Posts Tagged ‘corroboration’


In experiments, induction, justificationism on 20/08/2011 at 7:29 am

A philosophical problem has the form: I don’t know my way about. (Ludwig Wittgenstein)

Up until the late 19th century every observation was compatible with Newton’s theory of gravity. All these observations are also compatible with Einstein’s General Theory of Relativity. Two quite different theories were compatible with the same set of observations; therefore, one cannot know they have derived true theories from observations.

Assume we have a long series of numbers. They go on: 2, 4, 8 … What is the next number in the series?

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In empiricism, induction, justificationism on 19/07/2011 at 6:49 am

There is endless conjecture, and certainty is not to be counted upon (Kant, Critique of Pure Reason)

Some people treat evidence as something that accumulates over time, like sap from a tree. Once enough evidence is collected, you need only synthesize it into syrup, and then you’ve proved your point. “I have X amount of evidence for Y, therefore you ought to believe Y, otherwise you are behaving irrationally.” So the story goes.

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Newton & Einstein

In induction, popper on 15/06/2011 at 4:05 pm

“… (1) Newton’s theory is exceedingly well corroborated. (2) Einstein’s theory is at least equally well corroborated. (3) Newton’s and Einstein’s theories largely agree with each other; nevertheless, they are logically inconsistent with each other because, as for instance in the case of strongly eccentric planetary orbits, they lead to conflicting predictions. (4) Therefore, corroboration cannot be a probability (in the sense of the calculus of probabilities).

“… The proof is simple. If corroboration were a probability, then the corroboration of ‘Either Newton or Einstein’ would be equal to the sum of the two corroborations, for the two logically exclude each other. But as both are exceedingly well corroborated, they would both have had a greater probability than ½ (½ would mean: no corroboration). Thus, their sum would be greater than 1, which is impossible. It follows that corroboration cannot be a probability.

“… It would be interesting to hear what the theoreticians of induction … who identify the degree of corroboration (or the ‘degree of rational belief’) with a degree of probability — would have to say about this simple refutation of their theory.” (Popper, Karl. 2009. The Two Fundamental Problems of the Theory of Knowledge, xxivn. New York: Routledge.)