Monday, November 17, 2008

How We Reason

*......Either Jane is kneeling by the fire and she is looking at the TV, or else Mark is standing at the window and he is peering into the garden.

*......Jane is kneeling by the fire.
Does it follow that she is looking at the TV?
......Most individuals say, “yes”, see Walsh, C., and Johnson-Laird, P.N. (2004: Co-reference and reasoning. Memory & Cognition, 32, 96–106). Given the first premise, they think of two possibilities: in one, the first conjunction is true; and in the other, the second conjunction is true. They overlook that when the second conjunction is true, the first conjunction is false, and that one way in which it can be false is when only its first clause is true, i.e., Jane is kneeling by the fire but not looking at the TV. Hence, the correct answer to the question is: “no”.
That’s from ‘How We Reason: A view from Psychology’ in The Reasoner 2(3), 4–5. Philip Johnson-Laird’s book ‘How We Reason’ is out in paperback next month.
......Maybe that was an example of a fallacy, rather than a paradox, but I’ve labelled it under ‘paradox’ in view of how easy it is to see through those I’ve been looking at recently; and after all, I’d said “yes” myself. (There’s a nice list of fallacies in The Reasoner 2(5), 7–8.)

4 comments:

Brandon said...

Interesting. I imagine people simply read the disjunction to mean,

Either Jane is kneeling by the fire, looking at the TV,

or else

Mark is standing at the window, peering into the garden.

That is, the second conjunct in each case as not actually a conjunct at all, but a clarificatory note (reinforced by the pronoun use). In which case 'yes' would be the right answer. To strengthen each disjunct into an obvious logical conjunction would require more than just 'and' in each case.

Enigman said...

I naturally read the disjunction as EITHER Jane is kneeling by the fire OR ELSE Mark is standing at the window. The other conjuncts seem to add something like "and if so then she is definitely looking at the TV" and "and if so then he is definitely peering into the garden" respectively, and I can't think of any good reason why I would be reading it that way (aside from Philip's). I don't see the relevance of pronoun use though, or why more than 'and' is required. If Jane is kneeling by the fire and looking away from the TV, is the following true or false: "Jane is kneeling by the fire, looking at the TV." To me that seems false even without the 'and' being explicit (?)

Brandon said...

The pronouns can be read to suggest that the conjuncts are conflated, i.e., the second conjunct simply identifies something that goes along with the first, because they connect the conjuncts more closely than they otherwise might be connected. But the real issue is that the original disjunction naturally makes it sound as if there are only two possible scenarios from the get-go -- either Jane is kneeling by the fire, looking at the TV, or Mark is standing at the window, peering into the garden; the 'else' of the 'or else' suggests that it can't be both. So if there are only two possible scenarios,

A (which also involves C)
or
B (which also involves D)

then if we get A, we would naturally take it as saying C as well. And so here: Either

Jane is kneeling by the fire (she's also looking at the TV)

or

Mark is standing at the window (he's also peering into the garden)

and these are the only two possible scenarios, then if we know

Jane is kneeling by the fire

we know automatically that she is looking at the TV -- there is no possible scenario identified in which Jane is kneeling by the fire but not looking at the TV.

Enigman said...

Yes, that's pretty much how I read it. But the only thing I can see about the pronouns is that if 'Mark' and 'he' were replaced by 'she' then there would be no problem. If Jane is kneeling then she is not standing and so the first conjunct is true and so she is looking at the TV. What I now think happens is that when we are presented with the 'Either' we know to expect an 'or (else)' and so we skip quickly over the second conjunct of the first (exclusive) disjunct, pretty much as you say. We are setting up two possible worlds like fictional worlds, in that having gone into one (via the door of the initial conjunct) we believe everything we read about it. But perhaps what is most apposite is that we do that without knowing whether or not the second disjunct will be about Jane. We may well assume that it probably will be.