read my posts. I am actually insisting the opposite.
I’m the first to admit that google is not omniscient. So bear that in mind when you look at these search results: here, here, here, and here. At the time of writing, those four searches turned up a total of one result. In the last one, the relevant passages are on page eight, in the first two bullet points after “The KK-Thesis and the Limit”.
By way of comparison, “walrasian tatonnement” turned up 483 results. “Upper hemi-continuous” turned up 272 results.
That’s not to say that anything underhanded is going on, but I do question the cut-and-dry nature of the way “The Doxastic Axiom” has been presented, especially when the single result for “doxastic axiom” implies that we are dealing with a class of axioms rather than one particular axiom. (If the result is being proven, then why isn’t it “The Doxastic Theorem” or “Lemma”? Whereas if it is just an assumption, why should we accept it?)
Also for comparison, “swedish civil defense” and paradox turned up 42 results. I mention this because of two things. The first is that the best explanation of the paradox I’ve read is that you can’t always logic out what is in peoples’ heads.
The second is to consider some details of a brief survey of explanations, which you can read here. Notice how many involve parsing down definitions to very precise, but very narrow, statements. In doing so, one may solve the paradox, but lose the connection with the real world. In the case of The Doxastic Axiom, belief is a pretty sloppy idea. If one is defining a concept narrowly enough to create and use formal axioms, is one losing touch with the world we live in?
Here’s an example of where that question is important. In neoclassical consumer theory “rational” is defined so narrowly that it is essentially disconnected from its everyday meaning. Why then should we assume that it connects with everyday behavior? Well, economists have addressed that question. Through a series of mathematical if-and-only-if statements, they have shown that if an economic agent has rational preferences, then said agent’s choices will behave in a certain way. Additionally, if said agent’s choices behave in a certain way, then rational preferences are implied. As I understand it, experiments with rats, pigeons, children, and adults have shown that choices tend to correspond reasonably well, so that the rationality assumption, while not perfect, is a reasonable approximation.
Why should we assume that formal modal definitions of belief correspond to what we actually believe? If someone tells me that Banisteripsis Caapi is good for upset stomach, am I really obliged to believe that that statement is either true or false? When I had to go through radiation I had a terribly upset stomach. A nurse said that ginger, taken as ginger snaps or ginger ale, would help. She was a nurse at an oncology clinic, presumably she would know. However, when I actually consumed ginger, I can’t say that I had particularly spectacular results. Do I believe that ginger doesn’ work? No, not really. Do I believe that it does? No, not really. If someone is suffering from upset stomach, I’ll tell her that I’ve been told that ginger is supposed to be effective. If I have an upset stomach, sometimes I’ll try ginger snaps, sometimes not. Such behavior hardly corresponds to the dichotomy of The Doxastic Axiom.
If I am told that medicine X is effective, I don’t immediately decide that I believe it works or that I believe that it doesn’t work. I wait for more information. If I hear that there have been a number of double-blind studies showing its effectiveness, then I’ll believe it works. If I hear of a number of double-blind studies finding no significant effect, then I’ll believe it doesn’t work. Until such information is presented, I’ll just say, “Maybe it works, but I have no reason to think it does.”
These facts make me wonder just how well The Doxastic Axiom connects to the real world. The modal ontological argument has the same problem.
Let me start with a more physical example, again working from Bunch. In mathematics there is a controversial axiom called the axiom of choice. We needn’t worry what it says here, but let’s take it as given. It can then be proven that one can take a small sphere, disassemble it, and reassemble it into a larger sphere with no interior gaps. In other words, one can take apart a grapefruit, put it back together, and feed the world. Hmm, very interesting. The problem is that to do this, you have to be working in Euclidian space, i.e. like doing geometry on a flat table. The trouble is that we may not be living in Euclidian space, space might be like doing geometry on a ball or a saddle. So we have this wonderful result about feeding the world with a grapefruit, but it won’t work because modern physics seems to suggest that our universe isn’t Euclidian.
That, if I read it correctly, was the point of the Oppy article I provided earlier. One might be able to prove a god (for whatever it’s worth) in modal logical space, but we don’t know that we actually live in a modal logical space. According to Oppy, to decide if we live in a modal logical space we have to determine if there is a god. But now we’re going in circles! We need to prove we exist in a modal logical space to prove a god, and we need to prove a god to prove we live in a modal logical space.
Maybe Oppy is mistaken on that point, and there are other ways to prove that we inhabit a modal logical space. How is this to be done, and has it been done? With neoclassical consumer theory, we can show a connection through experimentation. Has such experimentation been done in modal logic?
Buck
I agree with much of what you said, but I do have a problem with this:
Everything about a rock — its identity, its description, its definition, its purpose, its context, even its existence — has been arbitrarily assigned by perceivers in exactly the same way that beauty has been assigned. Existence is a perceptual term, invented by philosophers to discuss the metaphysical status of a phenomenon. There is not necessarily any intrinsic property of “existence” to the universe or anything in it. So, how is it that without perceivers, rocks would still exist, or would even still be rocks?
I would say that a lot of the terms we assign to “rocks”–things like alkalinity, conductivity, melting point, solubility in water–describe processes that went on before we were here to describe them, and would continue on even if we were no longer around. Otherwise, where did we come from? I would put “That rock is beautiful” in a different category. (There may be or have been or will be non-human intelligences which might have some category we could recognize as equivalent to our “beauty”, or there may not.)
—p -> Bp is induced because it is assumed that a person will believe something that he knows is actually true.—
Wait, doesn’t that mean that p -> Bp is actually Kp -> Bp? Making the converse ~Bp -> ~Kp? That is, if knowledge of p implies belief in p, then lack of belief in p implies only a lack of knowledge of p, not knowledge or belief ~p. Indeed, none of this implies anything about p.
If it ISN’T Kp, then I can’t see why anyone would agree with the axiom. The actual truth of p doesn’t imply that anyone believes it is true.
And seeing as ~Bp and B~p are themselves both descriptions of people’s beliefs, not of anything relevant to the truth of p, I still don’t agree that “there is no difference” is a fair characterization.
Whether I B~p or ~Bp I can still posit p for the sake of any discussion of validity one cares to have, just as anyone else can. So in that sense, the sense seemingly relevant to discussion, there is no “difference” between ~Bp, B~p, OR Bp.
—I would say that a lot of the terms we assign to “rocks”–things like alkalinity, conductivity, melting point, solubility in water–describe processes that went on before we were here to describe them, and would continue on even if we were no longer around.—
Well, but how can we prove that?
I would instead note that I can’t change the base charateristics of a rock without manipulating it considerably, but I can change my opinion of whether it is beautiful just by looking at it. I don’t know what that implies, but it seems a signficant enough difference.
Likewise, I couldn’t change what cilantro looked, smelled, or tasted like, but I could change whether or not it was “tasty.”
Likewise, I couldn’t change what a country music recording sounds like, but I could come to appreciate that it (well, some of them) was beautiful.
Our existence is dependent on “rocks”–water molecules, phosphates, sodium ions, deoxyribonucleic acid, proteins–having certain properties. If, before we described those properties, DNA didn’t have the properties we observe it to have–say if the base pairs didn’t match up the way they do, if maybe they matched up entirely at random–then the “rocks” could never have evolved to the point where they could form complex systems which can describe their own physical properties.
Of course, I can’t prove this in some Euclidean sense. Maybe the whole Universe sprang into existence on April 28, 1970, at 11:33 a.m. Central Time.
Js_africanus
An impressive post, covering everything from Banisteriopsis Caapi to Swedish civil defense. 
The Doxastic Axiom follows naturally from the equivalent KD45 proposition, p -> Mp, where “M” is “<>”. It is weakened by the Doxastic Normality Principle which states that believing p to be true means believing p to be true in the most plausible possible worlds, epistemically speaking. Were it not weakened, Bp would imply p, just as Lp -> p, where “L” is “”.
What the axiom states is intuitively obvious. If p is actually true, then you will believe that p is true: thus, p -> Bp. Your concerns about taking medicine and such seem to indicate that you have it backwards, that Bp -> p, which is not the case.
You’re right (and I have said) that doxastic logic is seriously lacking in practical applications, since it has precious few axioms:
p -> Bp
Bp -> BBp
and
~Bp -> B~Bp
No one is saying that we live in modal space. Symbologies are intened to model the world, not replace it. We don’t tend to think of God as necessary existence; we tend to think of Him as Supreme Being. It so happens that necessary existence is an excellent way to model the notion of Supreme Being.
Oppy is an accomplished philosopher, and despite your assumptions to the contrary, I never intended to disparage him. But even he, like every other philosopher that I am aware of, considers the modal ontological argument to be valid. From your cite: “As Plantinga notes, this is a valid argument.” — Oppy.
That doesn’t mean he believes it is sound. Most atheists don’t. But soundness is in the eye of the beholder. If you do not accept, for example, that modal status is always necessary, then you will reject Becker’s Postulate (although Kierkegaard did not reject it).
Again I say that it is not incumbent upon us to be enemies merely because we hold two opposite views. You seem to think otherwise. You seem to find it necessary, not just to express your disagreement, but to prove me wrong — like a hippopotamus stomping out a campfire. But you have a whole lot of campfires to stomp out. Plantinga’s version of the argument (the one Oppy dealt with) is but one of scores.
Why can’t you and I just be friends, one of whom likes rock music and the other likes country-western?
Apos wrote:
No, but I can see why you thought that with my sloppy exposition. I apologize. “p” means “actual p”, not “knowledge of p” as I implied to you.
But I disagree with you that the axiom is unreasonable. If p is actually true, then it seems reasonable to believe p. It’s not an epistemic principle, but a doxastic one. Bp means believing p to be true in the most epistemically plausible possible worlds, but not necessarily any epistemically compelling world.
Apos
By way of clarification, see my post to Js_africanus, wherein I explain that the axiom is derived from p -> <>p in K logic. It is intensionally weak toward p.
—Our existence is dependent on “rocks”–water molecules, phosphates, sodium ions, deoxyribonucleic acid, proteins–having certain properties.—
Well… hey that’s a pretty good response. The major problem I can see with it is that it uses the properties we can observe now to create a theory that then requires those properties to have been the same when the theory was in operation. So in the end, it still begs the question: it has to assume the very consistency we were trying to establish in order for us to even care about any theory that explains our existence. Of course, if there was no consistency, it would be pretty hard for us to even think about “explaining” anything at all.
But insofar as we ignore the circularity of using a scientific theory to establish consistency (which isn’t always at issue anyone), it is true that chemicals had to have certain properties for us to exist, but as far as we can tell, there is no need for them, or any combination of them, to have been “beautiful.”
My example was more along the lines of the consistency not of objective existence outside perception, but of what the consistent features of my own perception are. Namely, I can’t, simply by percieving, change what color i percieve a rock to be. I can change whether or not it is beautiful.
Now you’re just being silly. You know darn well that it was 11:33 a.m. GMT. 
Buck wrote:
I don’t think anyone denies the gist of what you’re saying. I’m just saying that the properties you have assigned are properties of your perceptions and not of the rocks. A rock “having” a property is a metaphor. Rocks don’t really have anything. Even their existence is something we have established as a property.
Properties are perceptions we made up to help us make sense and order out of what we perceive. We speak of the inverse relations of wavelengths and frequency, for example, as though kilohertz were something intrinsic to radiation. But it isn’t. We drew up classes and measures and applied them to observations.
Here is an excellent treatise on existence from Stanford, and the distinctions between existence and reality. (In this fast and furious thread, I might already have given that link. If so, it bears repeating anyway. :))
—But I disagree with you that the axiom is unreasonable. If p is actually true, then it seems reasonable to believe p.—
I don’t understand how we insert talk about it being reasonable to believe until we make some connection between the truth of p and this truth having some affect on the believer. p is a statement about p. Bp is a statement about a person. We have a vast amount of examples wherein either p or ~p were definatively true (or at least we now know them to be true), but there were plenty of people both Bp and ~Bp and B~p all at once. What happened there, if p -> Bp?
If these questions sorts of aren’t relevant to the strictures of doxastic logic, then perhaps doxastic logic is an inappropriate model for what we are talking about, as below:
—It’s not an epistemic principle, but a doxastic one. Bp means believing p to be true in the most epistemically plausible possible worlds, but not necessarily any epistemically compelling world.—
Then perhaps this suggestion of a model of non-belief is generally inappropriate for what you are trying to describe. The above description makes ~Bp far far stronger a statement than “no belief in.” I mean, “no belief in” can apply equally well to a person who has not even considered the question, and has formed no ideas whatsoever about the epistemic plausibility of p.
** MEBuckner**
wrote:
It requires faith. That the material world exists is a belief not knowledge.
Is there any “objective evidence” of its existence ?
I agree, no more no less. But I don’t think its “objective evidence”
I think that’s the problem we don’t know what is “real” if anything. Although I think something has to be real, i.e. ”awareness”, for how can something “unreal” exist all on its own, so to speak ?
I am not sure where you are going with “thinking”, but we don’t have to “think” to be aware. After all what does a thought know ?
I said, * How can god be a mere percept ?*
It was in response to your statement:
**
I agree, hence, ‘god cannot be a mere percept.’
If god could be perceived I doubt it would be believable or tell us much about god.
An east India sage named Ramana Maharshi said, (paraphrase) “Whatever god you perceive is as real as you are.”
I think we agree. If Jesus returned to day, perceivable in the flesh (maybe he already has) would we know any more of a gods existence?
—Your concerns about taking medicine and such seem to indicate that you have it backwards, that Bp -> p, which is not the case.—
Wait:
the previous contentious implication was p-> Bp and thus ~Bp -> ~p
Doesn’t that also imply that ~p -> B~q and thus ~B~p -> ~~p?
Apos wrote:
You’re probably right. There’s an awful lot written on the shortcomings of doxastic logic, chiefly the exact sort of discussion that you and I are having now regarding the agency of belief. Even if p is actually true, it is not necessary that an agent B. Based on your argument, I’ll withdraw in general my remarks to Hawthorne, except to say this: if you behave as though you believe not, then you must not be surprised when someone discovers that you merely do not believe and wonders why you draw a distinction. Is that fair?
How? That doesn’t look like a contrapositive.
—Based on your argument, I’ll withdraw in general my remarks to Hawthorne, except to say this: if you behave as though you believe not, then you must not be surprised when someone discovers that you merely do not believe and wonders why you draw a distinction.—
Well, I’m not sure I it’s clear to me yet what “behave as though you believe not” would fully entail (since Hawthorne was just one example). If it entails running around saying “it’s stupid to believe p!” or “I expect that I’ll ~p” then I’d be the one surprised that the person even claims only to ~Bp. I’d then be more likely to Bp where p is “that guy is either confused, or full of it.”
Obviously, whether or not it make sense to draw the distinction is more a matter of the particular matter in question. If the matter in question is “what is your opinion of p?” the distinction is pretty important. If the matter in question is “prove ~p!” then the distinction is pretty important. If it’s “prove p” then it’s probably not.
Of course, in any case, the ideal is for any type of person to be able to criticize bad arguments regardless of their conclusions, and provisionally posit p or ~p to examine validity. In the ideal logical discussion about p, it should be irrelevant what anyone believes, only what we can all agree can validly be said about p.
—How? That doesn’t look like a contrapositive.—
What would be the contrapositive?
What if we wrote ~p as q? Then q -> Bq and ~Bq -> ~q, which is really ~B~p -> ~~p, or ~B~p -> p.
Or not.