Thursday, March 03, 2016

Signification and assertion

Every departmental science has a subject, and its literature talks about or refers to that subject. Physics talks about heavy bodies and momentum and energy, chemistry talks about compounds, biology talks about flora and fauna etc. What does semantics, the science of meaning, talk about?

And there is the problem. Sometimes we cannot refer to what we signify.

Frege recognised this problem in 1892, in his essay ‘On Concept and Object’. A sentence consists of words, each of which has a signification or sense. What the whole sentence signifies is thus a compound of the senses corresponding to the words. (See e.g. his undated letter to Jourdain, in Frege’s Philosophical and Mathematical Correspondence, ed Gabriel and Hermes, 1980). The possibility of understanding a sentence we have never heard before depends on this property. What the sentence signifies is something new and perhaps previously unknown to us, but the signification of the words of which it is composed must be known, otherwise we would be incapable of understanding the sentence. For example ‘Socrates is a man’ is composed of the expressions ‘Socrates’ and ‘is a man’, both of which we know and understand.

The problem that Frege grapples with in ‘On Concept and Object’ is that while we can talk about what ‘Socrates’ signifies, namely Socrates himself, we can’t talk about what ‘is a man’ signifies. Or suppose we can. Let’s refer to it by the expression ‘The signification of “is a man”’. Will that do? No, because that expression is what Frege calls an Object term, an expression that refers to an object like Socrates. Thus the sentence ‘The signification of “is a man” is an Object’ is true. But it cannot signify an object, otherwise the sentence ‘Socrates is a man’ would be composed of two terms for objects. But two such terms cannot compose a sentence, any more than ‘Socrates Plato’ can. The sentence would be a mere list of words. Frege says, enigmatically ‘the concept horse is not a concept’, and attributes it to ‘an awkwardness of language’.

There is a similar problem regarding what I call signs of assertion. Consider
It is false that Socrates is a horse
I have not asserted that Socrates is a horse. On the contrary, I have denied it. Yet the four words ‘Socrates is a horse’ occur inside the eight word sentence ‘It is false that Socrates is a horse’. Perhaps we can explain this as follows. The eight word sentence can be split into ‘It is false’ and ‘that Socrates is a horse’. The latter is what Frege calls an object term. It refers to something a mad person might assert as true, the very thing I stand in the relation of denying to. So the meaning of the eight word sentence is changed by putting ‘It is false’ in front, and so if the meaning of the whole sentence is a composite of the meaning of ‘it is false’ and ‘that Socrates is a horse’, the composite is what ‘It is false that Socrates is a horse’ signifies. But of course that can’t be so, for the very fact that we could signify that Socrates was not a horse, would require that Socrates not being a horse was a fact. Worse, ‘It is true that Socrates is a horse’ would signify Socrates being a horse, so would require the existence of Socrates being a horse. Both those contradictory facts would have to exist in order for the contradictory sentences to be significant. Impossible!

Frege alludes to this problem in a much later essay (‘Negation’) published in 1918. He distinguishes between a question (my example is ‘is Socrates a horse’) from the thought corresponding to an answer like ‘yes’ or ‘no’. For if the sense of the question contained the sense of ‘yes’ or ‘no’, then the question would contain its own answer. The question would express a thought ‘whose being consists in its being true’.
Grasping the sense [of the question] would at the same time be an act of judging, and the utterance of the interrogative sentence would at the same time be an assertion, and so an answer to the question. But in an interrogative sentence neither the truth nor the falsity of the sense may be asserted.
Fair enough, but Frege does not see this as a challenge to his compositional semantics. Consider ‘Is Socrates a horse? No’. The first part signifies the question. If adding the sign ‘No’ completes the sense, then what is signified by the whole thing, namely question plus answer, must indeed be something whose being consists in being true, which Frege apparently denies.

In summary, if the signification of the whole is made up of the signification of the parts, then we should be able to refer to the signification of the whole, if semantics is to be a proper science. But we can’t, otherwise the subject of our science would include items like Socrates not being a horse, as well as Socrates being a horse. Which is impossible. Therefore semantics is not a science, at least not a proper science.


David Brightly said...

Doesn't this all rather undermine the ordinary notion of 'signification'? We have the intuitive idea that a sentence (fragment) means something but when we ask what that something is, we just get back a sentence. Do you think anything can be salvaged from the idea?

Maybe semantics is an abstract science rather than a concrete science, more like geometry than botany. Rather than worry what significations are we should concentrate on their compositional relations. Let x denote the signification of an object expression and y the signification of a concept expression. Then,

TRUE DENY x y = DENY x y
QUERY x y NO = DENY x y


Edward Ockham said...

Hi David. I think

x = Socrates
y = being wise
x+y = Socrates being wise = that Socrates is wise

The problem with getting at the signification of 'Socrates is wise' is it would have to be the fact that Socrates was wise, but if that fact exists, then 'Socrates is wise' could not signify anything without being true.

I am not sure about the schemata you give above. Are you referring to expressions or significates?

David Brightly said...

>> ...but if that fact exists, then 'Socrates is wise' could not signify anything without being true.

Yes, exactly. Where does that leave the usual notion of 'signification' as reference to something external like a thing or a fact? It surely kicks it into touch. But can we find some other notion of signification that allows us to rescue the Fregean idea of compositionality as exemplified by the algebra?

Edward Ockham said...

I dropped you a line with some tentative thoughts. Tentative only. The question is whether referring to the combination itself brings about the combination. Hydrogen and oxygen once combined will explode. In the same way, the combination of the two parts of the proposition will cause an assertion. But can we refer to the two parts without causing the explosion?

David Brightly said...

>> But can we refer to the two parts without causing the explosion?

Yes, I think so. 'that Socrates is wise' seems to do the trick:

Socrates = m('Socrates') = OBJECT ('Socrates')
isWise = m('is wise') = PREDICATE ('is wise')
m('It's true that Socrates is wise') = ASSERTION (IDEA (Socrates, isWise))
m('It's false that Socrates is wise') = DENIAL (IDEA (Socrates, isWise))
m('Is it the case that Socrates is wise?') = QUERY (IDEA (Socrates, isWise))

and so on.

Edward Ockham said...

I don't follow the predication here. E.g.

Socrates = m('Socrates') = OBJECT ('Socrates')

Isn't OBJECT ('Socrates') a statement, rather than a term?

David Brightly said...

It's a semantic object. Think of the capitalised words as denoting functions that return semantic objects of certain types. They are called 'constructors' in the jargon.


is a semantic object of type ASSERTION constructed from an object of type IDEA, itself constructed from two further semantic objects, x and y.

OBJECT ('Socrates')

is thus a semantic object of type OBJECT (=singular concept) itself constructed from the linguistic name 'Socrates'. In practice we expect this object to be the semantic result of an earlier encounter with a sentence that introduces the name 'Socrates'. So in this case the 'construction' is more a case of looking up and returning from semantic memory the object associated with the name. Similarly, we expect to have already learned the meaning of the predicate 'is wise', which we take to be a semantic object of type PREDICATE (=general concept)

Edward Ockham said...

Ah right. Not quite like a propositional function then.