The Classical Definition of Knowledge
What does it mean to say that you know something is the case? We might begin by answering this question through the classical definition of knowledge which stems from Plato. It states that a person, A, knows that a proposition, P, holds if and only if the three following conditions are met:
(i) P is true,
(ii) A believes that P is the case, and
(iii) A is justified in believing that P is the case.
That P is true is to be understood in non-relative terms. That is to say, the concept of truth is treated as absolute. The proposition P is either true, or false, but not both at the same time.
The idea is that (i)-(iii) are individually necessary and jointly sufficient to have knowledge. The claim that they are jointly sufficient has been challenged, most famously by Edmund Gettier, but it nevertheless serves as a foundation for discussions about what constitutes knowledge. If something is not the case, then we cannot know that it is the case. If we do not believe something to be the case, then we do not know it, since knowing something (as per clause (ii)) entails that we believe it. Lastly, if we do not have good reasons for the belief that P is the case, then we do not know it either. We would scarcely like lady luck to decide for us whether we know something or not.
This classical definition deals with what can be called propositional knowledge. Propositional knowledge can roughly be likened to knowledge of facts. Propositional knowledge can in other words be distinguished from practical knowledge, for instance. I may know that the Earth is a spheroid in the first sense, whereas I may know how to ride a bike in the second sense. The distinction made in these two scenarios is precisely the one between propositional and non-propositional knowledge.
With these two types of knowledge in mind, we may return to the criteria (i)-(iii) listed above. That A believes that P means, simply put, that the person entertains a proposition and treats it as though it were the case. That the agent is justified in believing that P means that she has good epistemological reasons for entertaining it as though it were the case. Say that A believes the Earth to be spheroid on account of pictures being taken from satellites. This might constitute a good reason for believing this to be so. A picture taken of an equation such as “X + 1 = 3”, however, does not obviously constitute a good reason for believing that X is equal to 2. What would constitute good reason is some level of introspection grounded in some mathematical expertise.
Thus, we may speak of different forms of justification. We might make use of sense data and recordings of the causes of these in order to gain empirical knowledge. In another way, we might use our faculty of reason to justify beliefs about mathematics, language and logic, for example. The justificatory role is, we might say, domain-relative.
Aside from this, a person, A, who stands to review the photographs taken by satellites might be in a good position to believe that the Earth is spheroid. In other words, she is justified to believe this about the Earth’s shape. Imagine a scenario in the future when all technology and scientific knowledge has been wiped out from the face of the Earth. Say, because someone clumsily set off a number of nuclear devices. In this scenario, a person, B, might look as far as her eyes allow her to and still not have good reason to believe that the Earth is spheroid. This means that not only is justification domain-relative, it is also relative to individuals. The person A from our time has good reasons to believe something that the person B in the post-apocalyptic future does not.
What is more, assuming that A and B are similarly inclined to believe things on the basis of adequate evidence, we might find that A believes that the Earth is a spheroid, whereas B does not. This allows us to note that belief is relative to individuals as well. Indeed, I may believe many things you do not, and the reverse holds true as well. This is expected, but not self-evident until an analysis of the concept of belief has been supplied. Here, we may treat it as a subject-relative attitude of treating a possible state-of-affairs as an actual state-of-affairs.
To summarise, we have established that knowledge is (i) true, (ii) justified, (iii) belief. We have distinguished between propositional knowledge – knowledge of facts – and practical knowledge. We concluded that epistemic justification is domain-relative, and that justification is relative to individuals. Belief, as might be expected, is also relative to individuals. For instance, whereas I may believe that my fridge is empty, you might not believe that about my fridge, and vice versa.
 We’ll be making frequent use of variables throughout these sections. They will initially be introduced with some description, but these descriptions will not always accompany them afterwards. You can think of the letters as placeholders for other information. Sometimes (like here) they are shorthand for agents, sometimes for propositions. Sometimes for specific times, and other times they designate places. Variable symbols let us focus on the general form in our explications instead of being unnecessarily confused by the specific substantial things they refer to. They do so by clarifying what kinds of things we are interested in at different argument places without making use of particular instances of these kinds.