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Are all thought experiments simply another way to assert certain claims and examples or does it have inherent epistemological value?

Edit: is there any point that can't be made without thought experiments?

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    Yes, initially. (Some) thought experiments tap intuitions that have not been crystallized into a conceptual grasp yet. So what is relied on can not be expressed as explicit evidence supported claims and inferences for lack of requisite concepts, but can back plausible judgments. "First, thought experiments can disclose nature’s failure to conform to a previously held set of expectations. Second, they can suggest particular ways in which both expectation and theory must henceforth be revised", Kuhn. See SEP for extended discussion.
    – Conifold
    Apr 7 at 11:19
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Experiments distinguish between theories, between paradigms. Thought experiments can engage with paradigms directly.

Einstein's riding a light-ray. Maxwell's Demon. Schroedinger's cat. These all draw attention to a contradiction in general terms, between paradigms. There is also a degree of theatricality even hyperbole, and we remember not so much the experiments that addressed them, as how they have been resolved or not in the thought experiment's own terms - the new paradigm, rather than the result/s that led to it.

I think the Buddhist 'Parable of the mustard seed' and 'Parable of the poison arrow' should be regarded as thought experiments. They point towards experiential, embodied knowledge, from putting yourself in the situation of others, in a way less likely to be achieved by simply declaring the moral of a story.

Our actual politics and culture, is informed by what 'morals' or lessons we see in events, shifts on race politics or attitudes to sexual harassment propagate by witnessing and discussing real cases - and case law explicitly develops from it, like say Roe v. Wade. What lesson is drawn from events is very often affected by a compelling narrative drawn about it. This is a real kind of knowledge, where narrative & judgements rule over phenomena.

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I think your two questions are not equivalent, so I'll answer one and then the other.

First Question

A thought experiment is an analysis of what a theory claims will happen to a system assuming an initial state. A theory is about all possible situations; a thought experiment is about one specific situation. Here are some examples.

Theory: Newtonian Mechanics
Initial State: A moving box is on a frictionless surface and in a vacuum. Nothing about the interior of the box is known.
Prediction: The velocity of the box will be constant.

Theory: Thermodynamics
Initial State: Two chambers connected by a single tube contain identical gasses. A demon in this tube can open and close it at will. This demon has decided only fast molecules will be allowed to pass from left to right, while only slow molecules will be allowed to pass right to left.
Result: A temperature difference will develop between the two chambers. The entropy is constant due to the demon gaining knowledge.

These thought experiments do not generate any new knowledge. However, they are a excellent tool for communicating knowledge (i.e. teaching). There is a second type of thought experiments though. If a thought experiment shows that a paradox will result, it becomes a counter-example.

Theory: Backwards time travel is possible.
Initial State: A man uses backwards time travel to kill his grandfather before his father was born.
Result: The man was never born. The man killed his grandfather. People who are never born cannot kill anyone.

It is logically impossible for all three of the statements in the result to be true. Therefore, this thought experiment proves backwards time travel is impossible, or that initial state described can never occur. This thought experiment generated new knowledge, which I believe qualifies as "epistemological value". However, the epistemological value is not inherent to thought experiments (i.e. there exists thought experiments that do not have epistemological value, see above).

Thought experiments are just like physical experiments. If they support a hypothesis, they are best used as a teaching tool; if the contradict a hypothesis, they are best used as evidence that a hypothesis should be rejected. In other words, thought experiments can be used to "assert certain claim" and/or have "epistemological value".

Second Question
If on a test I were given the question "Prove the [insert polynomial] = [insert other polynomial]", I would answer the question with a sound argument that only used algebra. I have found a claim that can be supported by an argument that does not use thought experiments. Therefore, the claim "Is there any point that can't be made without thought experiments" is false.

P.S. My argument supporting the claim "I have found a claim that can be supported by an argument that does not use counter examples" is itself a thought experiment.
: )

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    There are a range of proposals about time. Closed time-like curves suggest travel back only to the point the 'time machine' is created might be possible. You imply absence of evidence proves it impossible, it doesn't.
    – CriglCragl
    Apr 8 at 11:40
  • I actually knew about that already, but I couldn't think of a better example. My general claim that we can use thought experiments to generate knowledge using reductio ad absurdum arguments stands though.
    – E Tam
    Apr 8 at 12:45

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