Suppose we list the things I believe to be true. For instance, I believe that I live in North America, that I had toast today for breakfast, and that I am a man. I also have metaphysical, ethical and political beliefs which largely make up my worldview. Suppose further that we list the collection of every belief I have in one big conjunctive fact. So for example:

I live in North America and
I had toast today for breakfast and
I am a man, etc.

Let's formalize this collection as (B1& B2 & B3 & ...Bn). This massive conjunction will be true if and only if every single belief i hold is also true. But it is surely plausible that not everything I believe is true. I'm not just trying to be humble here or appealing to some epistemic possibility. Indeed, I really have no significant doubts that something I believe is false---the contrary is outrageous. I'm unsure which belief is false, but I am certain that some belief is. However, in accepting that, I should therefore also accept that the totality of my beliefs is false, since that totality is true if and only if every belief of mine is true.

This strikes me as odd, because if you were to enumerate all of my beliefs one-by-one (B1, B2, B3,...Bn) and then ask me if I believe each belief itself to be true, then I'd say yes. They're my beliefs, after all! But each belief is true if and only if the conjunction of those beliefs is true.

Hmmm.

Beliefs may be fact or false.
Facts are true. And facts are evident because there is evidence to support them. They are objectively certain.

Mick wrote:Suppose we list the things I believe to be true. For instance, I believe that I live in North America, that I had toast today for breakfast, and that I am a man. I also have metaphysical, ethical and political beliefs which largely make up my worldview. Suppose further that we list the collection of every belief I have in one big conjunctive fact. So for example:

I live in North America and
I had toast today for breakfast and
I am a man, etc.

Let's formalize this collection as (B1& B2 & B3 & ...Bn). This massive conjunction will be true if and only if every single belief i hold is also true. But it is surely plausible that not everything I believe is true. I'm not just trying to be humble here or appealing to some epistemic possibility. Indeed, I really have no significant doubts that something I believe is false---the contrary is outrageous. I'm unsure which belief is false, but I am certain that some belief is. However, in accepting that, I should therefore also accept that the totality of my beliefs is false, since that totality is true if and only if every belief of mine is true.

This strikes me as odd, because if you were to enumerate all of my beliefs one-by-one (B1, B2, B3,...Bn) and then ask me if I believe each belief itself to be true, then I'd say yes. They're my beliefs, after all! But each belief is true if and only if the conjunction of those beliefs is true.

Hmmm.

This only makes sense if all the beliefs in your series had a necessary relationship with every other belief in your series, but since "You live in America" has no necessary relationship with "You had toast today" then one can exist without the other. The series is just shortened not nullified.

It is possible that some beliefs may be reliant, but the ones that are independent or in smaller sub-sets will not effect the rest of the series. For instance "I believe in God" will not effect anything outside of the supernatural. Even stating "I believe God must have created the universe" would not cause the universe to be untrue. It would only mean the manor in which it was created was untrue.

Just because you believe each of B1, ... , Bn individually it doesn't follow that you believe their conjunction.

I believe that 1, 14, 15, 23, 28, 33 will not be the next winning lottery numbers. The chance of that happening is very small indeed so I just don't believe it will. For the same reason if you gave me any 6 numbers and asked if I believed they will not be the ones on the winning ticket I would have to agree that I believe that. It doesn't follow that I believe that when the draw happens there will be no winning numbers.

logical bob wrote:Just because you believe each of B1, ... , Bn individually it doesn't follow that you believe their conjunction.

Of course that doesn't suggest I do. However, I don't need that to for this tension to be apparent. I can just point out that in modern (truth-functional) logic, the individually enumerated beliefs (B1, B2, B3,...Bn) are true if and only if the conjunction is true (B1&B2&B3&...Bn)

Are you saying that one of the beliefs B1, ... , Bn is the belief that one of the other beliefs in the set is false?

Hey. Mick's come to the philosophy forum and raised a philosophical question without any reference to his religion. In what way does it help to follow him around calling his beliefs bullshit when that isn't what this thread is about?

logical bob wrote:Are you saying that one of the beliefs B1, ... , Bn is the belief that one of the other beliefs in the set is false?

I didn't call it a set.

I'm noting that it is a contradiction on the basis of modern truth-functional logic. It seems then that I either must give up the belief that one of my beliefs is false or give up that every belief of mine is true or do not adhere to modern truth functional logic (or emend it in some way).

logical bob wrote:Hey. Mick's come to the philosophy forum and raised a philosophical question without any reference to his religion. In what way does it help to follow him around calling his beliefs bullshit when that isn't what this thread is about?

I have fans.

Mick wrote:

logical bob wrote:Are you saying that one of the beliefs B1, ... , Bn is the belief that one of the other beliefs in the set is false?

I didn't call it a set.

I'm noting that it is a contradiction on the basis of modern truth-functional logic. It seems then that I either must give up the belief that one of my beliefs is false or give up that every belief of mine is true or do not adhere to modern truth functional logic (or emend it in some way).

i dont need to believe that p&q is true iff p,q is true for the above to be true.

Mick wrote:

logical bob wrote:Are you saying that one of the beliefs B1, ... , Bn is the belief that one of the other beliefs in the set is false?

I didn't call it a set.

I'm noting that it is a contradiction on the basis of modern truth-functional logic. It seems then that I either must give up the belief that one of my beliefs is false or give up that every belief of mine is true or do not adhere to modern truth functional logic (or emend it in some way).

You can of course believe something like out of the set of all beliefs you have, 80/90/95/97.5/98.7/99.9/... are true. Of course, this belief will include this metabelief as well, so you accept that your guess as to the accuracy of the number you hold there. This kind of belief is less absolute, and therefore more useful in the real world.

Mick wrote:I'm noting that it is a contradiction on the basis of modern truth-functional logic.

Yes. If you wanted to formalise this properly, you would have to account for your less that 100% absolute confidence in your beliefs. You could use probabilities, for instance, which is where logical bob is presumably heading.

P(B1) = 0.9
P(B2) = 0.9
P(B3) = 0.9
...
P(B100) = 0.9

Therefore: P(B1 & B2 & B3 & ... & B100) is roughly 0.00002656. The confidence in the conjunction of all your beliefs is very low indeed.

All of this can be handled by a logic capable of basic arithmetic. Propositional (truth-functional) logic can't formalise this stuff generically, but then propositional logic can't do much.

Mick wrote:It seems then that I either must give up the belief that one of my beliefs is false...

If you believe that one of your beliefs is false then you hold contradictory beliefs so you couldn't really expect then all to be true.

Dwindling probabilities, yes? Plantinga made such an argument against probabilistic arguments for the resurrection, though I don't see why his case, if true, would be applicable to virtually any historical argument. He's been criticized by an individual far more capable in inductive logic than I am. Here's the link: http://homepages.wmich.edu/~mcgrew/plantinga.pdf

Oh bugger. There was me saying this wasn't about your religion...

logical bob wrote:Oh bugger. There was me saying this wasn't about your religion...

It's not. McGrew's point could be made for any historical case simply because Plantinga's object has that sort of scope.

logical bob wrote:

Mick wrote:It seems then that I either must give up the belief that one of my beliefs is false...

If you believe that one of your beliefs is false then you hold contradictory beliefs so you couldn't really expect then all to be true.

I know, but I don't want to give up either.

VazScep wrote:Therefore: P(B1 & B2 & B3 & ... & B100) is roughly 0.00002656. The confidence in the conjunction of all your beliefs is very low indeed.

I find this rather droll. We'd be all walking around knowing that our worldviews are improbable, or at least that we'd lack confidence in them.

Mick wrote:

VazScep wrote:Therefore: P(B1 & B2 & B3 & ... & B100) is roughly 0.00002656. The confidence in the conjunction of all your beliefs is very low indeed.

I find this rather droll. We'd be all walking around knowing that our worldviews are improbable, or at least that we'd lack confidence in them.

Not sure I've much time for the term "worldview" anyway. Nor do I take the concept of "belief" seriously enough to think that these observations about artificial formal systems have anything to do with the way my mind works.

Mick wrote:

VazScep wrote:Therefore: P(B1 & B2 & B3 & ... & B100) is roughly 0.00002656. The confidence in the conjunction of all your beliefs is very low indeed.

I find this rather droll. We'd be all walking around knowing that our worldviews are improbable, or at least that we'd lack confidence in them.

Why is that droll?