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Primary:
Gottlob Frege (1867) ‘On Sense and Reference’.[1]
Secondary: Beaney, Michael (1996) Frege: Making Sense, London; Duckworth. Dummett, Michael (1973) Frege: Philosophy of Language, London; Duckworth. Kenny, Anthony (1995) Frege, London; Harmondsworth. Noonan, Harold W. (2001) Frege: A Critical Introduction, Cambridge, UK; Polity.
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Frege’s Theory
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I’ll start by introducing Frege’s theory so that we know where the discussion that follows is going to end up. Frege thinks that terms don’t just have reference they also have something called a sense, and the sense of a term is what determines the reference. For Frege, in most cases, the sense could be called the ‘mode of presentation’ of the referent.
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Justify Sense
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Frege is concerned to investigate a theory of ‘meaning’, though he does not have a general term to describe that fuzzy concept. The word ‘Bedeutung’ is the usual word for meaning in German but Frege uses it in very specific ways, which make it clear that the thing he’s talking about is not the vague concept meaning but the slightly more precise concept of reference. To avoid some confusion if you’re going to read Frege you should be aware that Bedeutung is used in three senses in Frege’s writing, to refer to:
i. the relation between a word and the thing to which it refers, ii. the thing to which a referring term refers, and iii. the fact that the term refers to a particular thing.
Frege’s idea of a theory of meaning – or perhaps it should be called a philosophy of language – is that meaning is what is grasped when something is understood. It is better not to think of a ‘meaning’ as an object that has to be related to a term in some way – this is what Wittgenstein calls the hypostatization of / reification of meaning – but we should rather think of it as a way of talking about how we come to understand the things that are said to us and what comes to be understood. The warning need not be taken too seriously, since it doesn’t necessarily vitiate our researches if we understand meanings as objects, but it is said to help us look in the right places for meanings.
Reference
But Frege is writing, at least in part, against a supposition supported by some recent arguments that meaning is possibly identifiable with reference, so it behooves us to look first at what he says about reference. You’ll recall that Mill’s argument that reference was all that was relevant about meaning was derived from considerations of the truth or falsity of propositions in syllogistic logic. Frege took a similar beginning point for his studies, so let’s start with Frege’s view of logic and the discovery of truth and falsity in sentences.
Frege takes a view of logic which sees terms as built up from individual names of objects in a universe, variables which can range over objects, one and two place predicates which coordinate objects and pairs of objects, and one and two argument functions which take objects and pairs of objects to objects as values. An interpretation of a term or sentence is an assignment of objects and pairs of objects to names, predicates, and functions. To determine whether a term/sentence is true or not is a mere matter of working out whether the assignment does the sort of thing that the sentence claims. Does the object belong to the class of objects that the sentence says that it does. This view is the basis of the standard semantics (but it would have to wait until Tarski’s work for the details to be worked out), and it is entirely determined by the association of objects and terms – ie. reference. It is Frege’s contention that the reference of a complex term can be entirely explained by the references of its parts. In fact that principle of the compositionality of reference is one of the most fundamental parts of Frege’s theory of language.
The entire point of logic of course – and of interpretations of terms in a logical language – is to establish the rules whereby the truth or falsity of sentences can be established in terms of the truth or falsity of other sentences. Now since the T or F (the truth value) for a sentence can be worked out compositionally from the references of the terms of which it is composed, it occurred to Frege that perhaps his principle of compositionality applied also to the semantics of sentences: he proposed that sentences had references and that the reference of a sentence was its truth value. This is one of Frege’s more controversial proposals:
i. One criticism that is often made is that on this hypothesis all sentences refer to just one of two objects, so that the reference of ‘2 + 2 = 4’ is the same as the reference of ‘Napoleon was a military dictator’ ie. T; and the reference of ‘triangles are green’ is the same as the reference of ‘phlogiston is the cause of fire’, ie. F. Well, that’s not a very powerful objection because it relies upon a slide between our intuitions of what is intended by ‘reference’ à ‘what its about’ à ‘meaning’, and Frege’s going to show that there’s a distinction between the first and the last items in that series.
ii. There are also those who think that even if the reference of a sentence is compositional, so that the reference of ‘Australia is mostly desert’ has to be the same as the reference of a sentence in which the components are replaced by terms with identical reference such as ‘The savage island west of New Zealand is mostly desert’, it does not follow that the only candidate for such an invariant must be the truth value. Sometimes it’s proposed that ‘facts’ or ‘states of affairs’, or ‘propositions’ could play that role.
iii. A lot of people have thought that there was no call to talk of a reference for a sentence at all. The extension of the concept from (obviously referring) terms to the things that they go to make up may just be a fallacy.
Meaning
Notwithstanding all this, however, its clear that the fact of association or reference may well be sufficient for logic but it’s clearly insufficient for a theory of meaning because it says nothing about how the reference is to be fixed or determined. In fact, Frege doesn’t think that reference is any part of meaning, which is not to say that it is quite independent of meaning, for Frege thinks that it is meaning that determines the reference of a term.
One reason why we have trouble talking about meaning at all with Frege is that he didn’t see it as a uniform or well-defined concept. He probably thought of it as one of those terms we have in the language that are OK for everyday use but won’t really stand up to scrutiny. When we talk about meaning he thought we were talking about a bunch of things and any theory f meaning had to say something about at least these three:
i. tone, (colour, lightening): ‘Tone’ seems to have to do with the mental images that words bring up in the mind. We might call it the associative power of a word, so that ‘maid’ and ‘girl’ have different tones. He also thinks ‘dead’ and ‘deceased’ have different tones – but what difference do any of you feel in the mental images that arise. One of his favourite examples is the difference between ‘but’ and ‘and’ and I’m sure we can think of many ways in which the use of those two words has results in different impressions in the hearer. ‘but’ seems to indicate something contrastive or surprising or etc. – but can you think of any mental image that fits the case? He also talks about the tone being purely subjective, but this must be wrong because meaning is to do with the things that a word/sentence communicates between two speakers and so anything which is purely subjective can’t be part of meaning. Anyway who says mental images can’t be objective?
ii. Force: Force is another thing again, and it has problems too. But none of the problems with tone and force are really significant because what we’re interested in is the last part of meaning
iii. Sense: As usual, Frege’s not entirely consistent in the way he uses this term, so be warned. Tyler Burge[1], points out at least three functions of the senses that Frege talks about. Roughly speaking they are these:
1. The concept of the object being referred to by the term. 2. The information that a term conveys. It’s contribution to the truth or falsity conditions of a sentence in which it occurs. 3. The means by which the terms determines the referent.
It’s the last of these that is generally understood to be Frege’s great contribution, ad it’s the sense in which it’s mostly treated in the reading ‘Sense and Reference’ that is the place where he first developed the theory, so that we’ll simply accept from here on that The sense of a word is that means by which the reference of a term is to be determined.
Sense
a. Frege’s Puzzle
Frege uses the puzzle about identity statements to demonstrate that something beyond reference is being appealed to. That is why it is known as ‘Frege’s puzzle’. Remember what that puzzle was all about: when we compare a pair of statements like:
a. Venus is a planet b. Mars is a planet
We think that they have different meanings because it seems that we have to grasp different things when we understand them. In this case we know that the difference in meaning between the two is due to the fact that ‘Venus’ and ‘Mars’ have different meanings. The MV explain this by pointing out that V and M meanMV different things because V and M are proper names and their meaningsMV are just their references and they refer to different objects – to whit, Venus and Mars. So far, so good. But we also think that the following statements have different meanings:
c. Hesperus is Venus d. Phosphorus is Venus
and in this case the difference in meaning can’t be explained in purely referential terms because Hesperus and Phosphorus (the evening and the morning stars) both refer to the same thing (i.e. Venus). And, as we saw before, the difference is even clearer when we compare the sentences:
e. Venus is Venus f. Phosphorus is Venus
Now we can see how thinking of meaning in terms of understanding gives us the grounds to make the puzzle actually puzzling. What do we understand from A = B which we didn’t understand from A = A when A and B are names for the same thing? Reference can’t help. There must be something else that is grasped. Something that is different in the two cases.
The hypothesis of sense can dissolve this puzzle. Think of the sense of a term as being like the route to a referent: it is quite possible for two different routes to arrive at the same destination, and this is just what Frege believes is true of senses that differ and yet have the same referent. The sense of ‘Venus’ is different from the sense of ‘the evening star’ and different again from the senses of ‘Hesperus’, ‘phosphorus’, and ‘morning star’. Thus, says Frege, the sense of the sentence that is composed of those different parts will differ, even where the reference does not.
Note that this requires that there be a type of principle of compositionality for senses just as there was for references. We have to be able to say that the substitution into a sentence of terms that differ only in sense can, potentially, alter the sense of the sentence. Let’s just stop here for a moment to wonder what Frege meant by the ‘sense of a sentence’. Well we don’t have to wonder because he wrote a letter to Husserl that included a nice little diagram to show how the various parts of his philosophy of language were related to each other. It looks like this:
sentence proper name concept word
sense of the sense of the sense of the sentence proper name concept word (thought)
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reference of reference of reference of object falling the sentence the proper name the concept word à under the (truth value) (object) (concept) concept
If we think of the sense of a sentence as the thought that it expresses (to use a more usual expression), then its plausible that this, being whatever it is by which its reference – ie. the truth or falsity is to be determined, could be the sort of thing that is determined compositionally by the senses of the parts, being whatever it is that determinies their references – ie. the objects that the sentence is about. So let’s just accept that that’s a reasonable hypothesis. In fact it might even be necessary for this thesis to be true for Frege’s more fundamental thesis of the compositionality of reference to be true. On the other hand it looks like the compositionality of sense actually is sufficient for the compositionality of reference. Certainly some argument could be made for that. Have a look at the following schema:
term1 sense(term1) ≡ x(speaker, term1) = reference1 t2 s(t2) ≡ x(p, t2) = r2 t3 s(t3) ≡ x(p, t3) = r3 Sentence = g(t1, t2, t3) s(Sentence) = s(g(t1, t2, t3)) ≡ x(p, g(t1, t2, t3)) = r4 and by compositionality of sense s(g(t1, t2, t3)) = h(s(t1), s(t2), s(t3)) = h(x(p, t1), x(p, t2), x(p, t3)) = h (r1, r2, r3) r4 = h (r1, r2, r3)
The example he gives of the evening star and the morning star is hackneyed, and in fact, is somewhat ineffective because there are many who have thought that perhaps the name ‘the X star’ is best understood as a complex term in which the reference is set by the compositional rules that apply to the parts of the description ‘the X star’ and the contribution of each of those parts is referential. This, of course, is no good. Frege used a different example of two different names for a mountain that had been discovered by two different people and had different methods of fixing the reference. People who looked for the referent of ‘Chomolungma’ looked southward from Tibet, people who looked for the referent of ‘Annapurna’ looked northward from Nepal. (That example may be garbled as to fact – it’s a vague recollection of Quine’s adaptation of Frege’s Afla and Ateb example.)
Notice that those names and objects are rather special since there is only one route from Afla to the mountain it names and only one route from Ateb to the mountain that it names. But this is not generally the case, is it? Every person in this room may have a different method of determining the reference of the name ‘Brisbane’ from any other person in this room. This must mean that we all have a different sense to the same name. What is the difference we wonder between the sense of a name and the collection of all the things that we know about the bearer of that name. And isn’t there a problem here for the theory of sense, because the sense is supposed to be the objective thing that directs reference and yet the sense may just as well be restricted to each individual speaker, in which case it can’t be called objective – and therefore cant be called part of meaning’ – and the only thing that remains that is objectively identical in the various uses of Brisbane is the reference. But this means that if anything is gong to be the meaning it is going to be the reference. And we know that’s wrong.
There are similar problems with the fact that we think that someone can talk about Moses quite happily even if it turns out that most of what they think they know about him is not true. How much of what is thought to be true o Moses can be false before we decide that the sense – wherever in the knowledge of Moses that we possess it may lie – no longer determines a referent?, And is it possible that if there’s no overlap at all between the things that I believe about Moses and the things that my interlocutor believes about Moses it need not follow that I don’t believe that he can’t talk about Moses to me? We’ll come back to these issues next week. Anyway we might as well look now at the remaining problems for the direct reference theories.
(b) Talking about non-existents
You’ll remember that there was a problem with respect to statements about things that are known not to exist. When somebody tells you that Pegasus lives on Mt Helicon, or that Sherlock Holmes lives at 221B Baker Street you neither assume that Pegasus or Holmes exists nor collapse in puzzlement trying to understand what is meant by those sentences. But according to the direct reference people at least one of those reactions would be justified. Actually it is better in this case to retrict our attention to names of things that don’t exist but which are used in the full belief that they do exist, because there gets to be trouble when wondering just what is intended to be true of fictional names that people don’t have any inclination to really believe have referents. So let’s talk about the planet Vulcan instead.
Let’s say that that planet was supposed to exist and have a position in Earth’s orbit on the other side of the Sun, and was supposed to explain certain astronomical facts. This name certainly seems to have a sense, if only a sense that is the compositional result of the senses of the words in the description I’ve just given. It would certainly follow that if ‘Vulcan’ occurred in a sentence it would have a sense that could contribute to the sense of the sentence, and there is something that can be grasped to understand the term ‘Vulcan’ and the sentence in which it occurs. That’s why we can have thoughts about Vulcan. Nevertheless, the name lacks a referent – because there is no such planet - and the consequence is, apparently, that the sentence doesn’t have a referent – ie. it is neither true nor false. Of course this means that sentences made up of such sentences didn’t have truth values (referents) either, so that ‘Vulcan is a planet or Vulcan is not a planet’ couldn’t be declared to be true. Ditto ‘Vulcan does not exist.’
Frege thought that this was the right conclusion to draw about natural language – and for that reason we should not waste our time trying to regularise the semantics of such an unruly beast. We should make up a well-behaved language in which such things can’t happen and talk in that language instead. This sounds a little desperate, but I guess it’s a logically consistent thing to say.
(c) Talking opaquely
Let’s finally consider the question of opaque contexts. Recall the relevant problem: suppose we have the following:
a. Cicero was an orator. b. Cicero is Tully.
Then it follows that
c. Tully was an orator.
which we can conclude because the role that ‘Tully’ and ‘Cicero’ play in the sentences is pretty much exhausted by their referential role.
On the other hand, in the sentences:
d. John believes Cicero was an orator. e. Cicero is Tully.
it is pretty clear that here we can’t conclude that
f. John believes Tully was an orator.
because in those sentences reference is not all that is relevant to the truth or falsity of the sentence. As we said before, it’s pretty clear that the two sentences d. and f. don’t have the same meaning – or sense, we would say now – because it’s possible for one to be true and the other false – and if there’s anything that we’re sure of it’s that if two sentences can be true and false in different situations then they can’t have the same meaning. Here, if John doesn’t know that Cicero is Tully, then it’d be quite possible for him to believe that Cicero was an orator and yet not believe that Tully was an orator.
Frege’s solution to this sort of this looks like as ugly a piece of ad hockery as you’re ever likely to see – this week. He declared that we have to distinguish between the customary reference of a term and its indirect reference, and that in such oblique contexts the phrases do not have their normal reference, but instead has an indirect reference. The indirect references of two terms which have the same customary reference need not be identical, which would explain why substitution of coreferential terms into oblique contexts does not preserve truth (sentence reference).
Although this appears at first to be little more than an exercise in saving the appearances for his sense/reference theory it really isn’t. You’ll recall that I mentioned before that reference is supposed by Frege to be what the term or the sentence is talking about, so it’s not really an unjustifiable move to say that in these oblique contexts the terms are used to talk about something a little different from what they are used to talk about in normal contexts. After all, we wouldn’t think that words which are being quoted so that we can talk about them should be intersubtitutable, would we? Here’s an example (from Quine, I think):
g. “Cicero” has six letters. h. Cicero is Tully.
therefore
i. “Tully” has six letters.
One does not think so. The only real difficulty in this refinement of his system might be in understanding how we are going to systematically decide when we’re going to use the customary reference and when we’re going to use the indirect reference. But this isn’t really a problem because we accept that the reference is determinied by the sense of term, and the sense of terms is what we grasp when we understand them, and when we understand them then we know what they’re talking about – or at least, how to get at what they’re talking abut – and therefore we know how to understand the reference in the terms. In the sentences which have oblique contexts, the reference is determined by the sense, and the sense is compositionally derived from the senses of the parts (including the parts in those oblique contexts), and we understand the rules of the composition by which the sense of the sentence is created.
Frege reasons from the fact that coreferential terms ought to be intersubstitutable salva veritate, that the indirect reference of a term must be the sort of thing that if another term with the same indirect reference is substituted in the oblique context then the sentence’s truth is preserved. But what sorts of things can be substituted in oblique contexts while preserving the truth value of the whole? Now this is the clever bit: he proposes that the indirect reference of a term is its normal sense.
Now look at those sentences d and f again: the indirect reference of ‘Cicero was an orator’ is not the truth value of the sentence, which is its normal reference, instead it is the thought that Cicero was an orator., which is its normal sense. And the indirect reference of ‘Tully was an orator’ is its normal sense, the thought that Tully was an orator, which is quite a different thought from the thought that Cicero was an orator., and therefore can’t be expected to be substitutable for it in oblique contexts salva v. The sort of sentence which has the same indirect reference as ‘Cicero was an orator’ is something like ‘Cicero was a fine and persuasive public speaker’; and this can be substituted for ‘Cicero was an orator’ in the OC, s.v. QED.
[1] (1977) ‘Belief de re’, Journal of Philosophy, 74, p. 356.
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