Notional Attitudes 
(On Wishing, Seeking and Finding)*

Marie Duží

Resume.	Our knowledge, beliefs, doubts, etc., concern primarily logical constructions of propositions. If we assume that iterating ‘belief attitudes’ is valid, i.e., that the agent is perfectly introspective, he knows what he knows, believes, etc., then the so-called propositional attitudes are actually hyperintensional attitudes, i.e., they are relations of an agent to the construction–concept (of a proposition) expressed by the embedded clause. Their implicit counterparts, relations of an agent to the proposition denoted by the embedded clause, are just idealised cases of an agent with unlimited inferential abilities. 
On the other hand, our wishes, intentions, seeking, (attempts at) finding, etc., concern (in empirical cases) particular intensions (offices, properties, propositions), and the so-called notional attitudes (to empirical notions) are (despite calling them notional) not hyperintensional. In the paper we formulate some criteria for notional attitudes and examine basic categories of them. In general, notional attitudes are relations-in-intension between an agent and an object to which the agent is intentionally related. Even relations of an agent to a proposition can be notional ones, in case there is no salient constructional counterpart, the attitude is not influenced by agent’s inferential abilities. Another problem we meet is the ambiguity of sentences expressing notional attitudes. These statements can often be read both in the de dicto and in the de re way. Yet, a common feature that characterizes notional attitudes is using the construction of the respective intension in the de dicto way. The respective intension is mentioned; referring on such a situation, the reporter may use any of the equivalent constructions (concepts) of the intension, but not just a co-referring notion of another intension. Still, unlike the cases of relations of an agent to an individual when the respective individual office serves just as a pointer to the individual, when referring on notional attitudes the use of the respective notion of the intension is indispensable, which might perhaps justify calling such attitudes notional, though they actually are intensional. We also show that a passive form of a sentence cannot be usually read in the de dicto way (unless an idiom is used). Thus a common belief at the equivalence of the active and passive form of a statement is generally not justified.

Key words: Propositional / notional attitudes, hyper-intensions, de dicto / de re supposition, passive vs. active form.

1. Introduction
	Some expressions are ”sensitive” not only to the denotation of a related expression E but also to the logical structure, or more precisely to the meaning of E, in such a way that substitution salva veritate of an L-equivalent expression E’ denoting the same intension (/extension) fails. Such sensitive expressions are, e.g., some attitude verbs, like knowing, believing, counting,…, but also anaphora pronouns [17], etc., and the respective (indirect ”oblique”) contexts are called hyper-intensional [4], [32]. The problem has been noticed already by G. Frege who realized that his standard semantic scheme fails in indirect contexts, which led him to contextualistic solution (reference in ”normal” contexts and sense in indirect contexts). Moreover, Frege’s conception had been extensionalistic, and the notion of a sense had not been explicated and thus logically tractable.
	Due to the above sensitivity to a meaning (logical structure) of the embedded clause, the analysis of propositional attitudes has become a stumbling block for all the denotational semantic theories that take into account just the denoted entity. Since Frege’s times, many logicians strove after logically handling structured meanings, to name at least Russell’s  structured propositions, Carnap’s attempts at the formulation of a stronger criterion for the identity of belief, i.e. intensional isomorphism between substituted expressions, Cresswell’s tuples, etc., etc. Still, none of these attempts carries conviction of a full adequacy and correctness.
Pavel Tichý, the author of Transparent Intensional Logic (TIL), and Pavel Materna, its main protagonist, have presented a fundamental revision of Frege’s semantic scheme, which makes it possible to adequately explicate the ”behaviour” of expressions even in hyper-intensional contexts. Tichý’s solution respects the distinction between the meaning (sense) of an expression and the object denoted by the expression; but it differs from most current conceptions (incl. Montague’s [25]) in at least two points:
a)	it logically handles the hyperintensional structure of the meaning, sense is explicated as a hyperintensional entity (construction)
b)	No contextualism is present; expressions simply denote (either an intension / or an extension) via its sense. Empirical expressions denote always intensions, and where it seems that they denote extensions they only possess de re supposition.
Before presenting our main results applying TIL on the problem of notional attitudes, we first very briefly recapitulate TIL philosophy, and its main notions and definitions.
2. Transparent Intensional Logic.
In contrast to standard formal theory, which starts with a naked syntax and only subsequently proceeds to a semantic interpretation in a model, TIL is ‘transparent’ not only that it is anti-contextualistic but also not formalistic. Notion of a naked formal expression as a pure graphic shape can be arrived at only through abstracting its sense from it. In terms of conceptual priority, TIL starts with sense-endowed expressions, which is to say that the ”formal language” of TIL-constructions constitutes an ”interpreted formalism”. Every factor that is semantically salient is explicitly present in the respective formalism. This is evident, for instance, in the explicit typing of the theory, the types of TIL being exclusively objectual. So what qualifies the ”formal language” of TIL as transparent, inherently interpreted, is that a naked shape can be introduced as an expression only if it is paired off with a construction constructing an object of a particular type.
Definition 1 (Simple types of order 1):
(An objectual) base is a collection of mutually disjoint nonempty sets. 
i)	Every member of the base is a type over base.
ii)	Let a, b1,..., bm  be types over base, then (a b1... bm), i.e. the set of all m-ary (total and partial) functions with an argument (a tuple) áb1,...,bmñ, where bi  (1  i  m) is a member of the type bi, and at most one value of type a, is a type over base.
iii)	Nothing is a type over base unless it so follows from i) - ii).
An object O (that is a member) of a type  is called an -object, denoted O/.
According to Zalta ([30]), Russellian propositions play the desired role of complexes that result by ”plugging” objects into the gaps of properties and relations. In our opinion, properties, relations, i.e. functions in general, have no ”gaps”; particular objects simply are members of (the arguments of) these flat functions. But we can accept the possible-world semantics of propositions, while the demand of structured meanings is met by another entity: Between an expression and the denoted flat object there is a structured mode of presentation (construction in our terminology) of the object, i.e. meaning (perhaps the Fregean sense) of the expression. It is a complex, a procedure that consists in a creation of a function by abstracting over objects and/or in applying the function to its arguments. But particular (physical/abstract) objects cannot be ”plugged” into such a (conceptual) procedure; they must always be presented in an (albeit primitive) way, i.e., their concepts are constituents of the procedure. There are two such primitive modes of presentations that fill in the objects into the construction: variables and trivialisations. The other two kinds of constructions working over these ones are more complex; they are closure (creating a function by abstraction) and composition (applying a function to an argument).
TIL language of constructions can be viewed as a typed -calculus whose terms are names of (denote) constructions. Due to the perfect “isomorphism” between terms and constructions it is idle to mention the terms, and we transparently talk about the constructions. Thus, e.g., instead of claiming that ‘x [0> x 00]’ denotes the construction x [0> x 00] which constructs the class of positive numbers, we simply say x [0> x 00] is the construction.
Definition 2 (Constructions):
i)	Variables are constructions. Variables and constructions involving variables construct objects dependently on a valuation v, they v-construct.
ii)	If X is an entity whatsoever, even a construction, then 0X is a construction called trivialisation. Trivialisation 0X constructs X without any change. 
iii)	If X0 is a construction that v-constructs a function (mapping) F, i.e. an (a b1...bn)-object, and X1,...,Xn are constructions that v-construct b1-,...,bn-objects b1,...,bn, respectively, then [X0 X1 ... Xn] is a construction called composition. If F is defined on the argument áb1,...,bnñ, then composition [X0 X1...Xn] v-constructs the value of F on áb1,...,bnñ; otherwise it does not construct anything, it is v-improper.
iv)	Let x1,...,xn be pair-wise distinct variables that range over types b1,...,bn, and let X be a construction that v-constructs an a-object for some type . Then [lx1...xn X] is a construction called closure (abstraction). It v-constructs the following function F (of the type ( 1…n) ): Let v´ be a valuation that differs from v at most by assigning objects b1,...,bn (of the respective types) to variables x1,…,xn, respectively. Then the value of the function F on the argument áb1,...,bnñ is the object  v´-constructed by X. If X is v´-improper, then F is undefined on the given argument. 
v)	Nothing is a construction unless it so follows from i) - iv).
Notes: 
1.	The simplest constructions are variables; they are open constructions that construct objects dependently on valuation (they v-construct). They are no letters, characters, ‘x’, ‘y’, ‘z’, ... are names of variables.
2.	Trivialisation consists in grasping an object and its ”delivering” without any change. If X is an entity, then 0X is a presentation of X without a ”perspective”. The term ‘0X’ might be likened to a constant of a formal language. But unlike such a formal constant symbol, which can be interpreted in many ways so as to denote different entities and thus actually not being a constant but a ”variable construction”, ‘0X’ rigidly denotes construction 0X that constantly constructs X. A possible objection against such a conception might be: Well, your transparent approach is punctilious, but you lose the expressive power of model theories that enable us to examine common features of properties, relations and functions in particular models. Our answer is: Not at all; TIL transparent approach is more precise without losing anything; due to the infinite hierarchy of types we have at our disposal variables ranging over objects of any level, which makes it possible to render particular ”models” by valuations of (higher-level) variables.
3.	A composition corresponds to the traditional operation of application (of a function to an argument). (Only) composition may fail to construct anything, it may be (v-)improper, namely in two cases: First, the component X0  constructs a function F and components X1,...,Xn construct áb1,...,bnñ, but F is not defined on this argument. Second, some of the components X0, X1,...,Xn fail to construct an object (are v-improper). 
	(In case X1,...,Xn  do not construct objects of proper types to create an argument of F, the expression ‘[X0 X1 ... Xn]’ does not denote a construction.)
4.	Closure (l-abstraction) enables us to construct a function, and thus to analyse talking about the whole function (to ”mention” it), not only talking about a particular value on a given argument (to ”use” the function). Closure can never be improper, even if it constructs a (degenerated) function that is undefined on all its argument, like, e.g., x[0: x 00].
5.	Tichý’s definition of constructions comprises also single and double execution. We sometimes also adjust the definition by adding tuple and projection constructions. Since there is no need for them in this paper, we do not introduce these constructions.
Quantifiers - general  and existential $ - are functional objects of type (o(oa)). We will write xA, xA instead of [0a lx A], [0$a lx A], respectively. Quantifiers are ”totalising”, i.e. they always return a truth value when being applied to a class (even if the characteristic function of the class were undefined on some arguments), namely [0a lx A] returns True iff [lx A] constructs the whole type  (A constructs True for all x ranging over ), otherwise False, [0$a lx A] constructs True iff [lx A] constructs a non-empty subset of  (A constructs True for some x), otherwise False. Singulariser a is an object of type (a(oa)),  and instead of [0a lx A] we will use xA (the only x such that A); [0a lx A] constructs the only member of the class constructed by [lx A] iff [lx A] constructs a singleton, otherwise it is an improper construction. We will use a standard infix notation without trivialisation in case of using truth-value functions (, , …), less-than, greater-than and identity functions (, , =, …), but we have to keep in mind that these are just abbreviations that conceal the self-contained meaning of the respective ”logical symbols”. When a construction C constructs an object of type , we will often write C  .
	The bridge between an expression and a construction (logical analysis of the expression) is provided by a principle of subject-matter, which says, roughly, that an expression is about all and only those objects, incl. constructions, which receive mention in the expression (see [13]). Constructions are mentioned, e.g., in hyper-intensional contexts where the meaning, i.e. the expressed construction plays a crucial role. Thus a construction/meaning is a ”full-right entity” to talk about, and has to be of a definite (higher-order) type, which is not possible within the simple hierarchy of types.
Definition 3 (Ramified hierarchy of types)
Let B be an objectual base, i.e. a collection of mutually disjoint non-empty sets.
1. Types of order 1  
	Defined according to Definition 1.
2. Constructions of order n 	
(Cni)	Let a be a type of order n over B. If x is a variable that ranges over , then x is a construction of order n over B.
(Cnii)	If X is a member of a type of order n, then 0X is a construction of order n over B. 
(Cniii)	If X0, X1,..., Xm  are constructions of order n over B, then [X0 X1...Xm] is a construction of order n over B.
(Cniv)	If distinct variables x1, ..., xm, as well as X, are constructions of order n over B, then [lx1...xmX] is a construction of order n over B.
Let *n  be the collection of all constructions of order n over B. Types of order n+1 over B are defined as follow:
3. Types of order n+1
(Tn+1i)	 *n  and all the types of order n are types of order n+1 over B.
(Tn+1ii)	If a, b1, ..., bm are types of order n+1, then the set (a b1...bm) of all m-ary (total and partial) functions from b1 x... x bm to a is also a type of order n+1 over B.
(Tn+1iii)	Nothing is a type of order n+1 over B  unless it so follows from (Tn+1i) a (Tn+1ii).
	An objectual base is a special kind of base, over which (an infinite) hierarchy of functions and constructions can be built up, and our conceptual scheme can be adequately modelled within this system. This base consists of sets of objects of four basic categories: i, o, w, t, where i is a type (set) of individuals. The objectual base together with the interpretation of other elements constitutes an epistemic frame. Interpretation of its other elements is as follows: o is the type (set) of truth-values {T, F}; w is the type (set) of possible worlds, and t is the type (set) of time points (or real numbers). The collection of pre-theoretically given (basic) features (traits), using which all the other notions are defined, constitutes the intensional base of the given system.
Empirical expressions denote intensions, i.e. functions from possible worlds to chronologies of members of a type . Hence -intensions are functions of type (at)w), which will be abbreviated by atw. We will standardly use variable w as ranging over , and variable t as ranging over . If X is a construction that constructs an intension of type atw, then instead of [[Xw]t] we will write Xwt. 
Examples of intensions: 
Individual concepts (offices) are objects of type itw, properties of individuals are objects of type (oi)tw, binary relations-in-intensions between individuals are objects of type (oii)tw, propositions are objects of type otw. 
Since the terminology in the area of logical analysis of natural language is vague and ambiguous, we exploit the results of Tichý’s followers, as they have been presented, e.g., by Materna in [22], [23]. Just a brief summary: An expression expresses its sense (=meaning) that identifies (non-fregean) denotation. Hence an expression denotes (talks about) its denotation via its meaning-sense. The sense of an expression is in principle a structured ”procedure” – a closed construction (the concept specified by the expression). A construction identifies (constructs) the denoted object that is (in case of a ”successful” constructing, i.e. construction not being improper) either an intension or an extension (a first-order, set-theoretical object), or even a higher-order object (involving a construction). Empirical expressions always denote an intension, and in this case we also speak about a referent or reference of an expression, which is the value of the denoted intension in a given world/time. The relation between the first-order object (intension) and that what is in most semantic theories considered to be a reference of an expression (for instance an individual in space and time, a set of individuals, etc.) does not have a semantic character; it is influenced by an empirical factor – state of affairs, and thus it is not directly a subject of a semantic-theory investigation. Hence a co-reference of expressions is from the TIL viewpoint a contingent, empirical matter. Expressions can be equivalent when they denote one and the same object, but do not have (even in this case) to have the same sense, i.e. do not have to be synonymous. 

3. Propositional attitudes.
The problem of propositional attitudes has been a subject of much dispute in this journal, and we can claim that an adequate solution has been proposed. In general, propositional attitudes are expressed by verbs like to believe, to think that, to know, to doubt, etc., and they are relations-in-intension between an individual and the structured meaning of the embedded clause, viz. a construction, i.e. they are objects of type (*n). In belief contexts we are thus dealing with attitudes to constructions that construct propositions (or truth values in mathematics); hence they are attitudes to propositional constructions, and what has been called ”propositional attitudes” are just constructional attitudes to propositional constructions. If we assume that iterated attitudes are valid, i.e. that the agent is perfectly introspective, he knows what he knows, believes, etc, then what is known, believed, etc. concerns primarily meaning, i.e. concept, construction. This solution provides an adequate explication of the substitution failure in belief contexts and does not lead to the paradox of (mathematical/logical) omniscience. The fact that the following argument is obviously not valid: 	Charles knows that Bratislava has 500 000 inhabitants
500 000 = 25x56					
Charles knows that Bratislava has 25x56 inhabitants
is explained away. This argument uses a rule scheme of the form:
	[0Bwt  0X  0C1]
	[0=   C1 C2]
(R)	–––––––––––
[0Bwt  0X  0C2],
where B is an (propositional) attitude and C1, C2 are any constructions. Such a rule is not correct, because the second premise states only an equivalence of constructions (the identity of the constructed objects), but not the identity of the constructions themselves. The rule would be correct if constructions C1 and C2  not only constructed the same object but were also identical, i.e. the second premise would have to be:
	[0=   0C1 0C2].
It means that if the agent X has an attitude to a construction expressed by a sentence p, it does not mean that X has this attitude also to sentences that express logical consequences of the sentence p (they logically follow from p). This is due to the fact that X may have limited inferential abilities. Hence if the agent knows that 5 + 7 = 12, then he does not have to know all the mathematical truths; or, if he knows, e.g., the axioms of arithmetic, he does not have to know all the (provable) truths of arithmetic. Otherwise we would have to suppose that the language user is a logical and mathematical genius, that if he knows any mathematical truth then he knows also all its logical consequences, all the truths. This would not be in accordance with our intuitions and with the ”principle of Non-omniscience”. 
	On the other hand, however, the demand of the identity of constructions seems to be very restrictive. Identical constructions have to construct the same, but not only that; they must also be ”built up” from the very same constituents, subconstructions, in the very same way. Thus Charles’ believing that A and B would not lead to his believing that B and A, because 0[A  B]  0[B  A]. Actually, this solution deprives the agent of any inferential abilities. 
	We might eliminate this restrictiveness by conceiving attitudes to empirical embedded clauses as ”implicitly” relating the agent to propositions denoted by these clauses (to states-of-affairs). This would, however, mean that only two non-realistic (idealised) types of a language user are considered: either a logical and mathematical idiot (the former case), or a perfect language user who is a logical and mathematical genius (the latter case), and in this restricted sense omniscient [10]. Thus an ‘explicit’ propositional attitude would be distinguished from an ‘implicit’ (or ‘unconscious’) one [14]. Restrictive consequences of the constructional approach are reduced: in case of attitudes to empirical clauses we take into account also agent’s relation to the denoted states-of-affairs (type ()), not only to their constructions (type (*1)). The relation of an implicit propositional attitude is thus closed under the relation of logical consequence (the agent is in a way ”analytically” omniscient – if he, for instance, knows that p, then he also knows all the logical consequences of p, though he does not have to be aware of it, to know it ”explicitly”, i.e. to know all the constructions that identify p).

4. Notional attitudes.
	We have seen that when knowing, believing, doubting, etc., something – some proposition P, the agent is related to the proposition P only via the meaning of the respective clause C denoting P, and the substitution salva veritate of an equivalent clause C’ denoting the same proposition P may fail, because the agent is not able to perform the respective inference (logical and / or mathematical operation) on the meaning of C. 
	When analysing notional attitudes, we ask a similar question, namely to which kind of object is the agent related? And trying to answer this question, the substitution test should always justify the answer. But in this case there is another preliminary, more fundamental question: 
Which attitudes should be, in general, called notional ones? 
At first sight, the answer might seem to be simple. Well, these are attitudes to some notion, i.e. concept, but not a concept (i.e. construction) of a proposition. We will show that the answer is not as simple, and actually, since we doubt that an exhaustive answer can be given, in this brief study we just formulate some criteria and categories of notional attitudes. 
a) Attitudes to mathematical notions.
Consider the sentence 
(1)	Charles calculates 2 + 5.
To which object is Charles related? It cannot be the denotation of 2 + 5, for Charles does not calculate 7. It cannot be the respective expression ‘2 + 5’ as well (as might sententialists claim), because Charles can calculate 2 + 5 when being at the age of 5 (not knowing any such expression, or even a term of a formal language) and playing with the balls of an abacus. He is related to the respective construction, trying to perform the procedure and to find out, which object (number) is thus constructed. (Of course, we can describe the agent’s activity using sentence (1), which does not, however, mean that he was related to an expression.) Hence Calc(ulating) is an object of type (  *1) and the analysis of (1) is:
(1’)	wt [0Calcwt 0Ch 0[0+ 02 05]]	(Trivialisation of [0+ 02 05] is indispensable)
A similar way of reasoning can be used when analysing the sentence
(2)	Charles is thinking of the greatest prime. 
Since there is no greatest prime, Charles cannot be thinking of the denotation of this expression, he is related to the meaning of it (he is probably trying to find out whether the respective concept is empty, i.e., whether it does, or does not identify any number). Hence Th(inking) is here again an object of type (  *1). To analyse the sentence, we have to realise that the meaning of the simple expression ‘prime’ is the concept of the class of prime numbers, which cannot be just 0prime. This expression has been introduced to the mathematical language by a linguistic definition as an abbreviation:
Prime (numbers) =df  The class of natural numbers that have exactly two factors.
The respective concept is ( N(atural) / (), D(ivisible by) / (), Card / () ):
	x ([0Nat x]  ([0Card y [0Nat y]  [0D x y]] = 02))
Abbreviating, for the sake of simplicity, this concept by Prime, we get the analysis of (2):
(2’)	wt [ 0Thwt 0Ch 0[z ([Prime z]  z’([Prime z’]  (z  z’)))] ].
Generalising, we can claim that attitudes to mathematical notions are objects of type (*n), n being mostly equal to 1.
b) Attitudes to empirical notions.
	In this case the situation is rather more complicated, and we will show that in empirical contexts these attitudes are generally not hyper-intensional. First, simple relations 
(-in-intension) of an individual to another individual (of type ()), like, e.g., kicking, being in love, touching, talking to, etc., should not be considered as falling under the category of notional attitudes. For instance, in the following sentence 
(3)	Charles is talking to the Mayor of Dunedin
‘talking’ denotes a relation-in-intension of an individual to an individual – T(alk) / (), though no particular individual is mentioned in (3). The office MD /  of the Mayor of Dunedin serves only as a ‘pointer’ to the unspecified individual, and its construction (composed of the constructions of M(ayor) / () and D(unedin) / ) occurs de re. 
(3’)	wt [0Twt 0Ch [w*t* [0Mw*t* 0D]]wt ].
The two de re principles, i.e. the principle of existential presupposition and the principle of inter-substitutivity of coreferential expressions are valid. The Mayor of Dunedin has to exist, so as the sentence had any truth-value (existential presupposition), and the substitution salva veritate of a co-referential expression is possible. If Mr X is the Mayor, then Charles is talking to Mr X:
(S)	wt [0Twt 0Ch [w*t* [0Mw*t* 0D]]wt ]
wt ([w*t* [0Mw*t* 0D]]wt = 0X)
 wt [0Twt 0Ch 0X]
It may even be the case that Charles is talking to Mr X without knowing that this person is the Mayor of Dunedin (occupies the office), yet we may report on such a situation with perfect truth using (3). Hence, describing such a situation, the notion of the respective office is dispensable and (3) should not be considered as an example of a notional attitude, because Charles’ attitude of talking is related to Mr. X, an individual, not to the respective office (the notion of which is thus dispensable).
Consider, on the other hand, the sentence
(4)	Charles would like to talk to the Mayor of Dunedin.
Here we meet the problem of an ambiguity, which is often the case of (notional) attitude verbs. The sentence (4) may inform on situation similar to the case (3), Charles would simply like to talk to Mr X without any concern in his office, and the reporter just uses this office as a pointer to Mr X. Hence ‘would like to talk’ denotes an object of type (), and it is not the case of a notional attitude. But there is another, more interesting, and may be more adequate reading of (4). Our Charles may be discontent with public relations in the city of Dunedin, and he demands to meet and talk to the Mayor, not having any idea whoever he is, or even if there is one at all. Neglecting for a moment the meaning of ‘would like’, and denoting WLT / (  ) the object denoted by ‘would like to talk’, we get:
(4’)	wt [0WLTwt 0Ch [w*t* [0Mw*t* 0D]] ].
This time the construction of the office MD, namely [w*t* [0Mw*t* 0D]], occurs de dicto, the substitution argument (S) cannot be applied, i.e., we cannot deduce that Charles intends to talk to Mr X. It may even happen that the Mayer of Dunedin does not exist (there is no Mr X holding the office), and yet (4) may be true. There is no existential commitment here.
Hence the agent is related to the office itself, and reporting on such a situation the respective notion of the office is indispensable. In our opinion, such an attitude should be classified as a notional attitude (to the office of the Mayor). Still, a question arises: Should such an attitude not be analysed in a way analogous to propositional attitudes, that is, as a relation of the agent to the respective concept, i.e. construction of the office? We do not think so. Unlike knowledge, belief, doubting, etc., which concern primarily the mode in which the respective proposition is presented to the agent (whose deductive abilities, inferences, etc., i.e. in general agent’s knowledge, are strongly related to (depend on) the respective construction), intentional activities of the agent are primarily related to the office itself, regardless the way in which the office is reported to. If Charles intends to talk to the Pope, then he intends to talk to the Head of Roman Catholic Church, and vice versa. Even if Charles were an ignorant not knowing that the Pope and the Head of Roman Catholic Church are one and the same office, and demanded meeting the Pope, the speaker might truly report on the situation using the ‘Head of Roman Catholic Church’.
Anyway, we have to return to the analysis of (4). The proposed analysis (4’) is not the best one; it does not follow ‘Parmenides Principle’ of subject matter. Well, its constituents are concepts of those objects the sentence (4) talks about, and only of them, but not of all of them. We have to take into account semantically self-contained subexpressions ‘would like to’ and ‘talk to’, and construct the WLT object by composing their denotations. First, ‘talk to’ has to denote an object T / (), a relation of an individual to an individual (we cannot, of course, talk to an office). Second, construction of the office MD, namely [w*t* [0Mw*t* 0D]], still has to occur de dicto, as explained above. How can we overcome this discrepancy? There are two ways out; We can construct the property of talking to the Mayor of Dunedin
wt x [0Twt x [w*t* [0Mw*t* 0D]]wt ],
and analyse the sentence as claiming that Charles would like to obtain this property. Hence ‘would like’ denotes an object WL / (  ()) :
(4’’)	wt [0WLwt 0Ch [wt x [0Twt x [w*t* [0Mw*t* 0D]]wt ]] ]
Another possibility might be as follows (WL’ / (  ) : )
(4’’’)	wt [0WL’wt 0Ch [wt [0Twt 0Ch [w*t* [0Mw*t* 0D]]wt ]]) ] ],
which can be read as Charles would like (wishes that) he would talk to the Mayor of Dunedin. He has a relation to the respective proposition, namely of wishing that the proposition were (would be) true.
The latter is, however, rather free reformulation of the original sentence. (It means that the situation is such that he will probably not talk but he wishes that he would talk.) Still, the analysis using WL’  would be necessary when analysing sentences mentioning two agents, like:
Charles would like (wishes) that Peter would talk to the Mayor of Dunedin.
	wt [0WL’wt 0Ch wt [0Twt 0Peter [w*t* [0Mw*t* 0D]]wt ]]) ].
There is a question now whether WL’ should be characterised as an (implicit) propositional attitude, or as a notional attitude to a proposition (of wishing the proposition to be true). Unlike explicit propositional attitudes (of knowing, believing, ...), agent’s intentions, wishes, etc., are not sensitive to the way in which the proposition is reported to and these attitudes are closed under the relation of the logical consequence. If Charles wishes the above, then he, for instance, also wishes that there is somebody whom he would like Peter to talk to (we have to use a variable c ranging over offices , to obtain a correct inference):
	wt [0WL’wt 0Ch wt c [0Twt 0Peter cwt]) ].
Note that both (4’’) and (4’’’) meet the demand of de dicto supposition of the (concept of) Mayor of Dunedin – [w*t* [0Mw*t* 0D]], because both the (construction of) property of talking to the Mayor and the (construction of) proposition that Charles talks (will talk) to the Mayor are de dicto, which can be easily checked by performing respective -equivalent transformations (”renaming” -bound variables, see [12]):
(4’’)		wt [0WLwt 0Ch [w1t1 x [0Tw1t1 x [w*t* [0Mw*t* 0D]]w1t1 ] ] ]
(4’’’)		wt [0WL’wt 0Ch [w1t1 [0Tw1t1 0Ch [w*t* [0Mw*t* 0D]]w1t1 ]]) ] ],
from which we obtain (performing i-equivalent reduction, see [12]):
(4’’)	wt [0WLwt 0Ch [w1t1 x [0Tw1t1 x [0Mw1t1 0D] ] ] ]
(4’’’)	wt [0WL’wt 0Ch [w1t [0Tw1t1 0Ch [0Mw1t1 0D]]]) ] ]
The concept of the Mayor, i.e. [w*t* [0Mw*t* 0D]] is not composed with (”applied to”) the left-most w,t-pair (”reporter’s perspective”). Using WL and T, the relation WLT of Charles to the office MD is defined as 
[0WLTwt 0Ch [w*t* [0Mw*t* 0D]]  [0WLwt 0Ch [wt x [0Twt x [w*t* [0Mw*t* 0D]]wt] ] ], 
and using WL’ and T, we have
[0WL’Twt 0Ch [w*t* [0Mw*t* 0D]]  
			[0WL’wt 0Ch wt [0Twt 0Ch [w*t* [0Mw*t* 0D]]wt ]]) ].
Let us briefly return to the de re reading of our sentence (4). We have seen that on its de re reading ‘would like to talk’ denotes a WLTr object of type (). Thus the de re analysis of (4) is as follows:
(4r’)	wt [0WLTrwt 0Ch [w*t* [0Mw*t* 0D]]wt].
But a more fine-grained analysis has to take into account also the objects denoted by ‘would like’ (WL/WL’) and ‘talk’ (T). We have seen that WL (WL’) is a relation-in-intension to a property (proposition) and combining these together with T results in the de dicto supposition of the construction [w*t* [0Mw*t* 0D]] (concept of the Mayor) both in (4’’) and (4’’’). The way out is now not as easy. We might reformulate the sentence into
(4passive) The Mayor of Dunedin is the man to whom Charles would like to talk to
and denoting by WChT (/()) the property of individuals (‘being wanted by Charles to talk to’), we obtain:
	wt [0WChTwt [w*t* [0Mw*t* 0D]]wt],
which can be read as ‘the mayor of Dunedin has the property WChT’. To construct this property, we can choose WL (or WL’):	wt x [0WLwt 0Ch [wt y [0Twt y x]]]
Using the latter instead of  0WChT, we get:
(4r’’)	wt [ [wt x [0WLwt 0Ch [wt y [0Twt y x]]]]wt [w*t* [0Mw*t* 0D]]wt ], 
or i-reduced
(4r’’)	wt [x [0WLwt 0Ch  [wt y [0Twt y x]]] [0Mwt 0D] ],
which is the correct analysis of the de re reading of the sentence (4).
Remark: Note that the passive form of the sentence (4) cannot be read in the de dicto way. Thus the common belief at the equivalence of the active and passive form of a statement is not justified. The active form usually expresses the de dicto reading, whereas the passive form corresponds to the de re reading. While in case of notional attitudes one might object that even the passive form might be read de dicto (as, e.g., in ‘the doctor was sent for’, where ‘the doctor’ denotes an office / property that is not just a pointer, for the whole expression denotes an attitude of an anonymous agent to the office / property), it is not the case of propositional attitudes, where the passive form is exclusively de re.
We will not deal with the problem of ‘would like’, or generally wishes, intentions, any more, because its detailed solution is out of the scope of this study.
Imagine a similar situation, when 
(5)	Charles would like to marry a princess. 
There are again two readings of (5), namely the de re reading and the de dicto reading. The former, namely there is a (certain) princess that Charles wishes to marry, does not give rise to (notional) attitude to the property of being a princess (Princess / (), M(arry) / ()):
	wt x ( [0Princesswt x]  [0WLwt 0Ch [wt y [0Mwt y x]] ), 
(There is a princess and Charles wishes to obtain the property of being married to her) or alternatively
	wt x ( [0Princesswt x]  [0WL’wt 0Ch [wt [0Mwt 0Ch x]] )
(There is a princess and Charles wishes he were married to her).
The second reading: Charles’ intention concerns primarily the property of being a princess, not a particular princess, and using a similar way of reasoning as above, we get 
(WLM / (  ),  Princess / () ):
(5’)	wt [0WLMwt 0Ch 0Princess],
which is again a typical example of a notional attitude, because the ‘notion’ of the property Princess is indispensable here. A more fine-grained analysis results either in
(5’’)	wt [0WLwt 0Ch [wt y x ( [0Princesswt x]  [0Mwt y x] )	
	(Charles wishes to obtain the property of being married to some princess), or in
(5’’’) 	wt [0WL’wt 0Ch [wt x ( [0Princesswt x]  [0Mwt 0Ch x] )]
	(Charles wishes he were married to some princess).
	Consider another example:
(6)	Charles wants to become the president of USA
	Now there is no de re reading of (6), Charles cannot become George W. Bush; ‘wants to become’ denotes a relation WB of an individual to an individual office, which can be constructed by composing the object W(ant to) / (  ())) and B(ecome) / (  ), and we have again a case of notional attitude (P(resident of USA) / ):
(6’)	wt [0Wwt 0Ch [wt x [0Bwt x 0P]]], 	
0P (president) occurs de dicto, and WB is defined by the equivalence:
	[0WBwt 0Ch 0P]  [0Wwt 0Ch [wt x [0Bwt x 0P]]]
(Note that B(ecome) itself is a typical case of a notional attitude; sentence Charles became the President of USA would be analysed as follows: wt [0Bwt 0Ch 0P].) 
	Summarising, we can characterise expressions like ‘would like to talk to (the) F’, ‘wish to meet (the) F’, ‘try to marry (the) F’, etc., as being ambivalent. On their de dicto reading they denote objects of type (  ) or (  ()), which fall under the category of notional attitudes. There is not an existentional presupposition of the respective sentence (the F does not have to exist) and substitution salva veritate of an expression F’ co-referential to F is not possible. In general, intentions, attempts, wishes, and so like (expressed by the verbs like ‘would like to’, ‘want to’, ‘wish to’, ‘intend to’, ‘try to’, ‘seek to’) are relations (-in-intension) between an individual and an intension, which is either a property of individuals or a proposition. Such relations are (even in the latter case) characterised as the case of notional attitudes, because there is no constructional counterpart of them. 

5. Seeking and finding.
	Attitudes of seeking and finding have been dealt with and analysed using TIL in, e.g., [19], [8], [17]. Since none of these is an exhaustive study on the problem of seeking and finding, and some arguments claimed there are even flawed, our intention is to summarise, complete and in a way correct these results.
	We do not use ‘look for’ or ‘seek’ to talk about going to get something that we know what it is and where it is (at that case we use ‘fetch’ or ‘pick up’). In other words, we cannot seek something (somebody) the identity of which is well known to us. Hence, e.g., Charles can be looking for the author of Waverly, the policeman can be seeking the murderer, etc., if they do not know who the author (the murderer) is, and they are trying to find out who he is, who occupies the respective office. The agent is related to the office, and we have another example of a typical notional attitude:
(7)	Charles is seeking the murderer of X.
Assigning types to semantically self-contained subexpressions: Ch / , S(eek) / (  ), M(urderer) / ( ), X / , we get the analysis
(7’)	wt [0Swt 0Ch wt [0Mwt 0X]]
The concept of the murderer (wt [0Mwt 0X]]) occurs de dicto, there is no existential presupposition, Charles might conduct the search even if Mr.X were not actually murdered, and the substitution salva veritate of a co-referential expression is not allowed; if the gardener is the murderer, it does not follow that Charles is seeking the gardener.
	Still, ‘looking for’ and ‘seeking’ are again homonymous expressions, though. We can easily say that Václav Havel is looking for Dagmar. Does it mean that this search is an object of type (  ), a relation of an individual to an individual? No, it does not. This kind of search is different from the activity of seeking as stipulated above, for the existential question never arises for individuals, and Václav Havel certainly knows exactly which individual Dagmar Havel is. But Václav does not know where Dagmar is, he is trying to locate her, to find the current place of her. Let M be a particular place on the Earth. Letting aside the problem of type of the object M (let it be, for instance, a (continuous) set of 3-D co-ordinates with respect to the centre of Earth – () ) and assigning a type  to M, we can see that this search is again an attitude, this time to the -office. 
More precisely: V(aclav) / , D(agmar) / , L(ook for) / (  ), P(lace of) / ( ):
	wt [0Lwt 0V [wt [0Pwt 0D]] ], 		( [wt [0Pwt 0D]]   )
The sentence (7) is also ambiguous. It might be the case that the identity of the murderer of X is well known, let it be Mr.Y (police announced ”Y, the murderer, is wanted”), and Charles the policeman wants to find the place where Y is concealed:
(7’’) 	wt [0Lwt 0Ch w*t* [0Pw*t* [wt [0Mwt 0X]]w*t* ]]    ([wt [0Mwt 0X]] – de dicto)
Note that though the office of the murderer serves as a pointer to Y, its concept occurs de dicto in (7’’), and there is again no existential presupposition even on this reading of sentence (7). Charles may be trying to find out who the murderer is or where the murderer is (or both), in either cases the office of the murderer can be vacant. Charles may be trying to find or locate the murderer of X even if he does not know whether X had been murdered. Hence sentence (7) never implies that Charles is looking for Y.
	But consider a passive variant of (7)
(7*)	The murderer of X is looked for by Charles.
Now we are tempted to deduce that Mr.Y is looked for by Charles, which is correct. ‘Looking for’ in this passive form means trying to locate (  ) and we have a de re case of the notional attitude:
(7*’) 	wt [x [0Lwt 0Ch w*t* [0Pw*t*  x]] [wt [0Mwt 0X]]wt ]   ([wt [0Mwt 0X]] – de re)
Consider the classic
(8)	Schliemann sought the site of Troy.
	When Schliemann began his activity of search, he did not know whether Troy existed, though he had been pretty convinced of its existence. Hence Troy cannot be analysed as an individual, let it be for the sake of simplicity an office T /  (sought – S / (  ), site of – P / ())
(8’)	wt [0Swt 0Sch [w*t* [0Pw*t* 0Tw*t* ]] ]
Again, both the concept of the site of Troy and that of Troy occur de dicto. If Burbank were the site of Troy, then despite Kaplan Schliemann would not have been seeking Burbank. And even if he happened to come to the very location and stumbled at the ruins of Troy, he would ignore the place until he would have realised the connection between that and the offices. On the other hand, he might have successfully sought the site of Troy without ever standing at the respective place. He might have had an access to some sources which he knew to be truthful, and simply put two and two together and claim which place on the Earth the site of Troy is.
	Summarising, activities of seeking or looking for relate an individual to an office (a -object or - object), and according to the above preliminary characteristics these are notional attitudes of types (  ) or (  ). When we seek something or look for something, we are trying to find an occupant of the office (that does not have to exist, the office may be vacant). 
	Now, the search may be successful, which means that the seeker becomes the finder, the agent finds what he was looking for, or the search may be unsuccessful, the agent may fail in his effort, he does not find it. Hence if Charles were looking for the murderer of X, then one of the two following sentences has to be true and the other false:
(9)	Charles found the murderer of X
(10)	Charles did not find the murderer of X.
The latter may become true in two situations: Either Charles’ competency did not cope up with the murderer, or the murderer did not exist, X had not been murdered. It means that sentences on (intended) finding do not have existential presupposition on the holder of the respective office, and finding cannot relate an individual to an individual but to the office (that had been sought). These are again notional attitudes of types (  ) or (  ). (If there were the existential presupposition and the murderer did not exist, then neither (9) nor (10) had any truth value, Strawson [27].) Of course, if the search has been successful, i.e. (9) is true, then the murderer has to exist (existential commitment).
(9’)	wt [0Fwt 0Ch wt [0Mwt 0X]]
(10’)	wt [0Fwt 0Ch wt [0Mwt 0X]]
F(inding) is here an object of type (  ) and the concept of the murderer 
(wt [0Mwt 0X]]) possesses de dicto supposition. The two de re principles do not hold: In particular, if Mr.Y is the murderer of X, from (9’) it does not follow that Charles found (located) Y. Having performed successful search on the murderer (-office) only entails Charles’ finding out who is the murderer, but not where he is. 
	Similarly, it is true that Schliemann found the site of Troy, but another scenario is thinkable: If Troy did not exist, then it would be true that Schliemann’s search were not successful, i.e. that
(11)	Schliemann did not find the site of Troy
(11’)	wt [0Fwt 0Sch [w*t* [0Pw*t* 0Tw*t* ]] ]		(F / (  )).
	There is, however, another type of finding. Charles, on his way home, may trip over a stone, pick it up, and only on his coming home he finds out that the stone is the most beautiful diamond he has ever seen. We can report on the situation using (12):
(12)	Charles found the most beautiful diamond.
This time Charles is not related to the office of the most beautiful diamond, he did not intend to find it, he did not even look for it. We can see that (12) is ambiguous: it might express a notional attitude to the office of the most beautiful diamond, if Charles were looking for it before (intended finding F of type (  ) as above), or it may express a simple relation to an individual: This time (unintended) finding by chance is an object F’ of type (  ), and we have (MB / ( ()) – most beautiful, D(iamond) / ()):
(12’)	wt [0F’wt 0Ch [wt [0MBwt 0Dwt]]wt ]
We can see that the construction of the most beautiful diamond occurs de re, i.e. the two de re principles hold. In particular, if the most beautiful diamond is Charles’ most favourite stone (that made him rich), then Charles found his most favourite stone that made him rich.
	Sentences on seeking and finding are systematically ambiguous, for ‘seeking’ (‘looking for’) and ‘finding’ are homonymous. The former may denote an object S1/() in case the seeker is trying to find out who occupies the respective office, or an object S2/() in case the seeker is trying to find out where the respective individual (that may even be the occupant of the related office) is. Anyway, both S1 and S2 can be characterised as notional attitudes. On the other hand ‘finding’ may simply express an incidental (chance) finding, in this case it denotes an object F1 of type (  ), which is not a notional attitude. In case that finding (or possibly not finding) has been preceded by a search S1/() or S2/(), then it can be characterised as a notional attitude F2 / () or F3 / (), respectively.
6. Conclusion. 
	Our knowledge, beliefs, doubts, etc. concern primarily constructions. If we assume that iterating such attitudes is valid, i.e., that the agent is perfectly introspective, he knows what he knows, believes, etc., then the so-called propositional attitudes are actually hyperintensional attitudes, i.e. relations of an agent to the construction–concept (of a proposition) expressed by the embedded clause, i.e. they are objects of type (*n). Their implicit counterparts, relations (of type ()) of an agent to the proposition denoted by the embedded clause, are just idealised cases of an agent with unlimited inferential abilities. On the other hand, our wishes, intentions, attempts, etc., concern (in empirical cases) particular intensions (offices, properties, propositions), and the so-called notional attitudes (to empirical notions) are (despite calling them notional) not hyperintensional, they are objects of type (), for any type . Even relations of type () of an agent to a proposition can be notional ones, in case there is no salient constructional counterpart, the attitude is not influenced by agent’s inferential abilities. The respective intension is mentioned, it means that its concept must occur de dicto, and referring on such a situation, the reporter may use any of the equivalent constructions (concepts) of the respective intension. Still, unlike the case of relations of an agent to an individual when the office serves just as a pointer to the individual, when speaking about notional attitudes using the respective notion of the intension is indispensable, which might perhaps justify calling such attitudes notional, though they actually are intensional.
Acknowledgements: I am grateful to Pavel Materna and Björn Jespersen for their valuable comments, which improved the quality of the paper. 

VŠB–Technical University of Ostrava
Department of Computer Science
17. listopadu 15
708 33  Ostrava
Czech Republic

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