The term ' substance ' here stands for the set of all substances, and the conclusion of the syllogism reads : ' This individual dog is an element of the set of all substances ', which is equivalent to : ' This individual dog is a substance ' :
All individual (material) things are substances
This individual dog is an individual (material) thing
Therefore, this individual dog is a substance.
Here ' individual (material) thing (s) ' is middle term.
At least the minor must be demonstrated :
All mammals are individual (material) things
This individual dog is a mammal
Therefore, this individual dog is an individual (material) thing.
Here ' mammal(s) ' is middle term.
So between ' dog ' and ' substance ' we have the middle terms ' mammal ' and ' (material) thing '. Are there still more middle terms between ' dog ' and ' substance ' ? At least ' vertebrate ' is one. Are there an infinite number of middle terms between them?