Atheism, agnosticism and theism 2: What it is to have a belief

Previous posts in this series: One.

We talk a lot about believing this or that, and about faith and the content of faith, but we are often a little bit vague on what that actually entails and why. Philosophers, however, have a range of senses of “belief”, often shared by psychologists and artificial life researchers. For my purposes, I shall call a belief a conceptual stance. In other words, a belief is a concept (something that can be expressed as a sentence in some well-ordered language) towards which the believer holds some doxastic attitude (that is, accepts or rejects, defends or attacks, justifies or defeats). Shorn of the technical language, a belief is a sentence in your head that you think is true or false or something like that.

So a belief is a three-place predicate: any belief B is believed by a believer A, and has content C. In philosophy we call the content the intension of the belief. We can symbolise this as BA(C). Note that every belief has to be held by a believer. Beliefs do not float around unanchored in the world. This means that when we talk about “theism”, for example, we must restrict what we are talking about to an actual group of people, unless we are exploring a semantic possibility not as yet held by anyone. At some time, there was no monotheism, so it was at best a logical possibility only. Then somebody asserted it (Socrates?) and it became a belief held by actual believers. This will become important when we ask what options we are holding our own doxastic attitudes or stances towards.

What a belief consists in is open to dispute. In the classic Belief, Truth and Knowledge by David Armstrong, he identifies several accounts, including the conscious occurrence view of Hume, the dispositional view of Ryle, among others. He settles, as do I, for a view sometimes called representationalism but which he describes as Frank Ramsey’s view as beliefs are maps by which we steer. I think we can be representationists in this sense even if we also think to have a belief is to have a disposition to act in a particular way (by, for example, giving assent when presented with an idea), so representationalism is more general than the particular story one tells about what goes on in heads and actions.

But the map metaphor can be somewhat misleading. It suggests that our representation is “similar” pictorially to the way the world is as it is being believed. Instead, I would rather use what I call the graph theory of belief. A belief is a coordinate in a graph, a location in a space set up by the contrasts and issues of a certain time and place and group of interlocutors. Let me give an example.

Suppose I say that we have to choose between capitalism (open markets) and communism (closed and centrally controlled markets). That sets up the contrast. If I choose capitalism, which is to say I think capitalism is the best economic system, my belief in effect locates itself at that end of the spectrum:

Capiralism versus Communism

Now that spectrum is a one-dimensional graph, and it can either be discrete (two choices only) or continuous (some proportional mix of control versus free markets. These are the contrasts offered in a discourse. For this reason, this is sometimes also called contrastivism. A contrastivist thinks that any question only makes sense in terms of the contrast space in which it is posed, and that it presupposes a contrast (a notion in linguistics called presuppositionalism).

Now suppose I map that belief against another contrast, say whether society should be democratic or authoritarian:

Democracy and markets

You can see that there is now a field of possible coordinates/beliefs that a believer may hold. If each axis is discrete one might end up with a simple table of choices:

Political choices

However, if the field is continuous, the choices are harder to identify and label, and may end up as clusters rather than exact separate views. And that’s with only two contrasts. Typically such conceptual topics with have many contrasts, leading to an n-space, in which the number of axes/contrasts are higher than we can display simply as a graph. I mentally picture a graphic equaliser on a sound system, where each contrast is a distinct range that we can vary independently of the others. The “coordinate” or belief here is the shape of the “envelope”. If that doesn’t help you, consult your local mathematician.

A joke I heard told of Paul Erdos, but which probably was not originally about him, was when a mathematician was asked how to visualise a tesseract, a four-dimensional cube. “That’s easy,” he replied. “I just visualise a cube, and then I add a dimension.” This explains why mathematicians are never invited to philosophy conferences. So a semantic space is the “territory” in which beliefs are “located”. It can be a rather complex domain, but in this series I shall restrict myself to three dimensions, because I am constitutionally incapable of adding that extra dimension, and because it happens we only need three right now.

We might, for example, visualise the question of theism as a sequence of discrete integers, giving the number of deities from zero [atheism] to infinity. Obviously on that contrast, atheism and monotheism are most closely related than monotheism is, say, to Hinduism. That won’t do, so there must be more in play, but it illustrates the technique.

With this apparatus in play one more point needs to be made now. It is this: knowledge is a species of belief. Philosophers agree on very little but one thing there is (almost?) universal agreement on, it is this: knowledge is some kind of belief. Of course what kind is highly debated. Most agree that knowledge needs to be true belief. We can then get into a debate about what truth is, but not now. Another oft-made claim is that the believer, in order to say they know something, must be justified in believing it. It’s not enough to luck onto a belief that happens to be true; you also need reasons. However, this is still not enough, and epistemologists argue at length why and how to fix it. I shan’t because it doesn’t matter for our purposes.

I will therefore use the following symbolism: If A knows that P, then the claim A makes is KA(P). Roughly, “I, A, know that my belief P is true”. We can substitute quite complex formulae for P, and will later.

I’m going to use a simple version of symbolic logic known as QL, or quantified logic. Those who do not know this, or find it off-putting, can “bleep” over it and read the ordinary language translation I will put alongside it. It’s there so the professionals can see what I am doing (and disagree with me).

So, next we will consider one of these contrast spaces: claims of knowledge regarding gods.

The next post in this series: Three

38 thoughts on “Atheism, agnosticism and theism 2: What it is to have a belief

  1. The interesting thing is that this discussion is actually not only relevant within the philosophy (We actually believe we know nothing). For instance, changing the connotation of knowledge should/would have a radical effect in education. I was taught (about) knowledge, and I learned it as if it was mere truth. I de facto believed it all in the same way others believe in gods and creation myths. However, after dealing with some deal of knowledge I came to realize that doubt is more useful in gaining knowledge than knowledge itself (but both are needed). Maybe learning should be layered with a reasonable amount of doubt, to speed up the global process.

  2. Knowledge is a species of belief only in the trivial sense that we can’t “know” what we disbelieve. I call this trivial because it excludes from knowledge half of its essential nature, which is not merely empirical (confirmation of facts about the world) but also rational (articulation and multiplication of facts about the world–which I take to be Brandon’s point about Locke.)

    Chris Schoen

    I’d question how trivial that is. We don’t have absolute and complete knowledge of any aspect of the universe, our knowledge is inevitably incomplete, the extent of that incompleteness unknown to us. How deep does this “confirmation of facts about the world” and the “rational (articulation and multiplication of facts about the world…)” have to be in order for it to go from belief to knowledge?

    Even arriving at the point where you consider your empirical evidence to be sufficiently complete so as to enable you to classify your ideas as knowledge instead of belief is based in a rather great act of belief, considering the possible extent of what you don’t know.

    I used to think there was a real distinction between what was known and what was believed but I don’t believe that anymore. You can make an heroic effort to get to the point where you are justified in calling what you do “knowing” but not taking into account that you don’t have more than contingent “knowledge” and that anything you “know” is subject to being overturned certainly doesn’t make your “knowledge” more secure, though it might make your assertion of it more aggressive and insistent, your resistance to challenge less flexible to considering the substance of the challenge, which is the only, actual, substance of organized “skepticism”. Sometimes the opponents of organized “skepticism” are far more open to skeptical consideration of their beliefs than the “skeptics”. “Skeptics” seem to be pretty well stuck in the 18th century.

    1. Anthony,

      I don’t think you are construing me correctly. I wouldn’t disagree with you that under a definition that considered knowledge a species of belief it would be a difficult move to justify the exalted status of knowledge over belief, since the method of justification must always be contingent upon a belief in its soundness.

      I am arguing that knowledge is not a species of belief, that it is rather a different, separate, way to look at apprehension. Belief focuses on the aspect of dedication to a proposition, the degree to which we cleave to it. Knowledge focuses on the articulation of a proposition. How it fits in (or doesn’t) with other stories about the world. In this sense knowledge can exist entirely separately from belief. We need merely to be able to coherently describe a set of facts to know them. This is what novelists do, and no one would say novelists don’t know what’s going on in their own books, but neither would they say a novelist believed in her creation’s veridical truth. If a novelist believes in anything at all about her novel, it is that she wrote what she says she wrote. But such a belief has no real bearing on anything, It is trivial, compared to the knowledge itself, which is much greater than a justified true belief that she actually wrote the book.

  3. But all of the actions you use to characterize thinking as “knowing” requires accepting less than certain ideas as part of the process. The real distinction isn’t between two ways of thinking isn’t if it’s believed or known, it’s in how reliable you take the ideas and thinking to be.

    You can try to test and try to achieve higher degrees of reliability, science is a formal attempt to achieve higher degrees of reliability in regard to things which can be observed, measured and analyzed and to place that action within a social context where other people can accept your conclusions or to find problems with them. You can produce ideas that are the best available ways of thinking about some of those things within the contemporary context you happen to be in, as physics did. But as that context changes those ideas and even some of the most basic assumptions they are based on and assumptions they produce will either be modified or abandoned. The people who believed in the assumptions that the most rigorous science of their day certainly felt justified in thinking they knew what those ideas held. We might have other ideas about those things that we are justified in thinking we know, though as time goes on those ideas have a good chance of undergoing basic change. The category of “knowledge”, like all other ideas, are not fixed for all time, it is dependent on the agreement of what that means for our time, without even unanimous agreement today.

    It’s a lot less satisfying in some ways than the assumption of certainty, giving up that assumption on the basis of new information can be really upsetting, as Bertrand Russell apparently was when Eddington pointed out some of the necessary conclusions coming from quantum physics. Russell was quite glum about it, whereas Eddington and other scientists and even philosophers took it in stride. While it would seem to be better to be right than to be certain, the best available to us might be that it’s better to not presume we’re even able to know we’re right than it is to wrongly assume we can be certain of even that.

  4. Anthony,

    I don’t see how any of this engages my point. I don’t disagree with what you say here, inasmuch as you are making an essentially Kuhnian argument.

    My comment is that there is an aspect of knowledge (call it a generative aspect, for now) which is divorced entirely from matters of certainty and confirmation, and that this aspect plays an important role in what we “know.” Because of this, I think it is inaccurate to call knowledge “a species of belief,” since this would leave no room for the creation and articulation of logical and symbolic forms.

    I am not trying to make a point here about the epistemic superiority of knowledge over belief.

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