Being sceptical about 2+2: Sandifer v Day again


There is a section in the Sandifer-Day discussion (review here and transcript here)

Sandifer: Right, but when we’re talking about a world where people are – where there are subtle evils and mocking misrepresentations, isn’t a degree of skepticism a good thing? Isn’t a resistance to anyone’s demand that you should obey them a good thing?

Day: No! Not if what is being told is true! How is being skeptical about the truth a good thing? All that means is that you’re opening yourself up to something that is false. Are you skeptical about 2+2?

Sandifer: I am not skeptical about 2+2, but the question becomes…

Day: Right, but would you consider it to be good for someone to be skeptical about 2+2?

Sandifer: But at least within this story, we’re not talking…

Day: Then you agree with me.

Sandifer sensibly ignores Day’s point because it is a distraction. 2+2=4 is an analytical truth whereas the issues that Sandifer was referring to is not even obviously something to which truth values can be applied (whether you should obey your superior in general) but if it was would be a synthetic truth. However I would also say that she is wrong to be not skeptical about 2+2=4. The right thing to say is either “Yes, I am skeptical about 2+2=4 although I have strong reasons to regard it as true universally”. I’ll need to explain that particularly as I’m obviously very much in the pro-mathematics-isn’t-it-great-camp.

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