Monday, 1 August 2016

Denying the Conditional Premise: An Underrated Response to Skeptical Arguments

(This is a more focused re-write of a post from a couple of years ago, with better coverage of the literature.)

1. Introduction

Much ink has been spilled on skeptical arguments like the following:
  1. If you're a brain in a vat then you don't have hands
  2. You don't know that you're not a brain in a vat
  3. Therefore you don't know that you have hands
There are many variations on this sort of argument, and many issues have been raised about it, for example the issues of the closure of knowledge under implication, and the closure of knowledge under known implication.1

Here I will focus on the conditional premise part of this sort of argument. That is, on the premise which links a hypothesis according to which you are living in a simulation (e.g. the hypothesis that you are a brain in a vat (BIV)), to a seemingly-crazy hypothesis which flies directly in the face of things we normally think we know (e.g. the hypothesis that you don't have hands). Perhaps surprisingly, the truth of these premises is typically – we will consider a couple of exceptions below – taken for granted in contemporary discussions of such skeptical arguments.

For instance, Steup (2006, section 1) writes:

According to the BIV Hypothesis, you are a mere BIV without a normal body. This of course means, among other things, that you don't have hands.

Steup then goes on to consider five known kinds of responses to skeptical arguments. None of them, however, involves questioning (1), or questioning Steup's claim that '[t]his of course means, among other things, that you don't have hands'.

In this essay I want to argue against these conditional premises. I will try to be fairly non-technical and to avoid bringing in any very particular theoretical framework. I will focus on (1) in particular for the sake of definiteness, but the considerations will generalize in an obvious way to many similar conditionals.

In arguing that (1) and the like are not true, I am furnishing a way of avoiding the repugnant conclusions of skeptical arguments like the above without having to show that we do somehow know that we are not BIVs. We should instead, I say, just deny their conditional premises. This seems pre-theoretically attractive to me – it does intuitively seem to me that I do know that I have hands and that I do not know that I'm not a BIV. Or more carefully perhaps, and from a broadly contextualist perspective on knowledge-ascriptions2, it seems to me that there are contexts in which 'I know I have hands' comes out true while 'I know I'm not a BIV' comes out false.

Note that (1) and the like are generally supposed to be accepted readily, as though they were obvious (recall the Steup quote above). They just appear in skeptical arguments as premises which we're meant to accept without argument. Once you start scrutinizing (1) and the like as I propose, this can begin to seem rather odd. It can become hard to imagine what (1) ever had going for it. So, before arguing against it, let us first ask the question: why might (1) seem true?

Silly as it sounds – silly as it is – the answer appears to be something like this: when (1) strikes us as true, we are as it were picturing a brain sitting in a vat, and observing that there are no hands in that picture. Or we are picturing a brain sitting in a vat, and a mad scientist tending it, and noticing a striking contrast between the two figures – the scientist-figure has a body and hands, whereas the other figure is just an organ (in a vat). Something along those lines.

In this essay, I will argue that, by contrast, the denial of (1) has a good deal going for it. After first, in section 2, criticising and setting aside a superficial objection to (1), I will offer a volley of better arguments against it, beginning in section 3. In section 3 I will object that the question of whether a BIV has hands or not is better thought of as marking a different contrast from that between the BIV and the scientist above – a contrast such that some (possible) BIVs have hands and others do not. A possible doubt about this objection, which I will not try to allay in this essay, will lead us in section 4 to another objection based on it, which avoids the doubt. This objection, however, requires that when a BIV says 'I am a BIV' they are saying something true (however unknowable it might be to them). As natural as it is to accept this, it is contradicted by a famous argument of Putnam's, an argument designed to show that we are not BIVs. Accordingly, in this section I also examine and criticize Putnam's semantic ideas about 'I am a BIV' as said by a BIV, defending my objection against the threat from Putnam's argument. Then, beginning in section 5, I turn to a series of more intuitive arguments, designed to change the attitude of someone who is inclined to think (1) is true. In section 5 I make a case against (1) involving consideration of what is, and more importantly what isn't, implied by ordinary statements referring to hands. The idea here is to snap out of a false way of looking at such statements which we fall into when philosophizing about skepticism. In section 6, I contrast “normal” BIV scenarios with ones in which we are worse off epistemically, in order to motivate a view of “normal” BIV scenarios according to which their obtaining does not preclude our having hands. In section 7, I will suggest a reframing of the BIV hypothesis as a scientific one, and argue that from this point of view, the natural thing to do is to reject (1). This last suggestion will be seen to be essentially the position of Chalmers (2005), and therefore further supported by his arguments.3 I conclude briefly in section 8.

2. A Superficial Objection to (1) Rejected

Here I want to consider and put aside one particular line of attack on (1), to be found in Roush (2010). It is an almost comically literal-minded objection, which I found when I was searching the literature for previous attempts at calling propositions like (1) into question. Roush (2010) argues that it is not true that if you're a brain in a vat then you don't have hands, on the grounds that you might be a brain in a vat with hands just stuck on (!) – that is, where there are attached hands in the environment which contains the brain and the vat (as opposed to the environment simulated for the brain). Maybe the hands are just stuck on with glue and dangle there, or maybe they are delicately connected up with the brain, making for a queer straddling of two “worlds” (or environments, or levels of reality) on the part of the BIV.

There is something very frustrating about this objection. It is frustrating, I think, because if you just accepted this objection, deciding on its basis that (1) is false, and then walked away, you would have lost a valuable philosophical opportunity to understand (1) better. Furthermore, even if Roush's objection shows (1) to be false, the skeptical argument can easily be patched up by replacing (1) with 'If you're a brain in a vat without appendages as envisaged in Roush (2010), then you don't have hands'. Thus if we want to find objections to (1) in order to disarm skeptical arguments which threaten our putative knowledge that we have hands, we had better keep looking. We want an objection that is not so easily met with a patched conditional premise. (This is not to concede that the objection does show (1) to be false, by the way. For instance, we may ask whether a BIV with the envisaged appendages really counts as 'having hands', or whether this is really the best candidate meaning for 'having hands' in connection with a BIV.)

3. A Better Deserver of 'Having Hands' vs. 'Not Having Hands'?

We picture a BIV, and there are no hands in the picture. Then we picture a scientist tending the BIV and see a contrast between the figure of the scientist and the BIV-figure. And with this in mind, we might be tempted to say 'The BIV doesn't have hands and the scientist does'.

OK. But consider a different situation, in which we have two BIVs. It doesn't matter whether or not they are plugged into the same simulation. What does matter is that, in their lives in their simulation(s), one of them is an anatomically normal human, while the other has been in an accident and lost their hands. Mightn't we, if this was the first case we had considered, have been tempted to say 'One BIV has hands, the other does not'? And if we would be right in so saying, then we would be wrong to say (without shifting the meanings of relevant terms) that if you're a brain in a vat, you don't have hands; the first BIV would then be a counterexample to (1).

If we allow that we would be correct in saying, of the envisaged scenario, 'One BIV has hands, the other does not', this gives us an objection to (1). On this objection, 'has hands' vs. 'does not have hands', when applied to BIVs, is correctly used to mark this contrast, between BIVs like the first one and BIVs like the second one. Not the contrast between a BIV and a scientist tending it.

Here it might be objected that it would not be correct to say, unqualifiedly, 'One BIV has hands, the other does not' – rather, one would, to be both right and completely explicit, have to say something like 'One BIV has hands in its simulated environment, the other does not'.

In the present essay, I want to go along with – without endorsing – this objection to the present objection to (1), and use the present objection to (1) as inspiration for another objection, an objection which focuses on the truth-values of propositions uttered by a BIV in their simulated environment rather than on propositions we, standing outside a hypothetical scenario, might formulate about it. That is not to say there are no prospects for sticking with the present objection to (1) and arguing that the objection to it which we have just considered is mistaken – only that we will not pursue this here.

4. The BIV-or-Parity Argument

It may be that, of our first and second BIV above, we can't say with literal correctness that the first has hands and the second does not. But we can still ask about things the BIVs may say, in their simulations. And we could reason as follows: If the first BIV says, in the simulation, 'I have hands', they are, in the simulation, saying something true. And surely if they say, in the simulation, 'I am a BIV', they are, in the simulation, saying something true (even if they could never know it to be true). And thus, if they said 'If you're a brain in a vat then you don't have hands', they would be saying something false – something to which their very case is a counterexample. And if that's right, how could (1) fail to be false? How could our situation differ from the situation of the BIV in question in such a way that (1) for us is true, whereas their utterance – in the simulation – of 'If you're a brain in a vat then you don't have hands' – is not? I can see no way.4 So, I suggest the following overall argument. We are either BIVs or we are not BIVs. If we are BIVs, the above considerations about the truth-values of utterances made by an anatomically-normal BIV apply directly to us. If we are not BIVs, parity suggests that (1) for us has the same truth-value as the same sentence uttered by a BIV. Either way, (1) is false.

Now, the above reasoning seems natural, but of course it could be challenged. One way it could be challenged would be to follow Putnam's notorious (1981) in saying that, when the BIV says, in their simulation, 'I am a BIV', they are saying, in their simulation, something false, contra the above reasoning.

I do not have space here to lay out Putnam's arguments at length, but I think it is incumbent upon me to argue that Putnam is wrong on this point. I will now try to do this briefly and non-technically, but in a way that cuts quite deeply, perhaps more so than technical criticisms focusing on what might be non-essential features of Putnam's argument or reconstructions thereof. (For an overview of the literatue on Putnam's argument cf. Brueckner (2016).)

Putnam begins with a causal theory of reference, according to which what you're talking about when you say something is what stands in an appropriate causal relation with your utterance. He argues, from the causal theory, that since a BIV could have no causal contact with the brain they are, and the vat they are in, they could not be talking about that when they say 'I am a brain in a vat' – rather, their utterance is, according to Putnam, about 'vats-in-the-image', 'or something related (electronic impulses or program features)'5. And since they, the utterers, are not vats-in-the-image, i.e. not vats belonging to their simulation, nor the relevant 'related' things, what they thus say comes out false. Putnam goes on to argue, on this basis, that we are not BIVs, but we will stop here and just criticize this lemma – that a BIV saying 'I am a BIV' says something false – since the denial of that is all we need for our argument.

There are lots of things about this we could argue with – the idea that the BIV's talk might literally refer to electronic impulses or program features may seem crude and objectionable, for instance – but I will confine myself to a couple of key points.

Firstly, note that singular reference – reference to particular objects – isn't what is in question here. We are dealing with general terms like 'brain' and 'vat'. And what Putnam seems to be insisting on, in light of his causal theory of reference, is that, in order to really be about brains or vats, my talk needs to have an appropriate causal connection with some brains, or vats. So, going along with this way of thinking about what is required for talking about a kind of thing, in order for a BIV to think or say they are a BIV, it would seem that their thought or talk doesn't have to be causally connected with the particular brain they are or the particular vat they are in. It just has to be connected with some brains and some vats.

Now, why can't there be a general category marked with the word 'vat' which includes as members both “vats-in-the-image” - vats in simulations – and vats outside simulations? (And likewise for 'brain'.) I think we should say that there can be such a category. Consider things like happiness and intelligence: a BIV with a rich life is surely acquainted with these things, and causally connected with exemplars of them – and so they can have a category, for example marked 'expressions of happiness', and this category would include both things in their simulated environment and any appropriate things outside the simulation. And so Putnam's argument falls down here, by implicitly holding that the relevant reference classes – the 'brain' class and the 'vat' class – can only include things in the utterer's environment (or “level of reality”). Once we see this is not so, we can go along with Putnam's basic causal-theoretic starting point, but maintain that there is nothing stopping BIVs thinking they are BIVs, because they can form categories – by means of causal connections to brains and vats in their environment – which manage to include the brain they are and the vat they are in, despite those particular instances not being in their environment.

Now let us try to get a more positive sense of what is the matter with Putnam's argument, rather than just poking a hole in his reasoning. I want you to step back a bit, and just note how implausible and crude Putnam's interpretation of the BIV's utterance 'I am a BIV' is; it's supposed by Putnam to assert something which to the BIV would be obviously wrong – namely, something like: that they are brains in their environment in vats in their environment. And yet a reflective BIV might not find their utterance of it obviously wrong at all – on the contrary, it would be natural for them to regard it as something which it would be difficult or impossible for them to know the truth about. This suggests that something has gone awry. At a very general level, we may say that Putnam's problem is that he has inappropriately treated the language-game of talking about being a BIV as being just like an ordinary one about things in our environment. But it is plainly not that. Language, we might say, is playing a new trick here.6 We may not be able to come up with a theoretical understanding of this trick which would satisfy Putnam, but that does not mean he gets to falsify it.

So, I suggest that Putnam has not refuted the natural view that when a BIV says 'I am a BIV' they say something true, albeit something they may never be in a position to know. And thus the BIV-or-parity argument does not fail for that reason.

You may still be unconvinced, though, about the initial premise, i.e. that when an anatomically normal BIV – I mean their anatomy in the simulation, of course – says 'I have hands', they are saying something true. Accordingly, I will present further objections to (1) and the like which are supposed to convince you of this too, rather than just taking it as a premise. The general tendency of these arguments is to appeal to our common sense, as against the philosophical mood we are liable to be put into by skeptical arguments. (That this is a distinct mood is not something I am supposing to be obvious in advance, but if we are responsive to the appeal to common sense, I think we can see, in retrospect, that it was a distinct mood.)

5. Everyday Statements About Hands, And What They Do and Don't Imply

Consider statements made in ordinary, everyday conversation, statements which intuitively seem to imply that the utterer has hands. I want to urge that, intuitively, these seem not to imply that the utterer is not living in a simulation. That is, I think that is how it appears if we just regard these utterances with a normal, common sense attitude, instead of letting the skeptical argument put us in a philosophical mood in which our attitude changes and 'language goes on holiday'7. I suggest we accept these appearances, and conclude that (1) and the like are false.

For example, suppose someone asks me to help them with something and I say 'OK, one second - I'm just washing my hands'. This statement – that I'm washing my hands – surely implies that I have hands. Furthermore, I find it very intuitive – regarding the case from a common sense point of view – that it does not imply that I'm not living in a simulation, or that I'm not a BIV; that simply isn't at issue at all. That seems, I want to urge, quite independent of – extraneous to – the truth of what I said.

Going along with this: having hands is compatible with it not being the case that I'm not a BIV. And so, having hands is compatible with my being a BIV. And so it can't be true that if you're a BIV then you don't have hands.

6. That's Not A Nightmare. This Is a Nightmare!

The key intuition appealed to in the previous section – that my ordinary statement does not imply that I'm not living in a simulation – can, I suggest, be bolstered by thinking a bit about the space of different scenarios in which I am living in a simulation. Then we begin to see that it is possible to take an attitude to many of these scenarios which is quite unlike regarding them as epistemic nightmares, i.e. situations in which we're in really bad shape epistemically – where much of what we ordinarily think we know fails to be true. We can bring this out by contrasting “normal” scenarios in which we are in a simulation to what, by comparison, are the really nightmarish scenarios in which we are in a simulation. (Compare section 3, where we contrasted anatomically normal (in their simulation) BIVs with those who have been in accidents (in their simulation).)

Certainly we can imagine simulation-scenarios which are epistemic nightmares. We may be BIVs whose tending scientists are engaging in all kinds of foul play, planting false memories and moving things around on us. Also diabolical would be if some or all of the apparent agents we are interacting with are not sentient, or not as fully sentient as we think. I don't so much mean that they may not be constituted the way we are, or the way we think they are – after all, multiple realizability might be the case – but rather that maybe all there is to these agents is what's required to generate our interactions with them. Corners may be cut, so to speak – when we think they're off by themselves having a rich mental life, perhaps often nothing of the sort is true. But nightmarish scenarios like this are clearly a special subset of all simulation scenarios; in many of the latter, by contrast, I suggest that we may not be wrong about much of anything (or rather, not about anything to which the unknown fact that we are in a simulation would be relevant). It just might be the case that, unbeknownst to us, there is a higher level of reality “hosting” the one we inhabit, and this level may involve brains in vats.

Now, this of course raises the question: well, what about skeptical arguments which appeal to those really bad scenarios? Can't the skeptical arguments I am talking about just be patched up in light of this, thus making your criticisms no better than that of Roush, whom you criticised in section 2 for giving a superficial, easily avoided objection?

To this, I reply that, no, there is an important difference here. In the present case the 'patching up' is more complicated, and different BIV scenarios threaten different bits of what we normally think we know. It may be fairly easy to specify a scenario where certain supposed historical events in the simulation did not happen in the simulation, but the traces of them were put into the simulation in some other way. It may be fairly easy, but maybe a bit harder, to specify a BIV scenario where a BIV who hasn't been to France (in their simulation) is deceived about there being an Eiffel Tower (in their simulation). Harder still, but maybe doable, would it be to specify a scenario in which what a BIV takes to be other persons whom they know well are not actually fully persons, or do not always exist. As to what a BIV scenario where you are BIV who falsely thinks they have hands might really look like, I am not sure. I do not want to claim that no such scenario exists. The point is rather that, on the point of view I am advocating here, this would have to be quite a specific scenario – it merely being a scenario where you are a BIV doesn't automatically do the trick. This is, I think, a better, more nuanced way of thinking about BIV scenarios in relation to knowledge.

In further support of this viewpoint, I want to give one more suggestion, in the next section: that we reframe the BIV hypothesis as a broadly scientific one, rather than thinking of it as something like a threatening, sinister element in a story.

7. Reframing the BIV Hypothesis as a Scientific One

There is no need to respond to the news that you're a brain in a vat by revising your belief that you have hands. Why not treat the news instead as telling you, among other things, something new about your hands (and everything else in your environment), namely that they are “hosted” at a higher level of reality, or speaking crudely, are constituted by electrical impulses or program features. I say 'crudely' because the relation in question is obviously not the normal one of constitution from normal physical inquiry. Physics can be done in a simulation, too, and facts about the simulation being a simulation need not be regarded as belonging to that discipline. Nevertheless, I think it is quite natural to follow this suggestion and regard the BIV hypothesis as, in a broad sense, a scientific one. This seems to be a legitimate point of view. And once we take this point of view, it becomes natural to think of the hypothesis as one about the nature – in some sense – of your hands (and everything else in your environment), and thus not as a hypothesis which rules out your having hands. Compared with looking at these scenarios as something like sinister, threatening elements in a story, and then in that mood jumping to the conclusion that we don't have hands if those scenarios obtain, the point of view I am advocating seems the more clear-headed.

This last suggestion, that we regard BIV scenarios as scientific hypotheses, is substantially the same as Chalmers' suggestion in his (2005) that the hypothesis that we are in the same sort of situation as the main character Neo in the movie The Matrix is a metaphysical, rather than a skeptical hypothesis.8 (I prefer to use 'scientific' as the replacement category for 'skeptical', since I think we have a clearer idea of what science is, and of its successes, than we have of metaphysics. But presumably metaphysics is a kind of science, in a broad sense of 'science', so this is not a major disagreement.) Chalmers writes:

I think the Matrix Hypothesis should be regarded as a metaphysical hypothesis [...]. It makes a claim about the reality underlying physics, about the nature of our minds, and about the creation of the world. (Chalmers (2005), section 3.)

His argumentative strategy is (i) to formulate a 'metaphysical hypothesis' with three components, teased out in the way suggested by the last sentence quoted above, (ii) to argue that none of these components threatens to radically undermine what we think we know, and (iii) to argue that the metaphysical hypothesis is equivalent to the Matrix Hypothesis, in which case the latter does not radically undermine what we think we know either. Along the way, he responds to several possible objections.

In this section, I have simply outlined the idea of reframing the BIV hypothesis as a scientific one, and argued that it seems legitimate and more clear-headed than thinking of it as a threatening, sinister element in a story, i.e. the viewpoint we have when we think of it as a 'skeptical' scenario. Chalmers, modulo the minor differences between his discussion and mine outlined above, goes further on this front. Conversely, his discussion does not contain the earlier considerations of the present essay, such as the 'other contrast' argument of section 3, the 'BIV-or-parity' argument of section 4, the appeal in section 5 to common sense regarding everyday statements about hands, or the argument from contrast with really bad epistemic situations of section 69. Thus Chalmers' discussion and mine here are mutually supportive.

8. Conclusion

I have tried in this essay to make a good, multi-pronged case against (1) and similar conditionals, which feature as premises in much-discussed skeptical arguments. I hope I have convinced you that (1) and the like are false. Failing that, I hope I have at least convinced you that they are seriously open to question, not something which we should say 'of course' or 'obviously' about, as we saw Steup (2006) do.


Bouwsma, O. K. (1949). Descartes' evil genius. Philosophical Review 58 (2):141-151.

Brueckner, Tony. (2016). Skepticism and Content Externalism. The Stanford Encyclopedia of Philosophy (Summer 2016 Edition), Edward N. Zalta (ed.), URL = <>.

Chalmers, David J. (2005). The matrix as metaphysics. In Christopher Grau (ed.), Philosophers Explore the Matrix. Oxford: Oxford University Press.

Lewis, D.K. (1996). Elusive knowledge. Australasian Journal of Philosophy 74 (4):549 – 567.

Luper, Steven. (2016). Epistemic Closure. The Stanford Encyclopedia of Philosophy (Spring 2016 Edition), Edward N. Zalta (ed.), URL = <>.

Putnam, H. (1981). Brains in a Vat, in Reason, Truth, and History. Cambridge University Press.

Roush, S. (2010). Closure On Skepticism. Journal of Philosophy 107 (5):243-256.

Schaffer, J. (2015) Lewis on Knowledge Ascriptions, in A Companion to David Lewis (eds B. Loewer and J. Schaffer), John Wiley & Sons, Ltd, Oxford, UK.

Steup, Matthias. (2006). Knowledge and Skepticism. Supplement to 'The Analysis of Knowledge'. The Stanford Encyclopedia of Philosophy (Spring 2006 Edition), Edward N. Zalta (ed.), URL = <>.

Wittgenstein, L. (1953). Philosophical Investigations. Oxford: Blackwell.
Wittgenstein, Ludwig (1966). Lectures & Conversations on Aesthetics, Psychology and Religious Belief. Oxford: Blackwell.

1Cf. Luper (2016, section 5) for an overview of closure in relation to skepticism.

2. Cf. Lewis (1996). For an attempt to elaborate Lewis's core ideas about knowledge ascriptions more thoroughly and rigorously, cf. Schaffer (2015).

3. An important precursor to the present discussion and that of Chalmers (2005) is Bouwsma (1949). Bouwsma discusses, not a scenario in which we are living in a high-tech simulation, but an older kind of scenario in which an evil demon with supernatural powers is trying to deceive us. I have not tried to engage directly with Bouwsma's discussion here, since the evil demon scenario seems to me importantly different in a number of ways from a BIV scenario (and such differences aren't my focus here). Also, Bouwsma's piece is written in a literary, exploratory style, so that explicit commitments and arguments are not to the fore. Nonetheless, it is important to note that his piece exhibits, more than half a century earlier, the same overall tendency as the present discussion and Chalmers', i.e. to suggest that what may seem like epistemologically very threatening scenarios at first glance and in a certain philosophical mood, are more properly regarded as not so threatening.

4. At least, I can see no way which doesn't turn on us not being BIVs, not living in a simulation – and in that case, we wouldn't be able to know (1) without first knowing that we are not BIVs, in which case the skeptical argument could no longer be run.

5. (Putnam (1981), p. 15).

6. The phrase comes from Wittgenstein (1966), p. 1.

7. Wittgenstein (1953), section 118.

8. It is easy to miss Chalmers' piece when searching the literature for objections to (1), since Chalmers discusses, not the BIV scenario famous in recent philosophy, but the similar scenario depicted in the movie The Matrix (substantially the same as a BIV hypothesis, except Neo's brain outside the simulation is lodged in a body), and he doesn't explicitly frame his essay as an attack on the conditional premises of skeptical arguments, even though that is what it amounts to. (All this is in keeping with his piece having been written for a popular audience.)

9. Chalmers does touch on (Matrix-style counterparts of) what I in section 6 called 'really nightmarish scenarios in which I am in a simulation'. (In his section 5 he writes that '[t]here may be some respects in which the beings in a matrix are deceived. It may be that the creators of the matrix control and interfere with much of what happens in the simulated world.') But Chalmers does not touch on this in the service of a positive argument, by way of contrast, against (1) and the like. Rather, he discusses it defensively, as a possible threat to his claim that the Matrix Hypothesis is not a skeptical hypothesis; his point is just that this is orthogonal to the issue of whether you're in a matrix – being in a matrix doesn't by itself mean you're radically deceived, and the sort of 'interference' in question could also happen in life outside of a simulation.

Thursday, 7 July 2016

Reply to Adams and Clarke, and their Rejoinder

My recent Logos & Episteme paper, 'Two New Counterexamples to the Truth-Tracking Theory of Knowledge', has come in for criticism by Fred Adams and Murray Clarke. (Here is my original blog post about the paper.)

A recent issue of the journal contains a discussion note by Adams and Clarke entitled 'Two Non-Counterexamples to Truth-Tracking Theories of Knowledge'. Peter Baumann drew my attention to this and discussed it with me. I have also been happy to learn that Adams has given presentations where he talks about my paper and what he thinks is wrong with it.

The latest issue of the journal contains my reply to them, as well as a rejoinder by them.

The following is in response to their rejoinder:

Regarding the first counterexample, I am beginning to consider the possibility that the real lesson of our disagreement over it is that there are two possible concepts of knowledge which disagree about this case. Perhaps some people have one of these concepts, and some have the other, but this hasn't become clearly evident yet. Intuitively, I think that if a belief, even if it be true and truth-tracking in Nozick's sense, rests on a delusion in such a way that the delusion continues to be associated with it, and in such a way that if the delusion were removed, the belief would be relinquished, then that belief doesn't count as knowledge. If you have such a belief, I feel, you do not possess the truth about the matter in question, since your belief can be taken away from you just by correcting a delusion that you have. Adams and Clarke do not agree, and claim that everyone they have put the question to is on their side. I have certainly had people on my side too. So perhaps it is time to consider the possibility that there are two different concepts of knowledge here, and perhaps neither party is misapplying their concept in judging the example.

(Also, it may not be simply that some people have one concept of knowledge and other people have another. Some people, or even most, may have both. Or be disposed to form either (i.e. they may, in advance of considering this type of case, have just one concept which is in some sense indeterminate with respect to the case). Perhaps when I am talking to someone, urging the case as a counterexample, charity makes them select the concept of knowledge which behaves as I maintained in my original article, and perhaps when Adams or Clarke are talking to someone, urging their contrary judgement about my case, then charity makes their audience select the concept of knowledge which behaves as they maintain in their reply to me.)

Regarding the second counterexample, their latest argument seems to me very weak. In short, they contend that 'it seems intuitively likely that if p weren’t true, it might not be the case that Nutt speaks the truth regarding p [sic]' (p. 229).

This talk about what is likely true of a partially specified scenario is methodologically flawed. All I require is that there is a possible scenario, however unlikely, in which, if p weren't true, then Nutt - their name for the neighbour in my example - would still speak the truth about p, telling me that it is false. And this is the scenario I have tried to describe, by emphasizing that Nutt had a counterfactually robust desire - and ability, I might have added - to have me believe the truth about whether p is true or not. And my idea was that this desire and ability is counterfactually robust with respect to whether or not p is true. Surely this is possible. And in that case, it seems to me, Nozick's conditions are fulfilled and yet I do not have knowledge. That there is also a possible case nearby which doesn't make trouble for Nozick's theory is irrelevant.

Toward the end of their rejoinder, they seem to fall again into the misunderstanding of Nozick's theory that I tried to ward off in my reply:
[i]f one is to know something about tax law from a tax lawyer, it had better be the case that the tax lawyer would not say “p” about tax law unless p. (p. 230)

It looks here as though they mean that, if someone is to know something about tax law from a tax lawyer, it had better be the case that the tax lawyer would not assert any proposition about tax law unless it were true. As it happens, I am inclined to think this is false. But the point is that this requirement is not part of Nozick's theory. What Nozick's theory requires is that, to know something about tax law from a tax lawyer, it had better be the case that the tax lawyer would not assert that very thing unless it were true. And this is clearly a weaker requirement.

So, what Adams and Clarke say here does not succeed in neutralizing my counterexample to Nozick's theory. And their justification for saying it is cryptic and strained. They write:
Haze says that we are going rogue, and not staying true to Nozick's conditions. But as every constitutional lawyer knows, the letter of the law does not cover every application to every case. Some interpretation is required. Nozick's theory does not anticipate Haze's attempted counterexamples. But it is not hard to figure out how to apply the theory to the example and it goes as we suggest. (p. 230)

What does this claim, that 'Nozick's theory does not anticipate Haze's attempted counterexamples', mean? I don't really understand this, but it seems weaselly to me.

Monday, 20 June 2016

Forthcoming in Disputatio

My paper 'On Identity Statements: In Defense of a Sui Generis View' is forthcoming in Disputatio. The final draft is available at PhilPapers. It's the longest, most substantial paper I've gotten accepted for publication so far, and its argument is quite difficult and controversial. The first version of it was written in 2009 for a course taught by Adrian Heathcote. I presented its main arguments at the 2010 Australasian Association for Logic Conference and received a mostly encouraging response. I put it aside for a few years after a few failed attempts to publish it, and only recently began to try again. The Disputatio referee report was really good and has caused the paper to be miles better than it was.

Thursday, 16 June 2016

Modal Realism and Counterpossibles: A Tension in Lewis

David Lewis held that possible worlds are worlds as concrete as our own (cf. Lewis (1986)). He also held, in his work on counterfactuals (cf. Lewis (1973)), that all counterfactuals with impossible antecedents - 'counterpossibles' - are vacuously true. These two views do not fit together well. Embracing modal realism leads to especially compelling counterexamples - counterexamples given modal realism, that is - to the thesis that counterpossibles are all true. These take the form of conditionals whose antecedents are not intuitively impossible, but which are impossible given modal realism.

These arise because, according to modal realism, reality as a whole – that is, the totality of the posited worlds – is necessarily the way it is. Lewis is very upfront about this. Witness:

There is but one totality of worlds; it is not a world; it could not have been different. (Lewis 1986: 80.)

So, for example:

'If there had been two fewer men in reality as a whole than there actually are, there would have been fewer women.'

There is no reason to think this is true. And yet Lewis's thesis about counterpossibles, together with modal realism, implies that it is vacuously true.

Perhaps worse:

'If there had been fewer men in reality as a whole than there actually are, there would have been just as many men in reality as a whole as there actually are.'

This seems positively false.


Thanks to Quentin Ruyant for pointing out that the last counterfactual, given modal realism and the thesis that there are infinitely many worlds with men in them, actually seems to come out true in a funny way: if there had been two fewer men, there still would have been infinitely many. So this was a bad example. Consider instead:

'If there had been no Model-T Fords in reality as a whole, there still would have been some Model-T Fords in reality as a whole'.


Lewis, David K. (1973). Counterfactuals. Blackwell Publishers.

Lewis, David K. (1986). On the Plurality of Worlds. Blackwell Publishers.

Tuesday, 17 May 2016

Sufficient Conditions for Some Inference-Patterns Involving Conditionals

This is a continuation of the last post, which was a continuation of this article. The following three theorems show that, given a plausible assumption about the semantics of conditionals:

(1) You can't go wrong in applying hypothetical syllogism (transitivity for conditionals) so long as the set of relevant scenarios for the output conditional is a subset of that for the second input and the set of relevant scenarios for the second input is a subset of that for the first.

(2) You can't go wrong in applying contraposition so long as the set of relevant scenarios for the output conditional is a subset of that for the input.

(3) You can't go wrong in applying strengthening the antecedent so long as the same condition as in (2) is fulfilled.

Let us assume that a conditional A > C is true iff in all relevant scenarios the corresponding material conditional is true. 

I will use Sc(X) to denote the set of relevant scenarios for a conditional X .

Theorem 1. For any three conditionals A > B, B > C and A > C such that  Sc(B > C) ⊆ Sc(A > B) and Sc(A > C) ⊆ Sc(B > C), A > C will be true if A > B and B > C are true.

Proof: Take any three conditionals A > B, B > C and A > C such that Sc(B > C) ⊆ Sc(A > B) and Sc(A > C) ⊆ Sc(B > C).  Now suppose that A > B and A > C are true. Since all the relevant scenarios for A > C are also relevant for A > B and B > C, and A > B and B > C are true, the material conditionals A ⊃ B and ⊃ C will both be true at all the relevant scenarios for A > C (by the assumed semantics). Since transitivity holds for material conditionals, ⊃ C will be true at all the relevant scenarios for A > C, making A > C true (by the assumed semantics). Therefore, if A > B and A > C are true, A > C will be true.

IllustrationIf I had spoken to a cat then I would have spoken to an animal. If I had spoken to an animal I would have been happy. Therefore, if I had spoken to a cat then I would have been happy. (It is natural to think of the set of relevant scenarios for the first sentence as larger than that for the second. This could be further brought out by adding something like 'no matter what' to the first sentence.)

Theorem 2. For any two conditionals A > B and ~B > ~A such that Sc(~B > ~A) ⊆ Sc(A > B), ~B > ~A will be true if A > B is true.

Proof: Take any two conditionals A > B and ~B > ~A such that Sc(~B > ~A) ⊆ Sc(A > B). Now suppose that A > B is true. Since all the relevant scenarios for ~B > ~A are also relevant for A > B, and A > B is true, the material conditional A ⊃ B will be true at all the relevant scenarios for ~B > ~A (by the assumed semantics). Since contraposition holds for material conditionals, ~B  ~A will be true at all the relevant scenarios for ~B > ~A, making ~B > ~A true (by the assumed semantics). Therefore, if A > B is true, ~B > ~A will be true.

Illustration: (Assume for the following Q & A that it is analytic that all bachelors are men.)

Q: Do you think that, in view of the fact that we get energy from shooting men, if we don't shoot a man tonight, we won't shoot a bachelor? 

A: Of course: If we will shoot a bachelor tonight then, no matter what, we will shoot a man. And what you're asking about follows from that.

Theorem 3. For any two conditionals A > B and (A & C) > B such that Sc((A & C) > B⊆ Sc(A > B), (A & C) > B will be true if A > B is true.

Proof: (Same as for Theorem 2 but with (A & C) > B in place of ~B > ~A, (A & C)  B in place of ~B  ~A, and an appeal to the fact that strengthening the antecedent holds for material conditionals in place of the appeal to the fact that contraposition holds for material conditionals.)

(As with Theorem 2, assume for the following Q & A that it is analytic that all bachelors are men.)

Q: Do you think that we would have shot a man today if we had gone out and shot five bachelors and taken care to go for the masculine-looking ones?

A: If we had gone out and shot five bachelors, then, no matter what, we would have shot a man. So yes, of course we would have 
 shot a man today if we had gone out and shot five bachelors and taken care to go for the masculine-looking ones.

Thursday, 10 March 2016

Transitivity and Conditionals


Let us assume that a conditional A > C is true iff in all relevant scenarios the corresponding material conditional is true.

Let's leave it completely open here what makes a scenario relevant for a conditional. Let's also leave it open what scenarios are like.

(That something like the above is true for counterfactual or subjunctive conditionals seems more widely accepted than that something like it is true for indicatives, so the following will be most widely acceptable as an observation about the logic of counterfactuals. I think it probably applies to indicatives too. That it holds on the assumption of the above schematic semantics seems to me to be almost beyond dispute.)

In their 2008 paper 'Counterfactuals and Context', Brogaard and Salerno attempt to block a famous counterexample to transitivity for counterfactuals (cf. Lewis , p. 33) with the proposal that to have conditionals for which different scenarios are relevant figuring in the same argument is illicit.

But an inference from A > B and B > C to A > C will be truth-preserving as long as the set of relevant scenarios for the second is a subset of that for the first, and the set of relevant scenarios for the third is a subset of that for the second. (Note I don't say 'proper subset': they could all be the same set, but that's a special case.)

Illustration: If I had spoken to a cat then I would have spoken to an animal. If I had spoken to an animal I would have been happy. Therefore, if I had spoken to a cat then I would have been happy. (It is natural to think of the set of relevant scenarios for the first sentence as larger than that for the second. This could be further brought out by adding something like 'no matter what' to the first sentence.)

(This post builds on this.)


Brogaard, Berit & Salerno, Joe (2008). Counterfactuals and context. Analysis 68 (297):39–46.

Lewis, David K. (1973). Counterfactuals. Blackwell Publishers.

Wednesday, 9 March 2016

Five Objections to Sider's Quasi-Conventionalism About Modality

In a recent post I described Sider's quasi-conventionalism about modality, which in my view takes an important step forward with respsect to necessity de dicto but is mistaken in other ways. (My account of necessity de dicto shares a structure with it.) Here I give five objections to Sider's view.

None of these take the form of counterexamples. As Merricks (2013) observes:
[...] Sider’s general approach—as opposed to specific instances of that approach—is immune to counterexample. For suppose that Sider lists the “certain sorts.” You then come up with an absolutely compelling example of a proposition that is necessarily true and not of a sort on the list. Sider need not abandon his overall approach to reducing necessity. Instead, he could just add a new sort to the list to accommodate that example. Or suppose you come up with an absolutely compelling example of a true proposition that is not necessarily true and is of a sort on the list. Sider could just expunge that sort from the list.
1. Necessity does not seem disjunctive or arbitrary (at least, not to this extent).

This is an objection centering on our intuitive grasp of the concept of necessity de dicto. It seems like this is a notion we can grasp, with the help of Kripke’s characterizations as supplemented in this post. Now, when we grasp this idea, it seems we are grasping a single, unified concept: necessary truths could not have been otherwise, no matter how things had turned out. This just doesn’t seem like a disjunctive matter, and nor does it seem like the sort of thing we make one way or the other with any kind of arbitration - although of course there are unclear or borderline cases, which we may perhaps make stipulations about to some extent.

This is not a knock-down objection, of course. Sometimes philosophy can reveal things to be other than they might seem. But I think it is hard to deny, if we are willing and able to grasp the concept of necessity de dicto and careful to hold in abeyance any of our pet theoretical proclivities which may suggest otherwise, that the notion does seem more unitary and less arbitrary than Sider’s theory would have us believe. And I propose that that should count as a mark against Sider’s theory.

Furthermore, insofar as appearance really is different from what Sider says the reality is when it comes to necessity, there is some explanatory work for Sider, or more generally the would-be quasi-conventionalist, to do here: why the discrepancy? As far as I know, no answer has yet been given.

2. The ersatz substitute worry.

A starting point for this worry is the unapologetically ad hoc nature of Sider’s successive extensions of the toy version of his approach that he begins with (where the “certain sort” of propositions he takes as “modal axioms” are just the mathematical truths). This process seems to be one of going back and forth between a growing list of types of propositions, the list at the heart of an increasingly disjunctive account, and our grasp of the real modal notion of necessity. This gives rise to the worry that all we are doing is building an ersatz substitute for the real notion, by looking at the extensional behaviour of the latter and stipulating this behaviour into the account. No matter how far we pursue this strategy, the disjunctive notion we are building will remain fundamentally different in character from the notion whose behaviour we are modelling with it. Supposing that what we want from an ‘if and only if’ style account of necessity de dicto is not some substitute for that notion, but a biconditional which gives us insight into the notion itself, Sider’s approach will never satisfy.

Something of this worry is even suggested by what Sider says about family resemblances, rehearsed in the previous post as point (6). The quasi-conventionalist could simply insist that each of the items on their list of the types of propositions which count as modal axioms is there as a brute fact - that’s just how the notion of necessity works. But, Sider says, the quasi-conventionalist ‘need not be quite so flat-footed’, and is ‘free to exhibit similarities between various modal axioms, just as one might exhibit similarities between things that fall under our concept of a game, to use Wittgenstein’s example’. This move, offered as an optional extra for the quasi-conventionalist, is plausibly in tension with the way Sider’s successively extended accounts are formulated. Just as the concept of a game - allowing for the sake of argument that it is a family resemblance concept - is plausibly not actually captured by any particular disjunction, but is as we might say inherently open-ended, it is also plausible that we should admit that the real “certain sort” or “modal axiom” notion doing the all-important work in Sider’s account - allowing for the sake of argument that it is a family resemblance concept - is not captured by any particular disjunction either.

This of course suggests a variant of Sider’s approach, where it is held that the “modal axiom” notion is a family resemblance concept, and admitted that any definite, disjunctive list of types of propositions could only yield, when plugged into the overall account, an ersatz substitute for the notion of necessity de dicto. This variant is not, or at any rate less, vulnerable to the the ersatz substitute worry. But it is not clear whether it could really satisfy a philosopher who wants insight into the notion of necessity de dicto, let alone a philosopher with Sider’s motivations. For instance, can it really claim to be modally reductive? It might on the contrary seem that the family resemblance notion in question should be counted as thoroughly modal. Furthermore, it may seem to yield an account which is insufficiently insightful - essentially all we are now getting is (Schema) itself, together with the pronouncement that the condition C is given by a family resemblance concept. Is there nothing more which can be said? Relatedly, the question now arises: is it after all true that the notion in question is a family resemblance concept? What reason have we to believe that? (I will suggest, somewhat ironically given that I am on the whole much more admiring of Wittgenstein’s philosophy than Sider is, that it isn’t true. The notion playing this ‘condition C’ role, i.e. the notion which when combined with the notion of truth yields a notion playing Sider’s “modal axiom” role, can be defined in terms of a single necessary and sufficient condition.)

3. No iteration?

When Sider says early on in the modality chapter of his (2011) that the account he offers will be partial, there is a footnote to this remark which runs as follows:
(16) For example, the account defines a property of propositions that do not themselves concern modality, and thus is insufficient to interpret iterable modal operators.
This raises the question: how come, faced with this failure of coverage, Sider doesn’t simply make the same move with modal statements as he does with analyticities, “metaphysical” statements, and natural kind statements - namely include them expressly in the account?

Perhaps the answer is that this would threaten the account’s claim of reductiveness. For it seems that in order to include modal statements on the list, we need the concept ‘modal’.
The question then becomes: is ‘modal’ modal? If it is, Sider’s account is in serious trouble: it cannot, as a matter of principle, handle iterated modality. For remember, it is supposed to be modally reductive. And if iterated modality is a real, legitimate thing, then what use is a theory which gives us - by design - some extensionally correct answers but cannot handle this whole class of cases? It seems such a theory could give us an ersatz substitute for modality at best (to recall the above objection by that name). Its failure, if it is a failure, to be extendable to a salient class of cases should perhaps suggest to us that it is on the wrong track.

So, is ‘modal’ modal? It is an interesting question, and suggests interesting analogous questions about other kinds of concepts. One reason to think it is, is that we don’t seem to have a general way of saying what ‘modal’ means which doesn’t work by way of example. We seem to need examples of modal notions - necessity, or contingency, or possibility, or impossibility, or some combination of them - to do the job. To be sure, we could be said to be mentioning rather than using these notions in our explanations of ‘modal’, but is that any help? Don’t we need to use them in some broad sense in order to mention them in the appropriate way?

Another way out which may occur to the reader is to somehow delineate the modal statements using notions which are distinct from ‘modal’ and the like, but which fortuitously give the right extension. I am pessimistic about this. For a start, I can’t think of any good candidate notions. Furthermore, even if there were notions around which could do the job, wouldn’t using them for this purpose play further into the ersatz substitute worry described above? In particular, it seems like this strategy, while it may help Sider’s account deliver extensionally correct answers, would take the account (even) further from the real meaning of modal expressions, or the real nature of modal notions.

One possible strategy remains to be considered: accepting that ‘modal’ is modal and simply giving up the claim to full modal reductivity. From one angle, this seems not unreasonable; the way that ‘modal’ introduces modality, assuming it does, into the account, seems quite special and different from the way modality would be introduced if a notion of possibility or necessity were directly used. So perhaps there is room to claim that a broadly Siderian quasi-conventionalist account involving the notion of ‘modal’ as an unreduced modal element could still constitute a theoretical advance. I have no knockdown objection to this, but I do want to suggest that once this concession is made, other objections, such as the first two considered here - (i) that necessity does not seem as disjunctive or arbitrary as quasi-conventionalism would have us believe and (ii) the ersatz substitute worry - become all the more acute; I am not sympathetic with the following sort of move, but you might try to argue that biting those bullets is worth it if we get in return a complete reduction of modality, with its attendant payoff in eliminating puzzlement and vindicating certain sorts of metaphysical visions, but you can’t do that anymore under the present strategy. Indeed, the whole spirit of the quasi-conventionalist approach seems to be in tension with allowing such a modal element into the mix.

In sum, there is reason to suspect that iterated modality, and the failure of any existing version of Sider’s approach to cover it, poses a serious threat to Sider’s approach in general.

4. Reductivity a bug, not a feature.

Essentially this objection is raised against Sider’s theory by Merricks (2013). The objection is simply that, if we have reason to think that a modal notion like that of necessity de dicto cannot be reduced to non-modal notions, or if we just intuitively feel that to be right, then we should on that score alone be suspicious of Sider’s theory, since it purports to give a reduction. In making this objection, Merricks cites an argument he gives elsewhere (namely in Chapter 5 of his (2007)) for the conclusion that such modal notions indeed cannot be reduced to non-modal ones.

5. Questionable motivation.

As we said at the outset, Sider’s account is partly motivated by general puzzlement about modality, and partly by a metaphysical vision. Both these facets of the motivation can be made the focus of criticism. The following is not supposed to constitute a sharp, incisive objection, but rather to cast some doubt on these general features of Sider’s approach.

Regarding general puzzlement: yes, modality is puzzling to philosophers. But perhaps this puzzlement is not to be treated exclusively by means of reduction (or, for that matter, by ‘if and only if’ analysis whether modally reductive or not). Indeed, pursuing reduction can even be seen as pursuing an easy way out - albeit one which may be impossible in principle. Perhaps the only real way forward, with parts of our puzzlement at least, is, rather than trying to reduce modality to non-modal terms, to work on our way of looking at modal concepts themselves, using philosophical methods other than reductive analysis. (One method which comes to mind is the method, due to Wittgenstein, of imagining simplified language games and comparing and contrasting them to ours. In the Brown Book some steps are taken towards doing this with modality, but only cursorily. I mention this to give a particularly concrete and well-known example of a possibly helpful method, but this is just one among many - I do not mean to suggest it could suffice all by itself.) Non-modally-reductive accounts of necessity de dicto such as mine do not face this criticism, since they do not aim to clear up all of our puzzlement about modality, or even just some core of it, by means of an ‘if and only if’ style analysis. Nor do they aim even to point the way to such a clearing up. By being less ambitious on that front, they offer a more realistic hope of genuine theoretical progress on our understanding of de dicto modal notions - how they relate to other notions both modal and non-modal.

Regarding the metaphysical vision: it is beyond the scope of this post to criticize Sider’s Hume-influenced, Lewis-influenced metaphysical vision head-on. But we may note that, insofar as there may be grave problems with this sort of metaphysics for all we know given the present state of philosophical inquiry - nothing of the sort may be tenable, ultimately - there may also be problems with a highly ambitious approach to modality which is in service of this sort of metaphysics. More generally, perhaps there is reason to be dubious of any approach to modality based upon a metaphysical vision. One reason may be that the vision is, so to speak, too antecedent to modal considerations: perhaps one should let modal considerations shape one’s approach to metaphysical questions, rather than trying to explain modality (away, if you like) in terms of an approach to metaphysical questions which had its appeal quite apart from, or even in spite of, modal considerations. Another reason may be that the best way to make theoretical progress on the notion of necessity de dicto is to keep sweeping metaphysical visions out of it. We may do better to instead treat our topic along broadly logical lines. One way this may help is that it might free us up to throw a wider variety of conceptual resources at the problem - for instance, semantic notions or other modal notions which may seem problematic against some special metaphysical backdrop but are actually quite in order.

That concludes our list of objections or worries. For two further objections, see Merricks (2013).

I think the cumulative effect of the objections canvassed above should be for us to regard Sider’s theory as highly problematic. But note that none of these objections threaten (Schema). This raises the question: what if these were a more soberly motivated, more theoretically satisfying (Schema)-embodying account available? Some other candidate for the condition C in (Schema) which avoids these objections?

Merricks, Trenton (2007). Truth and Ontology. Oxford University Press.
Merricks, Trenton (2013). Three Comments on Writing the Book of the World. Analysis 73 (4):722-736.
Sider, Theodore (2003). Reductive theories of modality. In Michael J. Loux & Dean W. Zimmerman (eds.), The Oxford Handbook of Metaphysics. Oxford University Press 180-208.
Sider, Theodore (2011). Writing the Book of the World. Oxford University Press.
Sider, Theodore (2013). Symposium on Writing the Book of the World. Analysis 73 (4):751-770.