Great question!

Suppose there's a world W in which there's initially only one person X and only two beliefs, God and self (X).

Later, X invents sets. X then claims, that the set of his beliefs, B1 = {God, Self, Set}. Is B1 itself a belief? Yes, it is because sets like B1 are ultimately propositions.

Ergo,

B2 = {God, Self, Set, B1}

But then B2 is also a belief (a proposition)

Ergo,

B3 = {God, Self, Set, B1, B2}

B4 = {God, Self, Set, B1, B2, B3}

So on and so forth,

The set of beliefs is infinite!

B[infinity] = {God, Self, Set, B1, B2, B3,...}

I see no reason to get god involved, and whether or not there is an infinite set of beliefs is also not relevant, which you would know if you had read the relevant posts. Please post things that are salient, or create a new thread.

I see no reason to get god involved, and whether or not there is an infinite set of beliefs is also not relevant, which you would know if you had read the relevant posts. Please post things that are salient, or create a new thread. — ToothyMaw

My post is germane to your question. There are an infinite number of beliefs as demonstrated in my previous post. Thus the set of beliefs is an infinite set but whether infinite sets exist/not is controversial. So controversial in fact that the project of arguing for them was abandoned and mathematicians simply decided to make the existence of an infinite set an axiom.

Hence, if the set of beliefs is infinite, it is, can it be considered a set? Finitists would say no!

I know next to nothing about formal set theory; I'm working at a very basic level here, and I'm just going to go with the orthodox view that infinite sets exist.

Although I will get a book on set theory when I can.

Yeah, I understand your post now and see what you are saying. But why on earth is god necessary?

edit: the belief in god I mean

Not to mention how is the entire set B1 a singular proposition? It is a collection of elements - the elements God, Self, and Set.

B2 = {God, Self, Set, B1} is the same thing as B2 = {God, Self, Set, God, Self, Set}

You are representing a duplication of elements with each new proposition. It makes no sense.

It doesn't make sense?! A set can't contain another 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.”

First, let me recommend a book that presents the conceptual difficulties in developing this notion that beliefs correspond to brain states. The book is “Memory and Mind” by Norman Malcolm.

I will try to summarize these difficulties as follows:

1. First, we seek a natural correlation between the elements of the two domains, and not a stipulated correlation. For example, like the relation between tides and phases of the moon vs the relation between the english language and morse code. So, the isomorphism between experiences and brain states is one by nature not by convention. To determine if there is a natural isomorphism, we propose a hypothesis and thru observation see if it holds in the world.

2. Problem of defining the elements in the “Experience” domain. - Take the desire “wanting to catch a bus” and designate it as an element, call it “E” . The problems start to arise when one begins to think of all the different circumstance one would call “wanting to catch a bus”. We find there is not one common factor among all the cases. So, what brain state element is to connect to what “Experience” element?

3. Problem of duration - where mental states and brain states employ different concepts of duration. For example, Wittgenstein put forward the following example, “Indeed one scarcely ever says that one has believed, understood or intended something “uninterrupted” since yesterday. An interruption of belief would be a period of unbelief, not for example the withdrawing of attention from what one believes - e.g. as in sleep.” This would be unlike the duration of many physical events, say the motion of a ball across the floor could be observed and clocked. Thus, how could we ever determine if one element was simultaneous with other element when the one kind of duration is specific and the other duration is quite vague.

It can, but it doesn't result in an infinite number of beliefs is what I mean. You just keep adding the same elements over and over again with each new proposition. You treat them as if they are distinct when they aren't. Or am I wrong?

If we are talking about distinct beliefs and not duplicated beliefs then what I said applies I think.

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. — ToothyMaw

I value mystical ways of seeing things. I started a thread called "My favorite verses of the Tao Te Ching." I'm also an engineer - good at math and science. Booth ways of knowing are important to me and are central to my understanding of reality. Many people are tempted to mix the two. That almost always results in crap.

I can respect that.