As you talk about intervals, minor, major, diminished it is to assume that you know the names and terms of the eight intervals too, such as second, third, fourth, fifth etc.
Mind that the Arabic numbers are used referring to the chord tones: 135 (triad) 1357 (tetrad) etc.
Mind that the names of the intervals are used to sign the distances between to tones of a scale as-well for naming the degrees themselves.
To assign the degrees of a scale in music you have to use roman numbers.
your comment on Tim’s answer:
Was really struggling on how to phrase my question.
How to phrase your question:
C D EF G A BC D EF G A BC
(this is the scale of C, a “ladder” of 8 degrees, of which the 8th is named and sounding like the first again.)
We see that the intervals between the degrees are not all the same: there is 1 half step between ef and cb, all others are whole steps. The best representation is the keyboard where you can see that the steps EF and BC are closer together as there is no black key between these white keys.
what is here minor, major, diminished?
not all beginners know that major means actually big and larger and minor means small or smaller while diminished is probably known by math as even smaller, somewhat as reduced.
The terms minor and major are referring to the intervals as 2nd, 3rd, 6th and 7th.
If you consider these intervals there are two kind of 2nds:
EF -> half step (only one halftone between): minor 2nd
C D -> whole step (2 halftones between): major 2nd
now there are (for our concern) 2 kind of 3rds built of half and whole steps: (h or w)
W W = major
W H = minor (or H W)
(the same assumptions can be made for all other
Intervals mentioned above - counting half and whole steps...)
your question is concerning the 3rds or/and the triads built above the degrees:
2min 3min 4Maj 5Maj 6min 7dim
I ii iii IV V vi vii(dim)
uppercase = major
lowercase = minor
from here you can develop the answer to your question:
What determines that the intervals 2,3,6 are minor and the intervals 4,5 are major? I would assume the same applies to the diminished.
the thirds built above each degree are minor or major depending of the half steps a and whole steps they include.
The triads are major or minor depending of the 3rds built above the root tone:
major + minor third = major triad
minor + major third = minor triad
minor + minor third = diminished triad
(the latter is called diminished as the result of 2 minor thirds is a summary of a diminished 5th while all others triads are perfect fifths including 1 minor + 1 major 3rd or 1 minor + 1 major 3rd.