Opposition To Same Sex Unions Is Mathematically Wrong

Gary Hill

•Introduction•

Using basic principles of mathematical set theory, conservative Christian activist Andrew Schlafly has attempted to demonstrate the moral superiority of opposite-sex to same-sex unions on the basis that opposite sex unions create a larger set:

“Traditional marriage provides a greater set than otherwise: the union of A = {a, b, c, d} and B = {a, b, c, e} is merely {a, b, c, d, e}, while the union of M (man) = {a, b, c, d} and W (woman) = {e, f, g, h} is {a, b, c, d, e, f, g, h}, which is a broader and more diverse set.”

The glaring problem with his formulation is obvious: on what grounds does Schlafly maintain that a larger mathematical set is representative of, or equivalent to, a higher moral state of affairs than a smaller mathematical set? This is simply an assertion, there is obviously no empirical evidence for this claim and the logical deduction is not at all obvious. Note also that his formulation effectively quantifies two persons of the same biological sex as being 25% different and two persons of different biological sex as being 100% different, neither of which accords with either biology (although sex does normally exhibit as a bimodal distribution, both male and female do share an X chromosome) or clinical psychology or psychiatry (where a persons gender need not necessarily equate to their biological sex).

In response, two simple mathematically-based formulae are presented demonstrating that Schlafly's moral opposition to same-sex unions cannot logically work unless the prior assumption is made that one biological sex possesses a greater degree of moral and personal autonomous value than the other. Consider the following statements/propositions and their binary truth values:

S1: All human beings, regardless of their biological sex, hold equal value (true/false)
S2: Same-sex unions are inherently and always immoral (true/false)

I demonstrate mathematically/logically that one cannot hold to both S1 and S2 as being equally true moral statements. Specifically, if S1 is maintained to be true, then S2 must be false.

•Values Placed On The Moral Standing Of Possible Unions Between Two Biological Sexes•

Let:
M = male; F = female
X = a morally permissible union; Y = an immoral union

⇒ (M + F = X)
⇒ (M + M = Y)
⇒ (F + F = Y)
If (M + F = X) ⇒ (X = 1M + 1F)
If (M + M = Y) ⇒ (Y = 2M)
If (F + F = Y) ⇒ (Y = 0M)
(each case: Y is determined solely by M)
∴ (M > F; i.e., M possesses greater value in apportioning moral status to a union than F)
∴ If S1 is claimed to be true, S2 must be false

Solution:
(M + F = X) ⇔ (M + M = X) & (M + F = X) ⇔ (F + F = X)
S1 is true & S2 is false

•Values Placed On The Autonomous Person, Regardless Of Biological Sex•

Let:
M = male; F = female
P = personhood, i.e., autonomous personal being able to understand and consent to union
1 = numerical value assigned to P (∴ 0 = ¬ P)
∴ MP = 1; FP = 1

⇒ MP + FP = (1P + 1P)
⇒ MP + MP = (1P + 1P)
⇒ FP + FP = (1P + 1P)
∵ from (i): (M + F) ≠ (M + M) ⇒ (1P + 1P) ≠ (1P + 1P) ⇒ (MP ≠FP) & (MP > FP)
∵ from (i): (M + F) ≠ (F + F) ⇒ (1P + 1P) ≠ (1P + 1P) ⇒ (MP ≠ FP) & (MP > FP)
∴ (MP > FP; i.e., MP possesses greater value in apportioning moral status to a union than FP; MP possesses a higher degree of personhood than FP).
S1 is false

Solution:
From (i): (M + F + X) ⇔ (M + M = X) & (M + F = X) ⇔ (F + F = X)
∴ (MP + FP) = (MP + MP) & (MP + FP) = (FP + FP)
S1 is true, S2 is false

•Inevitable Conclusion•

Of course, both formulae can be redefined with biological sex transposed and the opposite result obtained (i.e., F > M or FP > FM). This does not, of course, refute the argument in any way; although the formulae would no longer reflect the attitude of those, like Schlafly, who are most active in objecting to same-sex unions, the mathematical processes and conclusion would be unaffected; if S1 is considered to be objectively true, then S2 is false.

'Opposition To Same Sex Unions Is Mathematically Wrong'. © Gary Hill 2018. All rights reserved. Not in public domain. If you wish to use my work for anything other than legal 'fair use' (i.e., non-profit educational or scholarly research or critique purposes) please contact me for permission first.