Is there a kind of "consensus" towards the meaning & intuition of the concept of "potential infinity" that goes back to Aristotle and is promoted by Edward Nelson, e.g. in the paper Hilbert's mistake?

Nelson distinguishes it strictly from "completed infinity", which is the kind of infinity mathematicians mostly refering to and which appears to be closer to what humans actually "intuitively" imagine under infinite entities, eg the naturals IN would be instance of an completely infinite object.

On the other hand, I have (as a mathematician) some troubles to develop an intuition for "potential infinity". Are there intuitional approaches to grasp this concept known?

Motivation: In comments below this answer Mikhail Katz explained that Nelson related the concept of potential infinity to concept of "numerals" - which in turn may be seen as a promising candidate to approach the concept of metalanguage integers.
Since originally my motivation was to develop an intuition for "metalanguage integers", I'm wondering if there is a philosophical consensus on how one may think of "potential infinity" before relating it to entities from (mathematical) metatheory.

Asking plainly, what is the precise contrast of potential infinity to "complete infinity" assuming one has say "school book intuition" for the latter?

Is there a kind of "consensus" towards the meaning & intuition of the concept of "potential infinity" that goes back to Aristotle and is promoted by Edward Nelson, e.g. in the paper Hilbert's mistake?

Nelson distinguishes it strictly from "completed infinity", which is the kind of infinity mathematicians mostly refering to and which appears to be closer to what humans actually "intuitively" imagine under infinite entities, eg the naturals IN would be instance of an completely infinite object.

On the other hand, I have (as a mathematician) some troubles to develop an intuition for "potential infinity". Are there intuitional approaches to grasp this concept known?

Motivation: In comments below this answer Mikhail Katz explained that Nelson related the concept of potential infinity to concept of "numerals" - which in turn may be seen as a promising candidate to approach the concept of metalanguage integers.
Since originally my motivation was to develop an intuition for "metalanguage integers", I'm wondering if there is a philosophical consensus on how one may think of "potential infinity" before relating it to entities from (mathematical) metatheory.

Asking plainly, what is the precise contrast of potential infinity to "complete infinity" assuming one has say "school book intuition" for the latter?

Is there a kind of "consensus" towards the meaning & intuition of the concept of "potential infinity" coined by Edward Nelson presumably originally coined already by Aristotile and "taken up" again by Edward Nelson, adressing it eg in the paper Hilbert's mistake. as "seminal reference"?

Nelson distinguishes it strictly from "completed infinity", which is the kind of infinity mathematicians mostly refering to and which appears to be closer to what humans actually "intuitively" imagine under infinite entities, eg the naturals IN would be instance of an completely infinite object.

On the other hand I have (as mathematician) some troubles to develop an intuition for Nelson's "potential infinity". Are there intuitional approaches to grasp this concept known?

Motivation: In comments below this answer Mikhail Katz explained that Nelson related the concept of potential infinity to concept of "numerals" - which in turn may be seen as a promising candidate to approach the concept of metalanguage integers.
Since originally my motivation was to develop an intuition for "metalanguage integers", I'm wondering if there is a philosophical consensus on how one may think of Nelson's "potential infinity" before relating it to entities from (mathematical) metatheory.

Asking plainly, what is the precise contrast of potential infinity to "complete infinity" assuming one has say "school book intuition" for the latter?

Is there a kind of "consensus" towards the meaning & intuition of the concept of "potential infinity" that goes back to Aristotle and is promoted by Edward Nelson, e.g. in the paper Hilbert's mistake?

Nelson distinguishes it strictly from "completed infinity", which is the kind of infinity mathematicians mostly refering to and which appears to be closer to what humans actually "intuitively" imagine under infinite entities, eg the naturals IN would be instance of an completely infinite object.

On the other hand, I have (as a mathematician) some troubles to develop an intuition for "potential infinity". Are there intuitional approaches to grasp this concept known?

Motivation: In comments below this answer Mikhail Katz explained that Nelson related the concept of potential infinity to concept of "numerals" - which in turn may be seen as a promising candidate to approach the concept of metalanguage integers.
Since originally my motivation was to develop an intuition for "metalanguage integers", I'm wondering if there is a philosophical consensus on how one may think of "potential infinity" before relating it to entities from (mathematical) metatheory.

Asking plainly, what is the precise contrast of potential infinity to "complete infinity" assuming one has say "school book intuition" for the latter?

Is there a kind of "consensus" towards the meaning & intuition of the concept of "potential infinity" coined by Edward Nelson, see eg the paper Hilbert's mistake. as "seminal reference"?

Nelson distinguishes it strictly from "completed infinity", which is the kind of infinity mathematicians mostly refering to and which appears to be closer to what humans actually "intuitively" imagine under infinite entities, eg the naturals $\mathbb N$ would be instance of an completely infinite object.

On the other hand I have (as mathematician) some troubles to develop an intuition for Nelson's "potential infinity". Are there intuitional approaches to grasp this concept known?

Motivation: In comments below this answer Mikhail Katz explained that Nelson related the concept of potential infinity to concept of "numerals" - which in turn may be seen as a promising candidate to approach the concept of metalanguage integers.
Since originally my motivation was to develop an intuition for "metalanguage integers", I'm wondering if there is a philosophical consensus on how one may think of Nelson's "potential infinity" before relating it to entities from (mathematical) metatheory.

Asking plainly, what is the precise contrast of potential infinity to "complete infinity" assuming one has say "school book intuition" for the latter?

Is there a kind of "consensus" towards the meaning & intuition of the concept of "potential infinity" coined by Edward Nelson presumably originally coined already by Aristotile and "taken up" again by Edward Nelson, adressing it eg in the paper Hilbert's mistake. as "seminal reference"?

Nelson distinguishes it strictly from "completed infinity", which is the kind of infinity mathematicians mostly refering to and which appears to be closer to what humans actually "intuitively" imagine under infinite entities, eg the naturals IN would be instance of an completely infinite object.

On the other hand I have (as mathematician) some troubles to develop an intuition for Nelson's "potential infinity". Are there intuitional approaches to grasp this concept known?

Motivation: In comments below this answer Mikhail Katz explained that Nelson related the concept of potential infinity to concept of "numerals" - which in turn may be seen as a promising candidate to approach the concept of metalanguage integers.
Since originally my motivation was to develop an intuition for "metalanguage integers", I'm wondering if there is a philosophical consensus on how one may think of Nelson's "potential infinity" before relating it to entities from (mathematical) metatheory.

Asking plainly, what is the precise contrast of potential infinity to "complete infinity" assuming one has say "school book intuition" for the latter?