Well, you could... I don't know - maybe explain better. — T Clark
The argument is over what kind of mathematical relation defines a logical dichotomy - a dichotomy being a relation that is mutually exclusive and jointly exhaustive.
MU wants to treat is as simple negation. A and not-A. The presence of some thing, and then its absence or its erasure. But that is question-begging as it doesn't go to any mutuality that could form the two poles of being, nor to the way the two poles then demonstrably exhaust all other possibilities.
So a dichotomy is about taking a difference - an asymmetry or symmetry-breaking - to an extreme. It must begin in sameness and wind up looking orthogonally opposed. You don't just have chance and its absence, you have chance and necessity - an opposition of two poles of being that then encompass everything else that could be "somewhere in-between" these complementary extremes.
So likewise every metaphysical-strength category. You don't just imagine discreteness and its absence. You can only imagine discreteness in terms of the absence of something else, its exact opposite of continuity. Stasis makes no sense unless understood in terms of being antithetical to flux. Oneness is not a meaningful concept except to the degree it contradicts multiplicity.
Then seeking a mathematical model of this relation, the best understanding is an inverse or reciprocal one.
MU's weak-arse negation is like addition and subtraction. Count up three places, then erase those three places to end up back where you started. It is like a mirror symmetry. Flip the image over to break the symmetry. Then flip it again and you are back where you started. It is a symmetry-breaking, but nothing much has really changed as it is so easy to return to unbrokenness by a single step reversal of your path. An A-sized step gets negated by a second A-sized step - just now in the other direction.
Mathematically, it is the symmetry-breaking of a zero. 1 + -1 = 0. It is about the least amount of symmetry-breaking you can get away with. It is the symmetry breaking that remains as close to nothing actually happening as possible.
A dichotomy then represents the opposite end of the symmetry-breaking scale - one that is as extreme or asymmetric as possible. And a reciprocal relation models this well as each move in one direction causes a matching move in the other. If one end of the relation grows, the other actually shrinks to the same degree. Two poles of being are in play, each acting on the other in mutual and exhaustive fashion.
Now the mathematics is a yo-yo around 1, not 0. It is a relation anchored on an actual unity - a foundational sameness - that then gets broken in two complementary directions. Hence it is a triadic or developmental relation being modelled.
So consider the development of a reciprocal in the form of a fraction - a numerical inverse.
We start with 1. This 1 is 1/1 (Aha, the latent symmetry breaking which so far has changed nothing!) Then we get 2, and so 1/2. Then keep counting. We get 3, and thus 1/3 as its reciprocal. Guess where this is going next. We get 3 and its formal inverse, 1/3. Every time one number gets bigger, it forces its partner number - anchored by this particular form of opposition - to get smaller. The values are being driven apart.
Extremetise the relation and we get infiinities and infinitesimals. The infinitesimal is 1/infiinity. The infinite is 1/infinitesimal. Every actual number - fractional or whole - is then contained within the limits of this canonical relation. The infinite and the infinitesimal emerge as the limits on the breaking of the symmetry represented by the ur-somethingness of the 1.
A relation has to relate things. A self-relation is tautologous. Just counting up or down is simply to add the minimal claim that "a something" exists to break the ultimate symmetry of a zero-ness. There is at least 1 thing now, and you can then imagine 1-1 to recover the initial symmetry from which this one-ness must have mysteriously arisen, or 1+1+1+1... as the operation to keep breaking this zero-ness in the vain hope of finding its other limit.
You can see all the usual metaphysical dilemmas that flow from this sound of one hand clapping. How did something arise from nothing? How could we have creatio ex nihilo?
But a reciprocal/dichotomistic logic derives complementary limits of difference from an initial absolute sameness. Now we do start with something - but it an undefined oneness, a vagueness, a firstness. It is as much everything as it is nothing. It needs no stronger definition than the claim that it is a unity, an unbroken symmetry.
And then we can imagine a fundamental division in mutually definitional directions. If this symmetry starts to show some discreteness, some discontinuity, then matchingly, there is the new-found definiteness in the continuity that it claims to be moving away from. If the action reverses its course, it will be heading back towards its actual opposite, not simply negating its existence.
If we say something is becoming more fractional - 1/3 is now 1/333 - then it is not just shrinking towards nothingness as one of the limits on oneness. It is moving ever further away from its own inverse, 333/1. It is expressing its tendency towards infinitesimality in terms of the countering possibility of the infinite.
So it boils down to monism vs triadicism.
Monism claims there is either nothing or, instead, the one thing. (So it is in fact reliant on a metaphysical dichotomy, but understands it as a dualism - a simple presence vs absence distinction).
Triadicism fixes this by seeing presence and absence as relative to the third thing of a vagueness or apeiron. There is the unity of an unbroken symmetry which is neither A nor not-A. The principle of contradiction does not yet apply. 1 = 1/1. And turn 1/1 upside down, multiply it how you like, and you see no difference.
But as soon as you allow the possibility of a difference, a symmetry-breaking, then you get a separation to opposing poles of being. If you can have 2/1, then you can have 1/2. A single step now causes a break in the actual scale of being. Growth is matched by shrinking, not merely by not-growth. The difference is a real one, not merely the unplaced notion of one hand clapping - an event with no context by which to measure itself against.