Are you familiar with the Rubin's Vase? It is basically a "double" image. There are many illusions like that and sometimes people have difficulty seeing both images. The mental switch that needs to occur to get them to recognize the second image is a Gestalt switch.
The most direct approach to debunking hormesis is to deal with it technically. But the hormesis propagandists can be very convincing and it can be difficult for someone to understand why it is bunk. It can sound like two sides of a controversy, which it isn't.
However, most rational people understand that homeopathy is bunk. They understand why it is illogical (massive dilution does not increase a dose response). The person who proposed radiation hormesis actually used homeopathy as part of a supportive argument. This should be a clear warning signal that that person cannot reason clearly, and should make you suspicious of any other claims.
Most rational people understand that Christianity is bunk. They understand why it is illogical (god sending his son/self to die to appease himself because he didn't know a woman would listen to a talking snake is nonsensical). Here is a book on radiation hormesis by an evangelical Christian. This should be a clear warning signal that that person cannot reason clearly, and should make you suspicious of any other claims.
I could go on. (Note that those two people are from the same town).
Now these types of associations in and of themselves don't necessarily mean radiation hormesis is wrong, only that the correct mental framework is to be skeptical of it.
Perhaps starting from this foundation and then, subsequently moving into the technical details may prove more useful in achieving a Gestalt switch with someone questioning LNT.
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