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I would like to introduce the reader to the Discontinuity Fallacy, and in particular how it applies to systemic racism in the United States of America.

The familiar argument is made as follows: America is a colorblind society, and any individual who wants to make it in this country can. The failure to succeed is therefore lain exclusively at the feet of those who are unable to make ends meet. In particular, people of color are held at fault for their impoverished state, which is taken as evidence of collective flaws in their character, such as lack of intelligence, laziness, or other shortcomings.

So, why is this a fallacy? For a very simple reason, really. In mathematics, continuity between two points in space and time means that a function must physically traverse the distance between them. It cannot magically teleport from one to the other. Doing so would violate that principle, and would be what we call "discontinuity".

In other words, if the United States was once plagued by systemic racism, and now it no longer is, it must have physically traversed that distance, and arrived at the latter paradise at some specific point in time. Which means someone who believes America is a colorblind society must be able to give the specific month, day and year when that occurred.

So, in summation, we know that in the 1860s America was plagued by racism, as people of color were essentially treated like furniture. We also know that a century later, in the 1960s, America was still beset by racism, as people of color were treated like they had the Bubonic Plague. So if you think that between then and now the situation has improved to the point where America has been completely healed of its racial wounds, the burden of proof therefore is upon you to divulge the specific month, day, and year when this miraculously happened. And if you cannot do so, how then can you realistically claim that such a date even exists? You cannot, nor can you assert that we have been a healed society.

And that my friends is the Discontinuity Fallacy in a nut shell.