child was one, I am another.’
[N] ‘If you are not that child, it will follow that you have had neither mother nor father, no! nor teacher. You cannot have been taught either learning, or behaviour, or wisdom. What, great king! is the mother of the embryo in the first stage different from the mother of the embryo in the second stage, or the third, or the fourth ? Is the mother of the baby a different person from the mother of the grown-up man? Is the person who goes to school one, and the same when he has finished his schooling another? Is it one who commits a crime, another who is punished by having his hands or feet cut off ?’
[K] ‘Certainly not. But what would you, Sir, say to that? ’
The Elder replied: ‘Neither I am what is now the grown up, nor was I what was the tender tiny baby, flat on its back. But all these are tied in one by means of this body.’
[K] ‘Give me an illustration.’
[N] ‘Suppose a man, O king, were to light a lamp, would it burn the night through?’
[K] ‘Yes, it might do so.’
[N] ‘Now, is it the same flame that burns in the first watch of the night, and in the second?’
[K] ‘No.’
[N] ‘Or the same that burns in the second watch and in the third?’
[K] ‘No.’
[N] ‘Then is there one lamp in the first watch, and another in the second, and another in the third?’
[K] ‘No Sir. But thanks to that lamp the light shined all the night through.’
[Nagasena:] ‘Just so, O king, does the continuity of dharmas connect. One emerges, another dissolves, connecting as it were without [a clear boundary between] the previous and the next, thus the former-consciousness and the next-consciousness cannot be categorized as either the same nor as different.’

This is then analyzed fabulously in all conceivable details by Nagarjuna in his Mulamadhyamakakarika. Basically, the idea here is that reality is not as discrete as the mind would like to believe. Things morph and develop continuously, rather like drifting clouds which only temporarily take certain recognizable shapes and are strictly speaking never the same nor are not themselves at any given point in time.
Strictly speaking, things and people don't have an immutable "core" or an atomic identity that would move through time from one moment to another. Each consequtive state of things develops from previous state through morphing, moving, and interacting - but the idea that it's still the same entity is imputed by us, it's not there. 
Another traditional simile, also used in Milindapanha, is that of the milk produce cycle. As milk goes sour, then becomes butter, then ghee - does it retain its identity or not? The Buddhist answer is that the identity is an imputation of the mind. To anyone interested in Western perspective on this, I recommend a short work called "Hierarchy Theory" by Valerie Ahl and T. F. H. Allen.

-1: <p>When the Pali suttas say that it is not the "same" bundle of psycho-physical properties that is born and dies what do they mean: do they mean that conventional desginators like "I" only refer to different concrete things (a baby, an old man) but they also mean something different? </p>

<p>Specifically: can we say, conventionally or otherwise, that the old man or the baby have aged, or that the baby grew up into an old man?</p>

<blockquote>
  <p>“Exactly so, venerable sir. As I understand the Dhamma taught by the
  Blessed One, it is <a href="https://www.dhammatalks.net/Books9/Bhikkhu_Bodhi_Mahatanhasankhaya_Sutta.htm" rel="nofollow noreferrer">the same</a> consciousness that runs and wanders
  through the round of rebirths, not another.”</p>
  
  <p>“What is that consciousness, Sāti?”</p>
  
  <p>“Venerable sir, it is that which speaks and feels and experiences here
  and there the result of good and bad actions.”</p>
  
  <p>“Misguided man, to whom have you ever known me to teach the Dhamma in
  that way?</p>
</blockquote>

<p>Hope I haven't misread it! He then goes on to describe dependent origination.</p>
 8157: <blockquote>
  <p><strong>When the Pali suttas say that it is not the "same" bundle of psycho-physical properties that is born and dies</strong></p>
</blockquote>

<p>The words "birth" ("jati") and "death" ("marana') are defined in SN 12.2 as producing or imputing the idea of "a being" ("satta") upon the manifestations or changing appearances of the aggregates. </p>

<p>What is important to understand is not so much the aggregates but how ideas of 'self', 'persons' or 'beings' are imputed upon the aggregates. </p>

<p>For example, when you see "my mother", "my father", "my wife", "my friend", "my enemy", "my favourite pop star", etc; and Arahant, in the same situation, sees only aggregates, elements and sense objects. </p>

<blockquote>
  <p><strong>Specifically: can we say, conventionally or otherwise, that the old man or the baby have aged, or that the baby grew up into an old man?</strong></p>
</blockquote>

<p>Convention is different than ultimate truth. In ultimate truth, only aggregates change &amp; cease. This is why there are so many suttas that says an arahant is not born, does not age, does not die (example, MN 140; SN 22.85; etc). </p>

<p>When there is no idea or view of a "self", "person" or "being", the ideas of birth &amp; death do not arise. </p>
 43: <p>This topic is analyzed a hundred times over in all schools. For example, in The Questions of King Milinda:</p>

<blockquote>
  <p>The king said: ‘He who is born, Nāgasena, does he remain the same or become another?’</p>
  
  <p>[Nagasena:] ‘Neither the same nor another.’</p>
  
  <p>[King:] ‘Give me an illustration.’</p>
  
  <p>[N] ‘Now what do you think, O king? You were once a baby, a tender thing, and small in size, lying flat on your back. Was that the same as you who are now grown up?’</p>
  
  <p>[K] ‘No. That child was one, I am another.’</p>
  
  <p>[N] ‘If you are not that child, it will follow that you have had neither mother nor father, no! nor teacher. You cannot have been taught either learning, or behaviour, or wisdom. What, great king! is the mother of the embryo in the first stage different from the mother of the embryo in the second stage, or the third, or the fourth ? Is the mother of the baby a different person from the mother of the grown-up man? Is the person who goes to school one, and the same when he has finished his schooling another? Is it one who commits a crime, another who is punished by having his hands or feet cut off ?’</p>
  
  <p>[K] ‘Certainly not. But what would you, Sir, say to that? ’</p>
  
  <p>The Elder replied: ‘Neither I am what is now the grown up, nor was I what was the tender tiny baby, flat on its back. But all these are tied in one by means of this body.’</p>
  
  <p>[K] ‘Give me an illustration.’</p>
  
  <p>[N] ‘Suppose a man, O king, were to light a lamp, would it burn the night through?’</p>
  
  <p>[K] ‘Yes, it might do so.’</p>
  
  <p>[N] ‘Now, is it the same flame that burns in the first watch of the night, and in the second?’</p>
  
  <p>[K] ‘No.’</p>
  
  <p>[N] ‘Or the same that burns in the second watch and in the third?’</p>
  
  <p>[K] ‘No.’</p>
  
  <p>[N] ‘Then is there one lamp in the first watch, and another in the second, and another in the third?’</p>
  
  <p>[K] ‘No Sir. But thanks to that lamp the light shined all the night through.’</p>
  
  <p>[Nagasena:] ‘Just so, O king, does the continuity of dharmas connect. One emerges, another dissolves, connecting as it were without [a clear boundary between] the previous and the next, thus the former-consciousness and the next-consciousness cannot be categorized as either the same nor as different.’</p>
</blockquote>

<p>This is then analyzed fabulously in all conceivable details by Nagarjuna in his Mulamadhyamakakarika. Basically, the idea here is that reality is not as discrete as the mind would like to believe. Things morph and develop continuously, rather like drifting clouds which only temporarily take certain recognizable shapes and are strictly speaking never the same nor are not themselves at any given point in time.</p>

<p>Strictly speaking, things and people don't have an immutable "core" or an atomic identity that would move through time from one moment to another. Each consequtive state of things develops from previous state through morphing, moving, and interacting - but the idea that it's still the same entity is imputed by us, it's not there. </p>

<p>Another traditional simile, also used in Milindapanha, is that of the milk produce cycle. As milk goes sour, then becomes butter, then ghee - does it retain its identity or not? The Buddhist answer is that the identity is an imputation of the mind. To anyone interested in Western perspective on this, I recommend a short work called "Hierarchy Theory" by Valerie Ahl and T. F. H. Allen.</p>
