Degrees of Belief

I’m not sure why this paper showed up and lingered in my tabs, but it did. I vague recall thinking “oh that sounds interesting!” then being disappointed.

It starts with a weird argument for why the topic (the metaphysical status of beliefs) is worth exploring. But the arguments seem pretty…weird. One is to help formal epistemologists avoid having to say “all out belief” or “binary belief” instead of just “belief” and then taking about degrees of confidence rather than degrees of belief. I guess I’m losing some aspect of being a philosopher because that sounds like a really dumb reason to write a paper.

We then see one rebuttal of a supposedly common argument:

Assumption 1: The property of having confidence that p is identical to the property of having belief that p.
Assumption 2: ‘Belief’ and ‘confidence’ pick out the same thing.

They then infer that since the property of having confidence, or the thing picked out by ‘confidence’, comes in degrees, it follows that belief comes in degrees.

However, no reasons are given for Assumptions 1 and 2. They seem to just be assumed. Now, on the face of things, belief and confidence do seem to be similar sorts of mental entities; perhaps they are identical. On the other hand, our having formed different words for them is some evidence that they are distinct. So, as it stands, I see no convincing argument here that beliefs come in degrees. We will have to look elsewhere for better arguments.6

Now I want to say, “are you kidding me”. First I want to know is how common this argument is. Next I want to know what problems this eliding causes, if it exists. Finally, I want to know whether the author has even seen a thesaurus. Multiple words for the same thing happens all the time.

But it gets worse:

Consider (i). One can talk of much hope, little confidence, much desire, and so on. For any paradigm propositional attitude that comes in degrees, higher or lower degrees of that attitude can be attributed to a person by way of an occurrence of a mass noun. This is inductive evidence for (i).

Consider (ii). One cannot ascribe higher or lower degrees of belief to a person with ‘belief’. (5) does ascribe belief by way of a mass noun, but this only ascribes a number of single beliefs to a population, not a degree of belief to a single individual. Whenever belief is ascribed to a single person by way of a noun, it is by the occurrence of a count noun and not a mass noun. That is why (3) and (4) do not make sense. From (i) and (ii), it follows that beliefs do not come in degrees.

Say what? We easily say that I have a strong or weak believe or that this belief is stronger than that one. And language is quirky! Consider temperature! It canonically comes in degrees! But I can’t say that I have much or little temperature!

Just no.

And, you know, people ask “Ok you believe P, but how much do you believe it?” “100%!”

“Do you believe it more or less than you believe the earth is round?” “Oh much less.”

So I remember now why I gave up with irritation. If you are going to argue from natural language to metaphysics (which I find weird in this day and age) and even if we accept confining yourself to English (which is bad) a minimal constraint should be a systematic linguistic analysis! Not a couple of cherry picked examples and some blather about mass vs count terms!

(Note that I don’t believe my example prove that belief does have degrees because I am not a silly person. I recognize that people might well talk about things in funny ways!)

In any case, I would have thought a metaphysical paper would have explored the, you know, metaphysics. Eg looked at the ontological aspects of beliefs. One might explore whether neuroscience dictates some aspect of the metaphysics of belief. (If beliefs supervenes on excitation dispositions they have a natural degree aspect in us independent of evidential strength.)

I’m so grouchy.


The Muddling of the Mental and the Physical

Nature also teaches me, through these sensations of pain, hunger, thirst and so on, that I (a thinking thing) am not merely in my body as a sailor is in a ship. Rather, I am closely joined to it—intermingled with it, so to speak—so that it and I form a unit. If this were not so, I wouldn’t feel pain when the body was hurt but would perceive the damage in an intellectual way, like a sailor seeing that his ship needs repairs. And when the body needed food or drink I would intellectually understand this fact instead of (as I do) having confused sensations of hunger and thirst. These sensations are confused mental events that arise from the union—the intermingling, as it were—of the mind with the body. Descartes, Meditation 6

Descartes is, of course, the arch-dualist. Mind and body are different substances with entirely different natures and can exist independently. Human beings, on the other hand, are not just their minds (even though the mind is the ego who’s existence we know first, and best). The things that teach us that we form a kind of unit — pain, hunger, thirst, etc. — are perceptions of the body which differ from how experience the rest of the world.

I was thinking about this because I’ve been feeling like crap for months now. Clearly there is a strong physical element, but equally so, there’s a strong mental component. They go back and forth in a complex dynamic but it’s not always clear which is which or even if they are fully separable. If I dry heave, it could be pure anxiety, a stomach virus, or a side effect of medication (perhaps for anxiety).

The most striking (for me) example in my personal history was the interaction between my inner ear issues and social anxiety. When I was a teen-ager, I developed an inner ear disorder that ranged from subtle to extremely overt (i.e., spinning for three days at a shot). But effect of the subtle variant was that in noisy environment with a fair bit of motion, my ability to distinguish my movement and other objects movement was diminished. (Think of being on a smooth and slow moving train when it just starts up and you’ve been distracted.) This can make you feel very uneasy and off balance and…anxious.

This inflected my experience of social gatherings…dances, parties, etc. When this got really going I would feel unsettled and uncomfortable and usually seek a quiet berth (kitchen, outside, or…not there). Part of this was undoubtably due to this inner ear phenomenon, but I had no idea that it even existed. So I interpreted this mostly physiological reaction as being a dislike of parties or part of my social anxiety. Which didn’t help the anxiety at all. On the contrary.

We know that many physical illness tend to have certain mental co-morbidities. Being sick sucks, so depression isn’t uncommon.

Our Cartesian unity…the fact that we are a big muddle of a complex system…makes life difficult. Our parts don’t swap easily.


Pan-blahism is the move to universalize some aspect of reality. Panpsychism is the obvious example, wherein everything is said to have mental properties (or be mind).

Perhaps it’s part of my procrastinatory ennui (and reading a bunch of philosophy, much of it I find unbearable in some deep way that’s hard to articulate), but I’m finding myself attracted to some pan-isms or, at least, some worries about pan-isms.

For example, all this problem/hard problem of consciousness stuff makes me wonder not “how can consciousness arise from physical stuff” but “why are there non-conscious things”? I know there are conscious things (e.g., me, at least for the moment). I’m pretty sure there are non-conscious things (e.g., me, somewhat later (if not in sleep, then in death), or the armchair on which I sit). But given that there are conscious things, why are there non-conscious things? Why is consciousness so hard to pop out?

Now, on one level, this is easily dispensed with: Brains have a lots of properties not found easily elsewhere in nature (or at least not in current chairs), so why feel there’s any special problem with consciousness (or qualia)? That sounds ok, but probably only if you don’t find consciousness mysterious in the first place. There does seem to be a problem with separability: It does seem  that consciousness is not necessarily tied to brain stuff, but then why should it be tied to complex functional organisations? Indeed, we can impose functional organisation (in our minds) on anything (draw a flow chart on the whiteboard and you have, in some sense, that functional organization imposed on the whiteboard, or, perhaps, on the white board and some hardware (say me) to run it on).

Well, I’m not going to argue all this, since it’s probably nonsense and a competent, au courant philosophy could, I’m sure, easily point out the nonsense and gross ignorance of this little meander. (But would that mean I’d lose the dispute? What would compel me to accept that my nonsense was nonsense? I mean, aside from being weary.)

So I turn to my other panism: pandialetheism. (I got here by reading Greg Littmann and Keith Simmons’ paper, which is pretty good in that Simmons way; note I was taught by Keith and overlapped a bit with Greg.) Dialetheism is the doctrine that there are true contradictions.  It’s usually the case that some contradictions are held to be not true and dialetheisim (and SCREW YOU Priest for this term!) usually hangs out with paraconsistent (i.e., non-explosive/inconsistency tolerant) logic.

But, meh. If I’m going to accept true contradictions, why should I give up good old fashioned classical logic? Let every contradiction be true and every statement contradictory! Take that Priest, you fuddy duddy logical conservative, you!

Well that sounds fun. And it is fun! Except, if I’m going to string the fun along, I have to come up with some sort of defence of this view. I suspect that I need a “climb the ladder” sort of defence ala Tractatus 6.54:

My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them—as steps—to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.)

Except I think we need to kick away the ladder while we’re climbing up it.

So, first question: Can we be a Pandialetheist? Is there a coherent view here?

Let’s start with a slightly relaxed view: There are contradictory formulae in first order logic. First order logic is explosive. So the deductive closure of P & ~P is going to be every WFF in FOL. This is not mysterious.

So, what can be my relationship to such a formula or to its deductive closure?

Clearly I can believe a contradiction at least for certain notions of belief. After all, I believe that other people believe contradictions (though perhaps not self-contradictions), indeed, most people, esp. philosophers, believe this and spend a lot of time trying to show this. But perhaps this belief isn’t a robust believing, e.g., I don’t realize that I’m committed  to a contradiction. Hence by showing me that my beliefs are contradictory, you force me to give something up or at least to go paraconsistent (i.e., I can try to isolate my contradiction).

There’s a lot of work being done by the idea that by bringing me to a certain sort of awareness about my contradictory belief something magical happens, the magic of rational rejection of contradiction. Or perhaps the rational acceptance that the contradiction isn’t true.

That the contradiction is false doesn’t prevent me from believing it. If anything is true, it’s that we all have a ton of false beliefs. Indeed, perhaps all my beliefs are false. But if all my beliefs can’t be false, why can’t they be false due to the fact that all propositions are false. I.e., there are no true propositions to believe?

I’m not sure if I have to yield to the thicker notions of belief. I just happen to have a relation to a set of propositions. Those propositions are expressed in FOL. This relation is such that if I am in that relation to a set of FOL formulae, then I am also in that relation (or a slightly weaker one) to the deductive closure of those formulae.

On this model, with some minor assumptions, we all believe everything. (But are we committed to everything?)

With weariness, I accept that this won’t do. It’s not enough that we have to be, in principle, able to have people with different beliefs, but, in fact, it’s going to be annoying to claim that people don’t have different beliefs. It’d be fun to claim that everyone agrees with me because everyone believes everything, but not all that much fun.

The usual (is it usual? it feels right to say “the usual” without any check that it is, in fact, usual) move is to add some thicker sorts of relations to the mix. E.g., “Yes, you have this ‘belief set’, but you aren’t committed to it.” or “You don’t really believe everything in your belief set.” We can even get trickier.

Let my set of “asserted” beliefs be B. By normal epistemic commitment, if I believe B then I’m at least “committed” to the consequences of B (Cn(B)). Let’s stipulate that everyone has at least on contradiction in their B. So we all have the same commitments (i.e., Cn(A & ~ A)) but we don’t have the same Bs! So, we can still make sense of our varying beliefs even though we all have precisely the same epistemic commitments.

Now we have a kind of game we play. We all pretend that our Bs are consistent. Disputation is basically grabbing some subset of our Bs and trying to force a contradiction. This is bad, because skilled disputers should be able to hide their contradictions from each other. If someone manages to flush out one of our contradictions, we pay the forefit by giving up one of the contraries. But that’s ok, we have plenty more contradictions in our head.

This doesn’t quite get me up to true contradictions. For that I need some semantics and probably some ontology. But…does it matter? I’m still committed to all contradictions and, ordinarily, that means I’m committed to them being true. The phenomenon is established (i.e., all contradictions are true, or, at least, we’re all committed to that), and the theory will have to follow.

Here I want to go a bit meta: Is this a reasonable bit of philosophy, or not? The logicy part, to the degree there is any, seems fine. I’m not making use of anything complicated. Indeed, I deliberately avoided anything logically complicated. The key question is whether I’m right about “belief” and “epistemic commitment”, and even there, I did the classic “thick and thin” move. The empirical bit (we all believe contradictions) isn’t really needed as I’m making a conceptual argument about what could be (could we all have contraries in our Bs? C’mon! Of course we can! Or if we can’t, we can construct minds so that they do.)

This sort of stuff is not so hard for me to generate. I can make it a bit harder by related work. I could dig out a bunch of relevant papers and “engage” in the arguments. Perhaps someone out there has advanced a similar line.

Is this nonsense only if I lack the confidence to believe it’s not? Is this argument a sort of Tinker Bell that needs my to clap sufficiently loudly to live and glow with the bright spark of profundity?

I’m certainly feeling that, at the moment. I suspect this is why I spiraled out in philosophy. This doesn’t necessarily make philosophy bogus. Lots of fields require some intellectual chuzpah, perhaps all of them.