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=== Full and partial === An important dispute in formal epistemology concerns the question of whether beliefs should be conceptualized as full beliefs or as partial beliefs. Full beliefs are all-or-nothing attitudes: either one has a belief in a proposition or one does not. This conception is sufficient to understand many belief ascriptions found in everyday language: for example, Pedro's belief that the Earth is bigger than the Moon. But some cases involving comparisons between beliefs are not easily captured through full beliefs alone: for example, that Pedro's belief that the Earth is bigger than the Moon is more certain than his belief that the Earth is bigger than Venus. Such cases are most naturally analyzed in terms of partial beliefs involving degrees of belief, so-called credences. The higher the degree of a belief, the more certain the believer is that the believed proposition is true. This is usually formalized by numbers between 0 and 1: a degree of 1 represents an absolutely certain belief, a belief of 0 corresponds to an absolutely certain disbelief and all the numbers in between correspond to intermediate degrees of certainty. In the Bayesian approach, these degrees are interpreted as subjective probabilities: e.g. a belief of degree 0.9 that it will rain tomorrow means that the agent thinks that the probability of rain tomorrow is 90%. Bayesianism uses this relation between beliefs and probability to define the norms of rationality in terms of the laws of probability. This includes both synchronic laws about what one should believe at any moment and diachronic laws about how one should revise one's beliefs upon receiving new evidence. The central question in the dispute between full and partial beliefs is whether these two types are really distinct types or whether one type can be explained in terms of the other. One answer to this question is called the Lockean thesis. It states that partial beliefs are basic and that full beliefs are to be conceived as partial beliefs above a certain threshold: for example, every belief above 0.9 is a full belief. Defenders of a primitive notion of full belief, on the other hand, have tried to explain partial beliefs as full beliefs about probabilities. On this view, having a partial belief of degree 0.9 that it will rain tomorrow is the same as having a full belief that the probability of rain tomorrow is 90%. Another approach circumvents the notion of probability altogether and replaces degrees of belief with degrees of disposition to revise one's full belief. From this perspective, both a belief of degree 0.6 and a belief of degree 0.9 may be seen as full beliefs. The difference between them is that the former belief can readily be changed upon receiving new evidence while the latter is more stable.

=== Belief-in and belief-that === Traditionally, philosophers have mainly focused in their inquiries concerning belief on the notion of belief-that. Belief-that can be characterized as a propositional attitude to a claim which is either true or false. Belief-in, on the other hand, is more closely related to notions like trust or faith in that it refers usually to an attitude to persons. Belief-in plays a central role in many religious traditions in which belief in God is one of the central virtues of their followers. The difference between belief-in and belief-that is sometimes blurry since various expressions using the term "belief in" seem to be translatable into corresponding expressions using the term "belief that" instead. For example, a belief in fairies may be said to be a belief that fairies exist. In this sense, belief-in is often used when the entity is not real, or its existence is in doubt. Typical examples would include: "he believes in witches and ghosts" or "many children believe in Santa Claus" or "I believe in a deity". Not all usages of belief-in concern the existence of something: some are commendatory in that they express a positive attitude towards their object. It has been suggested that these cases can also be accounted for in terms of belief-that. For example, a belief in marriage could be translated as a belief that marriage is good. Belief-in is used in a similar sense when expressing self-confidence or faith in one's self or one's abilities. Defenders of a reductive account of belief-in have used this line of thought to argue that belief in God can be analyzed in a similar way: e.g. that it amounts to a belief that God exists with his characteristic attributes, like omniscience and omnipotence. Opponents of this account often concede that belief-in may entail various forms of belief-that, but that there are additional aspects to belief-in that are not reducible to belief-that. For example, a belief in an ideal may involve the belief that this ideal is something good, but it additionally involves a positive evaluative attitude toward this ideal that goes beyond a mere propositional attitude. Applied to the belief in God, opponents of the reductive approach may hold that a belief that God exists may be a necessary pre-condition for belief in God, but that it is not sufficient.

=== De dicto and de re ===