Dale Tuggy floats an argument in his debate with Rob Bowman which has been criticized by a Trinitarian philosophical blogger named "Brandon." It goes thus:
1) The Father and the Son are the same God.
2) For any x and y, and for any kind F, if x and y are the same F, then x is an F, y is an F, and x = y. (x and y are numerically one)
3) The Father = the Son. (1, 2)
However, Brandon says 2) is "false" or begs the question (a logical fallacy) since it possibly contains an "equivocal" middle term or makes (unwarranted) assumptions. A middle term appears in the major and minor premise of an argument/syllogism, but does not appear in the conclusion of the argument.
He then provides a complicated "rebuttal" which amounts to (IMO) "we can't refute the Trinity doctrine by reasoning Dale Tuggy's way."
I'm not sure if Tuggy's argument goes through as it stands, but I've tried to construct a parallel version that is not susceptible to Brandon's criticism. Maybe:
1) Brahma and Vishnu are the same God.
2) For any x and y, and for any kind F, if x and y are the same F, then x is an F, y is an F, and x = y. (x and y are numerically one).
3) Brahma = Vishnu.