I also had trouble with the notation. Here’s how I’ve come to understand it:
Suppose I want to know whether the first person to drive a car was wearing shoes, just socks, or no footwear at all when they did so. I don’t know what the truth is, so I represent it with a random variable , which could be any of “the driver wore shoes,” “the driver wore socks” or “the driver was barefoot.”
This means that is a random variable equal to the probability I assign to the true hypothesis (it’s random because I don’t know which hypothesis is true). It’s distinct from and which are both the same constant, non-random value, namely the credence I have in the specific hypothesis (i.e. “the driver wore shoes”).
( is roughly “the credence I have that ‘the driver wore shoes’ is true,” while is “the credence I have that the driver wore shoes,” so they’re equal, and semantically equivalent if you’re a deflationist about truth)
Now suppose I find the driver’s great-great-granddaughter on Discord, and I ask her what she thinks her great-great-grandfather wore on his feet when he drove the car for the first time. I don’t know what her response will be, so I denote it with the random variable . Then is the credence I assign to the correct hypothesis after I hear whatever she has to say.
So is equivalent to and means “I shouldn’t expect my credence in ‘the driver wore shoes’ to change after I hear the great-great-granddaughter’s response,” while means “I should expect my credence in whatever is the correct hypothesis about the driver’s footwear to increase when I get the great-great-granddaughter’s response.”
I think there are two sources of confusion here. First, was not explicitly defined as “the true hypothesis” in the article. I had to infer that from the English translation of the inequality,
In English the theorem says that the probability we should expect to assign to the true value of H after observing the true value of D is greater than or equal to the expected probability we assign to the true value of H before observing the value of D,
and confirm with the author in private. Second, I remember seeing my probability theory professor use sloppy shorthand, and I initially interpreted as a sloppy shorthand for . Neither of these would have been a problem if I were more familiar with this area of study, but many people are less familiar than I am.
I’m trying to make sense of this. If I’m not mistaken you claim:
Autogynephilic sexual fantasies are causally responsible for late-onset not-purely-androphilic trans women’s motivations for transition
Some late-onset trans women have never had autogynephilic sexual fantasies
This obviously doesn’t make sense as-is. You briefly went into a theory of early-onset HSTS, late-onset not-otherwise-specified gender dysphoria, and you raised internalized misandry as a possible alternate instantiation of that “not-otherwise-specified”. And that could resolve the issue I’m pointing at.
This explanation makes a testable prediction. I’ve noticed that late-onset trans women tend to fall remarkably close together along a number of characteristics that aren’t obviously related to gender dysphoria or autogynephilia. Let me know if you don’t think that’s right, and I can go into more detail, but as a basic example, this group has way higher rates of ASD, and more people who were excellent programmers at a young age, compared to the male baseline. If you’re proposing that non-autogynephilic late-onset trans women have significantly different causal explanations for transitioning, then we wouldn’t expect to find them also in this autistic computer-kid cluster.
I notice that when offering Ziz as an example of a non-autogynephilic late-onset trans woman, you chose to mention that she’s “unusual along a lot of dimensions.” So I’m hopeful that I’m on the right track in inferring your thinking here.
From my perspective as a late-onset, not-purely-androphilic trans woman who’s on the spectrum and was an excellent programmer at a young age, but who lacks a history of autogynephilic sexual fantasies, I find the “not-otherwise-specified” explanation hard to believe.
Instead of supposing that most late-onset trans women were motivated to transition by their fetish, while I was motivated by some other factor, and that it’s just a coincidence that we happen to also share a lot of peculiar features, it would be more parsimonious to say that among these characteristics that we share is some psychological factor that motivated all of our transitions, and which also causes most of us to develop autogynephilic fetishes.
Maybe I’m wrong, and what I perceive as a clear cluster of unusual traits isn’t actually enough of a statistical anomaly to support my conclusions (I think it’s really anomalous though). Or maybe I’m a victim of social contagion — I ended up friends with a bunch of autogynephiles because we share all these characteristics, then they transitioned because of their autogynephilia, and then I did because I wanted to be ingroup (I’m quite happy with my transition though).
My explanation also has the advantage of matching the reports by most late-onset trans women about the relation between their gender dysphoria and autogynephilic fantasies. I agree there’s plenty of evidence that nobody is thinking sanely on this subject — motivated self-delusion is a believable explanation! But it does still incur a complexity penalty.