Jouni Lappi, having read the Substack article on Heidegger and Carnap, writes:
One thing I cannot get my head around is this part:’Nothing is F’ => ’Everything is not F’
Maybe there is some syntactic agreement behind the ’Everything is not F’, that I do not understand. In my layman ears it sounds strange and wrong. I would understand ’it is true for every thing, that it is not F’. Say in my universe there is A, B and F.’Nothing is F’ is false, ’Everything is not F’ is true.This is probably some newbie error in thinking. And especially because of that, I would appreciate if you could explain this to me and point out where I think wrong.
First of all, what you express as a conditional is really a biconditional. Thus
1) Nothing is F <=> Everything is not F.
Bear in mind that ‘F’ is a predicate. If it names anything, it names a property, not an individual. (Properties, by definition, are instantiable items; individuals are not.) So an instance of (1) is
2) Nothing is fragile if and only if everything is not fragile.
Surely (2) is true; indeed it is necessarily true. In a universe U in which there are exactly two individuals, a and b, and one property F-ness, if neither a nor b instantiates F-ness, then every/each individual in U does not instantiate F-ness, and vice versa.
Are you perhaps confusing individuals and properties? Or perhaps you do not appreciate that ‘everything’ is being used above as a distributive, not a collective term? ‘Everything’ means each thing; it does not mean the collection of things.
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