However, if T is an explanatory theory (e.g. ‘the sun is powered by nuclear fusion’), then its negation ~T (‘the sun is not powered by nuclear fusion’) is not an explanation at all.
The words “explanatory theory” seem to me to have a lot of fuzziness hiding behind them. But to the extent that “the sun is powered by nuclear fusion” is an explanatory theory I would say that the proposition ~T is just the union of many explanatory theories: “the sun is powered by oxidisation”, “the sun is powered by gravitational collapse”, and so on for all explanatory theories except “nuclear fusion”.
Therefore, suppose (implausibly, for the sake of argument) that one could quantify ‘the property that science strives to maximise’. If T had an amount q of that, then ~T would have none at all, not 1-q as the probability calculus would require if q were a probability.
There are lots of negative facts that are worth knowing and that scientists did good work to discover. When Michelson and Morley discovered that light did not travel through luminiferous aether that was a fact worth knowing, and lead to the discovery of special relativity. So even if you don’t call ~T an explanatory theory it seems like it still has a lot of “the property that science strives to maximise”
Also, the conjunction (T₁ & T₂) of two mutually inconsistent explanatory theories T₁ and T₂ (such as quantum theory and relativity) is provably false, and therefore has zero probability. Yet it embodies some understanding of the world and is definitely better than nothing.
A Bayesian might instead define theories T₁′ = “quantum theory leads to approximately correct results in the following circumstances …” and T₂′ “relativity leads to approximately correct results in the following circumstances …”. Then T₁′ and T₂′ would both have a high probability and be worth knowing, and so would their conjunction. The original conjunction, T₁ & T₂, would mean “both quantum theory and relativity are exactly true”. This of course is provably false, and so has probability 0.
Furthermore if we expect, with Popper, that all our best theories of fundamental physics are going to be superseded eventually, and we therefore believe their negations, it is still those false theories, not their true negations, that constitute all our deepest knowledge of physics.
Right, right. The statement T₁ is false; but the statement T₁′ is true.
What science really seeks to ‘maximise’ (or rather, create) is explanatory power.
Does Deutsch write anywhere about what a precise definition of “explanation” would be?
In short, explanations typically talk about why/how/because.
The words “explanatory theory” seem to me to have a lot of fuzziness hiding behind them. But to the extent that “the sun is powered by nuclear fusion” is an explanatory theory I would say that the proposition ~T is just the union of many explanatory theories: “the sun is powered by oxidisation”, “the sun is powered by gravitational collapse”, and so on for all explanatory theories except “nuclear fusion”.
Unless you’re claiming non-explanatory theories don’t exist at all, then ~T includes both explanations and non-explanations. It doesn’t consist of a union of many explanations.
A Bayesian might instead define theories T₁′ = “quantum theory leads to approximately correct results in the following circumstances …”
You’re changed it to an instrumentalist theory which focuses on prediction instead of explanation. Deutsch refutes instrumentalism in his first book, FoR, also at the link above.
Where’s the explanation? What do you think an explanation is? You said the theory gets “approximately correct results” in some circumstances – doesn’t that mean making approximately correct predictions?
The words “explanatory theory” seem to me to have a lot of fuzziness hiding behind them. But to the extent that “the sun is powered by nuclear fusion” is an explanatory theory I would say that the proposition ~T is just the union of many explanatory theories: “the sun is powered by oxidisation”, “the sun is powered by gravitational collapse”, and so on for all explanatory theories except “nuclear fusion”.
There are lots of negative facts that are worth knowing and that scientists did good work to discover. When Michelson and Morley discovered that light did not travel through luminiferous aether that was a fact worth knowing, and lead to the discovery of special relativity. So even if you don’t call ~T an explanatory theory it seems like it still has a lot of “the property that science strives to maximise”
A Bayesian might instead define theories T₁′ = “quantum theory leads to approximately correct results in the following circumstances …” and T₂′ “relativity leads to approximately correct results in the following circumstances …”. Then T₁′ and T₂′ would both have a high probability and be worth knowing, and so would their conjunction. The original conjunction, T₁ & T₂, would mean “both quantum theory and relativity are exactly true”. This of course is provably false, and so has probability 0.
Right, right. The statement T₁ is false; but the statement T₁′ is true.
Does Deutsch write anywhere about what a precise definition of “explanation” would be?
Yes, in BoI. http://beginningofinfinity.com/books
In short, explanations typically talk about why/how/because.
Unless you’re claiming non-explanatory theories don’t exist at all, then ~T includes both explanations and non-explanations. It doesn’t consist of a union of many explanations.
You’re changed it to an instrumentalist theory which focuses on prediction instead of explanation. Deutsch refutes instrumentalism in his first book, FoR, also at the link above.
How so? I think it’s still an explanatory theory, it just explains 99% of something instead of 100%.
Where’s the explanation? What do you think an explanation is? You said the theory gets “approximately correct results” in some circumstances – doesn’t that mean making approximately correct predictions?