## No evidence for singular thought

Teaching for this semester is finally over.

Last week I gave a talk in Umea at a workshop on singular thought. I was pleased to be invited because I don't really understand singular thought. Giving a talk, I hoped, would force me to have a closer look at the literature. But then I was too busy teaching.

People seem to mean different things by 'singular thought'. The target of my talk was the view that one can usefully understand the representational content of beliefs and other intentional states as attributing properties to individuals, without any intervening modes of presentation. This view is often associated with a certain interpretation of attitude reports: whenever we can truly say S believes (or knows etc.) that A is F', where A is a name, then supposedly the subject S stands in an interesting relation of belief (or knowledge etc.) to a proposition directly involving the bearer of that name.

I'm not denying that one can define some such concept of singular content. But I doubt it has any interesting use. In my talk, I argued that it is not useful for epistemology.

By epistemology', I mean the systematic study of what we can know and how we can come to know it. Do we know that carbon emissions cause climate change? If so, what is the relevant evidence, and how does it support that conclusion? If not, what is missing? What would we have to discover? How can we find out if vaping causes cancer? How should a doctor diagnose a patient based on their symptoms? I take these kinds of questions to be central to epistemology, although they are more commonly discussed in confirmation theory than in old-fashioned epistemology classes.

I raised three worries about doing epistemology with singular content. I suspect the worries are well known, but I couldn't see them mentioned or addressed in the literature I skimmed.

The first worry draws on the context-sensitivity of attitude reports. Suppose I draw a card from a deck, face down. Suzy is watching. She doesn't know which card I've drawn. She does know that my favourite card in this deck is the Ace of Diamonds. I happen to have drawn that card. Now Suzy leaves the room. Pointing at the face-down card, I exclaim:

(*) "Suzy doesn't know that this is my favourite card."

That seems true. Then I turn around the card, and we all see it is the Ace of Diamonds. Pointing at the card again, I utter (*) again. Now what I say is intuitively false

So does Suzy know the singular proposition that the card in question is my favourite card? If we go by our practice of knowledge reports, the answer depends on which way around I hold the card. But Suzy isn't in the room, so the card's orientation makes no difference to Suzy's evidence.

The singularist doctrine therefore violates the following constraint on a sensible epistemology:

What Suzy knows is not sensitive to how I hold the card.

My second worry draws on the fact that names can be introduced by description. As Kripke and many others have pointed out, this seems to open the door to a priori knowledge of contingent facts. More generally, and more worryingly I think, it seems to allow acquiring knowledge without doing relevant research.

For example, if you know that someone invented the zip, you can introduce a name ('Julius') for that person. Now you know that Julius invented the zip. So you know the singular proposition that Witcomb L. Judson invented the zip.

For another example, suppose Donald Trump will not be impeached. If you know that Obama will not be impeached, you can introduce the name Ronald' to denote Obama if Trump will be impeached and otherwise Obama. Now you know that Ronald will not be impeached. Assuming Trump will not be impeached, Ronald is Trump. So you know the singular proposition that Trump will not be impeached.

A sensible epistemology should not allow for such ways of gaining knowledge. It should respect the following principle:

If P is a contingent proposition about some subject matter (and one can rationally disbelieve P) then knowledge of P requires empirical enquiry into the relevant subject matter.

Relatedly, Alonzo Church once showed that every statement is logically equivalent to an identity statement. Let P be any proposition. Let N' denote the set { x : x=0 & P }. Then P is true iff N = { 0 }. Now the singular proposition { 0 } = { 0 } is knowable a priori. If P is true, it is the same proposition as { 0 } = N. But we know that N = { x : x=0 & P }. Together, these entail P.

On the singularist view, all truths therefore follow logically from a priori truths. A sensible epistemology should deny this.

Many truths are not logically entailed by propositions that can be known without empirical enquiry.

My third worry is the one I care most about, in part because it does not rely on any tricks.

Consider Oscar from the Twin Earth story. According to friends of singular thought, Oscar knows the singular proposition that there is water (H2O) in the lakes. But how could he know this, given that he hasn't done any chemical research? How does he know the stuff in the lakes isn't XYZ?

A sensible epistemology, I think should respect the following principle:

If two things A and B look the same, and you initially don't know whether you'll be confronting A or B, then you can't come to know that you're confronting A just by looking.

For example, you can't find out that a patient has disease A rather than B from their symptoms if the two diseases have the same symptoms.

One might respond that Oscar doesn't know that the stuff in the lakes is water rather than XYZ, because he doesn't even have the concept of XYZ. I don't think this addresses the worry. But in any case, we can easily adjust the story.

Suppose we show Oscar a cup of XYZ and tell him that it contains twin water. (We may or may not tell him that twin water is not water, I don't think it matters.) Now Oscar knows the singular propositions that H2O is in the lakes and that XYZ is in the cup. I want to know how he could have that knowledge. How does he know it's not the other way round? What is his evidence?

Well, you might respond, when Oscar looks at the lakes, he sees water, and not XYZ. Perceptual experience provides singular evidence.

But it doesn't. Suppose I tell you that I'm going to pour a dark red liquid into a cup. I have a number of such liquids to chose from, and haven't yet made the choice. On the current proposal, by looking into the cup, you will come to know the singular proposition that liquid ABC is in the cup, where ABC is the substance I'll actually choose. If you value knowledge, you should therefore pay for an opportunity to look into the cup. That's absurd.

If you already know that a cup contains a dark red liquid, you make no relevant epistemic progress concerning the nature of the liquid by looking into the cup.

My worry is not so much that the singularist doctrine has counter-intuitive consequences. My worry is that denying all the displayed assumptions is incompatible with any systematic account of what kind of research we need to undertake to acquire specific knowledge about the world.

# on 03 December 2019, 21:29

Regarding your first worry, when the card is face down you are talking about that card, the physical object, and Suzy did not know that it was the Ace, your favorite; but when it is face up you are talking about that card, the Ace, and Suzy did know that it was your favorite. What you are talking about depends on whether it is face up or face down. So there just seems to be an ambiguity about the meaning of "card" here.

Your second worry means little to me, as I do not hold to such theories of names; but I like your third worry. Similarly (as I blogged about a while back, having been thinking about Twin Earth), there seems to be the logical possibility of an exact copy of you. We simply assume that we are not being swapped instantaneously with such copies. We certainly cannot find out that we are not being so swapped empirically, as they would be exactly like us. And it does matter when it comes to reference and knowledge. If I see a copy of you waiting for a bus then I cannot know that you are waiting for a bus because you are not. And if I see you waiting for a bus then I can know that you are waiting for a bus even though I cannot possibly rule out it being your copy. This seems to make a mess of all of our reference and knowledge, until you realize that we simply assume that such swapping never does take place. That assumption is a hinge proposition (as Wittgenstein described such things). No?

# on 03 December 2019, 21:37

Thanks Martin,

I don't quite get the first point. The scenario is supposed to be one in which my favourite physical card object from the desk is the one we call Ace of Diamonds.

I agree that the swapping scenarios you describe should probably be treated like other radically sceptical scenarios: we're entitled to assume that they are not actual even though we don't have any relevant evidence. But a scenario in which the stuff in the lakes is XYZ is not of that kind. Here I think we need specific chemical evidence to know it's not actual.

# on 04 December 2019, 04:43

I'm sympathetic overall, but didn't quite get the first worry. Whether "Suzy knows that S" is true is sensitive to features of the context of utterance. These features of a context in which a knowledge attribution is made include lots of things that make no difference to Suzy's evidence. This includes what sorts of things are under discussion or salient in the context -- perhaps including what properties of a card are salient. So (*) is true in the first context but false in the second, even though Suzy's evidence remains the same.

Is the problem that an advocate of singular propositions can't adopt this sort of contextualist treatment? Or is it that even doing so wouldn't help given that "this is my favourite card" expresses the same singular proposition in both contexts?

# on 04 December 2019, 09:40

Hi Brian,

The worry isn't that knowledge reports are context-sensitive. It's that I don't want a certain kind of context-sensitivity in a systematic epistemology. (Maybe I want none at all, but there's room for debate on other cases.) I want an epistemology to tell us what kind of enquiry would put Suzy in a position to know any given proposition. With an all-or-nothing concept of knowledge, we may have to allow for some contextualism, letting the answer depend on the stakes or on whether we take skeptical possibilities into consideration. But the answer shouldn't depend on arbitrary features of our context, such as the orientation of the card in my hand.

I'm imagining this kind of setup: Here's an agent, here's a proposition (not a sentence); epistemology should tell us if the agent knows the proposition. Perhaps there is no unique answer because the agent may have "low-stakes knowledge" but not "high-stakes knowledge", and these are equally natural and useful concepts. But I don't think there is a natural and useful distinction between "face-up knowledge" and "face-down knowledge".

# on 04 December 2019, 20:18

Suppose I am in the room in the first scenario. I know that Suzy knows that your favorite card is the Ace, and I also know that you have drawn that card (I have marked all your cards in order to wow you with my card tricks later). So when you say (*) it does not seem true to me. But as Suzy is leaving the room, I slowly work out why you said it (I am a bit autistic, but wicked at card tricks). By the time you say (*) again, it does seem true to me.

What Suzy knows now seems to be sensitive, not to how you hold the card (I did not even notice you turning it over), but to who is in the audience. (I only do card tricks in fictions, sadly.)

# on 05 December 2019, 16:34

Hi Wo,

I'm not seeing why the first puzzle has anything crucially to do with singular thought. That is, you are suggesting that two utterances of (*) have different truth-values depending on how you hold the card. You also want to say that what Suzy knows is not sensitive to how you hold the card. I'm not seeing why it matters whether the that-clause of (*) expresses a singular or non-singular proposition.

Best, BP

# on 06 December 2019, 10:24

Hi Wo,

If XYZ was only a possibility, Oscar would be entitled to ignore that possibility, even if he knew of it.

Showing him a cup of the stuff does not necessarily change matters. If the XYZ came from a spaceship, he has no additional reason to doubt that our lakes contain H2O.

But it could move him toward a reasonable doubt. He might wonder whether aliens had done more than bring over a cup of the stuff. There would be a kind of evidence that he would need to gather, to allay his worries about that. For example, he might research UFO sightings.

I think that the more his doubts were reasonable doubts, the clearer it would be what sort of evidence he would need to gather, to allay those doubts.

# on 05 January 2020, 19:01

Hi Wo,

First, I wish you a happy new year!

I am not sure to understand what you meant when you wrote:

"Relatedly, Alonzo Church once showed that every statement is logically equivalent to an identity statement. Let P be any proposition. Let `N' denote the set {x : x=0 & P}. Then P is true iff N = {0}. Now the singular proposition {0} = {0} is knowable a priori. If P is true, it is the same proposition as {0} = N. But we know that N = {x:x=0 & P}. Together, these entail P."

If P is the formula: {0} = N, one gets N = {x:x=0 & ({0} = N)}. In my opinion, it is syntactically weird and I do not understand how P is entailed. Your help is welcome.

# on 21 January 2020, 15:18

Hi Joseph! Sorry, I only just saw this comment (which came in while I was travelling).

Just to clarify, in the argument, P is not supposed to be the formula {0}=N; rather, P is an arbitrary truth -- say, that it is cold in Edinburgh. Clearly, {x : x=0 & P } = {0} iff P is true. So P is logically equivalent to {0}=N. (I assume that {x : x=0 & it is cold in Edinburgh } is {0} because the only object x for which the following is true: "x=0 and it is cold in Edinburgh" is the number 0.)

Perhaps you're asking what happens if we deviously choose as P the proposition {0}=N, where N is defined as {x: x=0 & ({0}=N)}. We need to check if this apparently circular definition of N succeeds in defining anything. If N is {0}, then {x: x=0 & ({0}=N)} is {0}. If N is not {0}, then {x: x=0 & ({0}=N)} is the empty set. So the definition is compatible with N={0} and with N={}. So I'd say it doesn't succeed in defining anything, and so P is not a well-defined proposition.