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I tried to read and understand Frege's "The Thought" and came away with this question.

Frege argues mathematical theorems are thoughts which occupy a third realm independent from the physical or mental realms. Ideas are part of the mental realm, but a theorem/thought passes unchanged into our apprehensional capabilities of the mental. So when we apprehend the Pythagorean Theorem, it is done so without any change.

I believe this is accords with his final paragraph's:

When a thought is apprehended, it at first only brings about changes in the inner world of the apprehender, yet it remains untouched in its true essence, since the changes it undergoes involve only inessential properties http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Frege%20-%20The%20Thought%20a%20Logical%20Inquiry.pdf

I would think only direct realism would even be open to "unchanging essential properties" when something enters our minds. All other philosophies (epistemologies, ontologies, and metaphysics even) which are also not totally idealistic would seem to say essential properties of the hammer outside and hammer inside do change. And, I don't think even direct realism needs to maintain the external hammer and internal hammer have the same unchanged essential properties, but, only direct realism would be open to such a dynamic.

The way I see it, Frege wants externalism and unchanging essential properties. Even if these thoughts/theorems change our internal world according to his quote, the actual theorem is unchanged. The Pythagorean theorem always has the same words and structures whether apprehended or in the third realm, its most essential parts. This seems key as even if the PyTh thought changes the other two realms, that isn't the only thing being argued in his quote. The mind-dependent sentence of the PyTh and the independent proposition of the PyTh are too similar for any externalist philosophy I know of besides D.R. (but too similar would seem to push away from externalism as last paragraph). The essential parts of the hammer outside and the hammer inside, even for direct realism, seem to change, e.g. property dualism. But at least direct realism is closest out of the pack. And it seems like Frege would force us toward it by being the closest.

I don't think more general platonism/realism is the same as Frege's, as abstract objects may be much further removed/apprehension filters them much more than for Frege's version. In other external realisms where only inessential properties change, the inessential properties are different enough to speak of externalism. If that is collapsed, i.e. if the inessential properties are the only changes and they are so minute as Frege's realism, we are actually pushed away from externalism with the reasoning thus far. Externalism is proposed when the differences are pronounced (any essential changes or sufficient inessential changes). But Frege is externalist by being realist. What other solution could there be besides D.R.? Where does the tension push toward?

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