Saturday, April 6, 2019
Can you doubt that 2 + 3 = 5?
In his Given the possibility that he is dreaming or that an evil spirit might be causing him to hallucinate, he judges that whatever the senses tell him might in principle be false. In particular, the entire material world, including even his own body and brain, might be illusory. Hence claims about the material world, and empirical claims in general, cannot in Descartes’ view be among the foundations of knowledge., Descartes famously tries to push doubt as far as he can, in the hope of finding something that cannot be doubted and will thus provide a suitable foundation for the reconstruction of human knowledge.
Surprisingly for a rationalist, Descartes also suggests that even claims about basic arithmetic cannot be among the foundations. For he proposes that it is possible that God might make him go wrong when considering even something as elementary as the claim that 2 + 3 = 5 or the claim that a square has four sides. By the end of the first Meditation, he alters the scenario so that it is the evil spirit or Cartesian demon rather than God who is doing the deceiving, and later in the Meditations he argues that given God’s perfect goodness, he cannot be leading us astray in any way. The key point for present purposes, though, is that Descartes does suggest, at least initially, that it is as coherent to doubt basic arithmetical and geometrical claims as it is to doubt that one is awake or that matter exists. Is this true?
I think not. The way Descartes’ skeptical scenarios work is by proposing coherent alternatives – or purportedly coherent ones, anyway – to the way things appear to common sense. For example, given the experiences you are having right now, your common sense assumption would be that you are looking at a computer screen reading a blog post. However, there are, Descartes says, clearly possible alternative scenarios in which you are not really looking at a computer screen and reading a blog post at all. You could instead be in bed asleep and having a vivid dream about reading a blog post on a computer. Or you could be a disembodied spirit who is being caused by a Cartesian demon to hallucinate that you have a body that is sitting in front of a computer reading a blog post.
Put to one side for present purposes the question whether these particular scenarios really are, at the end of the day, coherent. (Some philosophers .) They are at least prima facie plausible insofar as we are familiar enough with dreams and hallucinations. It is possible to have a dream in which one is convinced one is awake and looking at a computer screen. It is possible to hallucinate. Hence it certainly seems like we have cases where things appear to be some way X but are really some other way Y. To be sure, one can (and should) question whether it is coherent to suppose that one is always dreaming or hallucinating, or whether a sensory experience of precisely the kind I am having right now could really be a dream or hallucination. But dreams and hallucinations are familiar enough that these particular skeptical arguments at least get off the ground, even if we can ultimately shoot them back down.
By contrast, it is not clear how skepticism about basic arithmetic can even get off the ground. For what we need is a coherent scenario in which it seems that (say) 2 + 3 = 5 but in reality the arithmetical facts are very different. For example, we need a coherent scenario in which 2 + 3 = 14 but God or the demon is making it seem otherwise. And the problem is that there is no such coherent scenario. We simply cannot coherently describe a case in which 2 and 3 really add up to 14, the way we can (arguably) coherently describe a case in which you are not really reading a blog post on a computer right now. For 2 and 3 adding up to 14 is a logical impossibility, whereas your not really reading a blog post on a computer right now is not a logical impossibility. The proposition that 2 + 3 = 14 entails contradictions, whereas the proposition that I am not really reading a blog post on a computer right now does not.
You might respond: “But maybe God or the demon is only making it seem to you to be a logical impossibility.” But that won’t work, for the same reason the original scenario won’t work. For now we need to be able to describe a scenario in which the proposition that it is logically possible that 2 + 3 = 14 is itself logically possible (and either God or the demon is only making it seem otherwise). And the problem is that that proposition is no more logically possible than the first one is.
There is, then, a crucial disanalogy between the examples involving arithmetic and the examples involving physical objects. We can, independently of what we know about dreams and hallucinations, make sense of a scenario in which a certain physical object is not present. (There are, after all, a great many places devoid of computer screens and blog posts – my back yard, the surface of the moon, the bottom of the Mariana Trench, etc.) Hence we can go on to contrast a dream or hallucination in which the object does at least seem to be present with the fact that it is not. But we cannot independently make sense of a scenario in which (say) 2 + 3 = 14. Hence we have nothing to contrast with a scenario in which God or the demon makes it seem as if 2 and 3 add up to something other than 14. We can’t really get the skeptical scenario going, the way we can with skeptical arguments involving dreams and hallucinations about the physical world.
So, it seems that, even if Descartes were correct to regard skepticism about the senses and the material world as coherent, he should not have regarded skepticism about basic arithmetic and the like as coherent. That is significant for the rest of his project in the Meditations. It has often been pointed out that, given the latter sort of skepticism, Descartes arguably shoots himself in the foot, making it impossible for him to get beyond the Cogito and maybe even impossible to get as far as the Cogito. For if I could be wrong even about something as seemingly self-evident as 2 + 3 = 5, why couldn’t I be wrong about something like Cogito, ergo sum (“I think, therefore I am”)? Or, even if I can’t be wrong about that, I still need to carry out some fairly complex reasoning to get from knowledge of my own existence to knowledge of God’s existence (as Descartes does later in the Meditations, before going on to appeal to God’s goodness as guarantor of the reliability of his rational faculties). And how can I be sure that I haven’t gone wrong somewhere in that reasoning, if I can be wrong about something as basic as 2 + 3 = 5?
It is a good thing for Descartes’ overall project, then, that the doubts raised in the first Meditation vis-à-vis basic arithmetic and the like are misplaced. (That’s not to say the project isn’t wrongheaded in other ways – it is – but at least this bit of it can be patched up.)