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In physics (and other natural sciences) you can ONLY prove negatives in fact, so to a physicist this statement is not surprising at all. Example: If we observe
by ThePhysicist 11y ago
In physics (and other natural sciences) you can ONLY prove negatives in fact, so to a physicist this statement is not surprising at all.
Example: If we observe an apple falling to the ground with the same acceleration many times we will try to generalize this observation and create a theory that explains this phenomenon and similar ones (such as Newton's laws and his theory of gravity). Unfortunately we can never prove such a theory in the mathematical sense since we can never be sure that the next time we perform a given experiment it will still yield the same result (it could be that the laws of physics change over time or work differently in other parts of the universe). However, we can easily falsify a given theory if we can produce even one single observation where the theory does not fit reality (which is precisely why general relativity was needed to replace the classical theory of gravity, which could not explain all experimental data [actually the new theory came even before the data in that case, which is amazing in itself]). So, in a sense, proving that something is not true is the only thing we can do with absolute certainty.
That said, theories that are proven wrong by experiment and replaced by other theories are still valid in their domain of applicability, so to say as an approxomation of the larger theory.
- scoofy 11y agoYou'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.
- Retra 11y agoWhat exactly do you mean by "positive knowledge" or "negative knowledge?"
- scoofy 11y agoPositive 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)
- Retra 11y agoSo you're not actually talking about knowledge, just the presence of the word 'not' in a sentence?
- scoofy 11y agoOf course i'm talking about knowledge. Empirical knowledge of a proposition being true or false.
- Retra 11y agoOk, 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?
- scoofy 11y agoYes, 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).
- Retra 11y ago"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.
- ThePhysicist 11y agoI 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".
- danielam 11y ago> However, we can easily falsify a given theory if we can produce even one single observation where the theory does not fit reality [...] Actually, strictly speaking, it's not that easy. The Duhem-Quine Thesis quite nicely shows how critical experiments aren't quite as decisive as some like to think, especially as theoretical depth increases. A theory can depend on numerous other theories being true. The reason a theory in question is the subject of a critical experiment is because of the principle of economy. Once supporting theories have been sufficiently corroborated, we justifiably tend to trust them more than the theory that we are currently considering.