From the questions on some of Gauss' philosophical ideas here at HSM stackexchange it's clear that Gauss had some major philosophical ideas that despite their profundity don't seem to have had much influence in the later developments of philosophy(perhaps philosophers with a mathematical inclination like Peirce were aware of some of them but didn't cite them). Is there any book or site where Gauss' collected philosophical writings are presented?
I'm not aware of any writings of Gauss that touched upon philosophical concerns. That doesn't mean that Gauss wasn't philosophically aware. He's been said to have read Kants Critique five times which probably isn't surprising given the esteem that Kant was held in the German consciousness of the time - rather like Hawking is held in ours.
And to me, it's clear that there was a possible influence of Kants analysis of space on his discovery of non-Euclidean geometry.
In fact, in Dunningtons Gauss: A Titan of Mathematics, we have:
Schleiden told the philosopher Rudolf Eucken that Gauss read Kant's Critique of Pure Reason five times. The fifth time he is reported to have said:"now it's dawning on me"...Gauss was interested in the manner in which Kant founded his concept of space and pioneered in the field of non-Euclidean geometry ...
Although Dunnington adds he also disagreed with Kant, where Gauss said:
The distinction between right and left cannot be defined, but only shown ...
But this is wrong as Kant in his 1768 essay, Concerning the Ultimate Foundation of the Differentiation of the Regions in Space, did exactly that - the essay is notoriously hard to understand, and Gauss may have just misunderstood it (we don't know if he had read this fives times!)
Donnington goes on to say:
Gauss and Kant thus differed in the manner of founding a theory of space, but there is scarcely any difference in their views about space. Gauss did not deny the a priori character of space.
Given the preceding, the difference is even slimmer than Donnington assumes here.