Why IQ shouldn't be considered an external factor

I think what you're saying is that if we want a coherent, nontrivial definition of "under our control" then the most natural one is "everything that depends on the neural signals from your brain". But this definition, while relatively clean from the outside, doesn't correspond to what we ordinarily mean; for example, if you have a mental illness, this would suggest that "stop having that illness!!" is reasonable advice, because your illness is "under your control".

I don't know enough neuroscience to give this a physical backing, but there are certain conscious decisions or mental moves that feel like they're very much under my control, and I'd say the things under my control are just those, plus the things I can reliably affect using them. I think the correct intuitive definition of "locus of control" is "those things you can do if you want to".

Regarding causal arrows between your IQ and your thoughts, I don't think this is a well-defined query. Causality is entirely about hypothetical interventions; to say "your way of thinking affects your IQ" is just to say that if I was to change your way of thinking, I could change your IQ.

But how would I change your way of thinking? There has to be an understanding of what is being held constant, or of what range of changes we're talking about. For instance we could change your way of thinking to any that you'd likely reach from different future influences, or to any that people similar to you have had, etc. Normally what we care about is the sort of intervention that we could actually do or draw predictions from, so the first one here is what we mean. And to some degree it's true, your IQ would be changed.

From the other end, what does it mean to say your way of thinking is affected by your IQ? It means if we were to "modify your IQ" without doing anything else to affect your thinking, then your way of thinking would be altered. This seems true, though hard to pin down, since IQ is normally thought of as a scalar, rather than a whole range of phenomena like your "way of thinking". IQ is sort of an amalgam of different abilities and qualities, so if we look closely enough we'll find that IQ can't directly affect anything at all, similarly to how g can't ("it wasn't your IQ that helped you come up with those ideas, it was your working memory, and creativity, and visualization ability!"); but on the other hand if most things that increase IQ make the same sort of difference (eg to academic success) then it's fairly compact and useful to say that IQ affects those things.

Causality with fuzzy concepts is tricky.

+1 for coming up with such an interesting argument

I think it's helpful to define terms for something like this. I realize you linked to another post describing them, but just to avoid any confusion:

internal locus of control - believing that my decisions are under my control external locus of control - believing that my decisions are not under my control

"Things under your control" (more generally, free will) is an ill-defined concept: you are an entity within physics; all of your actions and thoughts are fully determined by physical processes in your brain. Here, I will assume that "things under your control" are any things that are controlled by your brain, since it is a consistent definition, and it's what people usually mean when they talk about things under one's control.

Involuntary responses are not under your control and are not "determined by physical processes in your brain", but are considered actions. Voluntary responses are also influenced by factors occurring outside your brain. If you're tired, you are not likely to do any heavy exercise although you are able to choose to do so. If you see an explosion in front of you, you are likely to drop to the ground or run away.

maybe add physical traits, like height or attractiveness to the "internal factors" category

Yes, internal locus of control factors such as clothing, diet, or hair style are a major influence on attractiveness, but height; I have never heard anyone make that argument before. How is height under my control or what sort of arguments could be made in favor of such a belief? I recognize you are not actually arguing this is the case, but I'm not sure how you could even consider this to be a plausible argument.

It's true that one can measure his IQ, and that IQ rarely changes much, but still: if you consider IQ fixed and external factor out of your control, then you must consider your thought processes restricted to some set and therefore, not totally under your control. ... You shouldn't consider any functions of your current brain state as external when discussing locus of control, since such viewpoint is actually counterintuitive and, therefore, makes you prone to errors.

IQ places a limit on your ability to learn new things, true, but you are still able to determine what you choose to learn. I do not have a limitless amount of money, but I am still able to choose what I buy. Are you saying that income must also be considered completely internal, and if not the things I buy must be external? Everything is limited by something. I consider the limit to be external and out of my control, and the choices I make within those limits to be internal. I don't think that the limit and the choice are one and the same or grouped in some fashion that requires them to be kept together.

I suggest the following model. Consider yourself to be an agent of fixed optimization power but variable utility function. Then, "things under your control" are things that can be affected by the choice of the utility function.

In this model IQ is an external factor. But choosing to eat toast or cereals for breakfast is an internal factor. I think this corresponds better to the intuitive notion of internal/external factors.

But it's possible to ask, what can we change if we can change brain, conditional on the fixed IQ score. But then the "free will" intuition collapses; it's hard to imagine what we could change if our thought processes were restricted in some weird way.

Most people realize they don't have the brainpower to be the next Einstein. On the contrary, the general population has a phobia of anything involving math. I don't think this imposes much of an obstacle against free will. If you restrict to the "It's not exactly rocket science" domain, there are still plenty of choices to be made.

It's true that one can measure his IQ, and that IQ rarely changes much, but still: if you consider IQ fixed and external factor out of your control, then you must consider your thought processes restricted to some set and therefore, not totally under your control.

There are plenty of things restricting my thought processes. There are memory and speed limitations. There's my upbringing and cultural norms. I know my thinking to be prone to error. Free will isn't about being completely free of all constraints. Our courts already apply a "reasonable person" test where they examine what a rational person with ordinary intellectual capabilities could be expected to do. Limits to one's mental abilities have always been accepted along with free will. In fact, most Christian free-will apologists would consider it outright blasphemous to suggest perfect reasoning ability.

You shouldn't consider any functions of your current brain state as external when discussing locus of control

Epilepsy - and there's a very gradual slope of brain deficits which start seeming more "conscious" in nature from that point on And there's a similar slipper slope with non-brain body parts, over which we have varying degrees of conscious control.

Since this is mostly about framing, I'd recommend attempting to do away with free will intuitions entirely and intentionally failing to draw a clear boundary between self and non-self. Is it possible to simply perceive and act, without externalizing or internalizing?