You can of course very often express the negation of p by saying ‘it’s not the case that p’.
But some logicians in intro texts incautiously claim more — saying something like “This is cumbersome, but it works in every case” (that’s a quote, but no names, no pack drill!).
However it surely overshoots to claim that prefixing ‘it’s not the case that’ by itself produces the negation of what you start with in every case. Here are some examples:
- Jack loves Jill, or Jill is much mistaken about Jack’s feelings.
- It’s not the case that Jack loves Jill, or Jill is much mistaken about Jack’s feelings.
Aren’t both true if Jill is sadly mistaken?
- Jack loves Jill and it’s not the case that Jill loves Jack.
- It’s not the case that Jack loves Jill and it’s not the case that Jill loves Jack.
Aren’t both false if Jill loves Jack?
- Jones, who is a Russian agent, loves caviar.
- It’s not the case that Jones, who is a Russian agent, loves caviar.
Aren’t neither true if Jones isn’t a Russian agent?
So what are your favourite counterexamples to the claim that ‘it’s not the case that p’ always expresses the negation of p?
I will marry you if you change your religion.
It’s not the case that I will marry you if you change your religion.
This is at best ambiguous between ~(Q if P) and ~Q if P.
h/t Mark Sainsbury, Logical Forms.
Is the problem just that you can’t just stick “it’s not the case that” in front of arbitrary text that asserts something and get a result that would most naturally parse as the negation of the entire original assertion? Something like that is pretty much bound to go wrong in some cases, because of the way English syntax works.
1. “Jack loves Jill, or Jill is much mistaken about Jack’s feelings” is true if Jill is mistaken.
Using parens for grouping, 2 could naturally be parsed as:
2. (It’s not the case that Jack loves Jill), or Jill is much mistaken about Jack’s feelings.
which is also true if Jill is mistaken.
But
2′. “It’s not the case that (Jack loves Jill, or Jill is much mistaken about Jack’s feelings)”
looks false to me if Jill is mistaken (because the part in parens is true).
It looks like the same explanation works for 3 and 4.
5 and 6 are a bit trickier, though it’s still the same basic problem. The more natural parsing for 6 applies “it’s not the case that” to the part that says Jones loves caviar, leaving “who is a Russian agent” on the side. But it would have worked if 5 had been “Jones is a Russian agent who loves caviar.”
Indeed! The issue (as you basically say) is that an always-works negation prefix has to to take wide scope with respect to what follows it (govern the whole of what follows it), and it seems that that there are ordinary English uses of prefixed “It is not the case that” where on the most natural reading (indeed the only natural reading?) the prefix doesn’t govern the whole of what follows. So to get the desired negation we have to force the right scope by using more than a naked “It is not the case that”: we have to e.g. add brackets.
The middle example and a bit of diagnosis is in IFL1, §7.2. The first example is an obvious variant. The rather different third example is based on one of Tim Smiley’s. Any offers of different types of example?
I’m not sure these particular examples are convincing, but there could be problems when the original text contains the word “case”.
(a) I left on the train with the other case.
(b) It’s not the case that I left on the train with the other case.
Or where context makes a different meaning more salient:
(c) Holmes solved.
(d) It’s not the case that Holmes solved.
There also ought to be scope problems (as in your examples) with some uses of trailing comma-if, comma-unless, etc:
(e) Jack went to Glasgow, unless Jill rejected him.
(f) It’s not the case that Jack went to Glasgow, unless Jill rejected him.
(g) He told a lie, if he said the sky was blue.
(h) It’s not the case that he told a lie, if he said the sky was blue.
Or replace “if” in g/h with “because”, “unless”, …