Wednesday, 15 October 2014

Granularity and Relativism about Truth

The doctrine of semantic granularity can, I think, shed considerable light on the meaning and motivation of relativism about truth. It may even help resolve debates surrounding it.

In this post I will try to briefly indicate how I think this is so. I had a post on granularity and the paradox of analysis lined up for this month, but I will postpone it and get this one out now, in response to this related post on the blog language goes on holiday.

This may not be very clear to others yet, although I think I have it fairly clear in my own mind. Reading the other posts on granularity here, including future ones, will certainly help. (Soon I will do a granularity "roundup" post, collecting them all in one place and sumarizing their contents, but for now see the bottom of this post.) I will try my best under present constraints, in the hope that some reader gets something clear out of this.

Why bother? Well, I think this may be a pretty powerful and important application of granularity, since relativism about truth is such a vexed and widely ramified issue in our intellectual culture. Anyway, here goes.

Granularity and Relativism about Truth

Once the doctrine of granularity is on the table in its basic form, questions of this sort arise (among others): OK, meanings and the like can be carved up at different granularities, but what is the range of possible carvings up?

Surely there are limits; it is far from being the case that, for every two instances of thought or talk, there is a granularity at which they are counted as meaning the same. And it seems quite probable, although this is more debatable, that it also isn't the case that, for every two instances of thought or talk, there is a granularity at which they are counted as differing in meaning.

And do these different possible carvings up fall on a continuum, or are there multiple dimensions of what may count and what may not count towards difference in meaning? (I think the answer is that there are multiple dimensions, and I will try to say something about this in future.)

Now, these sorts of questions suggest a basic constraint on possible or "admissible" granularities for carving up propositions: if two instances of propositions are to be counted as meaning the same, they had better not differ in truth-value.

And now we can see relativism about truth in a new light, namely as the rejection of this constraint.

Furthermore, it is not hard to see how, in certain areas, it may be tempting to reject the constraint. Between two instances, there may be so much of the sort of stuff which usually counts toward sameness of meaning in common that it is really tempting to count them - at some granularity - as meaning the same, while nevertheless certain other important stuff differs so as to make (it best to say that) the truth-values come out differently in the two instances.

This may be particularly likely to happen with the rich and complicated concepts in the moral and aesthetic domains. And perhaps others too. And so we get a new perspective on the motivation of relativism about truth as well.

Of course, in many areas this sort of thing just won't happen - the motivation won't be there. It has often been observed (most saliently in my memory by my former teacher Adrian Heathcote, in unpublished writings) that relativism about truth appeals to people in some domains, such as morality and aesthetics, where it would never seem appealing in others. And so the general, woolly-seeming doctrine that all truth is relative can be and often is condemned as being based on a far too narrow diet of examples: you may be tempted to say such a thing after considering some moral or aesthetic matter (for instance), but with other matters such as basic geography or facts about how many chairs there are in some easily observable room, the notion that something may be true for me, while something else is true for you, would never occur to anyone, and seems completely absurd.

But relativism about truth need not be maintained that way - it may be maintained that in some areas, or with some propositions, truth is relative. Call this moderate relativism.

And, as I have tried to indicate, granularity considerations can shed some light on what this may mean, and what may motivate it. This in itself is, I think, a good advertisement for the power of granularity considerations, as relativism about truth is a big deal, especially in the borderlands of philosophy.

OK, good. But now a further question comes up: is it true? Are there, in some areas or with some kinds of propositions, admissible granularities on which two instances of propositions get counted as meaning the same but differing in truth-value?

I think that here we need to consider allowing the possibility of a kind of pluralism - slightly different sets of concepts such that, on one set, the issue gets decided one way, and on another set, the issue gets decided the other way. For instance, it could be that the maintainer of moderate relativism has a slightly broader or more flexible notion of meaning/proposition than the denier. And perhaps realizing that may enable them to resolve their dispute.

Still, it may give way to different disputes about how best to use certain words, and about which concepts to deploy where - but these may be more tractable.

(Here we get into the difficult and important topic of verbal disputes. Chalmers has recently had things to say on this topic, which was arguably being neglected before he did so. See his paper 'Verbal Disputes'.)

So, granularity considerations can be fruitfully applied to relativism about truth. They may help to (i) clarify its meaning, (ii) shed light on what motivates its adoption and (iii) help show the way to a resolution of debates over it.

Related Posts

Kripke's Puzzle and Semantic Granularity

Facts and Granularity

Granularity and Quine

Metaphysical Realism and Conceptual Relativity: An Application of Granularity

Philosophers' Carnival #168

Welcome to the 168th edition of the Philosophers' Carnival, a monthly digest of substantive analytic philosophy from around the blogosphere.

It seems like substantive philosophy blogging is in pretty good shape at the moment - but the landscape has been changing, so that things may not look healthy if you just stick to the old popular venues. Quite a few writers came out of the woodwork recently when Brian Weatherson started his new tumblr blog, And Another Thing. (He has a few posts on this theme, here, here and here.)

Tuesday, 14 October 2014

Raisins at Dawn #1

Topics this time include: logical space and Wittgenstein, method and semantic notions in philosophy, the idea of metaphysics, Lichtenberg on selfishness, modality, semantic granularity, and F.P. Ramsey on what the vastness of the universe doesn't mean for us.

Saturday, 20 September 2014

Modality and 'Epistemic' a preview of forthcoming analyses of a priority and analyticity.

This is a correspondence-inspired followup to 'Two Concepts of Metaphysical Modality'.

What I there called 'metaphysical modality in the broad sense' should probably be thought of as including what David Chalmers calls the logical or epistemic modality (also sometimes the 'indicative' modality), tied to what is a priori consistent. This despite my characterizing it in part with the term 'non-epistemic'.

What's going on? It may look like there is some disagreement between me and Chalmers about whether some modality has some status which we both call 'epistemic'.

I don't think this is so, however. It seems there are just different uses of 'epistemic' at work here. Chalmers doesn't think that what he calls the logical or epistemic modality depends upon our knowledge or conventions (any more than logic does). Whereas I was using 'epistemic' in 'non-epistemic' (and tend to use it elsewhere) to mean something like 'depending on or having to do with knowledge'.

This also connects with a bit in Chalmers's short piece on the tyranny of the subjunctive, where he fields the objection 'But indicative necessity is epistemic!' and says 'So?'.

For me that always seemed like a bullet that really didn't have to be bitten - in fact, on that ought not to have been. But this is probably because I was reading 'epistemic' to mean something like 'depending on, or having to do with, knowledge'. I now suspect I was reading it contrary to Chalmers's intention. One moral: take care using and interpreting overworked philosophical words!

Now for the preview...

For my part, I think the core notion behind the a priori/a posteriori distinction in propositional typology - which distinction is tied to what Chalmers calls the logical, epistemic or indicative modality - isn't really 'epistemic' in the sense that I tend to give that word. 'A priori' could of course be stipulated to be about knowability without experience or whatever, but what underlies and explains that knowability has to do with the nature of the proposition itself.

I'm working on cashing that out in terms of the internal meaning determining the truth value. And that sounds like analyticity, but to that I reply that it's the full internal meaning in question here, which need not be fully grasped in order to pass as understanding the proposition in question. To define analyticity, I want to use a notion of a 'meaning-radical' - something like a bit of conceptual structure such that having it on board suffices for you to count as understanding the proposition in question - and say that a proposition is analytic iff its meaning-radical determines its truth value. Or one of its meaning-radicals, if there can be more than one. (Meaning-radical/analyticity are pretty vague notions, I think.)

This also provides a nice pithy answer to Kant's big question; the synthetic a priori is possible because full internal meaning can outrun meaning-radicals. This connects to the idea of the linguistic division of labour, and Wittgensteinian points about the widely-scatteredness of the determinants of meaning.

Monday, 8 September 2014

Metaphysical Realism and Conceptual Relativity: An Application of Granularity

This is another instalment in the 'Applications of Granularity' series I introduced in the last post. To learn what is going on here, have a look at the first paragraphs of that, and the original post on Kripke's puzzle and semantic granularity.

Let us characterize metaphysical realism as the view that there is exactly one true and complete description of the world, and let us characterize conceptual relativity as the denial of that claim.

These two opposing views, at least in name, come from Putnam's discussions in, among other places, the books cited at the end of this post, and have since been discussed by many philosophers. It is not clear to me whether Putnam ever took the characterizations I have given as full characterizations, but they have certainly been for him at least part of what is involved in the two views.

Putnam used different characterizations at different times, and plenty of people have worked at sorting that out a bit. I'm not getting into any of that. I just want to stipulate the above characterizations, and briefly indicate how the doctrine of semantic granularity can dissolve the appearance of a hard- or impossible-to-resolve philosophical disagreement here.

It can do this as follows. If a complete description of a domain D is a set of propositions such that every proposition which says something true about D means the same as one of the propositions in the set (or a conjunction of them), then whether we say a description of the world is complete depends on the granularity we are operating at. Conceptual relativity may hold at a certain granularity, but once you make the granularity finer, it may collapse into metaphysical realism.

Seen in this way, where one claim, conceptual relativism, holds at one granularity or set thereof and the other, metaphysical realism, holds at another (finer) one or set thereof, they are not inconsistent with each other, and each has its own point.

Conceptual relativity as it were emphasizes the possibility of attaining the same or similar goals by different cognitive and linguistic means. Metaphysical realism on the oher hand emphasizes what we might call the sovereignty, the special individuality, of the different ways of doing things.

Relevant Works

Putnam, Hilary (1978). Meaning and the Moral Sciences, Routledge & K. Paul.

Putnam, Hilary (1981). Reason, Truth and History, Cambridge: Cambridge University Press.

Putnam, Hilary (1985). Realism and Reason, volume 3 of Philosophical Papers, Cambridge: Cambridge University Press.

Putnam, Hilary (1990). Realism with a Human Face, Cambridge, MA: Harvard University Press.

Not to mention the innumerable writings by others dealing with Putnam's philosophy.

Monday, 25 August 2014

Granularity and Quine

In a former post I introduced the idea that meanings and the like can be carved up at different granularities. This was motivated using Kripke's famous puzzle about belief, and introduced as offering the key to a solution.

I plan to develop this doctrine of semantic granularity further, adding detail and removing certain possible misconceptions, in future posts. For the time being, however, I will defer that and outline a further application of the doctrine (the original one being to Kripke's puzzle). Several more applications have occurred to me since arriving at the doctrine, each time bringing great joy and encouragement, since they seem to suggest that it really is a good idea. Accordingly, this will in all probability be the first of a series of posts which as a whole may be called 'Applications of Granularity'.

The application I want to outline this time is to Quine's famous skepticism about meaning and propositions. Quine's position is not so much that there are no such things as meanings or propositions (where these latter are construed as sentence-meanings) - although he does sometimes seem committed to that too - but rather that semantic notions such as that of meaning are somehow second-rate, badly-behaved, and not worthy of serious thought.

(Quine's peculiar conception of serious thought, first-rate concepts, real scientificality and the like - which could be called a scientistic conception, but is, to be fair to science, really much narrower than that; what we really have is a bias in favour of notions which Quine for his own peculiar reasons thinks of as first-rate scientific ones - is a very interesting matter which I would like one day to scrutinize here at some length. But this will have to wait till another time.)

Now, the application of the idea of semantic granularity I want to outline here is not to the refutation of Quine's position, although it may go some way toward breaking its grip. Rather, my focus is the explanation of Quine's position; what was going on with him when he came to it, and secondly, what is going on when other thinkers feel his arguments to have force.

Quine's skepticism focuses on the, to him, confusing individuation-behaviour of intuitive notions of meaning. To give a sense of his position, I will first quote from a section of McGrath's Stanford Encyclopedia of Philosophy entry on propositions, a section called 'The Individuation of Propositions', and then give a couple of illustrative quotes from Quine himself.

Some Quotes Illustrating Quine's Position

This section can be skipped or skimmed depending on how much of a sense one wants to get of Quine's position, or how much reminding one needs. To skip it, just scroll down to 'The Diagnosis'.

Probably needless to say, these quotations by themselves, to a reader unfamiliar with Quine's writings on the subject, will not give the full picture of what he had to say; it was an issue he picked up again and again and said a lot about.

Here is McGrath in the SEP:
Some philosophers, notably W.V.O. Quine, recognize the existence of certain sorts of abstract entities but not others at least partly on the basis of concerns about identity conditions. Quine granted the existence of sets, in part because they obey the extensionality axiom: sets are identical iff they have the same members. When it came to properties, relations and propositions, however, he found no such clear criterion of identity. The property of being a creature with a heart, he noted, is distinct from the property of being a creature with a kidney, even if all the same things exemplify the two properties. 
It is a controversial matter whether Quine was right to demand such rigorous criteria of identity as a condition for acceptance of a class of entities. However, even if Quine asks too much, any good theory of propositions ought to have something to say about when propositions are identical and when they are distinct. Developing theories which give such accounts in a way that fits well with intuitive data concerning propositional attitude ascriptions would enhance our reasons to accept propositions.

Now a few illustrative Quine quotes.

From 'Two Dogmas of Empiricism' (1951 edition):
For the theory of meaning the most conspicuous question is as to the nature of its objects: what sort of things are meanings? They are evidently intended to be ideas, somehow -- mental ideas for some semanticists, Platonic ideas for others. Objects of either sort are so elusive, not to say debatable, that there seems little hope of erecting a fruitful science about them. It is not even clear, granted meanings, when we have two and when we have one; it is not clear when linguistic forms should be regarded as synonymous, or alike in meaning, and when they should not.

This paragraph from a section of Philosophy of Logic boldly entitled 'Propositions Dismissed':
The uncritical acceptance of propositions as meanings of sentences is one manifestation of a widespread myth of meaning. It is as if there were a gallery of ideas, and each idea were tagged with the expression that means it; each proposition, in particular, with an appropriate sentence. In criticism of this attitude I have been airing the problem of individuation of propositions.

This passage from the 'Meaning' entry in the playful Quiddities:
[...] what is it for two expressions to have the same meaning? They cannot have exactly the same use, for when we use one we are not using the other. One wants to say rather that they have the same meaning if use of the one in place of the other does not make any relevant difference. The question of sameness of meaning, then, comes down to the question what to count as relevant difference.
I see no prospect of a precise answer, nor any need of one. Everything real and objective having to do with our use of expressions, and hence with their meaning, can be said without positing any relation of full synonymy ofexpressions, or sameness of meaning. In describing ways in which an expression is used we may be said still to be explaining its meaning, but there is no lingering trace of a museum of labeled ideas nor of any clear and simple relation of paraphrase or translation.
I urged at the end of the entry on IDEAS that there is no place in science for ideas, and under KNOWLEDGE that there is no place in the theory of knowledge for knowledge. Now we find me urging that there is no place in the theory of meaning for meanings, commonly so called.

Finally, if a bit more detail is wanted, here are selections (kept in order) from a more nuanced discussion in section 42 of Word and Object, 'Propositions as Meanings':
A large part of learning 'apple' or 'river' was learning what counts as the same apple or river reexposed and what counts as another. Similarly for 'proposition': little sense has been made of the term until we have before us some standard of when to speak of propositions as identical and when as distinct.
If we are content to define identity of propositions by synonymy of sentences, there is no evident objection to calling propositions meanings of eternal sentences. Misgivings as to what sort of object such a meaning might be could be allayed, if one pleases, by identifying it with the very class of all those mutually synonymous sentences that are said to have it. The worry that remains is the worry over a suitable notion of synonymy of eternal sentences. If propositions are to serve as objects of the propositional attitudes, then the broad sort of sentence synonymy talked of in § 14 [Details of that don't matter here - TH] would be unsatisfactory as a standard of identity of propositions even if adequately formulated. It would be too broad. For it would reckon all analytic sentences as meaning an identical proposition; yet surely one would not want to regard all analytic sentences as interchangeable in contexts of belief or indirect quotation, especially if all mathematical truths are regarded an analytic. Hence Lewis and Carnap have resorted to narrowed derivative relations of synonymy, or intensional isomorphism in Carnap's phrase, as better suited to interchange in contexts of propositional attitude.
Mates, Church, and Scheffler have argued that Carnap's intensional isomorphism (and Lewis's earlier construction of similar character) is still too broad for interchange in contexts of propositional attitude. Putnam and Church have responded with proposals for further tightening the relation. Scheffler still finds loopholes, but part of his criticism can be annulled [...]
We do have our analyticity intuition, but it grades off. [...] Now there is no objection to a graded notion of synonymy or of analyticity, supposing it made reasonably clear; but it is unlikely to contribute directly or indirectly to a standard of identity of propositions. For propositions have to be the same or distinct absolutely; identity, properly so-called, knows no gradations.
These reflections count only against hoping to base identity of propositions on some sort of intensional isomorphism derived from the broad sort of sentence synonymy which is interdefinable with analyticity. We might still hope to construct some approximation to intensional isomorphism suitable for identity of propositions, in some other way than from the elusive broad notion of sentence synonymy.
This last point [No need to worry about what that was - TH] has the germs of an argument not only against our specific plan of a structural synonymy concept as a standard of propositional identity, but against the whole idea of positing propositions. For, insofar as we take such a posit seriously, we thereby concede meaning, however inscrutable, to a synonymy relation that can be defined in general for eternal sentences of distinct languages as follows: sentences are synonymous that mean the same proposition. We would then have to suppose that among all the alternative systems of analytical hypotheses of translation (§§ 15, 16) which are compatible with the totality of dispositions to verbal behavior on the part of the speakers of two languages, some are "really" right and others wrong on behaviorally inscrutable grounds of propositional identity. Thus the conclusions reached in § 16 may of themselves be said implicitly to scout the whole notion of proposition, granted a generally scientific outlook. The difficulties cited earlier in the present section are merely by the way. The very question of conditions for identity of propositions presents not so much an unsolved problem as a mistaken ideal.

The Diagnosis

As we can see, Quine's objection to meanings, propositions, etc. was based on the idea that there is no single, clear criterion of identity for them. Given the doctrine of semantic granularity, this is no surprise and no objection. The individuation of these things differs at different granularities. In the grip of preconceptions about how language must properly work, Quine mistook a feature for a bug.

(I say that 'the individuation of these things differs at different granularities', but that form of expressing the point could be misleading and sound like some kind of antirealism - I will address that at length in a future post. For now: the point could be more carefully put in terms of the truth-values of synonymy or non-synonymy sentences, or of identity or distinctness statements about meanings, propositions etc.

This is connected with Quine's point in the Word and Object selection above, 'For propositions have to be the same or distinct absolutely; identity, properly so-called, knows no gradations.' On my approach, it is not that identity needs to have gradations, rather that identity statements with meaning- or proposition-designating phrases come out with different truth-values when operating at different granularities.)

It is instructive here to see how I, with my doctrine of granularity, can and indeed must agree with a lot of the things Quine says on the way to his hostile position, and how with the doctrine of semantic granularity on board, we can see that the hostile position doesn't follow.

For example: 'The very question of conditions for identity of propositions presents not so much an unsolved problem as a mistaken ideal' from the Word and Object selection. Indeed, if the question is construed as asking for a single, all-purpose set of conditions, it does present a mistaken ideal. What the doctrine of granularity says is that the conditions are different at different granularities, and that is part and parcel of the power and flexibility of semantic notions as bundlers and separators of linguistic items and occurrences.

And from Quiddities, 'The question of sameness of meaning, then, comes down to the question what to count as relevant difference. I see no prospect of a precise answer, nor any need of one.' Note the 'one'; the whole point of the doctrine of granularity is that there is no one answer here.

I hope I have conveyed in outline how the doctrine of semantic granularity can explain and perhaps help break the grip of Quine's hostility towards meanings, propositions and the like. This application will, if I am right, only become clearer and seem stronger with the development of the doctrine I intend to pursue in future posts.

Note finally that despite the focus here (especially in the Quine quotes) mostly being on propositions construed as sentence-meanings, all this applies just as much to sub- and super-sentential meanings as well, for instance with names and the individuation of their "meanings", which I construe as name-uses or individual concepts, or with the meanings of larger things like arguments or speeches or books.


McGrath, Matthew (2008). Propositions. Stanford Encyclopedia of Philosophy.

Quine, W.V.O. (1986). Philosophy of Logic. Harvard University Press.

Quine, W.V.O. (1987). Quiddities: An Intermittently Philosophical Dictionary. Belknap Press of Harvard University Press.

Quine, W.V.O. (1951). Two Dogmas of Empiricism. Philosophical Review 60 (1):20–43.

Quine, W.V.O. (1960). Word and Object. The MIT Press.

Saturday, 2 August 2014

Two Concepts of Metaphysical Modality

Here I want to distinguish two concepts of metaphysical modality and then give two reasons for thinking that this is an important distinction.

One concept, which I will call the concept of metaphysical modality in the narrow sense, crucially involves the subjunctive/indicative contrast, or the contrast between considering a scenario as counterfactual versus considering it as actual, and focuses on the subjunctive/counterfactual side. (This is why Chalmers is able, in 'The Foundations of Two-Dimensional Semantics' and other papers, to choose 'subjunctive necessity' as his preferred term for metaphysical necessity in the narrow sense.) It concerns how things could have been in a very broad sense. And so we can help fix the concept with familiar Kripkean talk like 'To be sure, we don't know a priori that Hesperus is Phosphorus. Given far-out enough empirical revelations, that could turn out to be wrong. But given that we're not mistaken about this - given that Hesperus is Phosphorus - then it could not have been otherwise. It is a necessary truth that Hesperus is Phosphorus'.

The other concept, which I will call the concept of metaphysical modality in the broad sense, doesn't involve this contrast. It may be roughly characterized as modality which is neither epistemic nor somehow conventional. Modal facts which are the way they are irrespective of anything to do with our knowledge, and irrespective of any conventions we might have, are metaphysical modal facts. And we might want to throw in something about the modality not being restricted as well.

To illustrate the difference, consider a proposition like 'This typewriter cannot have two of its keys depressed simultaneously' - or, to avoid the idea that this may be a case of some tacitly restricted modality, 'This typewriter cannot in the course of its proper functioning have two of its keys depressed simultaneously'. This proposition clearly has a modal element. Also, this modal element appears to have little to do with knowledge or some convention we have set up. If the proposition is true, then the typewriter in question has this modal property - that of not being able to have two of its keys depressed simulteneously in the course of its proper functioning - in virtue of the way it is, not in virtue of our state of knowledge or any convention we have set up. And so we might want to say that the modality in question is metaphysical in the broad sense. But it seems not to be an instance of metaphysical modality in the narrow sense. The subjunctive, or the consideration of scenarios as counterfactual, doesn't come into the matter; it is, we might say, about what the typewriter can actually do, not what it might have done had things gone differently (even if, in this case, there is a one-to-one correspondence between actual and counterfactual possibilities).

Another example of a proposition involving a modality which we should say is metaphysical in the broad sense but not in the narrow, is 'It is possible to win a game of chess in five moves'. Here the object of interest is something abstract (the game of chess), whereas in the first example the object of interest was a concrete mechanical thing.

Why is it important to realize that there are these two different concepts of metaphysical modality? One reason is that it seems very likely to be relevant to solving problems about the varieties of modality, a topic whose difficulty has become steadily more apparent in the decades following Naming and Necessity.

Another reason, which has been even closer to my concerns, is its relevance for the project of trying to analyze or give an account of metaphysical modality in the narrower sense. For instance, the account of this which I have been developing involves a notion which clearly has a modal component.

The account, which I will post on soon, says that a proposition is necessary iff it is, or is implied by, a proposition which is both inherently counterfactually invariant and true. And the notion of inherent counterfactual invariance is cashed out in terms of the counterfactual scenario descriptions producible by the language system to which the proposition in question belongs. Not those which it actually does produce in its career, but those which it can. (A proposition is inherently counterfactually invariant iff its negation does not appear in any of these producible counterfactual scenario descriptions.)

The question now arises: does the presence of this modal element - which should be a good sign to anyone who, like me, is suspicious that there could be any such thing as a reduction of a modal notion to non-modal notions - make the account circular? 'Circular' in this context seems like a dirty word, but note that if the answer is Yes, that wouldn't mean that the account is no good at all; it would still be far from obvious or trivial. It could then perhaps be seen as a recursive definition, presupposing some cases as a base, and explaining the rest in terms of it. But still, Yes might seem like the wrong answer. I suspect it is. Separating metaphysical modality in the broad sense from metaphysical modality in the narrow sense opens up a promising way of supporting a No; the account deals with metaphysical necessity in the narrow sense - subjunctive necessity, necessity when considering-as-counterfactual - and appeals, on the right hand side of the 'iff', to a distinct species of metaphysical modality in the broad sense. On this understanding, there is no circularity - or to put it more politely, recursiveness - in the account at all. Of course, it doesn't supply us with a key for analyzing modality away altogether, as some attempts at analyzing metaphysical necessity in the narrow sense (without perhaps isolating that sense sufficiently clearly) have tried to do, but that should probably be seen as one of its more important virtues.


Chalmers, David J. (2006). The foundations of two-dimensional semantics. In Manuel Garcia-Carpintero & Josep Macia (eds.), Two-Dimensional Semantics: Foundations and Applications. Oxford University Press. 55-140.

Kripke, Saul A. (1980). Naming and Necessity. Harvard University Press.