A theory can only be corroborated by the evidence when the negation of that evidence would falsify the theory. That is, the evidence must represent a test of the theory, and a test requires the possibility of failure. Tautologies and metaphysical hypotheses, then, are uncorroborable, since they cannot be falsified in principle.
Is Popper’s corroboration merely inductive support in disguise? No.
Consider the sunrise. My evidence of the sunrise each past morning corroborates my hypothesis that the sunrise will occur every morning, because if the sun had not risen on any of these days, then my hypothesis would be falsified. Every morning is a fresh test of my hypothesis. So far it has passed, and each further success corroborates my hypothesis a little more.
However, what about my expectation that the sun will rise tomorrow morning? Is this corroborated by evidence of sunrises in the past? That is, had the sun not risen on any previous day, would it contradict the claim that the sun will rise tomorrow morning? No. Evidence of past sunrises does not corroborate expectations of future sunrises, even though it does corroborate the general hypothesis that the sun will rise every morning.
The confusion stems from a fallacy of decomposition. That is, supposing what is true for the whole (sunrises in general) is true for its constituent parts (particular sunrises). In this case, while a theory may be highly corroborated, it does not follow that its logical consequences are also highly corroborated.
In other words, corroboration is not transmissible from premises to conclusion in a valid argument. In particular, evidence that corroborates a theory doesn’t also corroborate predictions derived from the theory. Corroboration is not ampliative; it’s more like a scorecard. That is, it’s just a measure of past performance and doesn’t entail anything about future success. Popper said this explicitly.
So when the inference or prediction from a theory eventuates one is entitled to say that the theory has not been proven wrong, so far. Testing has corroborated the theory. Every test is a fresh question of the theory. Each further success also corroborates the theory, but one remains aware that any degree of corroboration is dependent on the severity of the test and the ease with which the theory can fail testing. The survival of a difficult test could be more significant than mere repetitive passing of relatively non-demanding tests.
All theories remain conjectural, as do all inferences and predictions based on them.
In the case of the theory that the sun will rise, at non-polar latitudes, it seems to be less wrong than the theory that the sun will not rise. The theory that the sun will not rise also explains less and fits in with fewer other research programs than that of the sun rising.
Thanks for those thoughts Lee, this is a tricky area because the last resort for many inductivists is to fall back on the argument that Popper’s theory of corroboration depends on an assumption about the uniformity of nature which (they claim) is an inductive principle.
“In this case, while a theory may be highly corroborated, it does not follow that its logical consequences are also highly corroborated.”
But it has to if we’re talking about !logical! consequences. And since the “Sun will rise tomorrow” is a logical consequence of the “Sun always rises” we can say that it’s better corroborated than that it’s not going to rise. By the way they are all logical consequences of the Theory of General Relativity.
I think all Popper wanted to say is that corroboration is not an ampliative process of justification. Since the process of evaluating a scientific theory is not inductive, corroboration only means “so far the theory hasn’t been refuted”. That’s all we can say and no more.
Z,
No, the opposite of what you said.
Consider three propositions:
While P is corroborated by Q, R is not. The corroboration of P is not transmitted (like truth or probability) to its logical consequences. The corroboration of P given Q is indifferent to R.
It’s like confusing the average height of a population for the height of a specific individual. Corroboration is analogous to an average. That’s why you can get a hypothesis that is highly corroborated and a logical consequence of that hypothesis which isn’t corroborated at all.
A simple example would be a tautology. Every hypothesis includes among its logical consequences every tautology, and yet tautologies are entirely uncorroborable. Another example would be a metaphysical hypothesis like indeterminism, which is often said to follow from quantum mechanics. Putting aside the matter of whether this assumption is correct, the point is that corroborated hypotheses can have metaphysical implications, and these logical consequences are themselves uncorroborable.
Lee, you have got me thinking with respect to the fallacy of decomposition and I wonder if there it has a temporal analogue.
We call a theory corroborated if it has stood up to appraisal at a point/points of time with respect to a set of acceptable test statements. We should not infer from corroboration that the theory is “true” or “probably true” even though it is possible that it is true, nor can we say it is “true” that it will stand up to tests in the future, even though it possibly will. The notion of truth is timeless whereas our tests are always time bound. Theories, i.e. universal statements, make relatively timeless assertions whereas the basic test statements are time bound e.g. the theory is that the sun always rises, or will in the undetermined future. The test statement is that the sun will rise at a particular time e.g. tomorrow.
Our theory that the sun always rises is a universal statement that has been corroborated by passing observational testing at particular moments of time.
Lee, if what you’re saying is true then we would have to corroborate every logical consequence of General Relativity independently. I’m afraid we don’t have enough time to do that.
Z,
What I’m saying is true, but it doesn’t mean anything of the sort. We don’t have to corroborate every logical consequence of General Relativity. Indeed, that would be impossible, because infinitely many such consequences are uncorroborable, because they are tautological, metaphysical, or just prohibitively costly to test.
All this means is that General Relativity is a conjecture. It’s been well-tested, perhaps, and so is highly corroborated, but that neither makes it more probable nor implies that it will continue to survive testing tomorrow. All it really means is that General Relativity has not yet been falsified; it has survived criticism so far–and that’s all corroboration ever can say.
Now, we might become more confident that General Relativity will continue to yield true predictions in the future after passing severe tests, but that growing confidence does not correspond to the logic of corroboration.
In fact, this same argument applies to Bayes’s theorem and subjective interpretations of probability. If evidence only counts in support of a hypothesis when–in conjunction with initial conditions and background knowledge–it is a logical consequence, then the exact same problem arises. That is, the hypothesis becomes more probable, but its yet unverified predictions do not.
This obviously doesn’t describe how our confidence in a hypothesis and its logical consequences changes with favourable evidence, and so under such circumstances the subjective interpretation of probability is simply false.