What is a god or goddess?

My fantasy books include mythological creatures and, of course, gods and goddesses. I hit upon a problem though in trying to determine where some of my characters lie on the ‘god scale’. So I decided to define what I thought makes an entity into a god.

This strange piece below is what I have just come up with.

1 Without mortality

1.1 A god or goddess is not a mortal AND is more than simply non-mortal.
1.2 What is ‘not mortal’ can only then be defined by what is mortal. To be mortal is:
a) To live a life which is bounded by natural death.
b) To be vulnerable to death inflicted by other mortals.
c) To be constrained to mortal worlds.
d) To submit to physical rules, laws, and limits that affect all mortals.
1.3 A non-mortal may exhibit one or more traits beyond mortal life. To be non-mortal is to live a life which:
a) Is not bounded by natural death.
b) OR is not vulnerable to death inflicted by other mortals.
c) OR is not constrained to mortal worlds.
d) OR does not submit to physical rules, laws, and limits that affect all mortals.
1.4 From the above (1.1, 1.2, 1.3) it must be thus that A god or goddess :
a) Does not age and die.
b) AND cannot be killed by mortal hand.
c) AND is associated with a place where mortals cannot normally tread uninvited.
d) AND has specific powers or attributes that are not attainable by those who are mortal.

2 Recognition

2.1 A god must be known of mortals and recognised as not of them. This may involve worship, sacrifices, prayer, the building of temples, the consecration or dedication of land.
2.2 A god must be known of other gods and recognised as of them. This may involve the inclusion within a pantheon or the proclamation of another god.

3 It follows that

3.1 If a god or goddess cannot be killed by mortal hand (1.6) then one who kills a god or goddess cannot therefore be mortal.
3.2 A god or goddess cannot at the same time ever be mortal or simply non-mortal because a god or goddess is not mortal (1.1) and is more than simply non-mortal (1.4).
But this does not exclude that a god or goddess:
a) could once have been mortal or simply non-mortal
b) could, by a godly act, become mortal or simply non-mortal.
3.3 An entity which meets the criteria of 1.4 but does not meet the criteria of both 2.1 and 2.2 is not a god or goddess. Such an entity:
a) Must be non-mortal because of all conditions of 1.3 are naturally met.
b) May be considered to be more than simply non-mortal.
3.4 An entity which does not meet the criteria 1.4 but does meet that of 2.1 and/or 2.2 is not a god or goddess. Such an entity:
a) Might still meet the criteria of being non-mortal (1.3)
b) And, if meeting the criteria of 1.3 may be considered to be more than simply non-mortal.
3.5 An entity which is more than non-mortal and less than a god must be something that lies between them such as:
a) a demi-god,
b) an angel or servant to a god