Last updated on 22 Jun 2018
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:
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:
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:
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