the quote in the OP is claiming that having good reason to believe the premises doesn't constitute having good reason to believe the conclusion. — Pfhorrest
I don't take logical inference to be "ALL about" [all-caps added] good reasons for belief. Logical inference can take place in a machine that doesn't even have beliefs or reasons for belief. Modus ponens and other deductive forms have settings other than grounds for belief. — TonesInDeepFreeze
He said there is good reason to believe the premises, but not a reason to believe the conclusion. And that is true*. — TonesInDeepFreeze
If there is good reason to believe those premises, then there is reason (even good reason) to believe the conclusion — Pfhorrest
There might be something lurking in the notion of 'good reason' that has to do with degrees of good reason, which also relates to degrees of confidence in beliefs. And Pfhorrest broaches the matter of lack of certainty. I'm not inclined to it, but maybe a solution does lie in that direction. — TonesInDeepFreeze
I don't find that very convincing, at least, on the grounds that it can just be translated back -- it's logically equivalent. — Moliere
I'm saying that the nested conditional in logic does not behave like a string of two if-then statements in English -- so it's not a matter of applying rules of inference to the way premise 1 is set out, but trying to find a different, reasonable interpretation of the English sentence into a logical syntax that keeps MP intact. — Moliere
I only have this example. Does anyone have more? — Banno
[odd] 1: 80% [even] 2: 19% [odd] 3: 1%
In the broader context of all the die faces, the inference would be invalid — Andrew M
That's really good. It puts the puzzle in stark formal terms and takes out the background noise about the historical election facts. Thanks. — TonesInDeepFreeze
In the broader context of all the die faces, the inference would be invalid
— Andrew M
I don't get that. The logic is monotonic. So how can adding premises make the argument invalid? And how would we formalize the inclusion of a broader context? I surely see the point that not mentioning (2) relates to the problem, but I don't know how we would formulate that other than just mentioning it, and how it would overturn an argument in a monotonic logic. — TonesInDeepFreeze
Meanwhile, I'm inclined to think that a solution would center around problems with the notion of "good reason to believe". — TonesInDeepFreeze
I meant a context where we consider only the characteristics of the die where face 1, 2 and 3 are all possibilities — Andrew M
"If it's not 1 then it's 2". That's not a valid inference (since 3 is also remotely possible) — Andrew M
if Reagan doesn't win then Carter will. But it's not a valid inference — Andrew M
(background assumption) 1 — TonesInDeepFreeze
So my solution is that there is good reason to believe both ~R -> A and ~R -> C.
Though it is counterintuitive to believe ~R -> A.
So there is good reason to believe something that is counterintuitive. And that is counterintuitive. (Is it paradoxical?) And modus ponens ponens is not invalid. And I think the problem has more to do with disjunction than with modus ponens. That aligns with you and fdrake in the sense that the puzzle results from leaving off Carter in the disjunction. — TonesInDeepFreeze
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