About Richard Cohen, and Conventional, and (Somehow) Math

You've probably heard that Richard Cohen said some stupid, stupid words. I'm here to talk about one word in particular, and how I see it.

I'm a math major. I do the Maths, sometimes just for fun. And a lot of math, once you've seen your way past calculus and differential equations, doesn't look a whole lot like what you were doing before: you now have to prove stuff. And so I learn methods for doing certain types of things, including making general conclusions about a group¹ working only with the definition of that group. One specific tool I use for this type of thing is formally described in First Order Logic as Universal Introduction².

The basic process is this: take some group. Pick a random (read: typical or conventional) element in that group. If some general statement holds for that element, assuming nothing but inclusion in the group, then it holds for every element of the group. The key point is that there's nothing special about the element I chose; all I know about it comes from how the overall group is defined. So if I picked any other element from the group, I would have reached the exact same general statement. Therefore that statement must apply to every member of that group.

So, Cohen's "conventional" would apply back to the group he's picking from: the GOP, or maybe even a specific subset of that, of his own devising. He's going for what he thinks/claims he knows about the group: that a typical member of that group would see Mayor de Blasio's family as everything they feel is wrong in America, and thus the gag. Try replacing the "conventional views" with the phrase "views of a typical member of this group, the GOP". Now his horrible paragraph reads

"Today’s GOP is not racist, as Harry Belafonte alleged about the tea party, but it is deeply troubled — about the expansion of government, about immigration, about secularism, about the mainstreaming of what used to be the avant-garde. People with [views of a typical member of this group, the GOP] must repress a gag reflex when considering the mayor-elect of New York — a white man married to a black woman and with two biracial children. (Should I mention that Bill de Blasio’s wife, Chirlane McCray, used to be a lesbian?) This family represents the cultural changes that have enveloped parts — but not all — of America. To cultural conservatives, this doesn’t look like their country at all."

Let me say that I think he's still wrong. I would guess that a vast majority of today's GOP would feel fine with this marriage, and an even larger majority would say they feel fine with it. But to me, this is the first thing that popped into my head that even made an attempt at making sense of that abomination of a sentence. This paragraph now has a consistent internal structure.

tl;dr: Cohen's column is pretty bad. But we may be jumping to the wrong conclusion of what one single, specific word in it means.

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1 I use the word group in a standard, layman sense, not the precise mathematical sense, although it does apply to them too.^↩
2 See particularly pages 3 and 4.^↩