Second-Family Problems
Fixed Lenses
Many of the traditional problems of Western philosophy start with questions that have fixed elements. We might, for instance, ask ‘What is the relationship between mind and body?’ and take the preexisting categories of ‘mind’ and ‘body’ as our starting points.
Once a question like this has been asked, it can get a grip on our minds. We feel that there must be some relationship between ‘mind’ and ‘body’ that’s logically coherent and that fits the reality of the world. Over the centuries, philosophers have argued for all sorts of possibilities — ‘property dualism’ (which holds that the world is made up of a single type of stuff with distinct physical and mental properties) and ‘type physicalism’ (which holds that mental events are really just the same thing as the brain events that they are correlated with).
Despite all the theorising, however, no theory has emerged that has attracted a consensus among philosophers.
Flawed Questions
The form of these questions encourages us to treat the question’s elements as inviolable. We might, for instance, ask ‘Do we have free will?’ and assume that either ‘we do have free will’ or ‘we do not have free will’ has to provide a good account of reality.
In logic, the law of the excluded middle states that all propositions are true or false.1 So we might assume that, logically, we must either have free will or not have it. And when neither alternative is satisfying, it can seem as if there must be a serious flaw somewhere, perhaps in our understanding or perhaps in the fabric of reality itself. We get snagged by a philosophical problem.
The law of the excluded middle is perfectly valid when it is applied to the abstract systems that formal logic deals with, but when we are asking about the realm of experience there’s a third option — that neither of the alternatives hits the nail on the head. It could be that the concept of free will simply isn’t useful in exploring the relationship between consciousness and causation; that it doesn’t help us arrive at clarity. Likewise, the ‘mind’ and ‘body’ categories might simply not be helpful in understanding consciousness.
Paradoxes
The second-family problems arise where a question creates a paradox. It feels as if things should add up, but they don’t, and the more time we spend within the question’s system of ideas the harder it becomes to escape.
When we see any paradox from a proper perspective, however, we find that we’ve just been stuck in a mental eddy — in an unhelpful way to think about the matters at hand.
Take the ‘sorites paradox’, for instance. It invites us to imagine removing grains of sand, one by one, from a heap of sand and then asks when the heap would stop being ‘a heap’? It could never stop being a heap just by removing a single grain. But that would imply that the sand would form a heap even when there was only one grain left.
This paradox dissolves when we apply a proper understanding of how language works.2 A pile of sand doesn’t become a ‘heap’ through containing a certain number of grains. Whether or not it gets called a heap depends on the context. One person might look at a particular pile of sand, see that it is sufficient to mix a load of concrete, and think of it as a heap. Another person might look at the same pile of sand while wanting to fill enough sandbags to protect against an imminent flood. Disappointed, they might think that it’s not a heap at all.
Another classic philosophical paradox, Zeno’s Paradox of the Tortoise and Achilles, tells us to imagine Tortoise challenging Achilles to a race and asking only for a small head start. Common sense would suggest that Achilles — by far the faster runner — would easily overtake Tortoise. But according to Zeno this was not the case, for by the time Achilles reached Tortoise’s starting position Tortoise would have covered some ground himself. And when Achilles covered this ground, Tortoise would have again advanced, though admittedly a smaller distance. Every time Achilles caught up to where Tortoise had been, Tortoise would have moved a little further forwards and maintained his lead. So, according to Zeno, Achilles would never be able to overtake him.
This paradox dissolves when we find that the difficulty only arises through adopting an incoherent way of looking at the infinitely small. In the 17th century Newton and Leibniz independently developed integral calculus, which not only tells us that Achilles would overtake the tortoise, but allows us to calculate exactly when.
Nothing Philosophically Problematic
All paradoxes are similar in that, to those trapped inside them, they appear insoluble. This insolubility can feel strangely significant. But when we escape the grip of the paradox and see it from a proper perspective, its power melts away.
Like other paradoxes, second family problems don’t reveal anything truly problematic about the nature of the world or about the nature of thought. They just show us how easy it is to get ensnared by patterns of thinking that lead us away from clarity.
The best way to deal with such problems is to acknowledge that it would be counter-productive to try to answer the questions the way the questions beg to be answered, and then to either seek a better way to see the areas of the world that the questions point towards, or to simply resist the allure of the questions altogether and put them quietly aside. Nothing is lost through doing so.
- Bertrand Russell makes the law of the excluded middle central to his system of logic through the ‘self-evident’ principle that “all propositions are true or false”. Alfred North Whitehead and Bertrand Russell, Principia Mathematica To *56, Cambridge: Cambridge University Press, 1997, p. 38.
- “For a large class of cases—though not for all—in which we employ the word ‘meaning’ it can be defined thus: the meaning of a word is its use in the language.” Ludwig Wittgenstein, Philosophical Investigations, Oxford: Blackwell, 2001, §43