You're taking a political, or I dare even say religious point of view on the topic. You can't argument yourself. To think critically essentially means to use tools of logic, break down statements and analyze them one by one and their relationship. This is precisely what architectures like CoT and ToT do in models, and right before your eyes.

You can play word games and say "no, it doesn't think, because it's math", but that's just pathetic.

Note I'm not saying models always think critically. I said the exact opposite. And it applies to humans, as well. You had a knee jerk reaction here, you've had it many times in many replies to many social media. I can bet about it. You didn't use critical thinking. QED.

Yes, but the regurgitation can be thought of as memory.

Let it have more source information. Let it know who said the things it reads, let it know on what website it was published.

Then you can say 'Hallucinate comments like those by impossibleFork on news.ycombinator.com', and when the model knows what comes from where, maybe it can learn what users are reliable by which they should imitate to answer questions well. Strengthen the role of metadata during pretraining.

I have no reason to belive it'll work, I haven't tried it and usually details are incredibly important when do things with machine learning, but maybe you could even have critical phases during pretraining where you try to prune away behaviours that aren't useful for figuring out the answers to the questions you have in your high curated golden datasets. Then models could throw away a lot of lies and bullshit, except that which happens to be on particularly LLM-pedagogical maths websites.