AdeleneDawner comments on The benefits of madness: A positive account of arationality - Less Wrong
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Try "thinking is happening" and "observing is happening". No entity required.
Yeah, this clarifies what I thought on the matter - although it touches on anthropic reasoning, so I guess it isn't a standard answer.
For the record, it would look something like:
Putting this in formal logic, it only works if "being observed" is defined from the two-place predicate "x is observing y". We could also use a one-place predicate, "x is observed". So it's still not totally free of assumptions, so to speak.
The point is, Decart was supposedly doubting everything; so this particular argument, while decent, is not so unusually decent as to justify being held up as the one undoubted thing.
I feel like the existence of an observer is a necessary condition for "x is observed" to be true - but that is again anthropics, and so fully fleshing out this argument might take more than a comment,