Thoughts about ‘belief about’

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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

    Australasian Journal ofPhilosophyPublication details, including instructionsfor authors and subscription information:http://www.tandfonline.com/loi/rajp20

    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

    To link to this article: http://dx.doi.org/10.1080/00048407212341171

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    http://www.tandfonline.com/page/terms-and-conditionshttp://www.tandfonline.com/page/terms-and-conditions

  • 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...