On Carnap's 'Empiricism, Semantics, and Ontology' - Towards a More Nuanced View

Below are some notes on the first two sections Carnap's classic paper 'Empiricism, Semantics, and Ontology'. (Carnap's ideas in this paper have been very influential, and there has been a recent flurry of interest in them, as reflected in the 2016 publication of a volume entitled Ontology After Carnap. Thomas Hofweber, whose ontological project I have criticized, is a contemporary philosopher who has been very influenced by these ideas of Carnap.)

The notes below end up suggesting a more nuanced view of what is going wrong in metaphysical debates about the existence of ordinary things and numbers, according to which Carnap has correctly diagnosed that a kind of impossible jumping out of a framework is being attempted. But on the more nuanced view, this kind of jumping out is possible in some cases. (Carnap's view is that it never is, except as a potentially misleading way of switching to talk about the practical question of whether to adopt a linguistic framework.) That it is possible in some cases better explains why we so much as attempt it in the case of ordinary things and numbers.

* * *

'If someone wishes to speak in his language about a new kind of entities, he has to introduce a system of new ways of speaking, subject to new rules; we shall call this procedure the construction of a linguistic framework for the new entities in question.' - What is the status of this proposition? Is it meant to be a tautology? What does it take to be a 'new kind' of entity in the relevant sense? For in some reasonable sense it seems clear that we can begin to talk about a kind of entity which we have not previously been talking about without introducing a new linguistic framework. The framework can have, so to to speak, advance provisions for that in some cases.

'To recognize something as a real thing or event means to succeed in incorporating it into the system of things at a particular space-time position so that it fits together with the other things as real, according to the rules of the framework.' - Shades of pragmatism, or coherentism. Is 'recognize as F' a success verb here? Can't we have an idea of something which does fit well with our other current ideas but which is nevertheless the idea of something which doesn't actually exist?

Also, why a particular position? That seems false. Surely we can come to recognize the existence of something without knowing where it is. Also, the language Carnap uses here is quite unclear because while he is actually talking about changes on our end, i.e. in our linguistic representations and thoughts, he makes it sound like we are operating with the things themselves, incorporating them into a system.

- 'From these questions we must distinguish the external question of the reality of the thing world itself.' - This is a strong case for Carnap (who is talking here about the world of ordinary, observable physical objects), but one might wonder if it fails to generalize. Isn't there something special about our talk about the thing world? Carnap himself admits that the members of the thing world are 'the simplest kind of entities dealt with in the everyday language: the spatio-temporally ordered system of observable things and events'.

Couldn't it be this - the special foundational role played by talk of ordinary things - that makes it nonsense to ask whether they exist? (Or makes the question unsettlable?) Couldn't you have other cases where you've set up a framework which seems to licence certain "internal" existence statements, but where you can quite intelligibly and productively ask whether the things posited really exist at all? (And where this is not plausibly construed, as Carnap would want to construe it, as a practical question about whether to accept certain linguistic forms?)

It may be instructive to attempt to construct a clear, if artificial, example of this. (Here is a first thought, though there may well be much better examples available: a legal linguistic framework may treat the existence of a court as a basic assumption, without which the framework could not be applied. This doesn't mean we can't drop the legalese - step outside the legal linguistic framework - and ask about the existence of the court.)

Remember, linguistic frameworks can be embedded in larger linguistic frameworks. And in that way, we may be able to call the existence of the entities posited in some framework into question outside that framework, by remaining in a larger containing framework which allows us to treat the question in what Carnap would allow is a 'scientific, non-metaphysical' way. So that in the larger framework, the existence of the kind of entity in question is a question which may be answered empirically or a priori, in a non-trivial and non-metaphysical way, while in the embedded framework, the existence of the kind of entity in question is a basic assumption. I.e. something without which we can't really get off the ground with the embedded framework at all.

'The acceptance of the thing language leads on the basis of observations made, also to the acceptance, belief, and assertion of certain statements. But the thesis of the reality of the thing world cannot be among these statements, because it cannot be formulated in the thing language or, it seems, in any other theoretical language.' - Again, it seems like the thing language is a special case here, which makes Carnap overgeneralize. In the cases of less basic, less foundational frameworks, the latter disjunct 'or, it seems, in any other theoretical language' may be weak indeed.

Now Carnap turns to numbers, and again his case there is strong.

So, what I am saying is no threat to the core of Carnap's way of understanding what is wrong with metaphysical questions about the reality of ordinary things or the reality of numbers. Rather, it may lead to a nuancing of this and greater plausibility for it.

The problem isn't that you can never get outside a framework and ask about the reality of the things posited in the framework. On the contrary, you often can. And that helps explain why the attempt in the case of things and numbers is made at all.

So this more nuanced view has greater explanatory power. On Carnap's simpler view, according to which there is no such thing, ever, as getting outside a framework to ask about existence (literally, not as a disguised practical question), it is less clear why we would ever try.

Furthermore, the very idea of this going outside a framework, i.e. the very idea of what Carnap would call an 'external existence question', becomes clearer on the view I am suggesting. Rather than this mysterious thing which cannot in any possible case be done, it becomes something which can happen, and which we have examples of. On that basis, we may then argue that certain cases which bother philosophers are such that there is no properly analogous going-outside-the-framework to be done.

Forthcoming in Philosophia

My paper 'A Problem for Hofweber's Ontological Project' is forthcoming in Philosophia. It grew out of this blog post. The final draft is available at PhilPapers.

My preoccupation with arguing against Hofweber goes back further than that blog post, and he has always been very gracious and encouraging about it.

A Fallacy in Hofweber's Arguments in Ontology

[This is a draft of a paper.]

Hofweber's ontological project crucially involves inferring negative existential statements from statements of non-reference, i.e. statements that say that some term or terms do not refer. Here, after explaining the context of this move, I want to show that it is fallacious, and that this vitiates Hofweber's ontological project.

Thomas Hofweber has for several years been developing a distinctive approach to ontological and metaontological questions.

One of his starting points is the way some ontological questions in philosophy can apparently be settled with trivial arguments - for example, since mathematics has established that there are infinitely many prime numbers, it follows that there are numbers, and so there is no room for a special philosophical discipline of ontology (if it is to respect mathematics) to deal with this as a substantial question, the way ontologists of mathematics seem to try to do. Call this the puzzle about ontology.

Hofweber attempts to solve the puzzle about ontology by independently motivating a distinction between two different readings of quantifiers, or two sorts of quantification: internal and external. Internal quantificational statements, unlike external ones, do not work by placing conditions on a domain of objects. (To see that we might need something like this, consider the quantifier in 'Santa Claus doesn't exist, therefore there is something that doesn't exist'.) He then argues that the trivial arguments go through, but only when the quantifiers are given an internal reading. Give the quantifiers an external reading, and it is not clear that their premises have been established - in the case of 'There are infinitely many prime numbers', for instance, it might be that mathematics has established this on its internal reading, but not on its external reading.

Hofweber doesn't just want to solve the puzzle about ontology with his internal/external distinction, however. He also wants to use it to establish answers to certain (external) ontological questions - negative answers. This is what I call 'Hofweber's ontological project'.

Taking the number case, the project goes roughly like this. Hofweber argues that, if we can establish internalism about number-talk, including arithmetic (i.e. if we can establish that the quantifiers involved in number-talk, including arithmetic, are internal ones which do not place conditions on a domain of objects), we can show that the external question of whether numbers exist is left open by this talk, and is thus free for the taking by ontology.

Next, Hofweber argues that numerals, number words like 'four', and terms like 'the number 2' are not referring terms. I.e., that they are not in the business of referring to things. They sometimes assume the superficial grammatical position of referring terms for sophisticated linguistic reasons involving the notion of a 'focus construction' (and other considerations, depending on the kind of occurrence).

Then, on the basis that number terms don't refer, Hofweber concludes (via a principle designed to enable one to infer non-existence of things from statements of non-reference) that numbers don't exist, i.e. that there are no numbers (the quantifier here being intended externally), thus answering one of ontology's fundamental questions. I will good-naturedly call this last step 'the Howler'.

A couple of years ago, I inconclusively argued that Hofweber's distinction between internal and external quantification is ill-motivated. Here, I want to grant that distinction, and even grant that it enables Hofweber to explain the validity of the trivial arguments.

I want to make it clear that the Howler is a fallacious move, and that this vitiates Hofweber's project for answering certain ontological questions (e.g. about numbers, properties and propositions) in the negative. I will not be concerned here with whether Hofweber succeeds in establishing internalism about number-talk - my point is only that his argument from internalism to negative answers in ontology contains a fallacy.

The Howler appears in Hofweber's contribution to the influential 2009 anthology, Metametaphysics: New Essays on the Foundations of Ontology. The contribution is called 'Ambitious, Yet Modest, Metaphysics'. (I include other relevant papers in the bibliography, to help readers piece together a more detailed view of Hofweber's overall project, but he gives a good sense of it in the paper just mentioned.)

I think my criticism will be most effective if I quote the Howler along with the argument in which it appears, rather than reconstructing it and insisting that that is what Hofweber was doing. Here is the argument:

Let’s briefly reflect on what seems to be a central thesis about reference or denotation: 

(REF) If Fred exists then ‘Fred’ refers to Fred. 

Of course, I am assuming that ‘Fred’ is unambiguous, or at least used in the same way throughout. (REF) is uncontroversial, I take it, and probably a conceptual truth. Note that it implies the following: 

(REF∗) If ‘Fred’ doesn’t refer to Fred then Fred doesn’t exist. 

There are two ways for an expression not to refer. One is to aim to refer, but not to succeed. A classic case of this are empty names. Although the details of any example one might try to give of this are controversial, let’s nonetheless take ‘Sherlock’ to be an empty name of this kind. That is, suppose Sherlock is a name and thus has the semantic function of picking out an object. But it fails in carrying out that function. It thus doesn’t succeed in referring, and thus doesn’t refer. Thus Sherlock does not exist. Nothing in the world is Sherlock, no matter what in general the world contains. There could be all kinds of people, with all kinds of professions, but no matter how general properties are instantiated in the world, nothing in it is Sherlock. And nothing could be. If ‘Sherlock’ does not refer then Sherlock does not exist. This is all fairly trivial, but I go over it to make it vivid for our next case. 

Names aim to refer, but they can fail to succeed in what they aim for. The second way in which an expression might not refer is when it does not even aim to refer. Non-referential expressions, like ‘very’, don’t refer since they don’t even aim to refer. If internalism is correct about talk about numbers, properties, and propositions, then the relevant singular terms are non-referential. They do not aim to refer, and thus they do not refer. According to the above version of internalism ‘two’ is just like ‘most’. But since it doesn’t refer we know that there is no such thing as the number two. Since ‘two’ and ‘the number two’ are non-referring expressions nothing out there is (or can be) the number two. There can be all kinds of objects, abstract or concrete, they can have all kinds of properties and relations to each other. Nonetheless, none of them is (or can be) the number two. Or any of the other numbers. Internalism thus answers the ontological question.

Note first that Hofweber says that '[a]ccording to the above version of internalism "two" is just like "most"'. But what do we get if we substitute 'most' for 'Fred' in Hofweber's (REF*) principle?:

(REF*-Most) If 'most' doesn't refer to most then most doesn't exist.

But this seems like ungrammatical nonsense. Furthermore, it doesn't seem that 'Does most exist?' or 'Is there such a thing as most?' are substantial, sensible questions. It may be argued that 'Does most exist? No.' is not complete gibberish, if it is construed as a kind of metalinguistic point - it's not true to say 'Most exists'. This question-and-answer does not appear to be about whether the domain of our external quantifiers meets certain genuine conditions (and not simply metalinguistic conditions such as 'being referred to by the word "most"').

So if 'two' really is just like 'most' in all relevant respects, Hofweber has a problem. There is, of course, an important difference. Consider:

(REF*-Two) If 'the number two' doesn't refer to the number two then the number two doesn't exist.

Unlike (REF*-Most), (REF*-Two) is superficially grammatical. It even appears not to be nonsense (if we consider it independently of Hofweber's views). Do either of these two differences help?

Superficial grammaticality doesn't help; consider the nonsensical but superficially grammatical question 'Is there a rock of eggs?'. This doesn't seem to turn on whether a domain of objects meets some genuine condition, and 'Is there a rock of eggs? No.', like the 'most' case, seems to be a metalinguistic point at best.

The appearance of sense doesn't help either, for Hofweber has no way of explaining it except in terms of internalism; he explains occurrences of number-expressions always in terms of their being non-referring terms that appear in the syntactic guise of referring terms (for sophisticated linguistic reasons). And it is not at all clear what these could possibly be doing in an external quantificational context.

In general, the point might be captured by the following principle: non-existence of something only follows by semantic descent from non-reference when the non-referring term plays the semantic role of referring. Otherwise you can't semantically descend to a well-formed, sensical proposition.

(This is a necessary condition for the non-existence of something following by semantic descent from non-reference, but it may not be sufficient. I say 'follows by semantic descent' rather than simply 'follows' because '"X" does not refer' may be argued to always imply 'The referent of "X" does not exist' - but there is no semantic descent there, as there is in Hofweber's arguments.)

This seems like the natural view, in lieu of some special story, and Hofweber hasn't given any such story.

In a forthcoming post, I will argue that Hofweber's ontological project is impossible, for a different (though related) reason: internalism at the strength he requires it is inconsistent with the thesis that there is a substantial ontological question about numbers left open by arithmetic and other non-metaphysical number-talk, since such a question would constitute a counterexample to internalism. This mistake is, I think, more profound than the one exposed here - making it involves a kind of sawing-off of the branch one is sitting on.

Bibliography

Main reference: 

Hofweber, T. 2009. 'Ambitious, yet modest, metaphysics', in David John Chalmers, David Manley & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press.

Background reading for Hofweber's project:

Hofweber, T. 2005a. 'Number Determiners, Numbers, and Arithmetic', The Philosophical Review 114:2.

Hofweber, T. 2005b. 'A Puzzle about Ontology', Nôus 39:2.

Hofweber, T. 2007. 'Innocent Statements and their Metaphysically Loaded Counterparts', Philosophers' Imprint 7:1, <www.philosophersimprint.org/007001/>.

These papers are available on Hofweber's homepage:

http://web.mac.com/hofweber/Thomas_Hofwebers_homepage/Papers.html

A Note on Hofweber's Distinction between Internal and External Quantification

ABSTRACT: Thomas Hofweber's distinction between internal and external quantification is crucial to the solution he offers to his now well-known puzzle about ontology. Here I argue that this distinction is not well motivated by the considerations he employs.

In a series of interesting papers (2000, 2005b, 2007), Thomas Hofweber has identified a puzzle about ontology and developed a novel solution. Briefly, the puzzle is that questions such as 'Do numbers exist?' seem trivial from one point of view, but highly contentious from another. On the one hand, it is obvious that, e.g., there are even numbers smaller than 6. It follows trivially from this obvious statement that there are numbers. On the other hand, it is hotly disputed among philosophers whether or not there are numbers. Hofweber himself denies their existence. Nonetheless, he agrees that, e.g., there are even numbers smaller than 6.

Hofweber's solution to this puzzle crucially involves a distinction between two kinds of quantification which he calls 'internal' and 'external'. External quantification is familiar; externally quantified statements impose conditions on a domain of objects. Hofweber plausibly argues (2000, 2005b) that we must also recognize a kind of quantification which does not impose such conditions. His strategy is to highlight a certain 'inferential role' which quantifiers play in natural language, which enables them to function as place-holders for incomplete information; suppose we knew that Fred admires Thomas Edison, but then forgot this, remembering only that there is someone Fred admires. Hofweber argues that 'this situation is completely general', and that 'the only instances of the quantifier might be things that don't exist'.¹

With this distinction between internal and external quantification on board, Hofweber's solution to the puzzle about ontology is that the "trivial arguments" to the existence of contentious entities are indeed trivially valid, on the proviso that the quantifiers in their conclusions are given an internal reading. Questions about what there is, where 'what there is' is construed externally, thus remain as a non-trivial subject matter for ontology.

My object here is to show that the distinction Hofweber intends to make is not what it may appear to be at first glance, and furthermore that it cannot in fact be motivated solely by means of the considerations (indicated above) which he employs.

Let us begin with the question: why can't external quantification play the role of facilitating the expression of incomplete information? From the considerations offered, it seems that the only reason is that, as Hofweber says, the only instances of the quantifier might be things that don't exist. Thus we might think of internal quantifiers as characterised by the fact of ranging over both merely intentional objects and not-merely-intentional objects, in contrast to external quantifiers, which range over not-merely-intentional objects only. (I will call this 'the simple intentional-permissive understanding' of internal quantification.) This, however, is not how Hofweber conceives the distinction.

This becomes clear once we look at his views about arithmetical discourse with the distinction between the merely intentional and the not-merely-intentional in mind.² You can look for a prime between 24 and 28, and thus be looking for something. However, you will not find one: in this sense, there is no such thing. Hofweber fully recognizes this distinction, while nonetheless believing all quantification in arithmetic to be internal. Thus Hofweber's distinction between internal and external quantification cannot be understood in terms of the pre-existing distinction between the intentional and the not-merely-intentional. And yet this pre-existing distinction seems a natural and sufficient basis for a notion of quantification fit to play the inferential role Hofweber identifies. Therefore his consideration of this role is not by itself a good motivation for his internal-external distinction.

Note carefully that this argument does not require that the simple intentional-permissive understanding of internal quantification be a suitable basis for a solution to the puzzle about ontology. Furthermore, it does not rule out Hofweber's using the puzzle itself as a motivation for a special reading of quantification. The point is that he has not succeeded in establishing an independent motivation for such a reading.

It might be objected that I have not made an adequate case for the possibility of the simple intentional-permissive understanding of internal quantification. But I am not seeking to establish this conclusively; only, given that Hofweber has identified an inferential role which calls for a non-external reading of the quantifiers, the simple intentional-permissive conception is prima facie a better candidate than one based on Hofweber's internal-external distinction (considered apart from any puzzle about ontology). It may seem as though I'm not being quite fair, since I haven't really made his distinction clear in its own right. But I have no idea how to do this. Hofweber wants a reading of quantification such that the following comes out true:

There is an x such that x is not a merely intentional object, and x does not exist (in the external sense).

It has not been made sufficiently clear that such a reading is available.

Finally, one might wonder how Hofweber's internalism about arithmetical discourse avoids trivializing arithmetic. For on this conception, so-called "existence statements" about merely intentional objects (e.g. the largest prime) can easily come out true. Hofweber handles this with a supplementary doctrine to the effect that quantification in arithmetic is generally restricted to statements which have instances containing number words or numerals ('one', '46', etc.). However, and as Hofweber himself acknowledges, this sort of account cannot be extended to the reals, since we do not have number words for all of them.³ This gives rise to the worry that whatever the truth is about our quantification over the reals, it may also account for our quantification over natural numbers in arithmetic, rendering internalism about arithmetic theoretically superfluous.

Tristan Haze

The University of Sydney

References

Hofweber, T. 2000. 'Quantification and Non-Existent Objects', in Empty Names, Fiction and the Puzzles of Non-Existence, eds. Everett, A. and Hofweber, T. CSLI Publications.

Hofweber, T. 2005a. 'Number Determiners, Numbers, and Arithmetic', The Philosophical Review 114:2.

Hofweber, T. 2005b. 'A Puzzle about Ontology', Nôus 39:2.

Hofweber, T. 2007. 'Innocent Statements and their Metaphysically Loaded Counterparts', Philosophers' Imprint 7:1, <www.philosophersimprint.org/007001/>.

These papers are available on Hofweber's homepage: http://web.mac.com/hofweber/Thomas_Hofwebers_homepage/Papers.html

1 (2000), p 16.

2 These views are indicated in his (2005a).

3 Thanks to Thomas Hofweber for helpful correspondence on this and related points.