Is it possible to define the total number of possible beliefs that can be formed via interacting freely with one’s environment as a mathematical set? Or, even more simply, can things like beliefs even be expressed as belonging to a set? It seems to me that they can if beliefs or the forming of beliefs take the form of brain states or changes in the structure of the brain, but I’m not sure. I am trying to axiomatize something greater than this, so out of context this question might sound kind of bonkers. — ToothyMaw

I don't think beliefs actually exist as separate things that can be counted in any realistic sense. I see my understanding of the world as an interconnected, inseparable network of ideas, thoughts, beliefs, and attitudes. Any separation is artificial and I guess it would have to be associated with language. How many ways are there to slice the pie of my worldview?

I don't think beliefs actually exist as separate things that can be counted in any realistic sense. — T Clark

If they exist as part of the mind I would see the beliefs as existing as a brain state or change in brain structure. Sure - maybe the brain states are the result of and cause things but if they exist in people's brains they could be separately analyzed at a point in time it seems to me. I don't even need to know how to describe the objects (beliefs as brain states): all I need to know is if they can be put into a set.

if they exist in people's brains — ToothyMaw

I doubt they exist as separate brain states. I'd guess, without any specific justification, that no brain state ever repeats itself.

I doubt they exist as separate brain states. I'd guess, without any specific justification, that no brain state ever repeats itself. — T Clark

What exactly do we mean by separate? Separate from other phenomenon in the brain? Or never repeating and identifiable? I used the word because you did.

Furthermore, if there is a finite number of brain states brain states could potentially repeat I think.

edit: Actually even if there is an infinite number of brain states I think they could still repeat.

another edit: the possible number of brain states has nothing to do with whether or not they will repeat it seems to me.

What exactly do we mean by separate? Separate from other phenomenon in the brain? Or never repeating and identifiable? I used the word because you did. — ToothyMaw

Say I have a box of apples. The apples are separate from each other. I can pick them up, eat them, count them. I don't think ideas or beliefs are separable in that way. It seems much more artificial to me. More open to disagreement.

Furthermore, if there is a finite number of brain states brain states could potentially repeat I think. — ToothyMaw

Perhaps, but not in any practical sense. Given the number of neurons in a brain and all the possible interconnections, I think it is unlikely there would be a repeat in the lifetime of the universe, much less a person's lifetime. And that's assuming the persons brain was not constantly changing.

On the subject of brain states, we cannot simply assume brain states represent belief (as a subjective "thing" of some sort), as, if we're being rigorous which I assume is the purpose here, we have no proof of brains being conscious to begin with. Although, I also agree with criticism of the brain states approach (which would simply reduce to "very different brain states that nevertheless mean what I say they mean; i.e. different brain states represent the same belief, as long as we have -- totally different -- reasons for saying so, such as the words approach below").

For the general question of the OP, I think the more fruitful approach is to represent beliefs as "set's of words" made up of "sets of letters", and those easily form sets. So, insofar as beliefs can be represented with words, then they can be easily put into sets.

The problems would arise if you want to say different sets of words actually represent the same belief ("God exists" is the same belief as "Supreme being exists"). But this would be more of a linguistics problem than a set problem, and maybe you can simply work around it to make your greater project.

Say I have a box of apples. The apples are separate from each other. I can pick them up, eat them, count them. I don't think ideas or beliefs are separable in that way. It seems much more artificial to me. More open to disagreement. — T Clark

Okay, that makes things clearer. I don't think that beliefs need to be separate in such a way in order to count them as a brain state, or a quality of a brain state. We know that people have beliefs and that they exist in the brain, so even if the brain state isn't separately countable and can't be extracted we know that said person's belief is the result of a brain state - even if said brain state might never be repeated.

Not everyone would have to have the same brain state to believe the same thing, but those beliefs exist as brain states nonetheless.

If beliefs don't exist in the brain then where do they exist? And whether or not brains are conscious seems to be a different problem.

Not everyone would have to have the same brain state to believe the same thing, but those beliefs exist as brain states nonetheless. — ToothyMaw

I think this tangent I set us on is distracting from your main purpose. I'll leave it at that.

I actually thought we were getting somewhere.

I actually thought we were getting somewhere. — ToothyMaw

Ok. I was worried that I was distracting. I like to show respect for the intentions of the person who starts the thread.

This is the mind-body problem. It's been discussed for thousands of years.

Presumably (if other people are conscious, which we / I don't know) beliefs are associated with their brains (definitely seems to be the case), but that does not prove the subject experience is somehow "in" those brain states (as a collection of particles).

No equations governing particles in any of our laws of physics, in any arrangement whatever, predicts consciousness.

To say particle interaction "causes consciousness" is to say some particle description we can write down describes to us consciousness; that you can give me some paper with some descriptions of particles and, after review (even very lengthy) I (or any other diligent reviewer) would say "ah yes, these particles / field equations / whathave you, would be conscious in this description if such initial conditions, as clearly described here, were put into motion.

We do not have such a theory of physics. It is not even clear such a theory is even in principle possible.

Not everyone would have to have the same brain state to believe the same thing, but those beliefs exist as brain states nonetheless. — ToothyMaw

So, insofar as beliefs can be represented with words, then they can be easily put into sets. — boethius

I don't think saying that beliefs can be represented as groups of words gets us out of the hole. Similar ideas can be expressed with different words, but small differences in wording can change the meaning significantly. Example - there is currently a discussion on incest here on the forum. According to Thesaurus.com, "unacceptable" and "undesirable" are synonyms. Take these two statements of belief:

• I believe incest is unacceptable.
• I believe incest is undesirable.

Are they the same belief?

Also - what about groups of words that don't mean anything or that don't make sense.

For me, this isn't nitpicking. It goes to the heart of how I experience my mental life. It's a flowing current, not a set of blocks to be stacked.

Since we do not have any way, even in principle, to reduce consciousness to particles, the intellectually rigorous way is, presuming there is a phenomenon of consciousness (at least in my own case), is to postulate a consciousness field (that's what physicists do when they encounter new phenomenon that's not a prediction of the fields they already have: they add another one).

Now that we have postulated this consciousness field we can go ahead and say it somehow describes consciousness at different points in space, interacts with the other fields (of course, which way the causation goes is another question), and call it a day until someone invents a device that measures this consciousness field.

The lack of such a device is a problem for further development of the theory, but at least no made-up postulates without justification have been adopted. Of course, maybe such devices do exist after all, and we call them brains.

I knew of the mind-body problem, yes.

To say particle interaction "causes consciousness" is to say some particle description we can write down describes to us consciousness; that you can give me some paper with some descriptions of particles and, after review (even very lengthy) I (or any other diligent reviewer) would say "ah yes, these particles / field equations / whathave you, would be conscious in this description. — boethius

I grant all of that, but I think belief is different. Unless I'm mistaken we can actually model belief in the brain, whereas, as you say, we cannot mathematically model consciousness and do not know if it even can be modeled.

I thought about your linguistic solution and it seems pretty good - elegant even. But how could we know which beliefs (collections of words) are the result of freely interacting with the environment?

That is all very interesting stuff. Never would have thought of postulating a consciousness field (but of course I'm not a physicist; I don't know how such things work). That being said, I don't count myself as a philosopher either.

I don't think saying that beliefs can be represented as groups of words gets us out of the hole. Similar ideas can be expressed with different words, but small differences in wording can change the meaning significantly. — T Clark

That's why I said in the same post:

The problems would arise if you want to say different sets of words actually represent the same belief ("God exists" is the same belief as "Supreme being exists"). But this would be more of a linguistics problem than a set problem, and maybe you can simply work around it to make your greater project. — boethius

However, it depends what one wants to do with these sets of beliefs. If one's argument simply requires beliefs can form sets, then the word approach seems to me fine.

A belief can be counted by the number of statements held to be true or assented to.
So a set of beliefs would just be a collection of statements.

But I'm not sure the total number of possible beliefs, even in a context, is countable. Given that beliefs can be false, and can incorporate numbers (since beliefs are just statements which will be assented to), it seems to me that you could not separate beliefs into sets if the sets are thought to contain a finite number.

I thought about your linguistic solution and it seems pretty good - elegant even. But how could we know which beliefs (collections of words) are the result of freely interacting with the environment? — ToothyMaw

That actually doesn't matter; one can simply find out the conditions under which a belief is formed by a person.

But I'm not sure the total number of possible beliefs, even in a context, is countable. Given that beliefs can be false, and can incorporate numbers (since beliefs are just statements which will be assented to), it seems to me that you could not separate beliefs into sets if the sets are thought to contain a finite number. — Moliere

That doesn't matter; I just need to have a means of selecting beliefs from a set. Whether that set is finite or infinite doesn't matter, and whether they express quantities or can be false doesn't matter either; all that matters is that the belief is held and can lead to people making choices.

That is all very interesting stuff. Never would have thought of postulating a consciousness field (but of course I'm not a physicist; I don't know how such things work). — ToothyMaw

There's nothing mysterious to it. We know we can explore space, and we know "stuff" exists in space (otherwise we wouldn't know space exists of course). So, for every kind of stuff, we can postulate a field that covers space with that value of this stuff at any point.

By "stuff" is meant an observable phenomenon of some sort.

We can encounter elephants and postulate an "elephant field" which would tell us at each point of space if an elephant exists there or not.

Of course, if more general fields (such as that describe gravity, particles, etc.) can completely account for other fields (like our elephant field), then, although we can still have an elephant field to describe our elephant problems if we want, we would not say it is fundamental, even if maybe otherwise still useful (the typical example is temperature, which is reducible to particle motion, but nevertheless useful to work with fields representing temperature at different points in space, say the simulation of a part in a machine).

However, if a field isn't reducible to other fundamental fields, then it must be also fundamental. For instance, the Higgs field is assumed to exist because the other fields simply don't give rise to mass without postulating this other separate field.

A consciousness field seems to me the intellectually honest starting point, only after showing it is reducible to more fundamental fields (such as the elephant field, insofar as we're talking about elephants as collection of particles and not their conscious experience) can we say it is maybe a useful accounting of some aspects of reality (elephant field, temperature field, consciousness field), but not representing anything fundamentally physical.

That doesn't matter; I just need to have a means of selecting beliefs from a set. Whether that set is finite or infinite doesn't matter, and whether they express quantities or can be false doesn't matter either; all that matters is that the belief is held and can lead to people making choices. — ToothyMaw

It seems to me beliefs can be just words, and it seems pretty accurate that people make choices based on words in reality (that's as good a description as we can actually make; although "brain states" I would certainly agree affect decisions, it's not clear whether, apart from words, they do so by something we call beliefs; i.e. emotions certainly affect both beliefs and decisions, but it doesn't seem a given that they are themselves beliefs -- although, we can certainly have beliefs about our and others emotions).

But, if you just want beliefs to be in some reasonably constructed sets, then letters and words clearly can makeup sets, and it seems a very reasonable premise that people really do make decisions based on words (though, not exclusively; so, if this isn't a requirement, it's certainly a starting point).

I just need to have a means of selecting beliefs from a set — ToothyMaw

I'm not sure what you're asking for here. Are you wanting criteria? Because surely we have the means of selecting a belief from a set. All we need do is point to it! Or, if we want to be more formal, we could set up a map between two sets and then whenever you input whatever it is we're mapping to you output the belief.

the belief is held and can lead to people making choices. — ToothyMaw

That doesn't seem too controversial to me. People hold beliefs, and there are times when holding such and such a belief is the reason behind a choice.

But then you wouldn't be asking a question. What's the puzzle?

I'm not sure what you're asking for here. Are you wanting criteria? Because surely we have the means of selecting a belief from a set. All we need do is point to it! Or, if we want to be more formal, we could set up a map between two sets and then whenever you input whatever it is we're mapping to you output the belief. — Moliere

I just need a way of expressing beliefs as a set that can be selected from.

What's the puzzle? — Moliere

I'm trying to axiomatize the chain resulting from someone's beliefs that they are complicit in forming to the breaking of a very specific law, going from belief -> choice -> action breaking the law.

if we want to be more formal, we could set up a map between two sets and then whenever you input whatever it is we're mapping to you output the belief. — Moliere

Can you explain this? It seems to me I only need one set representing beliefs that can be drawn from and if a certain belief is known to have been formed at least partially by one's own free actions we can map that onto a very simple causal model determining moral culpability (in its most simple sense; I know there are degrees of moral culpability).

My main issue was the starting point, how to represent the collection of beliefs.

I need to specify: my idea is that if one is complicit in the forming of a belief and act on it then they are morally culpable; if they were not complicit in the forming of the belief they are not. Whether there are degrees matters, but at its base if one is complicit then they can be held accountable in some way, even if it is hard to say to what degree, and if they are not complicit then they cannot.

You might need to read part of my essay to fully understand what I'm trying to do here.

But, if you just want beliefs to be in some reasonably constructed sets, then letters and words clearly can makeup sets, and it seems a very reasonable premise that people really do make decisions based on words (though, not exclusively; so, if this isn't a requirement, it's certainly a starting point). — boethius

No, it doesn't have to be the case that decisions are made based on the words but rather that the words accurately express a belief that can be readily understood to have caused someone to act in such a way as to break a law.

Never would have thought of postulating a consciousness field (but of course I'm not a physicist — ToothyMaw

Perhaps the reason you wouldn't have thought of a "consciousness field" is that it's baloney. It's certainly not physics. Or psychology. It doesn't mean anything.

Obviously I don't know much about it. It sounded smart to me.

Apparently it is indeed pretty dubious, Deepak Chopra uses the term, and while that does not immediately discredit it, it goes a long ways towards raising suspicion that it is bullshit.