I find it difficult to see any trace of the idea in Euclid. Circles and straight lines, yes, but any abstract idea of shape in general, if it can be read into geometry at all, would only be in the modern axiomatisation. And done by mathematicians finding actual theorems, not by philosophers assuming there is an actual thing behind our use of the word, that it is their task to discover.
And done by mathematicians finding actual theorems, not by philosophers assuming there is an actual thing behind our use of the word, that it is their task to discover.
I don't mean to pick just on you, but I think philosophy is often unfairly criticized for being less productive than other fields, when the problem is just that philosophy is damned hard, and whenever we do discover, via philosophy, some good method for solving a particular class of problems, then people no longer consider that class of problems to belong to the realm of philosophy, and f...
Thagard (2012) contains a nicely compact passage on thought experiments: