Thursday, October 18, 2012


The following is plausible:

  1. x disbelieves p if and only if x believes not-p.
But suppose Jones believes snow is white. Then, surely, he disbelieves that it's not the case that snow is white. But then by (1) he has to believe that it is not the case that it's not the case that snow is white. But very few people have such double-negative beliefs, and there is no need to saddle Jones with it.

Now believing not-p is sufficient for disbelieving p. But it's not necessary. Perhaps then:

  1. x disbelieves p if and only if x believes a negation or negand of p.
(Negative propositions of the form not-p have p as their negand. Other propositions don't have negands.) But it seems that believing p to be false may also be sufficient for disbelief, even if you do not burden your mind with the further first-order belief that not-p. So:
  1. x disbelieves p if and only if x believes a negation or negand of p or x believes that p is false.
But this is really messy...


Unknown said...

Why not just stick with the first version ("x disbelieves p if and only if x believes not-p") and note that believing proposition not-p is the same thing as believing propositions logically equivalent to it. So if Jones believes that snow is white, then he also believes that it is not the case that it's not the case that snow is white. And this is true even if he wouldn't recognize his belief by assenting to the declarative sentence: "It is not the case that it's not the case that snow is white."

The fact that he doesn't assent to this sentence doesn't mean that he doesn't believe the proposition that we recognize as being expressed by that sentence. It may just be that the sentence is sufficiently unnatural and / or complex that Jones doesn't recognize it as expressing the proposition that he does in fact believe.

Unknown said...

Also, does the idea that "x disbelieves p if and only if x believes not-p" run into trouble once we recognize the possibility of holding contradictory beliefs?

It would seem to if "disbelieves" is synonymous with "doesn't believe". In that case, we have, "x doesn't believe p if and only if x believes not-p", which rules out the possibility in question.

Heath White said...

My views are much like Jonah's.

But suppose Jones believes snow is white. Then, surely, he disbelieves that it's not the case that snow is white.

Surely here is the problem? If Jones disbelieves that it’s not the case that snow is white, he believes that not-(it’s not the case that snow is white) [by definition]. But just because someone believes p, we need not attribute to them ANY further beliefs in the logical consequences of p. (Not even very simple ones, like that not not-p, or that p is true.) If we deny that, the messiness goes away.

We do open ourselves up to the possibility of obviously inconsistent beliefs. But that seems to me empirically accurate.

Alexander R Pruss said...

I might need to add a conjunct: "and not (x believes p)". I am not sure. If someone believes p and not-p, maybe we should say that they believe p and disbelieve p. If so, we don't need the conjunct.

I take Jonah's first suggestion to be that if you believe p, then you do believe ~~p, though you might not assent to a sentence expressing ~~p. (Maybe I am misunderstanding Jonah.) But that seems wrong. It implies that if we believe p, we believe ~~p, and ~~~~p, and so on.

Heath, is your suggestion that believing p (and, maybe, ~(believing ~p)) is not sufficient for disbelieving not-p?

Unknown said...

That is indeed my suggestion Alex. I'm still not seeing any problem with it. Specifically, I think it makes good sense to allow (indeed, to require) that if someone believes proposition p, then they believe proposition ~~p, ~~~~p, and so on. These are, after all, equivalent propositions. If propositions are sets of possible worlds, e.g., then each of the above picks out the same set.

I suspect that any intuitions to the contrary (e.g., the ones that you are trying to pump when you appeal to cases like p versus ~~p versus ~~~~p versus...) arise out of a confusion between propositions and the sentences that express them. At some point, the sentences become too opaque to be effective expressers of the proposition that p, for cognitively limited folk. And so people might well say that they believe "Snow is white" but that they do not believe "It is not the case that snow is not not not not not white", if only because they are just confused when it comes to what proposition is expressed by the latter sentence. Still the propositions that we logic-savvy folk take to be expressed by these two sentences are logically equivalent, and so we can confirm that if the person believes the 1st proposition, then he believes the 2nd proposition too -- because the 2nd proposition just is the 1st proposition.

Mike Almeida said...

But very few people have such double-negative beliefs, and there is no need to saddle Jones with it

That's not true. It's rather true that very few people would express the beliefs they have using double-negation. The belief that p just is the belief that ~~p. I don't think we'd want to fine grain beliefs in any way that makes the belief that p not the belief that ~~p.

Heath White said...

I thought the original line was a pretty good quasi-stipulative definition of ‘disbelieve’: x disbelieves p if and only if x believes not-p. That is, I disbelieve something if I actively believe its negation. (A slightly different definition would be: ...x believes p is false. I could also go for a disjunction of these: … x either believes not-p or believes p is false.)

Substituting in, we get that x disbelieves not-p iff x believes not-not-p [or x believes not-p is false]. But believing not-not-p (or that not-p is false) is different from believing p (or that p is true). So I misunderstood Jonah; my view is precisely the opposite of his. Beliefs should be fine-grained all the way.

I have an underlying reason for this. Frege’s original definition of a proposition was epistemic: two sentences express the same proposition iff everyone who understood one (or believed it to be true) would understand the other (or believe it to be true). So propositions correspond to equivalence classes for sentences, where the equivalence relation tracks something like mental transparency. The fact that there is NO pair of sentences with this relationship in every context drives all sorts of puzzles in philosophy of mind/language: London/Londres, the Twin Earth experiments, and several others. The right solution, in my heterodox view, is to say that the objects of belief are sentences, not propositions. We can continue to talk about propositions for convenience and because in large classes of ordinary cases, many pairs of sentences are such that you understand one precisely because you understand another.

Double negations (p, and not-not-p) are an obvious candidate. But people simply do not entertain beliefs with, say, fifty-odd “not”s on the front and there is some length of sentence which is humanly impossible to understand.

You could avoid this line of argument if you understood propositions not in epistemic terms but in, say, truth-conditional terms: they are sets of possible worlds for example. But then I think it will follow that we often do not know what propositions we believe (or disbelieve).

Dagmara Lizlovs said...

"But suppose Jones believes snow is white. Then, surely, he disbelieves that it's not the case that snow is white." The snow was white in the yard that is until Jones let his dog out. :-)

Alexander R Pruss said...


One good reason to make ~~p and p be different is that intuitionists would claim to be capable of believing the former without believing the latter. And do we have good reason to think they're wrong about what they believe?


I take the lesson of this line of thought to be that propositions are way more finegrained than people think. Even more finegrained than sentences, actually.

Alexander R Pruss said...

I should say something about why I care about this disbelief stuff.

Here is a rough characterization of lying: x lies that p iff x asserts that p and x disbelieves that p. This isn't right as a general characterization--there are counterexamples--but it seems right in the ordinary central cases of lying. But now I want to know what this disbelieving here is.

So, my functional characterization of disbelief that p is that it is that doxastic state that is typically involved in lying that p.

This is why I don't want to take Heath's solution that disbelief is belief that ~p. For if one believes that p and asserts that ~p, that's typically a central case of lying. So if we take Heath's way out, we now need something other than the notion of disbelief to give the typical mental state involved in lying.

Maybe it is the disjunctive one, though. After all, why should wrongful actions form natural kinds?

Dagmara Lizlovs said...

"For if one believes that p and asserts that ~p, that's typically a central case of lying."

That is right on the money. Let's keep this simple and straight forward. We can easily lie to ourselves more often than we think, more subtly than we think; and we can even believe our own lies and even become unaware that we are lying. I think a good article on sin, deceitfulness and self deception is found in this article in the Christian Post. A link to this article is here:

I agree with this statement from the article's author, Paul Tripp:

"Evil doesn't always look evil, and sin often looks so good – this is part of what makes it so bad. In order for sin to do its evil work, it must present itself as something that is anything but evil. Life in a fallen world is like attending the ultimate masquerade party. An impatient moment of yelling wears the costume of zeal for truth. Lust masquerades as a love for beauty. Gossip lives in the costume of concern and prayer. Craving for power and control wears the mask of biblical leadership. Fear of man gets dressed up as being a peacemaker or having a servant heart. Pride in always being right masquerades as a love for biblical wisdom.

You'll never understand sin's sleight of hand until you acknowledge that a significant part of the DNA of sin is deception. AS SINNERS WE'RE ALL VERY COMMITTED AND GIFTED SELF-SWINDLERS. No one is more influential in your life than you are, because you talk to yourself more than anyone else does. What you say to yourself is profoundly important. Your words either aid God's work of conviction and confession or they assist sin's system of deception. So it's important to humbly admit that we're all too skilled at looking at our own wrong and seeing good. We're all much better at seeing the sin, weakness, and failure of others than we are our own. We're all very good at being intolerant in others the very things that we willingly tolerate in ourselves. The bottom line is that sin causes us to not hear or see ourselves with accuracy. And we not only tend to be blind, but, to compound matters, we also tend to be blind to our blindness."

Dagmara Lizlovs said...

More on "For if one believes that p and asserts that ~p, that's typically a central case of lying." There is another factor I would like to add here and that is the apparent sincerity of the liar. I recall one situation while out goose hunting. There was an approaching storm, and the geese were looking for a place to land. The hunter in charge of our goose pit (who was also the caller) said to the geese "Don't go there you'll get killed (said in reference to one of our rival goose pits). Come over here, you'll be safe." His voice sounded so kind and sincere that even I for a second found myself believing his sincerity and apparent kindness towards the geese even though both of us and some six other people all had shotguns loaded with steel waterfowl shot and were covered from head to toe in camo.

Dagmara Lizlovs said...
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Dagmara Lizlovs said...
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Alexander R Pruss said...

I've removed a comment that, while raising a good question about whether dissembling of certain sorts is in fact a lie, contained material about apparent personal failings of a particular intellectual that was largely irrelevant to this discussion.