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thomblake comments on Guilt by Association - Less Wrong
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I'm not sure I'd grant that. The second can be sneaky, in that you can encounter countless arguments of that form with true premises and a true conclusion. In the first example, on the other hand, true premises guarantee that the conclusion is false.
I'm not sure if there's a word for the latter category, but there probably should be. "The conjunction of the premises is inconsistent with the conclusion" is not nearly as awesome as, say, "Antivalid"
In Bayesian reasoning,
and
are valid.
and
are invalid and antivalid.
Is "If P, then Q. P. Therefore, Not-Q." also just as basic and elemental an error as "P is Fermat's Last Theorem. Therefore, P is false."?
Related: Absence of Evidence is Evidence of Absence or Absence of Evidence Is Too Evidence of Absence (Usually) and Conservation of Expected Evidence.
No, it's far more basic. "Fermat's Last Theorem" is a very complicated concept which is only being referenced here. The full logical description of the concept - which is what's necessary to evaluate the argument - would be much longer.
In the words of a well known amateur pianist:
But Annoyance was talking about logic, not plausible reasoning or probability theory, right? In terms of Aristotelian deductive logic the two errors quoted are pretty much equivalent.
The statement "If P, then Q. Q. P is not ruled out." is correct logic. But it conveys very little information.
How much information is conveyed, the amount we need to update our prior for P, upon learning Q, may be considerable. It depends on p(Q|P) and p(Q|~P)
"Stupidity whose opposite really is intelligence."
That's why I edited the post (before your comment) to change "P" to "Therefore, P".
Subtle difference: if P is true, "P" (the statement that P is true) is true. But "Therefore, P" isn't necessarily true, because it references a preceding argument that may (or may not) permit the valid derivation of the conclusion.
In that particular argument, the conclusion does NOT follow from the premises and is false regardless of the value of P.
That's not really how "therefore" is usually used - it's a marker to show where the conclusion is, like drawing a line or using ∴. The point of having the distinction of invalidity is to understand where something might be wrong with an argument even if it has true premises and conclusion; taking "therefore" to mean something in a formal argument doesn't seem fruitful.
It just makes explicit what the other formulation implies: that the statement is said to follow from the premises.
The structure of the argument asserts that in the first version. The structure of the statement asserts it in the second. In terms of the totality of the argument, the two versions mean the same thing, but the shape of their presentation of truth is slightly different. Hopefully the second version reduces the tendency of people to confuse the truth of the statement with the truth of the conclusion.