Both euphemism and dysphemism are replacing words in order to make a point. With euphemism, you replace a word with another to make an idea sound better (often to be less offensive). With dysphemism, you replace a word with another to make an idea sound worse.
A great example of a rhetorical use of euphemism is the titles pro-life and pro-choice. Using the prefix 'pro' makes both of them sound like they are for something, instead of being against something. Additionally, it makes opposing the position sound bad (who wants to be against choice? Or life?). Therefore, naming your position can make your position sound better, while making the other position sound worse.
An example of dysphemism would be my calling unconditional election "arbitrary election". The word arbitrary makes the idea sound a lot worse (though I would argue that it is not inaccurate).
Euphemism and Dysphemism In Action
Probably the most obnoxious example of Calvinist euphemism is the term "Doctrines of Grace" which Calvinists use as a synonym for Calvinism. They do this because the word Calvinism is distasteful to some, and it sounds more like a label which isn't very chic. So they give it a new name to hide that it is a philosophical system, and to try and make it sound like they are only defending grace. It also is an attempt to try and own the word 'grace', as if that is a purely Calvinist concept (despite the fact that the defining doctrine in Calvinism is unconditional election while the defining doctrine of Arminianism is prevenient grace).
There are plenty of other examples: sovereign grace for irresistible grace, sovereignty for determinism, effectual atonement for limited atonement, etc...
There are lots of examples of dysphemism as well. For instance, the calumnious use of Pelagius wherever possible. Even the term Non-Calvinist is a bit of a dysphemism, since it paints Calvinism as the only solid idea (very far from the truth).
The End Result*
The end result is a lot of confusion, misdirection, and sometimes outright lies (though I will clarify the lie point at the end). What you usually have is what is known as poisoning the well. Poisoning the well is essentially creating a bias before any real conversation has taken place. For instance, the term "Doctrines of Grace" implies that other theologies don't really promote grace. While most Calvinists do believe this, by renaming Calvinism, one is now forcing the other side to argue against the "Doctrines of Grace" and making it sound as if the person is arguing against grace itself.
About what I said above about lying. There is nothing inherently deceitful about euphemism or dysphemism. Indeed, with the exception of the rampant dysphemistic use of 'pelagianism' or 'semipelagianism' I cannot think of a single example that is universally deceitful. However, it can be easily abused by those who do lie. There is a great article on SEA about Calvinism on the Sly regarding how many Calvinist pastors like to hide their theology until they gain a base, and then subvert the original leadership. This is not something I want to accuse all Calvinists of doing, or even most Calvinists, but it is interesting that it seems to be principally happening from the Calvinist camp right now. I think it is because the rampant use of euphemism and dysphemism by well meaning Calvinists give such power-mongers tools.
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