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Comment by scoofy | Hacker News Reader

You're reference for negative here is wrong. When you prove that something is not the case, then you do so by demonstrating an there exist something contrary to your hypothesis. This is positive knowledge, not negative knowledge.

This is a very convoluted philosophical concept, but it's essential Karl Popper's argument. We don't, and can't prove negatives, but what we mean by that, as i discuss below, is that we cannot apply the universal quantifier with any certainty.

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I see, so you talk about the case where we not observe any events at all? In that case I would indeed be surprised if it was possible to (mathematically) prove a theory using this negative knowledge.

We can make use of negative knowledge to draw conclusions about a given system though. For example, if we do not know whether an electron bound to an atom is in its ground state or not we might observe the system to see if it emits a photon or not. The longer we observe the system not emitting a photon, the more likely it is that it is in its ground state. So here we actually gain quantifiable knowledge about a system from the observation of a "non-event".

What exactly do you mean by "positive knowledge" or "negative knowledge?"

Positive knowledge is: there is an instance of x (where not existing is not a predicate of x, as existence is not a predicate)

Negative knowledge is: there is not an instance of x (where not existing is not a predicate of x)

So you're not actually talking about knowledge, just the presence of the word 'not' in a sentence?

Of course i'm talking about knowledge. Empirical knowledge of a proposition being true or false.

Ok, so you can know if a proposition is false, or you can know if it is true, and these two things fundamentally behave differently if the proposition contains the word 'not' in it?

Yes, because a proposition without it is a statement about a thing: "I exist." Whereas, with not in it is a statement about everything that exists: "Black swans do not exist." You need knowledge of one thing in the former, you need knowledge of everything in the latter.

It's not just the word "not" it's an odd number of nots (double negatives and all that).

"Black swans do not exist" isn't wholly a statement about everything that exists. It's a statement about the possibility of the property of "being a black swan" to exist.

It is a statement about an abstraction, not existence. Like saying "the cup is above the table" is a statement about the existence of the "above-ness with respect to the table" of the cup. One needn't survey all of reality to know if it is possible for some abstraction to exist. It need only be consistent with the rest of your language, so that's all you need to survey.

I would describe what you're talking about as "black swans cannot exist". That is an even stronger statement, because it also implies that black swans do not currently exist.

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