Linguistically, they are denoted by an embedded "that" clause, for example, 'Sally believed that she had won'.
Propositional attitudes have directions of fit: some are meant to reflect the world, others to influence it.
What sort of name shall we give to verbs like 'believe' and 'wish' and so forth? I should be inclined to call them 'propositional verbs'. This is merely a suggested name for convenience, because they are verbs which have the form of relating an object to a proposition. As I have been explaining, that is not what they really do, but it is convenient to call them propositional verbs. Of course you might call them 'attitudes', but I should not like that because it is a psychological term, and although all the instances in our experience are psychological, there is no reason to suppose that all the verbs I am talking of are psychological. There is never any reason to suppose that sort of thing. (Russell 1918, 227).
What a proposition is, is one thing. How we feel about it, or how we regard it, is another. We can accept it, assert it, believe it, command it, contest it, declare it, deny it, doubt it, enjoin it, exclaim it, expect it, imagine it, intend it, know it, observe it, prove it, question it, suggest it, or wish it were so. Different attitudes toward propositions are called propositional attitudes, and they are also discussed under the headings of intentionality and linguistic modality.
Many problematic situations in real life arise from the circumstance that many different propositions in many different modalities are in the air at once. In order to compare propositions of different colors and flavors, as it were, we have no basis for comparison but to examine the underlying propositions themselves. Thus we are brought back to matters of language and logic. Despite the name, propositional attitudes are not regarded as psychological attitudes proper, since the formal disciplines of linguistics and logic are concerned with nothing more concrete than what can be said in general about their formal properties and their patterns of interaction.
One topic of central concern is the relation between the modalities of assertion and belief, perhaps with intention thrown in for good measure. For example, we frequently find ourselves faced with the question of whether a person's assertions conform to his or her beliefs. Discrepancies here can occur for many reasons, but when the departure of assertion from belief is intentional, we usually call that a lie.
Other comparisons of multiple modalities that frequently arise are the relationships between belief and knowledge and the discrepancies that occur among observations, expectations, and intentions. Deviations of observations from expectations are commonly perceived as surprises, phenomena that call for explanations to reduce the shock of amazement. Deviations of observations from intentions are commonly experienced as problems, situations that call for plans of action to reduce the drive of dissatisfaction. Either type of discrepancy forms an impulse to inquiry (Awbrey & Awbrey 1995).
In logic, the formal properties of verbs like assert, believe, command, consider, deny, doubt, hunt, imagine, judge, know, want, wish, and a host of others that involve attitudes or intentions toward propositions are notorious for their recalcitrance to analysis. (Quine 1956).
In Generative linguistics a distinction is made between a semantic role that certain verbs discharge and that arguments receive ('argument' is a syntactic term corresponding to what Russell called an 'object' (in this context a logical, not a grammatical notion), which is sometimes also called an 'entity'), and the syntactic category that they select. For example, a verb like 'believe' discharges two semantic or 'thematic' roles: an AGENT-role and possibly a PROPOSITION-role, the former corresponding to the believer, and the latter corresponding to the proposition that is believed. At the same time, the verb selects syntactic categories - in this case a noun phrase and a sentence. The first theory is called Theta theory, pertaining to thematic roles, and the latter is called subcategorization, pertaining to the way syntactic categories combine. This way, an analysis of propositional verbs (as Russell preferred to call them) becomes possible.
One of the fundamental principles governing identity is that of substitutivity — or, as it might well be called, that of indiscernibility of identicals. It provides that, given a true statement of identity, one of its two terms may be substituted for the other in any true statement and the result will be true. It is easy to find cases contrary to this principle. For example, the statements:
are true; however, replacement of the name 'Giorgione' by the name 'Barbarelli' turns (2) into the falsehood:
(1) Giorgione = Barbarelli, (2) Giorgione was so-called because of his size
(Quine 1980 b, 139).
Barbarelli was so-called because of his size.
(The basis of the paradox here is the term "so" which in the one case refers to the name 'Giorgione' (note: to the name, not to the individual Giorgione) and in the other to the name 'Barbarelli'—such a paradox can be resolved by eliminating the use of pronouns. The reader will also note that Giorgione is an Italian name roughly glossed as "Big George." See also Liar's Paradox.)