Inductive logic: Every crow ever seen is black. Joe has a crow. Joe's crow is probably black.
Deductive logic: Every crow is black. Joe has a crow. Joe's crow is black.
It's set out now.
Statistical analysis is validated empirically and is therefore rooted in inductive logic. Primacy rests with inductive logic, not deductive. Deduction doesn't even tell us what crows are, black is, or who Joe is. — Hanover
As you know, though, false premises do not entail that deductive arguments are invalid, just that are unsound. — Janus
But even there some folk are asserting that stats is based on induction. — Banno
That's what I suggested happens in statistical inference. But even there some folk are asserting that stats is based on induction. — Banno
In rejecting Bayesianism and the method of inverse probabilities, Peirce argued that in fact no probability at all can be assigned to inductive arguments. Instead of probability, a different measure of imperfection of certitude must be assigned to inductive arguments: verisimilitude or likelihood. In explaining this notion Peirce offered an account of hypothesis-testing that is equivalent to standard statistical hypothesis-testing. In effect we get an account of confidence intervals and choices of statistical significance for rejecting null hypotheses. Such ideas became standard only in the twentieth century as a result of the work of R. A. Fisher, Jerzy Neyman, and others. But already by 1878, in his paper “The Probabilitiy of Induction,” Peirce had worked out the whole matter.
Corresponding to AAA-1 (deduction) we have the following argument: X% of Ms are Ps (Rule); all Ss are Ms (Case); therefore, X% of Ss are Ps (Result). Construing this argument, as we did before, as applying to drawing balls from urns, the argument becomes: X% of the balls in this urn are red; all the balls in this random sample are taken from this urn; therefore, X% of the balls in this random sample are red. Peirce still regards this argument as being a deduction, even though it is not—as the argument AAA-1 is—a necesary inference. He calls such an argument a “statistical deduction” or a “probabilistic deduction proper.”
One could imagine any number of self contained systems that can articulate itself without the need for external verification but sooner or later its relationship to other fields of endeavour must come into question. — Perplexed
Can you give any further details of such a conceptual analysis? Perhaps this would extend beyond the boundaries of science. — Perplexed
Note that this explanation that you are taking to undermine induction is itself inductively derived. It relies on that which it purports to undermine. — Janus
So do you say that to be free is to act only from internal forces? How does one begin the process of disassociating from external forces in order to follow internal ones? Would this change not violate determinism? — Perplexed
If the self is determined, from where does the power of choice arise? — Perplexed
Actually, all swans are still white; its just that Down Under, everything is upside-down and back to front and black is white and white is black. — unenlightened
This is not the case. Determinism is an explanation of choice which is completely lacking from those who propose free-will. — charleton
You ask what reason we could have for thinking the sun will not rise tomorrow — Janus
Are you suggesting that humans are able to act against the laws of cause and effect when the rest of the universe has to comply with it? — charleton
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