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From: Philip Johnson-Laird BA PhD Psychology (UCL), Stuart Professor of Psychology Emeritus at Princeton. (Author isn't a logician.) How We Reason (1st edn 2008). p. 344.

  A similar effect occurs with general knowledge. On the whole, if we’re faced with a choice of giving up a general principle or giving up a particular, but alleged, fact, then we abandon the alleged fact. We know that water freezes into ice. We have many reasons to believe this proposition. It fits with our other beliefs about winter, refrigerators, and mountaineering, and we have many observations to support it. Hence, if someone tells us: I froze some water, but it didn’t turn into ice. We tend to doubt the claim that they froze water rather than the general principle that freezing water turns it into ice.
  Is there perhaps an effect of the form of propositions? Some psychologists believe so. Suppose someone tells us:

If it was raining then Pat went to the cinema. It was raining.

Given a conflict, because Pat didn’t go to the cinema, which of these two propositions do we give up if they are equally entrenched? Suppose someone tells us:

Either Viv was late or else she didn’t go to the cinema. Viv wasn’t late.

Given a conflict, because Viv did go to the cinema, which of these propositions do we give up? The psychological evidence suggests that we tend to give up the conditional in the first case, and the disjunction in the second case. What is odd, however, is that conditionals and disjunctions are consistent with more possibilities than categorical propositions, and so they have a greater probability of being true. One reason for our judgment may be that we believe that speakers are less likely to be wrong about simple categorical facts. Their truth can be a matter of observation rather than inference. Hence, categorical propositions have an aura of certainty lacking from more complex assertions about relations between propositions.

Can someone please expound why the emboldened sentence is true?

  • A mistake in deductive reasoning would be to think all if.. . Then propositions called conditionals always express a sufficient or necessary relationship. Perhaps this is what is taught in mathematical logic. That is if the left side of the proposition before the term THEN is true necessitates that the right hand side must also be true. Reality says this is not so. Yes, it is possible some conditionals express a necessary or sufficient condition but some don’t. I can use a conditional for instance to express a threat: if you don’t give me your wallet, I’ll shoot you! I can shoot anyway. – Logikal Jul 11 '18 at 5:14
  • Because conditionals and disjunctions contain premises and disjuncts that can be given up without giving up them while categorical propositions do not and have to be given up altogether in the face of contrary evidence. Was that the question? – Conifold Jul 11 '18 at 15:58
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Consider the emboldened sentence that the OP quoted from Philip Johnson-Laird How We Reason (1st edn 2008) page 344.

What is odd, however, is that conditionals and disjunctions are consistent with more possibilities than categorical propositions, and so they have a greater probability of being true.

The question is "Can someone please expound why the emboldened sentence is true?"

Let P and Q be arbitrary categorical propositions. A disjunction connecting these two propositions would be "P or Q". A conditional connecting these two propositions would be "if P then Q" which is the same as the disjunction "not P or Q".

Note that these disjunctions are true if either of the propositions connected by the disjunctive connector "or" are true.

If we don't know anything about these propositions, which we don't because we labeled them arbitrarily as P and Q, we may assume the chance that any one of these propositions is true is the same as the chance of observing "heads" on a fair coin-toss. For each of the propositions, P and Q, we would flip the coin once. If we observed heads we would guess the proposition is true. If we observed tails we would guess the proposition is false.

Once we know our guess for P and Q, then we immediately know what our guess for the truth value of "P or Q" or "not P or Q" would be. However, that guess for these disjunctions involved two coin flips rather than one. That is, there are "more possibilities", as the emboldened sentence mentioned, for a guess of "true".

That would be a reason for agreeing with the emboldened sentence that conditionals and disjunctions have more possibilities than categorical propositions and so "they have a greater probability of being true".

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