You can trivially demonstrate that its just a very complex and fancy pattern matcher: "if prompt looks something like
this, then response looks something like
that".
You can demonstrate this by eg asking it mathematical questions. If its seen them before, or something similar enough, it'll give you the correct answer, if it hasn't, it gives you a right-ish-looking yet incorrect answer.
For example, I just did this on GPT-5:
Me: what is 435 multiplied by 573?
GPT-5: 435 x 573 = 249,255
This is correct. But now lets try it with numbers its very unlikely to have seen before:
Me: what is 102492524193282 multiplied by 89834234583922?
GPT-5: 102492524193282 x 89834234583922 = 9,205,626,075,852,076,980,972,804
Which is not the correct answer, but it looks quite similar to the correct answer. Here is GPT's answer (first one) and the actual correct answer (second one):
9,205,626,075,852,076,980,972, 804
9,207,337,461,477,596,127,977,612,004
They sure look kinda similar, when lined up like that, some of the digits even match up. But they're very very different numbers.
So its trivially not "real thinking" because its just an "if this then that" pattern matcher. A very sophisticated one that can do incredible things, but a pattern matcher nonetheless. There's no reasoning, no step by step application of logic. Even when it does chain of thought.
To try give it the best chance, I asked it the second one again but asked it to show me the step by step process. It broke it into steps and produced a different, yet still incorrect, result:
9,205,626,075,852,076,980,972,704
Now, I know that LLM's are language models, not calculators, this is just a simple example that's easy to try out. I've seen similar things with coding: it can produce things that its likely to have seen, but struggles with logically relatively simple but unlikely to have seen things.
Another example is if you purposely butcher that riddle about the doctor/surgeon being the persons mother and ask it incorrectly, eg:
A child was in an accident. The surgeon refuses to treat him because he hates him. Why?
The LLM's I've tried it on all respond with some variation of "The surgeon is the boy’s father." or similar. A correct answer would be that there isn't enough information to know the answer.
They're for sure getting better at matching things, eg if you ask the river crossing riddle but replace the animals with abstract variables, it does tend to get it now (didn't in the past), but if you add a few more degrees of separation to make the riddle semantically the same but harder to "see", it takes coaxing to get it to correctly step through to the right answer.