We all have beliefs, but not all beliefs are equally worth holding to be true or acting on the basis of. In order to help clarify what is meant by “truth” in various contexts I have divided beliefs into four basic types. Each of these types is a subset of the more general type, for example certain beliefs are a subset of consistent beliefs. So with no further ado here are the four types of belief:
The first type, which I simply call belief- (to distinguish it from the normal usage of the word belief), is simply anything a person can think is true. They can be inconsistent, irrational, and utterly without foundation. For example one morning I woke up and my throat was so try (this is an after the fact analysis) that I believed that I had staples in my mouth. Clearly this was an irrational belief; even so for a moment I felt strongly that it was true. Alien limb syndrome is another example of this type of belief. People suffering from alien limb syndrome are firmly convinced that one of their appendages is in fact not theirs, and will deny that it is theirs even when shown to be connected to their body. Even though it is provably false they nevertheless continue to believe it.
The second type I call consistent beliefs. A consistent belief (or set of beliefs) is when the belief is logically consistent. For example the belief that your dog is both all white and all black is not a consistent belief. In the context of mathematics consistency is generally held to be truth. That is to say that all mathematical statements are proved within a system of axioms, they are true when they are provable from those axioms and false when their negation can be proved. Although for convenience we often refer to the axioms as “true” they too are really just consistent with each other. Some might object to this account of mathematics, saying that mathematics is reflected in the physical world, and thus true or false in a stronger sense. This statement is not exactly accurate though, what is reflected in the physical world is a mathematical structure plus a set of correspondence rules, telling us which physical properties correspond with which mathematical statements, for example Minkowskian geometry’s correspondence with spacetime without gravity. However if later evidence shows that spacetime without gravity is not actually Minkowskian we would not say that Minkowskian geometry has been shown to be false, merely that it does not correspond with the physical world. If you argue that addition is shown to be true because when I stack two rocks on top of two rocks I have four rocks then what happens when I spit some of the rocks into smaller rocks? Have I shown addition to be false?
The third type is certain beliefs. For a belief to be certain there must be evidence supporting that belief, it must be falsifiable, and there must be no falsifying evidence. Most scientific theories fit into the category of certain beliefs, although it is possible that they may be falsified in the future will still feel confident acting on them as if they were absolutely correct. Generally beliefs that are certain are regarded as true for most purposes. An objection to my definition of certain beliefs might be as follows: you feel certain that relativity is generally correct, however you have never run the experiments yourself, so really you have no evidence for or against relativity, therefore you cannot be certain of it. To this I would answer that my evidence for relativity (and lack of refuting evidence) is provided by the writings of professional scientists. Although I haven’t done the experiments myself I have good reason to believe that the reports of these scientists are accurate, just as I have good reason to believe that the reports of the scanning tunneling microscope are accurate. Of course the potential to be falsified is also important for a belief to be certain, and the potential to be falsified can be identified by anyone. Why is falsification important? Well that would be the subject of a much longer paper, and since it is so widely accepted I will not bother to defend it here. Finally note that because of the necessity of evidence the content of a certain belief cannot be epiphenomenal.
Finally we have surety. Surety is the type of belief which cannot be false. For example, I believe that I exist. If you were a direct realist you would also feel that your personal observations were sure. Although your perceptions might be caused by hallucinations they are definitely real hallucinations in the sense that they had an effect on you. Surety is a category of belief that is rarely reached, and thus rarely talked about and rarely relevant; I include it here simply for completeness.
This brings us to an important question: is the standard for philosophical truth consistency or certainty? In my experience it is not one or the other, but depends on the topic that is under discussion and the results one wishes to achieve. For example sometimes an account of a phenomena is given with reference to certain assumptions simply to show that those assumptions do not deny the existence of the phenomena. Such an account is important because of its consistency, even though we are not certain of it. However anytime the content of a philosophical theory is something in the world and not an abstraction then certainty becomes the relevant standard of truth. Unfortunately in a single account the two may be mingled. For example in this very essay the “truth” of my categorization of beliefs is simply a consistency matter. On the other hand my claims about what kind of belief mathematical statements are is a claim that we should judge on the basis of certainty. (If examples could be provided where mathematical statements were judged by standards of certainty instead of standards of consistency then my claim about them would be falsified.) This is the reason why I felt that epiphenomenalism was a good reason to reject certain philosophical claims (again, here), because they purported to talk about aspects of the real world they needed to be judged on a basis of certainty, and I deemed them to be bad theories because they could not meet this standard.