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  • This article was downloaded by: [DUT Library]On: 07 October 2014, At: 16:22Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number:1072954 Registered office: Mortimer House, 37-41 Mortimer Street,London W1T 3JH, UK

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    Thoughts about beliefaboutL.F. Goble aa University of North Carolina , Chapel HillPublished online: 15 Sep 2006.

    To cite this article: L.F. Goble (1972) Thoughts about beliefabout, Australasian Journal of Philosophy, 50:2, 138-148, DOI:10.1080/00048407212341171

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  • Australasian Journal of Philosophy Vol. 50, No. 2; August, 1972

    L. F. GOBLE

    T H O U G H T S ABOUT 'BELIEF ABOUT'

    Drawing a distinction between opaque and transparent belief contexts is commonplace. Some arguments containing statements about belief, such as

    (A) (1) Jones believes that the oldest bank robber robbed a bank (2) The oldest bank robber = Smith

    .'. (3) Jones believes that Smith robbed a bank,

    are not valid. I f Jones is like most of us, as we may imagine, (1) is true. We may also suppose (2) to be true. Yet even so (3) may be false, as evi- denced by the fact that Jones sincerely denies that Smith robbed a bank. Thus the inference substituting identically referring terms is not generally valid when the substitution occurs within the scope of the belief operator. Similarly, f rom (1) one cannot infer that

    (4) There is someone of whom Jones believes that he robbed a bank,

    for that would only be Smith, contrary to the falsity of (3). Existential generalization also fails when it comes to statements about belief.

    Nevertheless some such arguments seem to be valid. Suppose that Jones has been witness to a bank robbery and is later called in to identify the robber from a police line-up. Jones looks, points out Smith, and says, 'That ' s the man; the man on the left robbed the bank' . I t is surely correct for the police sergeant to note for the record that Jones believes that Smith robbed the bank, since, let us suppose, Smith ---- the man on the left. The sergeant's argument is

    (B) (5) Jones believes that the man on the left robbed a bank (6) The man on the left = Smith

    .'. (3) Jones believes that Smith robbed a bank.

    Here we accept (3) even though Jones might still sincerely deny that Smith robbed a bank. Similarly, it seems fair to infer (4) from (5).

    We are confronted with two arguments, (A) and (B), which seem to be of the same form

    (7) Jones believes that a is F (8) a = b

    .'. (9) Jones believes that b is F.

    Yet one is valid and the other invalid. This wants an explanation. We should say that one of the arguments has been misrepresented, either (i) we

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  • Thoughts About "Belie] About"

    have got the structure of one or more of the statements wrong (but which ? and how should it be put?), or (ii) we have ignored an essential premiss in (B) (but what premiss 7), or (iii) we have an equivocation on the sense of the belief operator in (A) and (B). Thus, just as an argument of the sort

    p o r q

    P ~ q

    is valid if the 'o r ' is exclusive, invalid if it is inclusive, so arguments of the sort (7), (8) .'. (9) involving substitution of identically referring terms are valid when the belief operator is transparent, invalid when it is opaque. Similarly for the arguments involving existential generalization. This, it might be argued, is the difference between (B) and (A). Only when the operator is transparent does the statement (3), for example, report a belief about Smith; only when the operator is opaque is the evidence of Jones' assent or denial to statements of particular importance.

    To say that 'belief ' is ambiguous, and so statements such as (3) and argu- ments containing them are ambiguous, is a familiar move. I want to argue that it's wrong.

    Suppose that the operator ' - - believes t h a t . . . ' really were ambiguous, that it had a transparent sense and an opaque sense. How then could one explain how from

    Jones believes that the man on the left is older than the youngest child in town

    one might correctly infer Jones believes that Smith is older than the youngest child in town

    but not Jones believes that the man on the left is older than Baby Jane

    (given that the youngest child in town ----- Baby Jane). Jones might have no idea of the identity of the youngest child in town. I f the operator is trans- parent to admit the first inference, then it would admit the second; if it is opaque to block the second, it would block the first. Of course, one could say that for a sentence of the form

    S believes that a R b

    there are four senses of belief: opaque to both ' a ' and 'b ' ; transparent to 'a ' , opaque to 'b ' ; opaque to 'a ' , transparent to 'b ' ; and transparent to both. But then when the embedded sentence contains a triadic predicate there would have to be nine senses of 'belief', and so on. That cannot be right.

    Instead of speaking of transparent and opaque senses of the belief operator, we would do better to speak of transparent and opaque occurrences of terms within the scope of the operator. This may be indicated by subscrip- ting each occurrence of such a term with a ' t ' or an 'o ' . Thus, for now the ambiguity of (3) may be expressed by the difference between

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  • L. F. Goble

    (3') Jones believes that Smitht robbed a bank

    and (3 ~) Jones believes that Smitho robbed a bank.

    Only from (3') may one draw conclusions by substituting identically referring terms or by existential generalization; only (3') reports a belief about Smith.

    (In case there is an iteration o f operators there should be an iteration o f subscripts; for example

    The sergeant believes that Jones believes that Smitht.o robbed a bank would be distinct f rom

    The sergeant believes that Jones believes that Smitht,t robbed a bank.

    The former indicates that 'Smith ' has an opaque occurrence with respect to the sergeant 's belief, i.e. the first operator , and a transparent occurrence with respect to Jones' belief. The second indicates that 'Smith ' occurs trans- parently for both. F rom the first statement one may infer

    The sergeant believes that there is someone whom Jones believes robbed a bank.

    but not There is someone w h o m the sergeant believes Jones believes robbed a bank

    which may, however, be inferred f rom the second statement. I will not be concerned with iterated belief contexts any further.) 1

    I t is, o f course, possible that an occurrence o f a term in a belief context is opaque or transparent just because o f the sense o f the operator, but this now seems implausible. But if that is not the case, then the ambiguity o f a sentence like (3) is left unexplained.

    No t all ambiguity is semantical, i.e. due to some expression, such as the belief operator, in the ambiguous sentence having more than one meaning. Some is syntactical, i.e. due to the sentence's having more than one basic structure when all is said and done. For example, following Russell 's account o f definite descriptions, a sentence o f the form (i) a :~ 7 x . F x could be equiva- lent to either (ii) (Ex) (Fx & (y) (Fy ~ x = y) & a ~ x) or to (iii) ,'--~(Ex) (Fx & (y) (Fy ~ x = y) & a = x) which are not equivalent. Thus, in the absence of conventions to the contrary, (i) is ambiguous, but no one would suggest that the negation operator in it has more than one sense. The only difference is that in (ii) the negation lies within the scope o f the existential quantifier, while in (iii) it is outside.

    Perhaps the ambiguity with belief is similar. One o f Quine's early examples o f such an ambiguous belief sentence is 'Ra lph believes that some- one is a spy' which may be either o f the opaque form

    i So far as t know, Hintikka was the first to recognise clearly the problem of characterizing transparency for sentences containing more than one singular term within an epistemic context; he speaks of 'partially transparent senses of knowing' in [1] in response to criticism of Sleigh [6]. The device of subscripting occurrences of terms rather than indexing the operators is due to Sleigh [7].

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  • Thoughts About "Belief About"

    Ralph believes that (Ex) (x is a spy)

    (Ralph believes there are spies) or the transparent (Ex) (Ralph believes that x is a spy)

    (There is someone whom Ralph believes to be a spy). Here we have the same kind of play on the scopes of the two operators. (Cf. Quine [4]. p. 184.)

    Of course, there is no obvious reason why we should say that a sentence like (3) contains any quantification at all, so that scope difference would not tell the story between (3') and (3"). But at least (3') should be equivalent to

    (10) (Ex) (x ---- Smith & Jones believes that x robbed a bank)

    whereas (3") presumably is not, although it might amount to (10') Jones believes that (Ex) (x = Smith & x robbed a bank).

    (10) contains the desired quantification outside the scope of the belief operator as required for transparent belief. Indeed we might go so far as to say that (10) represents what the form of (3') really is. And more generally, we might say that the form of a sentence of the sort

    (7') Jones believes that at is F

    is really

    (11) (Ex) (x = a & Jones believes that x is F).

    Since the occurrence o f ' a ' in (11) is outside the scope of the belief operator, there is no problem with substituting another identically referring term, 'b ' , for it, to conclude

    (12) (Ex) (x = b & Jones believes that x is F) which would be the form of

    (9') Jones believes that bt is F.

    Similarly there is no problem generalizing from (11) or (12) to infer (13) (Ey) (Ex) (x = y & Jones believes that x is F)

    as we may from any term having transparent occurrence in a belief sentence.

    Since all the terms having transparent occurrence are thus removed from the scope of the operator, there is no longer the temptation to say that the operator must itself be ambiguous. Nevertheless, the root problem remains. For (11) requires an irreducible quantification into the belief context, and, as we know, it is difficult to make sense of such quantification.

    At this point there seem to be two ways to go. One could follow the neo-Fregean path proposed by, e.g. Sellars [5] or Kaplan [2], according to which the terms in belief contexts do not refer to what they ordinarily denote, but rather certain senses or intensions or individual concepts or even the expressions themselves. This avoids the problems with quantifying into the scope of the belief operator, but it raises a well known family of problems of its own. The other course is to try to develop an account of transparent belief and quantification into opaque contexts according to which terms still denote what they ordinarily do and variables range only over ordinary things. This is what I 'd like to begin here.

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  • L. F. Goble

    At first, however, I shall put forms like (1 I) aside in order not to risk presupposing what is eventually to be established. Instead I'll take trans- parent belief as a primitive notion, defining truth conditions for sentences of the form (7'), containing transparent occurrences of terms, in terms of sentences containing no such occurrences.

    Since behind a sentence like (3') there is generally one like (5), a natural first step in defining truth conditions for these sentences might be to say that

    (D.1) (7'), 'Jones believes that at is F ' , is true (on an interpretation) if and only if there is an expression, 'b', which denotes what "a" denotes and 'Jones believes that bo is F ' is true (on the inter- pretation).

    This, however, will not do. From the fact that Jones believes that the oldest bank robber robbed a bank it would then follow that he believes about Smith, that he robbed a bank; (3') would follow from (1), since 'the oldest bank robber' denotes what 'Smith' denotes, namely Smith.

    The difference between (5) and (1) which allows the inference to (3') in the one case but not in the other is that the name in (5), 'the man on the left', is used by Jones to pick out the man he believes robbed the bank; in (1) the name 'the oldest bank robber' really picks out no one, at least not for Jones. The inference from (1) to (3') will be blocked but the inference from (5) to (3') admitted if we require the term 'b' in (D.1) to be a name which 'picks out' the individual the belief is about. Borrowing a word from Kaplan ([4]. p. 203), let me speak of such an expression, 'a ' representing an object, o, for a subject, Jones. The expression will then be called a representa- tive name of o for Jones. (D.1) should then be modified to

    (D.2) (7') is true if and only if there is for Jones a representative name, 'b', of what 'a ' denotes such that 'Jones believes that bo is F ' is true.

    (D.2) is essentially Kaplan's characterization of belief about. The difference is that he would have our definiens (minus the ' ' - - ' is true') be the form of (7'), whereas here we are supposing only that it determines the truth condi- tions for (7'). Thus we do not have to suppose that sentences about beliefs are also sentences about words.

    I am not going to give an account here of what representation is. I will point out some things it's not.

    Certainly it is not sufficient for a name's being a representative name of o (for Jones) that it denote o. That would readmit 'the oldest bank robber'. Neither is it necessary. Consider the following, suppose that Jones has witnessed the robbery as before and is called to identify the robber. Now suppose, however, that Jones is a person who always confuses right and left, so that looking at the man on the left, Smith, he says, 'The man on the right robbed the bank'. Suppose, moreover, that the police sergeant and everyone else, except perhaps Jones himself, knows of Jones' disability. The sergeant would again be correct in noting for the record that Jones believes that Smith robbed the bank, in spite of the fact that Jones might sincerely refuse to assent to the sentence 'Smith robbed the bank' or even the sentence ' the man on the left robbed the bank' (since he would think that was about the

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  • Thoughts About "Belief About"

    man on the right). For Jones in this case the expression 'the man on the right' is a representative name of Smith, the man on the left, in spite of the fact that it does not denote Smith.

    It is neither necessary nor sufficient that a representative name be a gram- matically proper name. 'The man on the left' might well be Jones' represen- tative name of Smith; what's more we may have beliefs about objects which have no proper names at all. It is not sufficient either; suppose that Jones has overheard a man in a crowd saying to someone else, 'Smith robbed a bank'. Jones might go away thinking that what he heard was true even though he had no idea who Smith was. 'Smith' would not be a representa- tive name of Smith for Jones. We would not want to describe Jones as having a belief about Smith, though of course it might be true that he believes that Smitho robbed a bank. It does not even seem sufficient that the gram- matically proper name have been introduced by Jones by a baptism. Suppose that Jones believes that the oldest living bank robber who comes from Punxatawney, Pennsylvania and who once robbed the Kipton State Bank robbed a bank; Jones gets tired using this description, 'the oldest living bank robber from Punxatawney . . . etc.', so he decides to introduce the name 'Smith' in its place. Now we may say that Jones believes that Smith robbed a bank. But 'Smith' is no more a representative name than was 'the oldest living bank robber from Punxatawney, Pennsylvania who once robbed the Kipton State Bank'. Was the introduction a baptism? It 's hard to say. It would count as a baptism as some, e.g. Plantinga [3], have used that notion. (It would not be a 'dubbing' in the sense of Kaplan [2], p. 200.) It would not be a baptism in the eyes of the established church, but then neither would be the introduction of the name of a new born child by most parents.

    It is neither necessary nor sufficient that Jones be acquainted with the object represented, that he has ever directly perceived it.

    It is neither necessary nor sufficient that Jones be able to locate the repre- sented object in space and time. On one hand there may be representative names of non-spatio-temporal objects, but even when it is a physical object which is represented the task of actually finding or knowing where the object is may be insurmountable. On the other hand, some non-representative names may be expressions denoting individuals who could be located with very little detective work; for example, the expression might specify the location of the object to within a small area, as in 'the man right now nearest the geographical center of Times Square in N.Y.' which would not be likely to be a representative name of that man for anyone.

    I f one is to admit that one could have beliefs about future events or things, it must not be necessary that the object represented already exist or have existed. It does seem right to say that just as Jones could believe about the last solar eclipse that it was visible in the southeastern U.S., so he could believe about the next solar eclipse that it will be visible in northern Canada.

    (Kaplan requires that for a name to be a representative name of an object both that it denote that object and that it be of the object, which entails that the object already exist. Both of these conditions seem to me to be too strong.)

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    I should like to say that it is both necessary and sufficient for a name, 'a ' , to be a representative name of o for Jones that it be a name which Jones uses to refer to o. Certainly there is some connection between representation and a person's referring, but it is not so simple as this. I f Jones is now using ' a ' to refer to o, then perhaps it is all right to say that ' a ' represents o for him, at least right now. But what if he is not using the expression, it might still represent o for him. What we should count is what Jones would use to refer to o. But how are we to understand this subjunctive ? What Jones would use to refer depends on circumstances in ways that representation does not. Perhaps Jones would in fact never use ' a ' to refer to o because of facts ' a ' (it 's too long) or facts about himself (he's too polite), etc. Even so one would think that ' a ' could be a representative name for Jones.

    Even if one could specify the conditions on the subjunctive in a satisfactory way so that sensible necessary and sufficient conditions for representation are forthcoming, this still would not really clarify the sense of representation required here. For, I am inclined to think, the notion of a person's referring to an object requires an explication as much as the notion of a person's having a belief about an object. Indeed, it seems likely that an analysis o f this sort o f referring would need to refer to the subject having thoughts or beliefs about the object he refers to. Hence this will not help so far as our understanding of 'belief about ' goes.

    We should not suppose that if a person has two representative names, ' a ' and 'b ' , for one object o, that he must believe that a = b. But this presents a problem. Suppose that 'a ' and 'c ' are such names both representing, e.g. Smith, for Jones. I t might be that

    (14) Jones believes that a is F and

    (15) Jones does not believe that c is F

    are both true. From (15) it seems natural to conclude that Jones does not believe about c, i.e. Smith, that he is F. But from (14) we must conclude, according to (D.2) that he does believe about Smith that he is F. A con- tradiction? Perhaps.

    There are two situations which would account for a person's not believing about something that it is F. I t might be that (i) there is an expression, 'b ' , which is a representative name of that thing for the person although he, does not believe that b is F, or it might be that (ii) there is no such expression. 'b ' which both represents the object and such that be believes that b is F. I f these situations both present truth conditions for, for example,

    (16) Jones does not believe that at is F,

    then our interpretation takes us into a contradiction. But if (ii) alone describes truth conditions for (16) (and this is all that follows from (D.2)), then there seems to be no way to express what's given by (i) in our language of belief about. Either the language is inconsistent or it is incomplete.

    The only difficulty here is that our semantical meta-language is more flexible than the object-language; complex conditions define truth for

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  • Thoughts About "Belie[ About"

    seemingly simple sentences. The difficulty would be dispelled if we in- troduced a material mode counterpart to representation. Let us then say that Jones identifies a as b to indicate that he picks out a by calling it b. For example, in our early story Jones identified Smith as the man on the left; in the second story he identified him as the man on the right. The idea of 'identifying as' is that a sentence

    (17) Jones identifies a as b

    is true if and only if 'b ' is a representative name for Jones of the object denoted by 'a ' .

    I f Jones identifies a as b and if he believes that b is F, then we should say that he believes about a that it is F. The converse, o f course, is not true, for Jones might believe of a that it is F but not identify a as b; he might identify it in some other way. But presumably there must be some way in which he does identify a. This suggests that we might now define trans- parent belief contexts in this way

    (18) Jones believes that at is F if an only if (Ex) (Jones identifies a as x & Jones believes that x is F).

    The situations described in (i) and (ii) above would then correspond to the truth of

    (19) (Ex) (Jones identifies a as x & Jones does not believe that x is F)

    and (20) ~,~(Ex) (Jones identifies a as x and Jones believes that x is F),

    respectively, and there is no problem about (19) being true while (20) is false. Hence there is no problem with (14) and (15).

    Notice, however, that (18) commits one to quantifying into an opaque context once again. We seem to have come full circle. This may stand out even more as we think about the 'relation' of identifying as. In a sentence of the sort (17) the occurrence of ' a ' is of course transparent; the occurrence of 'b ' must be opaque. This means that we cannot equate (17) with, for example, the sentence 'Jones believes that a = b', unless the occurrence of ' a ' there is transparent, making (18) useless as a definition. But we could tentatively take (17) to be equivalent to

    (21) (Ex) (x = a & Jones believes that x = b).

    More quantification into a belief context! It is time now to define truth conditions for sentences such as (20) or (21) which do involve this kind of quantification.

    For simplicity's sake I shall imagine that we have already defined truth conditions for all sentences not containing belief operators; this in terms of an interpretation, I, specifying a domain and an extension for every constant, and a function, v, assigning values in the domain to all individual variables. I shall also suppose that truth conditions have been given for all sentences in which there are only closed formulas within the scope of belief operators. In other words, I am now only concerned with sentences, such as '(Ex) (Jones believes that x is F) ' and its cousins, containing quantification into a belief

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  • L . F. Gob le

    context. We may imagine that we are happy with such things as the failure of Leibniz' Law to apply to opaque belief, that is, the failure of Leibniz' Law to be valid when the substitutions are made within the scope of a belief operator; we may also expect existential generalization to fail in these cases as well.

    Let us now say that, if xz . . . . . Xn are all the free variables in a formula " a x s . X n ' ,

    (D.3) 'Jones believes that AXz . . . x n ' is true on an interpretation, I, for an assignment of values to variables, v, if and only if there are expressions, 'as', ., 'an', such that 'as', ., 'an' are representative names of v(xl) . . . . . v(xn) respectively and 'Jones believes that A a z . an' is true on I and v,

    (where ' A a z . . . an' is the result of substituting each 'at ' for all free occurrences of xi in ' A x z . . . Xn').

    Then we may stipulate that, as usual, (D.4) ' ( E x ) A " is true on I and v if and only if there is an assignment of

    values to variables, v', which is just like v except, perhaps, for its assignment to 'x ' such that 'A' is true on I and v',

    where 'A' is any well formed formula, even one containing free variables within the scope of a belief operator. Generally then a formula is true (on I) if and only if it is true (on I) for every assignment of values to variables.

    In this way we can define truth for sentences containing quantification into belief contexts and so, via (18), define truth conditions for sentences con- taining transparent occurrences of terms without having to suppose a special ' t ransparent ' sense of belief.

    It might be objected, however, that (D.3) and (D.4) commit us to a substitu- tion interpretation of the quantifiers, for a sentence (i) '(Ex) (Jones believes that x is F) ' would be true (on an interpretation) if and only if there was a substitution instance of it, (ii) "Jones believes that a is F ' , which was true on the interpretation (where ' a ' is a representative name). This observation concerning (i) is correct. However, inspection of (D.4) makes it clear that no special interpretation is given to quantifiers when they extend over belief contexts and, moreover, it is just the familiar denotation or domain of values interpretation which is employed here.

    Even in classical, fully extensional logic it may be that any sentence " ( E x ) F x ' is true if and only if an instance, "Fa' of it is true. This would be the case whenever the language being interpreted contains a name for every object in the domain of the interpretation. In general, of course, this won' t happen; there may be unnamed objects, especially if, for example, the domain contains all real numbers. What (D.3) and (D.4) suggest is just that, while there may be unnamed objects in the domain, one cannot have any beliefs a b o u t them. One might very well believe that all real numbers between 0 and 1 are less than 1 ; one could not believe about each and every real number between 0 and 1 that it was less than 1.

    Of course, it must be born in mind that there is nothing very remarkable about being a representative name of an object and so one might well have

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  • Thoughts About "'Belie'] About"

    beliefs about objects for which he could not give a special distinguished name. Fo r example, Jones ' representative name for Smith was just ' the man on the left ' ; he needn' t know that Smith's true name is 'Bank Robber Smith' ( 'Rob ' to his friends). Representative names may come and go. Smith may move to the front o f the line, whereupon Jones would no longer identify him as the man on the left; ' the man in front" would become his representative name for Smith, while ' the man on the left ' ceased to be so. Smith may have a son w h o m Jones identifies as Smith 's son; later Jones may learn that in fact Smith has two sons. He may now want to represent the boy by the name 'Smith 's eldest son' or ' the one I used to call Smith 's son' , etc. 'Smith 's son ' would, presumably, no longer be a representative name for Jones, though of course it could be. (Cases like this suggest that we should not require a representative name to denote the object represented, since 'Smith 's son" is, in this case, an improper description.) Jones may even have representative names like ' the tune I am now imagining' (as he imagines a tune) which allows that he may have beliefs about things like tunes whose name he doesn ' t know and which he can ' t otherwise easily describe.

    One has a great deal o f freedom in acquiring and adapt ing representative names. This takes care o f the problem of how, according to (D.3) and (D.4), one could have beliefs about objects which, off hand, one might think he couldn ' t really name.

    Given (D.3) and (D.4) we may now see how ident i fy ing as is equivalent to representation, at least if we make two fairly innocent assumptions. As suggested earlier we define

    (17) Jones identifies a as b

    as

    (21) ( E x ) ( x = a & Jones believes that x = b).

    Let us assume (I) for all representative names, 'c ' , for Jones that ' Jones believes that c = c ' is true. Then if 'b ' is a representative name o f a for Jones, Jones believes that b = b; let v be an assignment o f values to variables such that v(x) = a. 'x = a ' is true on this v; ' Jones believes that x = b' is also true on v, since there is a representative name o f v(x) which when substituted for x yields a truth. So '(Ex) (x = a & Jones believes that x = b)' is true on this, or any, v. Consequently, if 'b ' is a representative name of a for Jones, Jones identifies a as b. To show the converse, that if Jones identifies a as b, then 'b ' is a representative name of a for Jones, we must assume (II) that, in general, if ' c ' is a representative name of an object, a, for Jones, and if Jones believes that c ~ d, then ' d ' is a representative name of a for Jones. For then, if ' (Ex) (x = a & Jones believes that x = b)' is true, then for some v, 'x = a ' and 'Jones believes that x = b' are true on v. But that would be the case only if there is a representative name, ' c ' o f v(x) such that Jones believes that c = b. By (II) that makes 'b ' a representa- tive name of v(x) which is a.

    Since these assumptions, (I) and (II), seem required o f any plausible theory o f representative names, (21) seems an adequate explication o f (17).

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  • L. F. Goble

    Earlier , with (18), it was suggested t ha t the sentence (7'), ' Jones believes tha t at is F ' defined as ' (Ex) (Jones identifies a as x & Jones believes that x is F) ' . Tha t now comes to

    (22) (Ex) (Ey) (a = y & Jones believes tha t y = x & Jones believes that x is F) .

    Given assumpt ion (I) above , (22) is equivalent to

    (11) (Ex) (x = a & Jones believes that x is F) .

    Thus (7') is equivalent to (11). This is what we wanted initially. We have got ten it wi thout any special commi t tmen t to s t range in tensional entit ies o r to strange senses o f belief.

    Look ing back at the a rguments wi th which we began, we m a y now see tha t the a rgument (B), f rom (5) and (6) to (3), is val id so long as either (a) (5) is unders tood in such a way that the occurrence o f ' the m a n on the left ' is t ransparen t and so real ly out o f the scope o f the bel ief opera to r , or else (b) another premise be added to the argument , a premise to the effect tha t Jones identifies the man on the left as the man on the left, i.e. ' (Ex) (x = the m a n on the left & Jones believes tha t x = the man on the left) ' . This a d d e d premise guarantees tha t the expression ' the man on the left ' is for Jones a representat ive name o f the one who is the man on the left, and this licenses the inference f rom (5), ' Jones believes that the man on the left robbed a b a n k ' in which ' the man on the left ' does lie within the scope o f the opera tor , to

    (5') (Ex) x = the m a n on the left & Jones believes tha t x robbed a bank)

    in which the descr ip t ion is outside. F r o m this and (6) (3) fol lows directly, so long as it is under s tood as (3') wi th the occurrence o f 'Smi th ' t ransparent .

    This takes care o f ' b e l i e f abou t ' . W h a t remains now is to give an adequate account o f fully opaque bel ief sentences and an account o f representa t ion.

    Received Augus t 1971 University o f North Carolina, Chapel Hill.

    REFERENCES

    [1] Hintikka, J., 'Partially Transparent Senses of Knowing', Philosophical Studies, v. 20 (1969), pp. 4-8.

    [2] Kaplan, D., 'Quantifying In', Synthese, v. 19 (1968-69), pp. 178-214. [3] Plantinga, A., "De Re et De Dicto', No~s, v. 3 (1969), pp. 235-258. [4] Quine, W. V. O., 'Quantifiers and Propositional Attitudes', in The Ways of Paradox,

    N.Y., 1966, pp. 183-194. [5] Sellars, W., 'Some Problems about Belief', Synthese, v. 19 (1968-69), pp. 158-177. [6] Sleigh, R., 'A Note on an Argument of Hintikka's', Philosophical Studies, v. 18 (1967),

    pp. 12-14. [7] Sleigh, R., 'On a Proposed System of Epistemic Logic', No(~s, v. 2 (1968), pp. 391-398.

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