Thursday, March 29, 2012

Reference and supposition

I made a start here on an account of medieval 'supposition theory', although there is a lot more to do. I was getting irritated with the Wikipedia article, although it is not bad by Wikipedia standards, having been written in 2006 by someone who is actually a professor of philosophy. Brian is not an expert though (few people are in this arcane branch of logic) and the article has a few problems. It's sad too that he could not continue his work on Wikipedia because work for inaccessible peer-reviewed journals was more important, according to his Dean of studies. (I know him from the days I was naively trying to recruit academics to Wikipedia).

Anyway, one of the problems with the article is the way it compares supposition theory to modern theories of reference. That's actually not a problem for Wikipedia – most standard reference works say exactly the same. But Catarina Dutilh Novaes has objected, in a number of published works including her Ph.D. thesis, that this is an anachronism. She doesn't think the concepts of supposition and reference are comparable at all, and part of the problem, she says, is that modern philosophical logicians do not understand medieval theories of supposition, and medieval scholars do not understand the concepts of modern philosophical logic such as reference. Each is comparing something they do understand to something they don't understand, and it's all wrong.

I used to think she was right about this, but now I don't. The problem is that modern philosophical logicians don't really agree on what 'reference' is, and the definitions they give are extremely vague. Consider the definition from the much-better-than-Wikipedia SEP:
Reference is a relation that obtains between expressions and what speakers use expressions to talk about. When I assert ‘George W. Bush is a Republican’, I use the proper name ‘George W. Bush’ to refer to a particular individual, an individual about whom I go on to speak. [...] More picturesquely, we are able to use language to talk about the world because words, at least certain types of words, somehow ‘hook on to’ things in the world — things like George W. Bush. Proper names — expressions like ‘George W. Bush’ — are widely regarded as paradigmatic referring expressions.
What does all that mean? One of Catarina's objections to comparing supposition to reference is that in classical supposition theory, common terms as well as proper names have supposition. 'Man' supposits for all men, 'Socrates' supposits for just Socrates. But according to the SEP definition above, it seems like common terms can refer. If reference is 'talking about', then we can use the expression 'every man' to talk about every man, and when we assert 'every man is an animal' we use the quantified expression 'every man' to talk about a particular group of individuals, individuals about whom we go on to speak.

Now Frege had an objection to this (and Frege is the source of all our modern ideas about reference).
If I utter a sentence with the grammatical subject 'all men', I do not wish to say something about some Central African chief wholly unknown to me. It is thus utterly false that I am in any way designating [my emphasis] this chief when I use the word 'man', or that this chief belongs in any way to what the word 'man' means.
Which is not correct at all. When you use the expression 'every man' or 'all men', you certainly are saying something about this individual, even though he is unknown to you. And why is it false that you are designating him? It depends what mean by designation, but then you are back to the problem of defining 'reference'. And the chief does belong in some way to what the name means. If it meant something different, e.g. if the English word 'man' meant only European men, then the sentence wouldn't be about this chief, would it?

In summary, there is nothing about the definition of reference as given by at least two authoritative sources (the SEP and Frege) that distinguishes it from the medieval concept of supposition. More later.


David Brightly said...

Hi Ed,

Your last para has thrown me a bit. If 'reference' a la SEP is rather weakly defined as mere 'talking about' then it would seem to agree with medieval 'supposition'. But reference a la Frege would seem to be a more refined notion. In particular,
'man' denotes a concept rather than the things that fall under it in some context. Doesn't this distinguish it from supposition, contrary to your claim?

Jason Hills said...

Enjoying this and the previous technical posts.....

Edward Ockham said...

>>But reference a la Frege would seem to be a more refined notion. In particular, 'man' denotes a concept rather than the things that fall under it in some context.

Possibly, but in that case 'reference' is not simply 'talking about'.

>>Doesn't this distinguish it from supposition, contrary to your claim?

Well it does, but I think that Frege is trying, but failing, to get at something else here.

Edward Ockham said...

Perhaps Frege is getting at something when he says that it is not the case that "this chief belongs in any way to what the word 'man' means."

But then we have the problem, which we've discussed before, of what 'Socrates' means. Does Socrates belong in any way to what his name means? If so, then Socrates is part of the meaning of his name, which as I've argued before is absurd.

Anthony said...

Socrates is what "Socrates" means.

David Brightly said...

Here is Peter King on Supposition Theory in the Oxford Companion to Philosophy (in full, my emphasis):

Medieval philosophers developed supposition theory in the late twelfth century to specify the reference of a term in various propositional contexts. A term has personal supposition when it is used to talk about what it signifies, for example 'lion' in 'She is feeding the lion now'. A term has material supposition when it is used autonomously to talk about its inscription or utterance, as in 'Lion has four letters.' A term has formal supposition when it stands for a concept or universal, as in 'Lion is a species'. The modes of personal supposition specify how many objects a term is used to talk about: either exactly one (discrete supposition) or at least one (determinate supposition); if the latter, either all instances (distributive supposition) or several (non-distributive confused supposition). Supposition theory was used to codify and explain the inferential relations among sentences. It was an important part of medieval theories of truth, quantification, entailment, and fallacy.

Bear in mind that I haven't come across supposition theory before. The Thomists at BV's may have brought it up a while back but that whole discussion ran above my head. Is it fair to say that the medievals needed supposition theory in order to compensate for the ambiguities inherent in their language? It's as if they worked backwards: given some sentences purporting to be a valid argument, they found it necessary to make more precise the meanings of the premisses and conclusion. It's as if they are annotating terms with further information, in particular, as King makes clear above, information as to quantity. This amounts to embedding their original language in an extended version. So though supposition is concerned with issues of reference it's by no means a theory of reference, as we would understand that phrase. It's actually progressing towards a logical language more fit for its purpose.

Edward Ockham said...

Hmm the definition of personal supposition is not correct - in material and simple supposition the terms also stands for what it signifies, in a different way. I the LM article I used the expression 'ultimate significate' which comes from Buridan.

But that is roughly right. On what supposition theory is, that is a bit beyond the scope of a blog. It's clearly a theory of quantification. On ambiguity, yes - they didn't have any formalisation to speak of except for the A and B in 'every A is B'. To account for donkey sentences and the like, and many other cases of ambiguity, they developed a complex series of rules - dozens of them. Modern logic prefers, rightly, a very simple set of rules and a formal language.

On the other hand, the medievals were more interested in ordinary language as such, so that's fine too.