A Framework for Intentions

Intended States of Affairs

Boris Hennig, 10. 10. 1996

Introductory Remarks to Nuel Belnap

(1) You may wonder how a revised version of my paper (Tracing through Worlds, Ms. Leipzig 1. 7. 1996) could be titled 'A Framework for Intentions'. Indeed, as I read my paper once again, I could hardly find anything substantial in it except for the attempt to formulate a de dicto / de re distinction (that Werner Stelzner gives in De Dicto, De Re und Quantifikation in der alethischen Modallogik; Untersuchungen zur Logik und Methodolgie 2, p. 54) in terms of Gupta. In a recent lecture, however, Klaus Jakobi convinced me that there is no use in spelling out this distinction in technical, that is, linguistic terms (Potentialität und Possibilität, unpublished lecture held at the 17th german congress for philosophy, XVII. Deutscher Kongreß für Philosophie, Leipzig 23. - 27. September 1996, Leipzig septembre 25th).
Some of it will appear in my text. The better basis for technical explication seems to be the Abaelardian distinction between the reading of ambiguous sentences secundum conpositionem vs. secundum divisionem.
(Cf. Minio-Paluello p. 13f. No [18].)
Jakobi prepares a more complete edition of the text (Logica ingredientibus III or Super Peri Hermeneias) to be published in the Corpus Christianorum, Continuatio Medievalis. The remaining best approach of a distinction between de dicto and de re modality seems to be the one of Gerard J. Hughes (The Nature of God, London 1994, p. 16f.): The terms shall be understood litterally. So, de dicto modality simply deals with linguistic, de re modality with nonlinguistic entities of all kinds. But I don't want to write too much on these issues here, for neither distinction has to do much with Gupta's book.
The substantial part of my previous paper thus disappeared suddenly and I was admittedly helpless about how to write a philosophical paper in the remaining two weeks. I therefore decided to resort to a sort of Wittgensteinian concept of 'philosophy' as 'lucid presentation' (übersichtliche Darstellung, Philosophical Investigations par. 122f.) and deliberately leave the most questions open. A lucid presentation was indeed the kind of thing my previous paper was not.

(2) Unfinished as the following paper is (for instance, I could not even take into account 'Intention' of G. E. M. Anscombe, Oxford 1959 and 'Intentionality' of J. Searle, Cambridge 1983), rough and fundamental critical remarks will be the most helpful reply to it. Please do not withhold your very own opinioun on the subject; for my 'framework' will previously not be filled within the next 6 months, that will not prevent me from thinking myself.

(3) I wrote this text without any tutorial advice. I can only hope that there is no comlete nonsense in it, as regards the English language or formal logics.

The Purpose of Modal Logics

I felt that the first question in a system of modal logics must be its application. There is obviously no use in debating about the status of possible worlds, unless they can be hoped to solve a particular problem. Aldo Bressan has developed a very complete and multi-purpose calculus in his book, and as a nonphysician I have nothing to add to his book as regards physics. Since it is highly general and can be translated into extensional logics, every calculus based on his is at least legitimate, concerning the technical matter. Besides the admittedly very important concept of physical modality, however, I think there are two generalkinds of intelligible approaches (Cf. Loux p. 259):
The one of Gupta, who attempts to translate pieces of natural language, and others who contribute to an explanation of social and psychological phenomena.
(in N11 of his 'On Gupta's Book The Logic of Common Nouns', Journal of Philosophical Logic 22, 1993 pp. 335-383, Aldo Bressan holds that his calculus is the more general one and therefore more suitable to translate sentences of natural language. This must be admitted, but certain restrictions for some parts of natural language have to be considered, for the user-friendliness of Bressans logic suffers from its generality).
The latter have to deal primarily with other concepts than mass-points or natural numbers. So, they have to model themselves on common-sense notions, but they do not have to follow Gupta's distinction between common nouns and predicates.
Aristotle apparently tried to realign physical modalities with these common sense notions (of his Categoriae) in Metaphysics Z, Cf. Loux 7. III.

The notion of 'intending something' is surely a central and fundamental one in most kinds of social science. Theories of communication, consciousness and agency use it frequently as a basic concept, so that a worthwhile purpose for modal logics might be to provide technical requisites for formulating 'intended states'. It may be helpful to get a certain distance to the natural language, for the question whether it is possible to intend something without being able to describe it in a language is not trivial. Initially, however, it seems rather clear that only states of affairs can be the objects of intentions. Even a description like 'A wants the thing x' appears to be better replaced by 'A wants to have x'. A sentence of the kind 'A intends the thing x' does not seem intelligible -at least not in German. There are several possibilities to argue that this kind of intended entity has a merely 'linguistic' being, for it is precisely the 'content of some (uttered or implicitly accepted) sentence'.
- Anm.: There is an argument in Geach, Logic Matters (Berkeley, Los Angeles 1972, p. 22f. and 259) that there are no states of affairs 'outside' in rebus; Chisholm in two of his articles (Nous 4 and 5, 1971/72)explicates states of affairs as contents of sentences. Something like this can also be found in Abaelards ethics, that is, his distinction between voluntas (as the nonlinguistic content of a will) and intentio (as the linguistic one), see his Ethica seu Liber Scito Teipsum (published by Victor Cousin in Petri Abaelardi Opera, tomus posterior, Paris 1856; likewise the edition of Luscombe, Oxford 1971).
I have elsewhere (Intention und Sprache, Ms. August 7th) tried to support the thesis, that intention without language is not intelligible, but this claim may be too strong. A passage in an article of Davidson, that seems to support the contrary -that is, that building an intention is completely different from saying something --- does not convince me. For a start, I will leave the decision open by using the phrase 'state of affairs' to be interpreted de dicto (as the content of a sentence) or de re (as a manner material things behave to each other).

A Classification of Modal Entities

The traditional distinction between possibilitas and potentialitas can be rendered by two different kinds of sentence schemata. I am indebted to Klaus Jakobi for this view. The distinction that is drawn by this means is independent from two other possible distinctions: the one between using 'can/must' and 'possible/necessary' to articulate modality, and the other one between modalities de dicto and de re. It is illuminating to consider first a latin formulation of the mentioned sentence schemata:

(1) Possibile est Socratem currere,
(2) Socrates potest currere.

Similar sentences can be construed for the case of necessity or contingency, and a distinction according to the one between possibility and potentiality can be used here, too.Sentence (1) ascribes possibility to a state of affairs, the modality in (2) appears to be rather the power or potency of the subject Socrates.Schema (1), in which the modality is attached to the 'oblique' sentence Socratem currere can be rendered by two less elegant formulations:
(1a) id est possibile quod Socrates currit and
(1b) possibile est ita contingere ut hec propositio dicit 'Socrates currit' (Minio-Paluello p. 13, No [18]), so that the modality is (as regards syntax) either predicated of an unpersonal subject 'id' or of the propositional content 'Socrates currit'.
This is what can be described as applying modality on a state of affairs. As regards the distinction between 'can/must' and 'possible/necessary', the two schemata can be stated thus:

It can be that F(a),
It is possible that F(a)

versus

a can be F,
For a to be F is possible.
(It may be formally more correct to say 'For a it is possible to be identical to a certain x such that F(x)'.)

Again, the first two sentences can be said to attribute possibility to states of affairs, the second to state potencies or powers of certain things (that may be denoted extensionally). Although G. H. von Wright takes exactly this to be the distinction between de dicto and de re modalities (Essay on Modal Logic, Studies in Logic and the Foundations of Mathematics, North Holland, Amsterdam 1951, p. 28 and passim) the latter can easily be combined with the two schemata:

	Possibility -	- Potentiality
De Dicto -	- propositions -	- individuals
De Re -	- states of affairs -	- things

In this tabular I have inserted the respective entities of which modality is predicated. By 'individual' I sum up the content or sense of all kinds of linguistic means to refer to (sets of) individual things, that is proper names, rigid designators, definite descriptors, individual variables and constants, common nouns and the like. As I already said, the question whether there are states of affairs different from (or even independent of) propositions will be left open. Therefore, every entity to which possibility is attached can be called 'state of affairs'. The horizontal distinction can be compared with the Fregean difference between sense and reference, but anyway I will be concerned with the vertical one between possible states and possible predications.

Intentions

Intentional Action

I have not yet dealt with the full range of requirements that are given with the task of explicating the phrase 'A intends X'. In the context of this paper, I will have to restrict the investigation on the concept of modality to be used. In order to clear the environment in which this is to be done, I will simply quote the explication of 'intentional action' that Tuomela uses in his recent book, and add a few remarks.

An agent A intends to perform X only if

1. A believes (and has not temporarily forgotten that he believes) that he, at least with some non-negligable probability, can perform X (or at least can learn so to perform X);
2. A wants (and has not temporarily forgotten that he wants) to perform X;
3. A either has no stronger incompatible want (or set of incompatible wants whose combined strength is at least as great), or if A does have such a want or set of wants, he has temporarily forgotten that he wants the object(s) in question, or does not believe he wants the object(s), or has temporarily forgotten his belief that he cannot both realize the object(s) and perform X.

This quotation is from Tuomela's 1977 book (Human Action and its Explanation, Dordrecht, Reidel 1977, p. 133). In The Importance of Us, he adds the following analysis of intentional action:

An action performed by a single agent was intentional (in the core sense) relative to D if and only if, relative to D, the result of that action was something the agent aimed to bring about by his acting (...); and the action was performed approximately as planned (p. 69).

Here, D stands for a description of the intended state.Obviously, these analyses still have to be analysed.

The Object of Intentions

Tuomela's talk about the status of the intended entities is not very careful, especially in his use of 'object'. I have to admit that it is hardly possible to avoid to speak of objects of intentions: I did so myself above. Intentions, as I have said, do not aim at individual things, but rather at states or manners of things, and Tuomela does not seem to claim anything different. Therefore, 'object' must not only be taken in its widest possible sense, it must rather be taken in a sense that ex cludes 'things' from its range. Indeed, in Tuomelas first analysis 'realize an object' and 'perform X' seem to have at least the same syntactic category. In these clauses, 'object' denotes an action. But as regards the meaning of 'object' in phrases like 'A wants the object in question', there seems to be a shift from states to things. Even if this is to be passed over, Tuomela appears to draw a distinction by this difference that I do not want to adopt. He seems to suppose that states of affairs can be wanted, but only the results of actions can be intended. At least, the result of a performance can be 'wanted', and I think it should be possible to 'intend' certain states that are no direct results of one's own actions. Generally, I prefer a threefold distinction between 'wants', 'wishes' and 'intentions'. It may be that an intention involves a commitment to act, and by that way always aim at some result of an action. But that specifies the difference between 'wishes' and 'intentions'. 'Wants', I want to claim, need not even aim at some particular state of affairs, let alone, a resulting state of affairs.

Both analyses deal with the notion of 'intending to perform X' or 'performing X intentionally' instead of 'intending Y'. There is a difference between an intentional action and an intended one. An intentional action is an action by wich an agent intends something (possibly different from the action), and this is what Tuomela claims to analyse in the second quotation. So the latter analysis deals with the intended state of affairs rather than with an intended action. As 'in contrast to wants and desires, intentions can be regarded as commitments to action' (The Importance of Us, p. 53), it seems plausible that every kind of intending is covered by this second analysis. One can imagine, however, to intend passive rather than active, as in 'A intends to do nothings against Y'. The more general formulation will be 'A intends the state of affairs X', where it must be added, that one can only intend states of affairs one is (in any kind) involved in. I am not quite sure whether 'A intends the result of performing X' is equivalent to 'A intends the state of affairs X he is (in any kind) involved in' --- maybe the concept of 'performance' can be widened sufficiently. But even the notion of involvement must be modified: A need not be involved in the intended strate itself, but only in making it possible. I summarize these points by making the following claim:

A intends X only if A can be involved in making X possible.

To give an example concerning the degree of involvement: A borderline case of an intended state could be, that A intends that some other person B suffers from a desease D by withholding the message that an epidemic is spreading. The content of the intention will be: 'B suffers from D'.

Hopes vs. Beliefs

Stekeler-Weithofer remarks that it is not useful to speak of believes in this case, for 'to believe something' is not to be confused with some attitude to a possible state. (Zum Problem gemeinsamen und kommunikativen Handelns bei gemeinsamen Zielen, unpublished lecture on the occasion of Tuomela's participation in workshop 8 of the 17th. german congress for philosophy, XVII. Deutscher Kongreß für Philosophie, 23. - 27. September 1996 in Leipzig. He contributes this point (without explicit reference) to Nuel Belnap, but his according manuscript is 'not to be cited'.)
I am not completely convinced of his argument, that a belief can only be held about an actual state of affairs, but not a possible one. Stekeler proposes to use 'to hope that X will obtain' in the latter case, and for I will be concerned with precisely the involved notion of possibility, I will keep this in mind. So,

A intends X only if A hopes that X will obtain.

Intentions and Driving Forces

In the first quotation, Tuomela is careful enough to state merely the 'only if'-side of an according definition. Indeed, I do not believe that the coincidence of a belief and a want is sufficient for an intention. Roughly, Tuomela seems to approach the notion of 'A intends X' by adding (i) a belief and (ii) a consistency clause to the according 'A wants X'. It seems plausible that it is possible to 'want' inconsistent sets of states, but not to 'intend' them. The concept of 'wanting', however, is not a sufficiently clear one. To get things lucid, it is convening to seperate 'wants' as far as possible from 'intentions'. Therefore, a want may be posited on a level together with driving forces, urges, impulses and unconscious desires. So it may be possible to want (a) impossible things, (b) things one believes to be evil and indecent, (c) undescribable things and the like. Intuitively, I think it is further possible to want individual things, as different from wanting states of affairs to obtain. 'To want' can be described as to be driven into some direction.

The categorical difference to another form of endeavouring can be seen in a somehow more detailed representation of the wanted item. This could be called 'will' or 'want₂ '. The important feature of this higher-level want₂ seems to be that it imposes a complete 'virtual' difference between the objects: on one side there are the objects that fulfill the want₂, on the other side the ones that do not. It is essential that this difference can be known in advance, that is, independent of the actual circumstances. For instance, one can imagine two kinds of 'wanting something to eat': hunger and appetite. Hunger may be satisfied by taking appetite suppressants, while appetite for something particular cannot be really satisfied this way, but only brought to an end. This is nearly a cognitive or linguistical property, for there remains only a small step to such entities that divide the 'logical space' in verifying and falsifying states of affairs, like a sentence may be claimed to do (Wittgenstein, Tractatus 3.4). Intention seems to be a rather fundamental want₂ of the latter sort. I think it is possible to explain 'verifying a sentence' and 'saturating a concept' by regarding sentences as special kinds of intentions. There is a long tradition of using the latin 'intentio' for 'meaning', i.e. the greek kataphasis (Boethius in De Interpretatione) and the arabic ma'na (Michael Scotus in the Avicenna latinus), cf. also Ockham's Summa Logicae I,12.
To state explicitely, where and how this new category of wants₂ emerges, is sometimes said to be the main task of epistemology (cf. Gerold Prauss, e.g., in his books on Kant) and it is an extremely difficult task. Despite these difficulties, it seems plausible to state that 'intending X' at least requires (a) a primitive driving force, that is, an impulse in a vague direction, and (b) a more 'civilized' driving force, that might even have to be consistent with the other 'civilized' impulses. It is obviously not possible really to intend some state and not to be driven in any suitable direction. Tuomela, however, confuses this fundamental difference between wants (a) and intentions (b) by using them both with X as their object. That is, his approach is not merely an addition of (i) a belief and (ii) a consistency clause to the notion of a primitive driving force, it is rather first setting 'to want' on a level where it already contains a detailed model X of the aimed state of affairs. Either X is stated unsharp, then it cannot be intended, or it is sharpened, then there is no real difference between wanting and intending any more. Nevertheless, I will be myself concerned with 'sharpened' objects of some want₂. I close this section with the following claim:

Besides some driving forces into a suitable direction, every intention must at least implicitly contain a description X of a possible state of affairs.

It is important, that this description uses intensional concepts: it is possible to intend states of affairs that are merely possible, but will never happen to be actual. Generally, there will be no use in describing aims for already obtaining states of affairs.

Modality Applied

Where to apply Modality

There are two occasions for applying intensional language. First, the agent must believe that the intended state of affairs can ontain. Such a belief must have the form

A believes that X_B can obtain,
A believes that It is possible that X_B obtains.

Here, the state of affairs occurs in a belief-context and is therefore marked X_B. In order to keep the truth conditions of the whole sentence constant, several things must be considered. For instance: If A has a belief about a certain x, does he know all the relevant properties of x, especially that it is identical to some y?

The intention itself must be articulated in an intensional language, too. That does not have to take place in a particular belief-sentence. It must be intelligible to say of someone else 'He intends X', although one does not share the according beliefs. The reference to intentions of other agents is independent from their respective knowledge or linguistic competence. When a state of affairs appears in such an intention-sentence, therefore, it can be dealt with less restriction:

A intends the state of affairs X_I.

It gets obvious, by the way, that no intention is reducible to a driving force and a corresponding belief: Intention can be described without the notion of belief and is still more than a mere driving force.

Things and States of Affairs

To decide which kind of modalitiy has to be used is not as easy as it seems. There are two arguments:

(a) The object of an intention must be a state of affairs. Therefore the modality must be a possibilitas.
(b) An agent can only aim at 'actual possibilities', but not at mere 'possible actualities', and he must be somehow involved in actualizing the intended state. Therefore we have to use the notion of potentialitas.

The distinction between 'actual possibilities' and 'possible actualities' is taken from Robert Musil (Robert Musil, Der Mann ohne Eigenschaften, Reinbek 1978, Chapter 4: Wenn es Wirklichkeitssinn gibt, muß es auch Möglichkeitssinn geben). An actual possibility can be described as a possible combination of existing entities, whereas a 'possible actuality' can involve nonexisting entities and even disregard some laws of nature.
- Anm.: There is much confusion in possible-worlds-semantics, when possible worlds are taken as merely 'possible actualities', that is, any maximal consistent set of sentences. Some of this distinction can be articulated by using the verbs 'intend' and 'wish'. It is possible that I 'wish I were you', but not possible that I 'intend to be you' (in a litteral sense). In this way, every intended state must be an 'actual possible' one. If we are to follow Jakobi's classification, however, this kind of modality has to be oriented at the potentialities of given things. So, the actual situation has to be considered first and then various potencies of the relevant things have to be introduced. It might be even better to formulate the concept of intention thus:

(*) A intends a to be an x such that F(x).

But there is a further difficulty: Suppose that an agent A intends to have a white marriage, but does not want to marry a particular person yet. That seems plainly intelligible: A can be supposed to say later to his wife (or husband): 'I always wanted to have a white marriage'. Of course, this is a higher level want₂, and adding the plausible belief (that a white marriage is possible), there was indeed an intention without an object. It could be analysed according to (*) in the following way:

A intends himself to be an x such that F(x),

but the involvement of the agent himself was already obvious (by saying that he intends something). Further, there might be intended states that do not themselves include A (for instance, the help for developing countries). Anyway, in Bressans calculus the far more elegant solution is already provided: both a and F(x) have to be intensional concepts.

I. If A wants to have a white marriage, this marriage cannot be described as an actual marriage with other persons involved in. It may be that A sees such an event somewhere and says to himself 'when I grow up, I want to do the same'. But 'the same' cannot be reached by elimininating the concerning individuals and replacing them by A and his wife (her husband). In such a procedure,

Peter marries Susan in the particular manner M, therefore
x₁ marries x₂ in the particular manner M, therefore
A marries x₂ in the particular manner M,

the manner M cannot be extensionally the same. It is obviously not the marriage of Peter and Susan in which A and x₂ enter instead of Peter and Susan. It is rather some counterpart of this actual marriage. Therefore, a logic of intentions must be able to determine counterparts of events, independent of the concerned individuals. Even the agent himself is not in general to be excepted from this: it is possible to intend states of affairs with out being part these very states of affairs. A father can intend, for instance, that his unborn son visits the highschool. There is a similar example in Davidson, p. 137. Consider also the schema 'A intends X under all circumstances'.

II. There is another, more farfetched, argument for event-counterparts. Anil Gupta (p. 11) construes common nouns by a very special kind of predication. He analyses a sentence like

Any man who owns a donkey beats it

by seperating the attribution of a certain kind from that of a predicate:

(for all D, x) (for all (M, y) Oyx, z) Bzx.

The only ordinary predication takes place in the phrase Bzx, that is, 'z beats x'. The other predications, D 'to be a donkey', M 'to be a man' and Oyx 'y owns x' are done by common noun-clauses (According to Definition 1 (vii), p. 7, '(M, y) Oyx, z' is a single common noun). By such a clause, it can be said, a 'this' (x) is transformed into a 'this something (Loux, p. 134), that is, into an x of a particular kind. This can be called 'species-predication' in contrast to 'form-predication' (which transforms a 'this' into a 'this such'). Cf. Loux p. 120 and 137: 'forms lack their own built-in principle of individuation'. Kinds or species are presupposed, not themselves stated. In the words of Aristotle: they are not open to contrariety (Categoriae 3b24, Loux 7, II p. 239ff.). They are the ousiai (substances) that are involved: For an ousia is an entity that is not predicated of another, but of which others are predicated (Categoriae 2a11, Metaphysics Z 1038b15-16; Loux p. 14: 'the idea that ousia function analogous to a kind term seems to underlie one important (in the Categories, certainly, the most important) use of the term'). Indeed, the following argument appears to rely on Aristotle himself:

Even that some x is of the kind K is a predication.

In a wide sense, (there is a K, x) is indeed a predication: there is a certain 'this' which is a K. The x cannot be omitted, far it is essential to distinguish a certain (K, x) from another (K, y) (Loux p. 229 and Metaphysics Z 1034a5-8). This requirement is given with the contingency that is even involved in some x's being of a certain kind. Since members of kinds come into being and pass away, they cannot be necessary of the respective kind in the last consequence. In the context of Aristotle's Metaphysics Z:

... because we want to accomodate the fact that the familiar particulars of the Categories [i.e. man or horse] can come to be and pass away, we construe them as composites of matter and form (Loux p. 160).

From this point of view, however, to be of a certain kind is to have some contingent properties. The according modal logic will have to underlie intensional concepts like mass-points and natural numbers in order to determine counterparts of the respective parcels of matter. To transform such a contingent form- into a species-predication amounts to the suggestion: 'this time, I do not want to talk about the form K an x has, but rather about the form F a certain (K, x) has'. That is not to be confused with arbitrarily inventing necessary predications. In some cases, there may be no sense in talking of a certain (K, x). Aristotle himself seems to have a firm grasp of 'right' and 'wrong' species-predication: the predicates of being a man or being a horse can be said to be ousiai , but not some artificial predicates like 'white man' (Metaphysics Z 4, 1029b28, Loux p. 274: 'We have to know, for example, that man is a genuine substance sortal and that cloak [to be defined as 'white man'] is not; that geraniums are ousiai and that hoplites are not').

III. Further, I think that a tracing-principle for states of affairs contributes to a problem that Davidson poses in the context of a reconstruction of action-descriptions (Handlung und Ereignis, p. 165ff.). The according paper, The Logical Form of Action Sentences, was first published by Nicholas Rescher in 'The Logic of Decision and Action', University of Pittsburgh Press 1967. Davidson remarks that an action can be described by different sentences and asks, how it could be justified, that two such sentences deal with the same state of affairs. In contrast, Davidson sees no such problem in denoting a certain thing and then predicating various properties of this very thing. His example: 'There is a house such that I bought it, it is situated in the city, it has four bedrooms,...'. Given a complete and unique counterpart relation for states of affairs, there seems to be no problem either: a state of affairs can be denoted under all possible circumstances. Second, there need not be any worry about substitution of involved particulars salva veritate: this is only relevant for stating the belief of the agent, not for denoting the state of affairs. For belief contexts, Cresswell has given a rather complete approach in his 'Structured Meanings', Cambr. Mass./ London 1985.

Towards a Calculus

Since Gupta's calculus is a kind of restriction of Bressan's, it is convenient to return to the latter one. So I will allow counterpart-relations for predicates and relations, that is, for states of affairs. Since intentions are had in the actual world and can only aim at situations that can be reached in a finite number of steps, we need two things in particular:

1. an (alleged) real world r,
2. a tracing principle for situations, predicates and relations, that is a construction that amounts to Gupta's underlying common noun.

To deal with conditional intentions we might have to label a related possible world s as 'supposed' real world s_r. That is, if we want to deal with the schema 'After I have reached goal G₁, I want to get G₂', we have to suppose as a starting point the situation s_rin which G₁ is reached. It might be impossible to reach G₂ in the actual world r.

Omitting Belief

First, I want to consider the distinction between 'to belief X' and 'to hope that X' that Stekeler-Weithofer draws. Davidson has pointed out, that it is possible to intend something without being sure about ones ability to bring it about (Davidson p. 141). Therefore, a belief of the form 'I can bring X about' may be too strong. Whereas it is not intelligible to intend X, but to belief that one cannot bring it about, it seems possible not to belief that one can bring it about.
The content of a hope seems to be as explicit as the content of a belief. A can be said to believe or hope p if he is at least disposed to utter p when he is asked. Therefore, it is the kind of attitude to an equally explicit goal that is different. An example that displays this, is that A has the firm intention to marry B, but knows that B does not like him. He can even publish his intention in a newspaper but nevertheless not belief that he will have success. If there is a little chance of success, however, this attitude should be called 'intending' rather than mere 'wishing' --- and the according attitude 'hope' rather than 'belief'.
To hope means to take a risk, not to act merely rational. That appears to be the main difference to belief-attitudes: the mere belief that one can do X is not risky, but rather the action according to this belief. What is believed can be spelled 'There is the probability p that I can do X'. In contrast, the content of an according hope is: 'I will manage to do X'. Hope seems to be a neglect of contingency, in other words: a commitment to act. As regards belief sentences as 'the probability that I do X is such and such', they are not relevant for the intention.
Unlike Stekeler-Weithofer, I do not belief in a fundamental difference between 'hopes' and 'beliefs'. Hope is still a belief, but with neglect of uncertainty. The concept of 'hope' should nevertheless be used instead of 'belief', for it excludes several irrelevant 'beliefs' and focuses on beliefs that are commitments to actions. Commitments to actions, however, can be described in an objective language. Together with the possibilty to resort on a group-relative set of beliefs (Balzer) the problems concerning belief sentences can be avoided. Of the two intention-contents X_B and X_I, there will be only one left (X), that can be described in an intensional language based on the description of the real situation r.

A Fragment of Intensional Logic

This is roughly how I suggest to proceed:

• We first describe a real situation r in a (fragment of a) contemporary extensional language. r will be a set of sentences like F(a) where a is supposed to represent a certain individual and F(...) is a predicate.
• These sentences are then divided into two classes: (i) the predications that are supposed to be changeable and (ii) the predications that are taken to be the 'substance' of the considered situation.
• Then, more complex predicates can be defined by sets of extensions in r.
• The construction of related situations depends on the changes that are possible. The number n of combinations of possible changes determines the number of relevant situations s₁, ... , s_n.
• The substantial sentences are assigned a unique counterpart in every related situation. In general, every 'this' should have one substantial predicate and every substantial predication one counterpart in every related situation.

Syntax

(1) It seems plausible to describe the situation r in terms the intending person can take into account. Most of the individuals can be denoted by constants. For a start, only one-place predicates will be considered, but the language can be easily extended to n-place predicates. A predication like F(c) will be called 'atomic'.
It seems desirable to avoid the notion of an individual thing, but rather to start with predications and divide them into form-predications and substance-predications. Constants and variables could to be taken as standing for the phrases 'this' and 'one of these', or even not to denote individuals at all. To get a distinction between denoting things and 'real' states of affairs, the logic will have to model on the aristotelian distinction between a 'this such' predication (for states of affairs) and another predication of the form 'this something' (for things). Perhaps, the resulting calculus can omit the usage of constants and variables completely. Instead of individual symbols (constants and variables), predicates could be used as the only basic concept. But there are several complications, that I did not manage so far. At least for technical reasons, every predication must consist of two thing: a predicate and a subject. A distinction between quantifying over form- or substance-predications will still have to be drawn. Further, the syntactical distinction between form- and substance-predications can only be drawn by semantical means, for they have the same symbolic structure.
In the following, I continued in using individual symbols in the syntax, but avoided to interpret them as individual things semtantically. A step further, the theory of truth for predicate logic will have to be changed. A sentence F(c) will not be true any more iff the thing denoted by c has the property F(\cdots), for c does not denote a thing. I did not pursue this point.

To keep things simple, descriptions can also be assigned to sets of agents. The criterion for gathering agents in sets may be their social position, which can be determined by typical actions. As a result, the description need not be in terms of beliefs of a single agent, and restrictions concerning the knowledge and linguistic competence of particular persons can be relaxed.
(Balzer, p. 72, p. 80: 'The Summary of all [personal] components of an internal model to one unit, that is a [single] internal model considerably more lucid. (...) [we will] reduce the variety of internal models by assigning them directly to groups, and not to individuals'. Balzer's 'internal model' is similar to my 'description'. There are also several English publications of Balzer on this matter, e.g. A Basic Model of Social Institutions, Journal of mathematical Sociology 16, 1990, 1-29; A Theory of Power in Small Groups, in H. Westmeyer (ed.), The Structuralist Program in Psychology: Foundations and Applications, Bern 1992.)

(2) The decision whether an atomic predication is substantial or not is not an arbitrary one: it may be wrong. It need not arouse too much suspicion, for it is as easy or maybe as deceptive as describing the situation r. For particular (groups of) persons, only those predications need to be regarded as changeable which the considered person can be involved in changing. Both the set of atomic predications and the assignment of a subclass of substance-predications is called description.

1. If c is a constant or variable and F is a one-place predicate, then F(c) is an atomic predication.
2. 1. If c is a constant and it is supposed to be possible that not F(c), then F(c) is an atomic form-predication.
   2. If c is a constant or variable, F(c) is an atomic substance-predication. If x is a variable, then [for all x ... K(x) ... ] is an atomic substance-predication.

3. Atomic substance-predications are called terms, atomic form-predications are called dispositions .

An atomic disposition should contain no variables. In some cases, the variables may be identified with a constant. For complex form-predications, a quantifier will be introduced together with a substance predicate.

(3) Both complex form-predications and complex substance-predications are introduced. There are four kinds of complex substance-predications, and perhaps some of them should not be allowed.

1. First, if C and D are terms, then C=D is a substance-predication.
2. If K₁(x) and K₂(y) are terms, then K₁(K₂(y)) and K₂(K₁(x)) can be either substance- or form-predications. That depends on the extensions of K₁(x) and K₂(y) in the related situations s₁ ... s_n.
3. If K₁(x) ... K_k(x) are terms and F(y₁ ... y_k) is a k-place form-predication (k > 0), then F(K₁ (x₁) ... K_k (x_k)) is a substance predication, when it is taken to be substantial.

The decision between substantial predications and changeable ones seems to have to be made once again. But the terms K₁(x) ... K_k(x) are already given, and F(K₁(x₁) ...K_k(x_k)) should be substantial when it holds in r. If it is true, it has to be a substance-predication.

Likewise, 'not C' and 'C and D' could be defined as complex terms where C and D are terms. There may be, however, some doubts about 'not C'. I introduce it, because together with 'C and D' it allows to define other complex terms like 'not (C implies D)' or 'C or D'.
(remark: Niklas Luhmann bases his theory of social systems on an intuitive notion of 'not (C implies D)', that is 'C and not D'.)
Another possibility is to replace complex predicates by a reduction rule of the form 'F(C and D) reduces to F(C) and F(D)', but I am not quite sure whether 'A intends to drink coffee and milk' is equivalent to 'A intends to drink coffee and to drink milk'.

Perhaps the doubts concerning negation can be countered with a lattice theoretical construction. For instance, Balzers descriptions (internal models) consist mainly in a propositional space < P, *-* > (where *-* is an informal notion of entailment or implication) and a representation of believed causal relations verursacht (i.e. 'to cause'). The propositions are fitted with a 'minimal formal structure', that contains parts of propositional logic. They seem to amount to our atomic predications. Balzer uses lattice theory to proceed in defining the infimum(p, p') and suprenum(p, p') of two propositions p, p' according to *-* (Balzer p. 94ff). After the infimum over all propositions is set 0 and the suprenum over all propositions 1, a proposition q is defined as the negation of p iff the infimum(p,q) = 0 and suprenum(p,q) = 1. As an alternative, negation could be defined as p *-* 0 = not p. There remain difficulties, however, in determining a linear order of the type *-*.

In the case of mere form-predications, the things are more easy:

1. If F(...) and G(...) are form-predications, then F(G(...), G(F(...), 'not F(...)' and 'F(...) and G(...)' are form-predications.
2. If either C or D is a disposition, then C=D is a disposition.
3. If x is a variable, K(...) a substance-predication and F(...) a form-predication, then for all x ... F(K(x)) is a complex form-predication.

The other functors are introduced as usual.

Semantics

(4) A related situation contains every substance-predication and either every disposition or its negation. The difference to Carnaps notion of a state-description (Meaning and Necessity, Midway reprint 1988, p. 9) is the limit on dispositions. Another difference will be, that there can be individuals that do not exist in r. It will be useful (a) to consider only relevant predications and (b) to keep most of them substantial, that is, not to be changed. For every particular intention, there will naturally be such fixed values, for it is more intelligible to intend one change at a time. At least, it is impossible to intend everything to be changed, since then no understandable description of the intended state could be given. Aristotle, Metaphysics Z 8, points out that a change can only take place when both matter and form keep constant and change their mutual relations.

As an abbreviation, the set of variables or canstants x₁ ... x_m is set to x_1-m.

There are two possibilities of varying the dispositions of a situation r.
(i) The intension of a form-predication F(x_1-m) is given as an ordered n+1-tupel < F(x_1-m), F(x_1-m¹), ... , F(x_1-mⁿ) > , where x_1-m, x_1-m¹, ... , x_1-mⁿ are extensions and n=the number of related situations s₁,..., s_n.
(ii) The intension of a form-predication F(x_1-m) is given as < F(x_1-m), F₁ (x_1-m), ... , F_n (x_1-m) >.
I prefer the first one (i). In both cases, the intension of a substance predication K(x) will be K(x_1-m), ..., K(x_1-m) n+1 times.

(5) If K(c) is a substance-predication, every counterpart of c is an x such that K(x). If F(c) or F(K(c)) is a form-predication (where K(c) is a term), to assign a counterpart means roughly to determine which other individuals can possibly be an F(x).

It seems natural to take, e.g., the counterpart of an empty cup to be a filled cup, the counterpart of a woman a mother of twins. But in case of intentions, the things are different. The object of an intention is not a filled cup, but rather the filling of a cup. Therefore, it must be asked whether some actual dicta could involve another (possible) individual. This is rather clear for intentions like the one 'to care for a yet unborn child': there is no individual in r that has the child as its counterpart. The solution Bressan and Gupta give, that is, to construe an artificial nonexisting entity *, seems to be suspicious, for the silliest things might be the counterpart of * in r in some related situation s. The nonexisting entity therefore must not be 'completely' nonexisting. In the case of the unborn child, it may be required that a certain woman is in trouble. To avoid impossibilities that are imposed with such a restriction, there can be labeled a related world s_r, that can be reached by other means and contain the predication in question. It is obvious that the number of involved individuals cannot keep constant for every related situation, for living beings simply have the ability to breed, and other entities can be supposed to multiply, too (for instance, the books in my room). The possible predications are nevertheless determined by 'actual possibilities', that is, dispositions in r.

Time As an addition, time may be required, for intentions always aim at the future. The related situations s₁, ... , s_n can be ordered by a temporal relation <_t, such that < S, <_t > will be a linear order of situations s_i in S. For the real situation r, it must be supposed that there is no s in S that obtains at the same time. That is, the relation must be r <_t s for every s.

Interpretation In this approach both states of affairs and individual things will be assigned to predications.
Usually, things are assigned to constants and variables, and sets of things to predicates. Taking Aristotle as an exponent of common sense, however, 'to be' can only mean 'to be of a certain kind'. In his lecture 'Pragmatism and Common sense', William James regards the aristotelian Tradition as representative for common sense (Pragmatism, Dover Thrift Editions, London New York 1995, p. 63ff. For Aristotle, see Metaphysics H 6, 1045b6 and perhaps H 2, 1042b25f. Cf. Loux p. 271 and 84f. and Gupta p. 9).
Therefore, constants and variables should not be regarded as denoting things, but rather as providing an individuation principle. They are assigned to things in combination with substance-predications.Roughly, I suggest the following assignment:

1. If y is a constant, K₁(y) is a substance-predication and < K(x_1-m), ... , K(x_1-m) > (n+1 times) the intension of a substance-predication, then
   \langle K(K₁ (y_i)), ... , K(K₁ (y_i)) > (n+1 times) denotes a thing in r, s₁, ... , s_n respectively.
2. If x_1-m is a set of bound variables, K₁(y_1-m) is a substance-predication and < K(x_1-m), ... , K(x_1-m) > (n+1 times) the intension of a substance-predication, then < K(K₁ (y_i)), ... , K(K₁(y_i)) < (n+1 times) denotes a thing in
   r, s₁, ... , s_n respectively.
3. If K(y_1-m), ... , K(y_1-m) is the intension of a substance predication, then
   K₁(K(y_i)), ... , K₁(K(y_i) denotes a thing in r, s₁, ... , s_n respectively.
4. If c, c₁ ... c_n are constants, K(d), K(d₁) ... K(d_n) are substance-predications containing a constant or a term containing bound variables (to be taken as replaced by d, d₁ ... d_n) and < F(x_1-m), F(x_1-m¹), , F(x_1-m¹) > is the intension of a form-predication, then both < F(c), F(c₁), ... , F(c_n) > and < F(K(d)), F(K(d₁)), ... , F(K(d_n)) > denote states of affairs in r, s₁, ... , s_n respectively.
5. Complex form-predications denote states of affairs.

Alternatively, a further distinction can be drawn between form-predications that denote changeable things, and other form-predications that denote states of affairs. I did not pursue this point.
- Anm.: To pursue this might lead to a revision of the whole language.

Tracing states of affairs

There are mainly three possibilities to trace a state of affairs:
(i) If the predication in question is a term, there is already a counterpart in every related situation.
(ii) There can be complex predications that are substantial in virtue of their parts.
(iii) As regards particular intentions, there can be fixed values, that is, intention-relative needs. These are presuppositions of the intended state, external obligations that are not called into question, and predications that do not vary in the considered situations for other reasons.

The example of A, who wants to have a white marriage, can be dealt with in the following way: In western countries, the existence of several institutions is necessary in order to have a white marriage. That are the church, a registry office, witnesses and the like. In the relevant situations, these institutions are not called into question, that is, every situation contains a predication like 'c is a registry officer', 'd is a priest', etc. According to Balzer, these senstences can be analysed into sentences like 'c has the social task of doing X₁' (Balzer p. 74, cf. also Tuomela, The Importance of Us, p. 35 and 174. Certainly, there can be agents who want to abolish all these institutions, but the situations that are taken into account by A have to contain the according predications. The intention to have a white marriage should not be formulated like 'I want to have a white marriage when there are still the relevant institutions'. Such an intention content would be as strange as 'A bintends (X if he doesn't change his mind)' (Davidson p. 141). In contrast, an agent who strongly wants a white marriage will do the relevant things against the abolishment of the according institutions. To conclude, the white marriage that A has in a related situation is neither the same nor a direct counterpart of some white marriage actually taking place. But it is a complex predication in virtue of relevant substances of a subset of considered situations. The according terms, again, can be 'traced'.

Modalities

Several different kinds of necessity can be distinguished:

1. A complex state of affairs like 'not (X=Y and not Y=X) can be necessary in virtue of his logical components,
2. A state of affairs like G(F(c)) may be an analytic truth if F(c) is a term and the predication of F entails the predication of G,
3. A predication may be called necessary when it is true in every related situation.
4. Especially, an agent A can be obliged not to change a certain state of affairs F(c),
5. It can be necessary not to change F(c) in order to reach the intended state.
6. Finally, every substance-predication is necessary.

The first two cases display the familiar concepts of analyticity of Quine and Kant respectively. To determine necessity by the truth in every related situation is not really the same definition as Carnap gives, for the set of 'actual possibilities' is only a subset of the 'possible actualities'. What is true in every world depends not only on the logical components, but also on (a) the decision which predications are to be taken substantial and (b) the presuppositions of a particular intention. The last concept of necessity is fairly similar to Aristotle's concept of ousia.

Similar considerations will have to be made in case of possibility. The main types of modality are (1) logical modality, (2) description relative-modality (3) agent-relative modality (i.e. modality relative to a social position or group) and (4) intention-relative modality. Logical necessities (i.e. necessary states of affairs)are a subset of description-relative necessitities and need not include analytic necessity. (The decision is left open.) Description-relative necessities are a subset of intention-relative necessities. When descriptions are assigned to agents, description-relative and agent-relative necessities are the same.

In all cases, the same holds for possibilities. There can be circumstances, that is, certain relations to other situations, where the description has to be changed, and thereby the description-relative modalities. Analytic necessity (of the above-mentioned kind) may also be called into questions by such changes.

Result

The phrase 'A intends X' can be rendered by:

A intends S⁺.

S⁺ stands for the set of related situations, that fulfill the intention. Thereby, the direct reference to a sentence in natural or formal language is avoided.

Intention can be described as a mapping from the set of related situations s₁ ... s_n in S to the values < +, - >. S is the set of situations that are assigned to +. The group or social position of the intending agent A and his ability to achieve the intended state is reflected in the construction of the related situations s₁ ... s_n. The reference to an according belief can be omitted for the given reasons. As regards the driving forces of A and the consistency of his different intentions, they are included in the content of the intention.

s_i in S₁⁺ only if there is no driving force that is not compatible with s_i.

The notion of a driving force is left vague. It is not possible to relate driving forces directly to some s, for they do not contain a model of the intended state. The above amouts to the claim that intentions are mainly cultural phenomena. It is supposed, that a driving force must be cultivated in order to stand plainly against an intention. This, however, is rather contained in the following consistency-clause:

s_i in S₁ ⁺ only if there is no other Sigma_j such that s_i is in S_j⁺.

Here, both S₁⁺ and S₁⁺ are intentions of the same agent or group of agents. This can be symolized by adding a further index, as in S_i^(a)+. Before labeling group-specific intentions S_i^(a)+, however, the group-relative sets of S_i^(a)+ have to be determined by describing the according situations r^(a).

Literature

• Balzer Wolfgang Balzer, Soziale Institutionen, Berlin/New York 1993.
• Bressan Aldo Bressan, A General Interpreted Modal Calculus, New Haven/London 1972.
• Davidson Donald Davidson, Intending, published in Davidson, Handlung und Ereignis, Frankfurt 1985 (German translation) and Yirmiaku Yovel, Philosophy of History and Action, Reidel, Magnes Press, The Hebrew University 1978.
• Gupta Anil Gupta, The Logic of Common Nouns, New Haven/London 1980.
• Loux Michael J. Loux, Primary Ousia, An Essay on Aristotle's Metaphysics Z and H, Ithaka/London 1991.
• Minio-Paluello Lorenzo Minio-Paluello, Twelfth Century Logic, Texts and Studies II, Abaelardiana Inedita, Roma 1958.
• Tuomela Raimo Tuomela, The Importance of Us, A Philosophical Study of Basic Social Notions, Stanford 1995.