In a 1965 paper, Gilbert Harman explained that enumerative induction is not an autonomous phenomenon, but is simply a disguised consequence of Inference to the Best Explanation (IBE). — Wikipedia - Inductive reasoning
But to me, stats, being a branch of mathematics, is a certain science and would thus be deduction. Of course the stats result in a probability, but (stay with me on this) it's resulting probability is certain. E.g. If 95% of swans are white, then for the next swan picked at random, it is certain that there is a 95% chance it will be white. So this definition of induction is really just deduction.the best way to distinguish between induction and abduction is this: [...] in abduction there is an implicit or explicit appeal to explanatory considerations, whereas in induction there is not; in induction, there is only an appeal to observed frequencies or statistics. — SEP - Abduction
Yes. As the original hypothesis is in contradiction with the new data, then it is necessarily false. So this is deduction.We go looking for more swans and see a black one, so our hypothesis is falsified. — aletheist
As the original hypothesis is not in contradiction with the new data, then it is not necessarily false. This is also deduction.If we were never to see a black swan, then the hypothesis would not be falsified, but that does not warrant certainty that it is true since we only ever observe a finite sample of swans. — aletheist
No, it is not necessarily false, it is contingently false--it is contradicted by experience, not logic. That is what makes it inductive, rather than deductive.As the original hypothesis is in contradiction with the new data, then it is necessarily false. So this is deduction. — Samuel Lacrampe
Again, if the conclusion is not logically necessary, then it is not a deductive inference.As the original hypothesis is not in contradiction with the new data, then it is not necessarily false. This is also deduction. — Samuel Lacrampe
No, it is not necessarily false, it is contingently false--it is contradicted by experience, not logic. That is what makes it inductive, rather than deductive. — aletheist
If some swans are black, the explication that necessarily follows is that the hypothesis "all swans are white" is false. So we falsify the hypothesis with deduction as you've defined it.Deduction is the explication of what would follow necessarily from that hypothesis if it were true. — aletheist
No, we falsify the hypothesis by observing a black swan. "If some swans are black, then not all swans are white" is deductively valid regardless of whether there actually are any black swans. Induction is the method that tells us to keep checking whether we ever see a non-white swan. Its validity lies in the fact that if there are any, we would eventually find one if we were to keep looking indefinitely.So we falsify the hypothesis with deduction as you've defined it. — Samuel Lacrampe
Indeed, experience only contributes to the premisses, not the conclusion. Deduction derives necessary conclusions based strictly on formal considerations. It takes no experience at all, just competence in the English language, to deduce that there are no married bachelors. Induction is not required, since looking for a counterexample would be pointless.Otherwise, in general, all deductions must contain some experience since it checks for possible contradictions between premises that are built from experience. — Samuel Lacrampe
I accept that claim. Thanks.Deduction derives necessary conclusions based strictly on formal considerations. — aletheist
Abduction is formulating a hypothesis, while induction is testing a hypothesis. Abduction offers a plausible explanation of a previously observed phenomenon, while induction evaluates whether that explanation is actually borne out by additional experience.But now, how is induction different from abduction? — Samuel Lacrampe
No, all three types of reasoning can be illustrated with syllogisms having two premisses and a conclusion. The key difference is how the conclusion follows from the premisses in accordance with what Charles Sanders Peirce called the "logical leading principle." He helpfully characterized the three propositions as rule, case, and result.Premises are built from abduction, and conclusions are built from deduction. — Samuel Lacrampe
This distinction is in the function but not in the act. It seems to me that both are IBE, which is used both to build the hypothesis and to test it against new data.Abduction is formulating a hypothesis, while induction is testing a hypothesis. — aletheist
Yes I'm familiar with how Peirce described it (I gave the link to this example in the OP). In which case, it seems to me that both abduction and induction are IBE, and the distinction is that induction is a general explanation whereas abduction is a specific one.[...] He helpfully characterized the three propositions as rule, case, and result. — aletheist
the best way to distinguish between induction and abduction is this: both are ampliative, meaning that the conclusion goes beyond what is (logically) contained in the premises (which is why they are non-necessary inferences), but in abduction there is an implicit or explicit appeal to explanatory considerations, whereas in induction there is not; in induction, there is only an appeal to observed frequencies or statistics.
96 per cent of the Flemish college students speak both Dutch and French.
Louise is a Flemish college student.
Hence, Louise speaks both Dutch and French.
You may have observed many gray elephants and no non-gray ones, and infer from this that all elephants are gray, because that would provide the best explanation for why you have observed so many gray elephants and no non-gray ones.
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