In our recent interview with Martha Bueno, we delve deep into the broader implications of the drug war. We discuss how many Americans lack the critical thinking skills needed to oppose it logically and consistently.

Full Episode: https://thefreethoughtproject.com/podcast/podcast-martha-bueno-ross-ulbrichts-injustice-the-power-of-cannabis-healing-americas-divide

Matt Walsh, the conservative podcaster man, made that documentary. And ever since, there's been nothing but seething. And this article especially rubbed me the wrong way.

Firstly, there's this:

Yeah, how dare a "random African tribe" have an opinion on gender! The reason why Walsh "picked a random African tribe" is because for well over a decade now, gender theorists and online commentators have claimed that the sex binary is a white colonialist invention. That's why. And here you are sniffing that it's so "unhinged" to ask African people what they think. I think Matt Walsh is an absolute fucking racist, but you're over here dismissing the opinions of rural Africans out of hand, without having even heard what those opinions are.

This is an entire video and article response to the documentary, and you're not going to watch it? You'd literally rather put cat pee in your mouth than hear an opinion you know you'll disagree with??

The next five paragraphs go into the dishonesty of creationists. The author actually says, "why am I talking so much about evolution?" The answer to that is that the theory of natural selection is backed up by science, and the idea that you can change your biological sex with exogenous hormones and experimental surgeries is not. So it's more convenient for you to conflate the two and pretend that males can be women, if they really want to be.

Okay, so finally, at the end of the video, the answer to the question, "what is a woman?" It's supposed to be non-circular and not reliant on sex stereotypes.

"a person society associates with the female sex" sounds better than "anyone who identifies as a woman." But how does society associate a person with the female sex? Gender roles. As in, this is just saying "a woman is anyone who performs sufficient femininity and/or can be clearly recognized as an adult human female." To define women by femininity is sexist toward women. To even deny us a cohesive class, especially when our abusers and oppressors can clearly place us there, is sexist.

But anyone who has been in the community knows another glaring problem with this statement: the person making it is inadvertently excluding transwomen who don't pass. In fact, that takes the identity away from transwomen and puts it back to society. That means misgendering doesn't exist anymore. I've seen you, I'm part of society, I've decided whether or not you're a woman. Additionally, how does this jibe with the notion that transwomen not only are, but always have been women?

Even this youtuber is adding in caveats (about fifteen minutes worth) to this supposed simple, one-sentence definition, and saying it doesn't cover all the circumstances. No shit. When "woman" has to be a term open to anyone who claims it, but closed to anyone who doesn't claim it (yet), it'll sound like this.

So, if Mike is asserting that if you lie about one thing we’re entitled to disbelieve your entire testimony, what does that say about his many half-truths and falsehoods?

What I will never respect are "pro-lifers" who are only okay with abortion in cases of incest or rape. Those who would deny school lunch programs, ban easily-accessible non-abortifacient contraception (aka: the pill, the patch, the shot, the ring, the implant etc), cut funding to food stamps and medical care for women and their children, oppose legislature making paid maternity/paternity leave mandatory. You are the sorts I will never respect.

It is well known that adding unrestricted kind polymorphism to the higher-order polymorphic lambda calculus, a.k.a. System $ F_\omega $, leads to logically inconsistent paradoxes. For those in dependently typed theorem proving community, this is non of their concern, since dependently typed proof assistants are usually based on predicative calculus with stratified universes. However, there is an alternative approach that has not been well explored yet.

Consider taking an alternative approach of starting from a more traditional functional language based on impredicative polymorphism and turning that into a theorem proving system. For instance consider a certain subset of Haskell with GHC extensions such as RankNTypes and ImpredicativeTypes (after all, core of GHC is an extension of $ F_\omega $ ), and trying to carve out a logically consistent language. This is exactly the motivation of my Ph.D. thesis, and its resulting artifact is the Nax language. To make the long story short, we should be able to have a logically consistent subset of say Haskell with GHC extension including GADTs and PolyKind. The benefit of such design is that we can reuse all the facilities that have already been built around functional languages like Haskell, which has far more sophisticated and well-optimized compilers than most theorem proving systems.

If we take this route, we should figure out a safe way to extend impredicative polymorphism with a restricted form of kind polymorphism. I believe that extending $ F_\omega $ with Rank 1 polymorphic kind bindings for finite number of globally defined type constructor variables is safe. That is, the resulting calculus with this extension is logically consistent. Proof of logical consistency of this extended calculus should be quite straightforward by mapping the extended calculus back into $ F_\omega$ by inlining.

Here is the syntax of the extended calculus: $$ \sigma ::= \kappa \mid \forall \chi.\kappa $$ $$ \kappa ::= \chi \mid * \mid \kappa \to \kappa' $$ $$ A, B, F, G ::= X \mid A \to B \mid \lambda X^{\kappa}.F \mid F~G \mid \forall X^{\kappa}.B $$ $$ \Sigma ::= \cdot \mid T^\sigma,\Sigma $$ $$ \Gamma ::= \cdot \mid X^{\kappa} \mid x:A $$ $$ t, r, s ::= x \mid \lambda x.t \mid r~s $$

A type constructor name $T$ is no different than a type variable $X$. It is just a notional convention to emphasize that the variable stands for a globally defined name for a type constructor. From a list of globally defined type constructors $ T_1 = F_1, T_2 = F_2, \ldots, T_n = F_n $ a global context $\Sigma$ can be obtained such that $ \Sigma = T_1^{\sigma_1}, T_2^{\sigma_2}, \ldots, T_n^{\sigma_n} $ Each $\sigma_i$ is a polymorphic kind of $F_i$. For instance, the polymorphic kind scheme of $F_1 = \lambda X^{\chi}.X$ is $\sigma_1 = \forall \chi.\chi \to \chi$.

For simplicity, let us consider just one global definition where $T_1 = F_1$. Assuming $F_1$ is well kinded, we get $\Sigma = T_1^{\sigma_1]}$. In the derivation tree of a typing judgment $ T_1^{\sigma_1};\Gamma \vdash t : A $, we inline each occurrence of $T_1$ with an instantiation of its definition $F_1$, instantiating all the free kind variables in $F_1$ appropriately for each occurrence. For instance, if we had $F_1 = \lambda X^{\chi}.X$, we might instantiate it to $ \lambda X^{*}.X$, $ \lambda X^{ * \to * }.X$, or any appropriate instantiation of $\chi$ as needed. Once we have inlined every occurrence of $T_1$, the global context $\Sigma$ becomes irrelevant. Therefore, we can simply ignore $\Sigma$, and the resulting derivation tree is exactly the derivation tree for a typing judgment in $ F_\omega $.

Generalizing the inlining for $n$ definitions is not so hard. The only additional thing to consider is that the previously defined type constructor names can be used in the latter definitions. Consider $ T_1 = F_1, T_2 = F_2, \ldots, T_n = F_n $. The first name $T_1$ can appear in any of $F_2, \ldots, F_n$. So, inlining should be performed in a cascading manner starting from $T_1$, inlining inside $\Sigma$ as well as other parts of the derivation tree.