This post assumes prior knowledge of philosophical vocabulary, concepts and quantified modal logic.
In the last century, against the backdrop of his own deep suspicion of modality, Willard Van Orman Quine took part in one of the most interesting debates in the philosophy of language.
He took a stance against de re modality (the view that objects can have essential or necessary properties), alongside the likes of David Lewis and against the likes of Saul Kripke who had is quantified modal logic to defend. Quine concluded that we must shun the view that objects can have essential properties.
I decided to revisit some of the research I completed as a student to explain Quine's view.
Groundwork: Intensionalism and Extensionalism
Extensional and intensional definitions are two ways in which we can define objects or concepts.
Intensional definitions give us the necessary and sufficient conditions for a term to be used correctly. For example, an intensional definition of 'bachelor' is 'unmarried man'.
Extensional definitions define things by listing all of the things that fall under that name. An extensional definition of 'bachelor' is a list of all unmarried men.
Now, Quine was an advocate of extensionalism. There were a number of things he liked about extensionalism, including its simplistic benefits and the thought that first order logic is scientifically superior. But we won't get into that here.
Here's an important techincal definition of extensionalism that we'll use later:
Extensionalism: a context is extensional iff when a term is replaced with a coextensive one, the truth value doesn't change.
As we will see, de re modality flouts extensionalism.
Three grades of modal involvement
Quine distinguished between three grades of "modal involvement" within sentences. The first is unproblematic. The second can be reduced to the first. But the third is unacceptable.
Why? Spoiler! It turns out that the third type requires essentialism. ********************
Quine considers the three grades by considering three formulations of the mathematical claim that:
9 is greater than 5
A: ◻'9>5'
B: ◻(9>5)
C: ∃x◻(x>5)
Or, to put it in a nicer way:
A*: The sentence '9 is greater than 5' expresses a necessary truth
B*: It is necessarily true that 9 is greater than 5
C*: Something is necessarily greater than 5
Predicates vs Statement Operators
To understand the linguistic and metaphysical differences between these, we should bear in mind the difference between predicates and statement operators.
Predicates are the necessary constituents of sentence which attach to singular terms. We can then say whether or not a sentence is true. For example, '___ is fickle' is a (one-place) predicate. We can attach a subject such as 'Alice' and creates a whole sentence.
Alice is fickle
...or formally:
Fa
Statement operators attach to whole sentences to form new ones.
It is necessary that Alice is fickle
...or formally:
◻Fa
Now let's go back to Sentence A - ◻'9>5'. The quotation marks around 9>5 tell us that's a linguistic expression, and that '◻' is the predicate. In our English version, '___ expresses a necessary truth' is our predicate.
But Sentence B treats '◻' as a statement operator. The sentence is like this: 'it is necessarily true that ___'.
Why sentences like A and B are unproblematic
Quine doesn't think sentences like B are problematic. Why? Well, let's think about what is needed to create whole sentences from a predicate and statement operator.
In place of Sentence A, we might have written:
A': The sentence 'Manchester' expresses a necessary truth
And that's fine, because we'll just say that it's false ("Manchester" doesn't express a necessary truth..!) But if we translate this into Sentence B format, the sentence becomes ungrammatical
B': It is necessarily true that 'Manchester'.
Now, A is consistent with extensionalism, but B doesn't look like it is. But Quine argues that Sentence B* is actually formed like this:
B**: It is necessarily true that-9-is-greater-than-5
Why does this help? Well, the name 9 isn't in the sentence at all. It's just an orthographic accident, in the same way that 'Java' doesn't really appear in 'JavaScript'. Suddenly Sentence B becomes an inoffensive predicate.
Interlude: Leibniz's Law
Leibniz's Law, also known as the Identity of Indiscernibles, roughly says that no two objects can have exactly the same properties. Formally:
∀x∀y(x=y => ∀F(Fx <=> Fy) && ∀F(Fx <=> Fy) => x=y)
Or if you prefer: for any x and any y, x is identical to y iff for any property x has, y has, and for any property y has, x has.
We're about to use this!
The Problem with C
Let's remind ourselves of Sentence C.
C: ∃x◻(x>5)
Here, '◻' is acting as an operator which quantifies into the sentence.
Now, remembering Leibniz's Law, look at these sentences.
P1 The number of planets = 9
P2 9 is greater than 5
P3 The number of planets is greater than 5.
Looks pretty good so far. But look what happens when we substitute P2 for B*:
B*: It is necessarily true that 9 is greater than 5
With Leibniz's Law, look what happens...
P4 It is necessarily true that the number of planets is greater than 5
This looks REALLY BAD! From obviously true sentences, we've created one that is obviously false. Quine uses this to say that all names, like '9', are referentially opaque. Necessity has to be a linguistic construct, not something which says anything about the world itself. We can't substitute these two coextensive terms salva veritate.
And this flouts extensionality.
Variables have to be purely referential. Why? We test quantification in logic for each bound variable by assigning objects in that domain. Let's test this against Quine's third grade of modality by imagining that we can treat C* like B**:
B**: It is necessarily true that-9-is-greater-than-5
C**: There is an x such that-x-is-necessarily-greater-than-5
Something isn't quite right here. It isn't an accurate translation. The 'x' in (x>5) is bound to the ∃x. It isn't merely the 24th letter of the alphabet, not merely an orthographic accident. Sentence C really claims
C*!: There is an object of which it is necessarily true that the object is greater than 5
This forces a de re sentence in which we say something is true of the object. We can't reduce the operator to the simple predicate '◻' like we did with Sentence B.
Because we can't "quantify across modal operators", as Quine puts it, we should only use analytic sentences, in quotation marks. This entails what's known as Aristotelian Essentialism - that objects can have properties necessarily. But Quine doesn't like this at all. He believes modal concepts are strictly linguistic, they don't correspond to the world. In other words, they're de dicto claims rather than de re.
Interlude: Barcan Formula
For the next section, it will be useful to understand the Barcan Formula. It goes like this:
Barcan Formula: If everything is necessarily F, then it is necessary that everything is F.
∀x◻Fx => ◻∀xFx
For our purposes in understanding Quine, this means that de dicto claims imply their de re counterparts.
The Barcan Formula isn't undisputed - for example, it entails that there are no merely possible objects. But for now, let's run with it.
Why not de re modality?
R: Ralph believes that someone is a spy
The de re version of R is:
R*: There is someone whom Ralph believes to be a spy
Imagine for a moment that there's a chap on the beach, and he is the man in the brown hat. Ralph doesn't think the former is a spy, but believes the latter is. We can't be sure whether it's really true that he believes someone is a spy.
Quine moves by saying that Ralph believes of x the intension of being a spy. But this isn't sufficient. Intensions are not scientific notions. So he replaces belif with 'believing-true'.
R**: Ralph believes-true 'x is a spy' of the man in the brown hat.
Now recall the Barcan Formula. If Ralph believes that (in general) there are spies, and that he also believes there's someone who is the shortest spy. He believes the shortest spy is a spy. Note how the predicate '___ is believed by Ralph to be a spy' represents different properties depending on the term places before the predicate.
Now, given the Barcan scheme, Ralph believes there is someone (a particular person) of whom it is true that he is a spy. But that isn't the case. And that, Quine said, is absurd.
Against Essentialism
We might say that mathematicians are necessarily rational and not necessarily two-legged. Meanwhile, we might say that cyclists are not necessarily rational and necessarily two-legged.
What, Quine wonders, of an individual who both cycles and is a mathematician? It seems silly to consider her necessarily rational and coincidentially two-legged.
Since there's no good account of when properties are essential as opposed to accidental, as with our mathematician and cyclist, de re modality requires a distinction that Quine labels 'invidious'.
Therefore, Quine continues, there can be no de re modality.
Has he done enough?
Whether Quine has done enough is a question for another post (which I intend to write).
This one's already rather long (and somewhat complex).
For what it's worth, I'm not sure Quine is right, but I'm not sure his rivals (Kripke, for example) are either. I'd be willing to bite some bullets that others might find rather large when it comes to denying the truth of sentences we intruitively believe to be true.
In fact, understood my way, almost all sentences would be strictly false.
Enough of that, for now though!
Further reading
- Quine (1960) Word and Object
- Quine (1966) Three Grades of Modal Involvement
- Quine (1953) From a Logical Point of View
- Quine (1990) The Pursuit of Truth
- Quine (1995) From Stimulus to Science
- Kripke (1980) Naming and Necessity
- Lewis (1986) On the Plurality of Worlds
