user13282: In SN 35.93 quoted below, it reads intellect-consciousness arises in dependence on the intellect and ideas, but if this consciousness is also a thinking about the work of intellect on ideas then it in itself is an intellect. and if so we have to look for another consciousness which higher and the search continues ad-infinitum.
This, of course, is not my own though it's a classic platonic thinkers response to Descartes's misguided saying Cogito ergo sum ( I think, therefore I am),  quoted below is from Plotinos Ennead Book Nine explaining the relation of intellect and consciousness.

SN 35.93 Dvaya Sutta: A Pair

"In dependence on the intellect & ideas, there arises
  intellect-consciousness. The intellect is inconstant, changeable, of a
  nature to become otherwise. Ideas are inconstant, changeable, of a
  nature to become otherwise. Thus this pair is both wavering &
  fluctuating — inconstant, changeable, of a nature to become otherwise.


PLOTINOS: - SECOND ENNEAD, BOOK NINE.

Though there be a difference between thinking, and thinking that one
  thinks, these two nevertheless constitute a single intuitive
  consciousness of its actualizations. It would be ridiculous to deny
  such a consciousness to veritable Intelligence. It is, therefore, the
  same Intelligence that thinks, and that thinks that it thinks.
  Otherwise, there would be two principles, of which the one would have
  thought, and the other consciousness of thought. The second would
  doubtless differ from the first, but would not be the real thinking
  principle. A mere logical distinction between thought and
  consciousness of thought would not establish the (actual) differences
  between two . Further, we shall have to
  consider whether it be possible to conceive of an Intelligence which
  would exclusively think, without any accompanying consciousness of its
  thought. If we ourselves who are entirely devoted to practical
  activity and discursive reason were in such a condition, we would,
  even if otherwise considered sensible, be insane. But as true
  Intelligence thinks itself in its thoughts, and as the
  intelligible, far from being outside of Intelligence, is Intelligence
  itself, Intelligence, by thinking, possesses itself, and necessarily
  sees itself. When Intelligence sees itself, it does not see itself
  as unintelligent, but as intelligent. Therefore in the first
  actualization of thought, Intelligence has the thought and
  consciousness of thought, two things that form but a single one; not
  even logically is this a duality. If Intelligence always thinks what
  it is, is there any reason to separate, even by a simple logical
  distinction, thought from the consciousness of thought? The absurdity
  of the doctrine we are controverting will be still more evident if we
  suppose that a third intelligence is conscious that the second
  intelligence is conscious of the thought of the first; we might thus
  go on to infinity


user8157: Consciousness ('vinnana') is not thinking. Consciousness is experiencing or knowing. 

Dependent on intellect & ideas, intellect-consciousness arises. The meeting of the three is contact. With contact as a requisite
  condition, there is feeling. What one feels, one perceives (labels in
  the mind). What one perceives, one thinks about. What one thinks
  about, one objectifies.
MN 18

The term 'intellect-consciousness' is merely a name for a certain type of consciousness (knowing), similar to when describing different types of paint as 'red paint', 'blue paint', 'house paint', 'wall paint', 'outdoor paint', etc. Intellect-consciousness' refers to a consciousness that arises to experience the intellect & its products. 
The 'intellect' (called 'mano') is not 'the power of knowing'. 'Mano' refers to the power of intelligence, reason, thinking & decision making, such as described in verse 1 of the Dhammapada: 

Manopubbaṅgamā dhammā manoseṭṭhā manomayā. Manasā ce paduṭṭhena bhāsati vā karoti vā Tato naṃ dukkhamanveti cakkaṃ'va
  vahato padaṃ.
Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with an impure mind a person speaks or acts suffering
  follows him like the wheel that follows the foot of the ox.

As described, above, 'mano' (translated as 'intellect') is that which thinks & acts rather than is that which knows & experiences. 
It helps understanding to view 'consciousness' as a 'mirror' and to view 'intellect & ideas' as objects reflected in that mirror. 

user43: This is just bad translation. "Consciousness" is the common word for vijnana. A better translation of vijnana is "(subjective) experience". Meaning, you see something => you recognize it => you make sense of it => you experience it.
"Intellect" is how they usually translate manas or mind.
So "Intellect-consciousness" or mano-vijnana, is therefore the subjective experience of what's going on one's own mind. It's when you "see" what you're thinking about etc. I think it's called re-representation in modern cognitive science.
It does not require a higher mind or anything like that. Based on my meditation experience, it works as a cycle. Normally the input from sense organs goes to memory to find matching associations, this is how recognition happens, the basis of vijnana. With manovijnana, instead of the sensory organs, our attention grabs data from short term memory, finds matches in long term memory, puts that back in short term memory - voila, manovijnana.

13282: <p>In SN 35.93 quoted below, it reads intellect-consciousness arises in dependence on the intellect and ideas, but if this consciousness is also a thinking about the work of intellect on ideas then it in itself is an intellect. and if so we have to look for another consciousness which higher and the search continues ad-infinitum.</p>

<p>This, of course, is not my own though it's a classic platonic thinkers response to Descartes's misguided saying Cogito ergo sum ( I think, therefore I am),  quoted below is from Plotinos Ennead Book Nine explaining the relation of intellect and consciousness.</p>

<hr>

<p><a href="https://www.accesstoinsight.org/tipitaka/sn/sn35/sn35.093.than.html" rel="nofollow noreferrer">SN 35.93 Dvaya Sutta: A Pair</a></p>

<blockquote>
  <p>"In dependence on the intellect &amp; ideas, there arises
  intellect-consciousness. The intellect is inconstant, changeable, of a
  nature to become otherwise. Ideas are inconstant, changeable, of a
  nature to become otherwise. Thus this pair is both wavering &amp;
  fluctuating — inconstant, changeable, of a nature to become otherwise.</p>
</blockquote>

<hr>

<p><em>PLOTINOS: - SECOND ENNEAD, BOOK NINE.</em></p>

<blockquote>
  <p>Though there be a difference between thinking, and thinking that one
  thinks, these two nevertheless constitute a single intuitive
  consciousness of its actualizations. It would be ridiculous to deny
  such a consciousness to veritable Intelligence. It is, therefore, the
  same Intelligence that thinks, and that thinks that it thinks.
  Otherwise, there would be two principles, of which the one would have
  thought, and the other consciousness of thought. The second would
  doubtless differ from the first, but would not be the real thinking
  principle. A mere logical distinction between thought and
  consciousness of thought would not establish the (actual) differences
  between two . Further, we shall have to
  consider whether it be possible to conceive of an Intelligence which
  would exclusively think, without any accompanying consciousness of its
  thought. If we ourselves who are entirely devoted to practical
  activity and discursive reason were in such a condition, we would,
  even if otherwise considered sensible, be insane. But as true
  Intelligence thinks itself in its thoughts, and as the
  intelligible, far from being outside of Intelligence, is Intelligence
  itself, Intelligence, by thinking, possesses itself, and necessarily
  sees itself. When Intelligence sees itself, it does not see itself
  as unintelligent, but as intelligent. Therefore in the first
  actualization of thought, Intelligence has the thought and
  consciousness of thought, two things that form but a single one; not
  even logically is this a duality. If Intelligence always thinks what
  it is, is there any reason to separate, even by a simple logical
  distinction, thought from the consciousness of thought? The absurdity
  of the doctrine we are controverting will be still more evident if we
  suppose that a third intelligence is conscious that the second
  intelligence is conscious of the thought of the first; we might thus
  go on to infinity</p>
</blockquote>
 8157: <p>Consciousness ('vinnana') is not thinking. Consciousness is experiencing or knowing. </p>

<blockquote>
  <p><em>Dependent on intellect &amp; ideas, intellect-consciousness arises. The meeting of the three is contact. With contact as a requisite
  condition, there is feeling. What one feels, one perceives (labels in
  the mind). What one perceives, one thinks about. What one thinks
  about, one objectifies.</em></p>
  
  <p><em>MN 18</em></p>
</blockquote>

<p>The term 'intellect-consciousness' is merely a name for a certain type of consciousness (knowing), similar to when describing different types of paint as 'red paint', 'blue paint', 'house paint', 'wall paint', 'outdoor paint', etc. Intellect-consciousness' refers to a consciousness that arises to experience the intellect &amp; its products. </p>

<p>The 'intellect' (called 'mano') is not 'the power of knowing'. 'Mano' refers to the power of intelligence, reason, thinking &amp; decision making, such as described in verse 1 of the Dhammapada: </p>

<blockquote>
  <p><strong><em>Mano</strong>pubbaṅgamā dhammā <strong>mano</strong>seṭṭhā <strong>mano</strong>mayā. <strong>Mana</strong>sā ce paduṭṭhena bhāsati vā karoti vā Tato naṃ dukkhamanveti cakkaṃ'va
  vahato padaṃ.</em></p>
  
  <p><em>Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with an impure mind a person speaks or acts suffering
  follows him like the wheel that follows the foot of the ox.</em></p>
</blockquote>

<p>As described, above, 'mano' (translated as 'intellect') is that which thinks &amp; acts rather than is that which knows &amp; experiences. </p>

<p>It helps understanding to view '<em>consciousness</em>' as a '<em>mirror</em>' and to view '<em>intellect &amp; ideas</em>' as objects reflected in that mirror. </p>
 43: <p>This is just bad translation. "Consciousness" is the common word for <code>vijnana</code>. A better translation of <code>vijnana</code> is "(subjective) experience". Meaning, you see something => you recognize it => you make sense of it => you experience it.</p>

<p>"Intellect" is how they usually translate <code>manas</code> or mind.</p>

<p>So "Intellect-consciousness" or <code>mano-vijnana</code>, is therefore the subjective experience of what's going on one's own mind. It's when you "see" what you're thinking about etc. I think it's called re-representation in modern cognitive science.</p>

<p>It does not require a higher mind or anything like that. Based on my meditation experience, it works as a cycle. Normally the input from sense organs goes to memory to find matching associations, this is how recognition happens, the basis of <code>vijnana</code>. With manovijnana, instead of the sensory organs, our attention grabs data from short term memory, finds matches in long term memory, puts that back in short term memory - voila, manovijnana.</p>
