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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
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
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