I’m starting to warm up to the idea that there may be a kind of rational inference (apart from disjunctive syllogism) from a known disjunction.
This is very half-baked, but here’s the idea – suppose you’ve got a known disjunction (P or Q). Suppose you know that P is possible, but you’re not sure whether or not Q is possible. Suppose you cannot conceive of how Q could be true, but you have a clear idea how P could be true. Would that be enough to reasonably infer P? I lean toward, yes.
We could frame this as an epistemic principle.
(DM) If S is justified in believing that (P or Q), S is justified in believing that P is possible, and S is not justified in believing that Q is possible, then S is justified in believing P.
Quick Clarification: “S is not justified in believing that Q is possible” should not be confused with “S is justified in believing that Q is not possible” – if it were the latter, then that would amount to knowing (P or Q) and being justified in believing not-Q – you could run an ordinary disjunctive syllogism.
I’m imagining a scenario where S is not justified in believing not-Q and S is not justified in believing Q. The scenario is such that you should suspend judgment about Q. (Also, keep in mind that this is the inclusive-or that we’re talking about)
If you’re on board with (DM) we could push the envelope. Imagine S is justified in believing both that P is possible and that Q is possible, but S’s justification for believing that P is possible is much higher than S’s justification for believing that Q is possible. Is that enough to reasonably conclude that P is true? In other words, is (DM*) true?
(DM*) If S knows that (P or Q) and S’s degree of justification for believing that P is possible is higher than S’s justification for believing that Q is possible, then it is justified in believing P.
Homework:
- Has anyone encountered an argument that employed this kind of reasoning?
- What decisive counterexamples can we construct? I’m looking forward to either a completely decisive counterexample, or nit-picky one that would force us to Chisholm away at either of the above principles.
Where is this going?
I think we could do some pretty interesting philosophical work with either of these two principles – especially (DM*)
[p.s. Madison is kind of awesome]
Andy, I was wondering if the color blindness counterexample I proposed to refute reliabilism could be turned to be used as a counter example against (DM*) as well. Here is the thought experiment summarized:
Color Blind?: “What if John has had perfect color perception since he was born; he sees each shade of red perfectly and so forth. Obviously he has memories of his visual perception never letting him down; when he sees an apple he knows the precise shade of red and when he sees a school bus he knows the precise shade of yellow. This continues until he is twenty years old. Suddenly one night when John is sleeping, God decides that colors are not aesthetically pleasing to him anymore and makes everything in the universe a shade on the gray scale. When John wakes up, he sees everything in terms of black and white or the in between gray shades; rightfully so, he thinks he’s gone color blind. But in actuality, he still is seeing everything perfectly; his faculty is still functioning properly.”
So, when John wakes up he has the intuition that it is the case that either he is color blind or he is not color blind, and he is justified that either one is possible. But, given that God has (unbeknownst to John) taken color out of the world, to John it seems that the proposition that he is color blind is much more possible than that he is not. But obviously his belief is false; he is seeing every shade perfectly still. Is John justified in believing that he is color blind?
If yes, it still seems that John could not possibly know the proposition that he is color blind (because P would not be true).
If no, then John would undoubtedly have to suspend judgment about both propositions. If he’s still not justified in believing proposition p, and that seems like the more plausible choice (but perhaps it’s not conclusive enough), I don’t think he could accept either choice as true.
This just popped in my head so forgive the half-baked analysis. I just wanted to see if you had any thoughts on the matter.
[p.s. glad you’re enjoying Madison]
Justin,
This is an interesting case.
My intuition about this case is that John is justified in believing that he is color blind.
Note at the beginning of your comment you say…
“When John wakes up, he sees everything in terms of black and white or the in between gray shades; rightfully so, he thinks he’s gone color blind.”
What do you mean by saying “rightfully so” if not “justified”?
Also, you take care to emphasize that that John’s belief that he is color-blind is false. Unless one thinks that it is impossible to have false justified beliefs, the mere fact that John’s belief is false should have any bearing on whether or not it is justified.
Maybe it will depend on the difference in the degrees of justification in believing in P and Q?
The smaller the difference is, the less justified seems believing in P will be.
If there are 3 doors, and prize behind just one of them, would we be justified in believing that it is either behind door number 1 or door number 2? (as we are more justified in believing that, than believing that it is behind door number 3)?
Tanasije,
That seems right. I’d be willing to accept that the degree to which you’re justified in believing P would be a function of the difference in the degrees of justification for believing that P is possible and Q is possible respectively.
Hey Andrew,
Regarding (DM*):
Let P be Goldbach’s Conjecture, and Q be the negation of Goldbach’s Conjecture.
Suppose that I know very little about mathematics. I do know, though, that (P or Q). I receive testimonial evidence from a source I know not to be an expert in mathematics for P. In that case, it seems to me that I have a bit of evidence for P. And, I have a bit more evidence for P than I do for Q. Still, I’m not justified in believing P.
One more thing related to 3 doors example…
It doesn’t seem to me right to say that we are justified in believing that P:the prize is behind doors number 1 or 2, because we are less justified in believing that Q:the prize is behind door number 3 , and because P or Q is true.
Because if we by DM* conclude that we are justified in believing that P, we would be justified in believing that the prize isn’t behind door number 3. But also similarly by DM*, we can group doors 1 and 3 vs. door 2, and conclude that we are justified in believing that the prize isn’t behind number 2, and also by similar reasoning that we are justified in believing that the prize isn’t behind number 1.
In this case, it is not just that it is relative degrees of justification, because we could do the same with any number of doors. For example with 100 doors, we could take P:The prize is behind door number 1 or 2 or …. or 99 Q:The prize is behind door number 100. By similar reasoning as previous, we would end up being justified believing for each door, that the prize isn’t behind it.
So, it seems to me that some additional requirement is needed to eliminate those kind of cases, to ensure something like DM*.
anonymous,
This may not apply to the issue Andy is considering. For one thing, you are certainly justified in believing (P or Q), but this is not really the inclusive “or”, since it is impossible that (P and Q). Really, this amounts to saying that for any P, you’re justified in believing (P or ~P), and that if you get some (weak) testimonial evidence for P, you are still not really justified in believing P. This is probably not very controversial.
Thanks Anonymous,
This is a good case to think about. At the very least it forces us to clarify the principle.
Following up on the last Justin’s point.
We could strengthen the antecendent so that one must at least be justified in believing that P is possible.
If that were the case, you might think that mere testimonial evidence from a known non-expert isn’t sufficient to give you reason to think that P is possible.
Tanasije,
That’s really good! You’re right there is something suspicious about this kind of reasoning that DM* would allow for.
Notice – It looks OK in a single case. I wouldn’t have a problem if DM* allowed, in one isolated instance, for someone to conclude that the prize was not behind door number 3.
But if DM* allows you to generalize and conclude FOR EACH door that the prize is not behind it – that’s bad.
Here are two ways to go on your example
One: This doesn’t seem any more problematic than puzzles about lotteries and the thesis that justification is closed under logical entailment. Whatever we say in those cases, we might be able to say something here.
Two:
Let P = The prize is behind door number 1 or the prize is behind door number 2.
Let Q = The prize is behind door number 3.
You might think that P is possible and your justification that Q is possible are the same.
What is clearly different is your justification about probabilities. So you might think that one doesn’t satisfy the antecedent in prize door case.
Justin,
Ok. I’m fine with the point not being very controversial. In that case, it’s not very controversial that (DM*) is false.
Andrew,
So, the revised principle is the following?
(DM**) If S knows that (P or Q), S is justified in believing that P is possible, and S’s justification for believing that P is possible is higher than S’s justification that Q is possible, then S is justified in believing P.
Anonymous,
I think Andrew’s suggestion is that DM* be revised as follows:
(DM**1)If S knows that (P or Q), S is justified in believing that Q is possible, and S’s justification for believing that P is possible is higher than S’s justification that Q is possible, then S is justified in believing P.
Although, he might want it revised as follows:
(DM**2)If S knows that (P or Q), S is justified in believing that P is possible and that Q is possible, and S’s justification for believing that P is possible is higher than S’s justification that Q is possible, then S is justified in believing P.
Joshua
Both of Joshua’s revisions seem intuitively plausible to me.
Here is a modification of the case given by Anon. I suppose someone could be justified in believing some rather strange things about modality. For example, someone might be justified in believing that some things are possibly necessary yet are not the case. So, suppose that Joe justifiably believes that Goldbach’s conjecture is possibly true and that the negation is possibly true as well. Maybe he believes this because he justifiably believes that every proposition is possibly true.
It just so happens that, today, Joe’s friend, someone who knows very little about mathematics, testified to him that Goldbach’s conjecture is possibly true. Joe now has whatever prior reasons he had for believing in the possibility of Goldbach’s conjecture and for believing in its negation. But, he now also has the testimonial evidence for the possibility Goldbach’s conjecture as well. It seems that he is more justified in believing in the possibility of Goldbach’s conjecture than in the possibility of the negation of that conjecture. But it is not clear to me that he is justified in believing that Goldbach’s conjecture is true. After all, he rejects that the possible necessity of a proposition entails the truth of that proposition.
I think the point of anonymous might still stand. We just need this bit more complicated case to show it.
Joshua
Here is another case. Suppose that Fred, Joe, and Charlie are all trustworthy individuals. Fred testifies to me that either P or Q is true so that I justifiably believe that either P or Q. Joe testifies that possibly P is true and Charlie testifies that Possibly Q is true, thus making me justified in believing each of their possibilities.
It just so happens that, although I justifiably find each of them to be trustworthy individuals, I justifiably find Charlie to be a bit more trustworthy than Joe. Now, it doesn’t seem to me that I have reason to believe that Q is true just because my evidence for its possibility comes from a slightly more trustworthy source than my evidence for the possibility of P.
Joshua
Joshua,
Both of those cases are great. I only see two options to save the principle.
Bite the bullet and say that it’s a very small reason in favor of Q. Which might be OK, because testimony that Goldbach conjecture is possible from a non-expert (but trustworthy source) strikes me as a very small reason in favor of the possibility.
(I don’t particularly like this option)
The other option would be to Chisholm away and require that there be some bigger gap between the justification for believing that P was possible and Q was possible. (I’m not sure how well a testimony case would work against that…but I think it might still sway me even here)