“In order to be able to think up a hypothesis which has a significant chance of being correct, I must already possess a sufficient quantity of information” is obvious, following immediately from the mathematics of information. But that’s emphatically not the same thing as “I obtain my hypothesis by applying a ‘principle of induction’ to generalize the data I have so far.”
The way induction was supposed to work was that your observation statements served as the premises of a kind of inference. Just as one can use deductive logic to infer “Swan[1] is white” from “All swans are white”, so one was supposed to be able to infer “All swans are (probably) white” from (“Swan[1] is white”, …, “Swan[N] is white”) for sufficiently large N.
But there is no such thing as a “method of induction” which finds hypotheses for you. Consider those swans: In order to even write down the data we needed to have the concepts ‘white’ and ‘swan’, and something must have motivated us to look specifically at swans and note down specifically what colour they are. In other words, by the time we get round to actually applying our “method of induction” we must already have formed the very hypothesis that the method was supposed to return, or something close to it (like “all swans are some colour—perhaps white”).
This becomes comical when we turn to GR:
Our raw, unprocessed ‘sense data’ comes streaming in: (“The precession of Mercury’s perihelion looks exactly as if (long description of the mathematics of general relativity)”, “The apparent position of this star as the sun moves in front of it changes in a manner that looks exactly as if (long description of the mathematics of general relativity)”, “A clock aboard this high-flying plane runs slightly faster than one on earth, exactly as if (long description of general relativity)”) … and then, as if by magic, the Method Of Induction selects for us the appropriate hypothesis: (long description of the mathematics of general relativity).
There must be a process to turn data into hypotheses. It may be that that process in our brains is biased towards dealing with things like animal colors, but even that came from evolution being handed raw data.
The thing to keep in mind is that all the intermediate sensory processing may also be part of the process of induction (or a biased version of it.) If the data is pre-selected, then that just means that much of the inductive work has already been done. The selection could not have happened otherwise.
A less biased, more raw system might systematically look for correlations between variables, including computed variables like “What species is this?” Which can themselves be inferred from the raw data.
But there is no such thing as a “method of induction” which finds hypotheses for you.
Yes there is although one must of course already have some kind of vocabulary within which to represent hypotheses. It is finding a hypothesis out of an infinite number of hypothesis that such a method is useful for.
No there isn’t, because as I have illustrated above, an ‘inductive inference’ pointing to a hypothesis presupposes a set of data selectively chosen and written down in such a way that the hypothesis is already present.
I think you probably have something else in mind, perhaps “abductive inference” (i.e. “inference to the best explanation”).
Yes, abductive inference or some form of analogical thinking are how powerful hypotheses are really generated. Neither of the posts linked to in number 4 above even mention induction, so I’m not sure why the author thought they were evidence for the thesis.
Number 4 is totally wrong.
“In order to be able to think up a hypothesis which has a significant chance of being correct, I must already possess a sufficient quantity of information” is obvious, following immediately from the mathematics of information. But that’s emphatically not the same thing as “I obtain my hypothesis by applying a ‘principle of induction’ to generalize the data I have so far.”
The way induction was supposed to work was that your observation statements served as the premises of a kind of inference. Just as one can use deductive logic to infer “Swan[1] is white” from “All swans are white”, so one was supposed to be able to infer “All swans are (probably) white” from (“Swan[1] is white”, …, “Swan[N] is white”) for sufficiently large N.
But there is no such thing as a “method of induction” which finds hypotheses for you. Consider those swans: In order to even write down the data we needed to have the concepts ‘white’ and ‘swan’, and something must have motivated us to look specifically at swans and note down specifically what colour they are. In other words, by the time we get round to actually applying our “method of induction” we must already have formed the very hypothesis that the method was supposed to return, or something close to it (like “all swans are some colour—perhaps white”).
This becomes comical when we turn to GR:
Our raw, unprocessed ‘sense data’ comes streaming in: (“The precession of Mercury’s perihelion looks exactly as if (long description of the mathematics of general relativity)”, “The apparent position of this star as the sun moves in front of it changes in a manner that looks exactly as if (long description of the mathematics of general relativity)”, “A clock aboard this high-flying plane runs slightly faster than one on earth, exactly as if (long description of general relativity)”) … and then, as if by magic, the Method Of Induction selects for us the appropriate hypothesis: (long description of the mathematics of general relativity).
No.
There must be a process to turn data into hypotheses. It may be that that process in our brains is biased towards dealing with things like animal colors, but even that came from evolution being handed raw data.
The thing to keep in mind is that all the intermediate sensory processing may also be part of the process of induction (or a biased version of it.) If the data is pre-selected, then that just means that much of the inductive work has already been done. The selection could not have happened otherwise.
A less biased, more raw system might systematically look for correlations between variables, including computed variables like “What species is this?” Which can themselves be inferred from the raw data.
Doing this efficiently is a trick.
Yes there is although one must of course already have some kind of vocabulary within which to represent hypotheses. It is finding a hypothesis out of an infinite number of hypothesis that such a method is useful for.
No there isn’t, because as I have illustrated above, an ‘inductive inference’ pointing to a hypothesis presupposes a set of data selectively chosen and written down in such a way that the hypothesis is already present.
I think you probably have something else in mind, perhaps “abductive inference” (i.e. “inference to the best explanation”).
That’s the kind of science aliens use.
Yes, abductive inference or some form of analogical thinking are how powerful hypotheses are really generated. Neither of the posts linked to in number 4 above even mention induction, so I’m not sure why the author thought they were evidence for the thesis.
I speak of the sense used in “4”, that which you were objecting to. Louie is right and you are wrong.