I'm way overthinking this, but I'm going with finite. It could be an unfathomably large number, but gender is a human construct and there are a finite number of humans. Let's say each human that ever lives has a unique gender identity - there could be billions or trillions, but it would still be finite.
Countries have been trying gamification and incentivization to increase birth rates, when they should have been appealing to our pedantic impulses all along.
There are finite number of possible humans due to there being a finite number of states a brain can be in.
There is an argument for moral realism that takes advantage of finiteness and computability of mental processes to show that there could be an objective morality
there are infinite ways to arrange and configure finite neurons
computability of mental processes
are mental processes entirely computable though? you kind of run into a halting-problem-style issue because if you can compute your response to anything that should imply that you can never make a decision that surprises the computation. but if you feed knowledge of the computation's result into your decision making process you can just pick the opposite
If mental states are finite, then the space of all possible human minds is finite and includes the one that believes they have knowledge of the computation's result. It is possible for mental states of 2 minds to be different but extensionally behave like the same person. We would exclude human minds whose models don't map well onto the physics of our universe though. You might not be willing to pick the opposite if we are talking about morality also @askbeehaw
It's possible that brains act stochastically such that two discrete identical brains produce a range of outputs under identical conditions. In that case, mental states would be confined by the space of outputs of minds, and if that's the real numbers then it would be uncountably many.
I was going to write up a similar argument, but does a gender exist if no one has it? Because then we might be able to "fill in the gaps" and get it to uncountably infinite.
I thought something similar, but the human brain is finite, so I don't think a single person could have an uncountably infinite gender; unfathomably large, maybe, but it would still be finite.
Edit: I'm not trying to be bigoted here. If someone does identify that way I don't want to discredit your identity.
I'm no mathematician, but I don't think that's how it works. A quick Google says there are 100 billion neurons. So you would have 100000000000! possible combinations, unfathomably large, but finite. Granted, a human brain is more complex than the configuration of neurons, but I don't know how it becomes infinite.
yeah, but the relative positions and relative lengths and relative widths and relative densities and relative conductivities of those neurons are real numbers
I fucking love where this went, as I was thinking the exact same responses while reading this thread! Love it when a question about gender results in fundamental ideas surrounding mathematics and the nature of reality.