Thinking Without Limits

Is human comprehension limitless?

Simon Saunders is currently Professor of Philosophy of Physics at the University of Oxford, and Fellow of Linacre College. He is noted for his work on quantum mechanics (particularly the many-worlds interpretation), on identity and indiscernibility in physics, and on structural realism.


What do you think the idea of thinking the unthinkable actually amounts to? When we discuss “thought”, what do we actually mean?

I think it’s about limits to thought vis-a-vis something like states of affairs. To set it up, one might ask, “are there extraordinary facts about the universe that somehow are going to be forever beyond our comprehension?”

So the important question is whether or not we can have knowledge of every state of affairs? 

Right. I think there are other aspects to the question which are also interesting – issues of experiential knowledge etc. It comes up in the philosophy of mind: for example, qualitative experience called qualia. Is redness a property that we can have access to through science? Or is it something that we really have to directly experience ourselves?

The great example here is Mary, the colour-blind scientist. She knows everything there is to know about colour. She spends her life incarcerated in a black and white room, she communicates with a black and white video monitor. There are no mirrors. And then one day she leaves the room, and for the first time in her life she sees red. She thought she was learning something new. It was something she was incapable of getting at merely through a scientific understanding of colour – things like refractive properties of surfaces, electromagnetic structures, wavelengths of light, relations among wavelengths, that sort of thing.

If that's the topic, then of course there are all sorts of things that in a sense we can never have an experiential concept of. Take ultraviolet, or a deep infrared – these are parts of the spectrum that we can't directly experience. We can study them scientifically, but lacking that first-person experiential concept we can't necessarily know what ultraviolet light is like. Or other examples: what is it like to be a bat? There are lots of examples like that where it seems there are going to be limits to what we can understand via experience. There are limits to our sensory modality, that’s really what it boils down to.

In response to the challenge from philosopher Mark Rowlands, you said that while other animals cannot fully comprehend the world, they can get a rough understanding of things – what exactly do you mean by this?

The point about animals is a good one. A lot of my overall interest in the topic is whether or not there are good arguments to suggest that there are things we can't know. My general fear is that there are no good arguments, but if there is one, this is perhaps the best. It proceeds from the observation that we clearly have an understanding of things we know – stuff that no dog can know, no cat can know, no lizard can know. I think the issue of the monkey is a little bit borderline. Granted we are somehow able to know things, all kinds of things, that these other mammals and reptiles and insects couldn't possibly know. So, are we not in that situation vis-a-vis some morally sophisticated life form?

There was a suggestion by Mark that, if there's a god, then it knows things that are unthinkable to us. I find that slightly curious. I'm not sure if one needs god, it just needs to be something more sophisticated and real.

If you take the surface of the Earth, which is a very large domain that we know a great deal about and surely know more than any animal does, but there are still going to be some animals which probably do have a good understanding of what exists on the surface of the Earth – its spherical character, geography, all kinds of things, and probably much more so that the great majority of humans. I’m thinking particularly of migratory birds, who really get around and travel widely over the planet and know a great deal about nature.

The point is: can we break down this intuition that just as we surpass the competencies of lower life forms, there will be some superior life form that surpasses us? Another aspect to breaking that down is, undoubtedly, to question the level of detail. I think it's very plausible that in fact we're not going to know all sorts of things about highly complex systems or the ultramicroscopic, or what goes on sufficiently far away from us.

I think the urgent question is, isn't it just more of the same? In particular when it comes to remote parts of the universe. Sure, we aren't going to get there. We're not going to have direct data relating to it. But isn't it going to be in some way similar to the parts of the universe that we do have access to? There are issues with that. There are theories according to which sufficiently remote parts of the universe actually have very different physical laws from ours. If that's the point, we can even get at some extent to what those different physical laws would be, and can, to some extent, understand what might be going on in those parts of the universe.

I'm not sure if this is an interesting sort of unthinkability. I think the idea is rather that there's a whole way of thinking about reality that is unavailable to us, there are hugely important aspects to reality that aren’t accessible to us. That's what I see as the interesting question, and I would like to argue the case that we have no reason to think so. And the case of animals not having our competencies doesn't really deliver. Again, the example of birds that travel the Earth, they know an enormous amount about the Earth, even given their tiny brains.

It seems like a lot of what you're saying is that, when people make arguments for the fact that we might have limits to understanding, they often come down to contingent limitation. Like you say, we can't know about the other side of universe, because we can't get there, but it's not because we couldn't in theory think about it.

Right. It's not just contingent, but that kind of understanding that isn't available to us is perhaps one of detail. A bird will traverse the Earth's surface and know a great deal about its geography, or know a great deal about local fragments of that geography, perhaps it typically forages there, nests and so forth. They're not going to know about the internal structure of plants, except for what they eat. There will be limits of detail, and they're not going to have the medical concepts, computational concepts that we have. But they have a reasonable understanding.

Of course this stuff is very controversial. Some people deny that animals other than humans have any understanding at all. But I take the view that animals actually do have something close to what we call understanding, even if they can't learn language and so forth.

And they have a grasp of that state of affairs?


You’ve said previously that there are no good arguments for the limits of thought. Is it futile to discuss the limits of thought – surely if there are things beyond us they are things we are not going to be able to talk about?

There's a fairly obvious sense in which, if there is a limit still, we're not going to pass over that. I'm not going to be able to report on the stuff that we're never going to be able to think about. But I think, and as your question brings up, there have long been long been philosophers, sometimes scientists, who argue that this is why we cannot get beyond our human sphere. There's an argument, and that argument is intended to show that something is forever beyond our reach.

Again, Mark Rowlands gave a quite good example in that he talked about relations, quoting Russell. Indeed there's that whole tradition in philosophy that goes back well beyond Russell. To give a brief summary: we are only aware of things by virtue of their impact on our senses. We mirror the relations among things in the world in terms of the relations among the sensory data that we have. Sequences of sensory impacts mirror sequences of events that cause those sensory impacts. That's the idea. So somehow all we have is a structural, relational grasp of what goes on outside of our skin. That's the picture. And I think it’s a bad argument, but it’s been quite a compelling one, and people have been grappling with it for a long time.

I think it's a bad argument and part of the reason is that whatever basis we have to conclude that we only have knowledge of the world by virtue of impacts on our sensory surfaces, that comes from science itself. That comes from the impersonal perspective of science, which, you know, we've kind of imagined ourselves as being objects of scientific inquiry, conclude, “oh, this object of certain inquiry, namely the human subject, can only know anything insofar as something interacts with its skin, or its retina, or eardrums”. But that picture comes from science, and it can't as it were undermine science.

Of course science is entirely descriptive, not only of the human organism but the environment, and all of the interactions among the objects that impact on the human organism. In a certain sense, it just can't work to undercut that scientific picture of the world. That scientific picture of the world absolutely is not confined to structural relations among sensory data. There were scientists who tried to do that. They thought science ought to only be about sensations, because only those were somehow indubitable, or that we have this special kind of access to them. But I think that's a bad way of thinking both about science and about how we have knowledge of things.

Other examples, a very famous one is from Kant. Actually, there are several from Kant. Kant argued that we can only ever know about appearances of things; we can never know things in themselves. Here's one argument: many of our concepts are grounded on sensation and we cannot dispense with that origin, that source in human perceptual sensibility. Because these concepts are so fundamental to science, they're supposed to show that science is only ever to do with the objects of human sensibility. We've got to engage in things through sensibility, we can't do it directly through cognition. That puts a huge limitation on anything that we can ever know.

The example is infinity, as bound up in spatial concepts. Can we ever have an intellectual grasp of what infinity is? Or is it something that we can only know it in intuition? Through sensibility?

Actually when you think about it, it's a pretty weird idea, because one thing you might think you never see is infinity. We only ever see bounded things. He had a quasi-logical argument to say that you can enumerate any finite number of things, and you can enumerate them in thought but you can't complete the series, you can't go to infinity. But somehow intuitively we can directly cognize infinity.

His example was a kind of compass and rope construction. You draw two parallel lines and you connect them at a right angle. Then take a line that intersects that right angle and connects the two lines diagonally, and then tilt that diagonal line down a little bit, tilt it down a bit more, tilt it down a bit more, and the line gets longer and longer as you connect the two straight lines. It’s the sort of thing that you can do visually much better than you can put into words. And this is supposed to show somehow that we can grasp infinity, but that we can only do it through this construction, and we have to actually see the construction in order to get the picture.

His development in the late 19th century with Frege and formal logic, which says we can grasp infinity and we can express it without any recourse to sensibility. We can express it in logical terms. You do so in terms of something like a relation, a non-reflexive relation, like "greater than.'' So A can't be greater than A. A can be greater than B, B can be greater than C. It's transitive, therefore A is greater than C. But A can't be greater than A. Well take that relation, "greater than,'' and let me now express infinity to you. I'll put it in words, but it's a logical notion. For all X there exists a Y such that Y is greater than X.

Yes, a thing is always bigger than everything else.

Well, no, it's not saying there exists a Y such that for all X, Y is bigger than X. That's the thing which is bigger than anything else. No. What it says is, for all X there exists a Y such that Y is greater than X. You give me any X you like, I can find a Y that is bigger. It's kind of trivial. I think we could explain this to a five-year-old. I'm not sure the five-year-old would get the force of “any X”.

Does this require some big formal revolution in knowledge to understand this? Could not Kant have hit upon this?  Sometimes I think we're kind of overdignifying these discoveries by calling them a revolution in logic. But at the same time, some very fundamental conceptual discoveries are a matter of seeing something that's obvious all along, but correctly diagnosing it. Maybe that's what was going on here. In other words, fairly trivial though this construction is, it's showing us that there's a logic of analysis of what infinite means that's entirely straightforward and fairly simple and within our grasp. And we don't have to proceed through intuition. That's one example of Kant.

Another example, it's kind of fun, this, one. The left hand and the right hand. He asks us to imagine a left hand in a universe all on its own. So how would we characterise it as left rather than right? What characteristic does it have that makes it left rather than right? It would seem that in terms of all of the angles, lengths of lines that connect points the left hand, they're all replicated in the right hand. There's a symmetry operating. We can't get at what makes something left rather than right. And this extends right through mathematics, the issue of handedness in mathematical structures. How can we mathematically characterise something as being left-handed instead of right-handed?

And it's a fundamental problem if you like. Kant took this to mean that there’s something given in sensibility and intuition which can't be intellectually grasped. As soon as you have a constraint like that in place it suggests that there’s going to be all sorts of stuff that we can't intellectually grasp, because we can't engage with it in sensibility. That would set limits to what is thinkable. We cannot out-think our sensory operators, as we need our sensory operators in order to deal in the fundamental part of cognition. That's what cognition is. I think that's a bad argument from Kant, the so-called argument from incongruent counterparts. And I think the issue of infinity is also a bad argument from Kant. Reasonable at the time, but we now see it as just a bad argument.

It seems to me that the there’s a lot of that in the history of philosophy. It's not so much that philosophers are determined to say we're limited in these ways. I think philosophers have always been attentive to the question of, “do we overreach ourselves?” Part of this is brought up by metaphysics, because metaphysics asks all kinds of questions that seem completely unanswerable. There's been a repeated attempt to say, “well, we've got this quandary with metaphysics." But the reason we're in this mess is because we're trying to ask about stuff that we can't ever get at. If we could only recognise that then we could give up posing these tragic questions that drive us all nuts.

I think that's partly why philosophers repeatedly come back to the issue of whether there is something that we can't do intellectually? They try to develop arguments. I've given three or four examples now, and I think those arguments are all bad ones. I really don't know of a good one. Perhaps the best one is that just as we have surpassed the capabilities of lower animals, then there'll be some superior being who can outclass us.

Actually, on that thought, what about artificial intelligence? Anyone who's a fan of Iain M. Banks will have been impressed, I think, with what machine intelligence may be capable of and how it may interact with human intelligence. I think surely it is already happening in all kinds of ways that machine competences in a way outstrip our own. All the time we're using Google and computers and so forth to augment our ability to answer questions, but increasingly, to organize ourselves and our lives.

I think we could fairly quickly get into a situation where we are, as it were, having our hands held by computational backup. I'm presently waiting for the Google eyeglass thing, whereby you get facial recognition, some little voice whispering into your ear someone's name and so forth. What an experience that might be, to walk through a crowded street and have information available about pretty well anyone that you look at. That would be extraordinary. And who knows how far that will go. There are issues of limitations of what we can think and so forth, by virtue of complexity, well why not use what artificial intelligence will be able to teach us? I think that's an interesting way to puzzle a bit more about these issues.

What about other kinds of understanding? You say that language goes beyond thought, and thought beyond language. So something being inexplicable doesn’t necessarily mean that it is unthinkable?

I was also thinking about what can be put into words as opposed to what can otherwise be grasped. I think that's an interesting question. In connection to that is the idea that thought goes beyond language in all kinds of ways. Also, language can often fool us into thinking that we're thinking something when we're not. Perhaps a good example of that is the, "why is there something rather than nothing?" That's a question that philosophers sometimes have asked.

What is the thought about nothingness, and do we really have a thought about nothingness? Typically what people think of when they think of nothingness is a big, empty, dark space. But space is a geometric structure and it's not nothing. What is nothingness which isn't just a big, dark, empty space? I'm not sure if we really know. I think what we may have is just a form of words. That's the suggestion.

I think, also, that a lot of understanding that goes on in mathematics can't really be put into words. I think a lot of understanding goes on in physics, that can't really be put into words either. So there are ways in which thought goes beyond language. But perhaps that's not so controversial.

Is that perhaps part of the examples you're giving from Kant about our intellectual limitations versus experiential limitations? We're tricked into thinking we have limitations because we can't talk about these things?

I think that's right. What makes Kant's claims much more problematic, and I think in a sense it's fairly straightforward that mathematics goes beyond words, but for Kant, when he talked about not being able to intellectually “get” the concept of infinity, he did talk about discursive concepts.

The contrast is with intuition: discursiveness versus intuition. With intuition you just passively receive something, whereas with intellectual cognition, we do it. It's not imposed upon us. We do it, it's freewheeling, and it's discursive. By that he didn't just want to constrain it to words - he meant mathematics, too. For him, non-Euclidean geometry might be a kind of “play of representations”, that's the phrase that he used. We might algebraically manage to characterise non-Euclidean geometry as something without content. Somehow what was required to give any cognition like that content is to engage it with sensibility. And he thought that we could not imagine intuition of a geometry that was not Euclidean.

Actually, that was an important part of the undermining of Kant's philosophy in the late 19th century, where you get people like Hermann von Helmholtz, who worked out ways in which we might be able to have sensible intuitive engagement with non-Euclidean geometry. It's a bit like saying, "Here's what it would be like to live in a non-Euclidean world.'' And that really seemed to be a seriously damaging blow to Kant's general framework. By the early 19th century, mathematicians had developed consistent geometries that were non-Euclidean.

The last thing to ask is whether you're feeling optimistic about the things we can and can't uncover? Is there anything you'd be interested for us to get our thoughts on and we haven't managed to get a grasp of yet?

I do come back to Mary the colour-blindscientist who's confined to a black and white room. I think there is something here fairly close to the centre of the mind-body problem. The mind-body problem does seem to me really intractable. What is at issue is how can a physical process have an awareness and if does have awareness, can we ever get at the nature of that awareness just from an understanding of the physical process? Or do you have to, as it were, “be” that physical process in order to know what it's like? I think that question is a pretty fundamental one. I would like us to make progress with it.



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