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Of course, it has to be an invention more like the invention of English than like the invention of, say, a religion. Both our native language and the language of mathematics affect how we think to such extent that it is virtually impossible to think otherwise without falling into contradiction. And while it is correct that whether or not we have two things before us depends on what we count as things, all the same, if we agree that we have one antelope and another antelope in front of us, we have to agree that we have two antelope in front of us. The point of my saying that it is a form of our intuition (and synthetic a priori) is that, while it may or may not map on to what is really 'out there', it does describe something accurately and universally -- the way we think about what's out there.
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"Die Deutschen meinen, daß die Kraft sich in Härte und Grausamkeit offenbaren müsse, sie unterwerfen sich dann gerne und mit Bewunderung:[...]. Daß es Kraft giebt in der Milde und Stille, das glauben sie nicht leicht."
"The Germans believe that power must reveal itself in hardness and cruelty and then submit themselves gladly and with admiration[...]. They do not believe readily that there is power in meekness and calm."
-- Friedrich Nietzsche
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