One criticism that I often read of Popper is that some ideas are just obvious, and so there is no need to take all this fallibilist stuff too seriously. As an example, people often say 1+1 = 2 is obvious or something like that. But 1+1 = 2 is not obvious.

Let’s start by considering the fact that 1+1 = 2 is a very abstract statement. It’s not the same as saying “I have one cow in my barn and I have put another cow in my barn, so now there are two cows in my barn.” People have been able to do this sort of thing for a long time. But 1 does not stand for a cow in a barn. It’s a number. It happens that cows in barns instantiate certain abstract mathematical relationships like 1+1 = 2, but so do peas in a pod, ducks in a pond and so on. It takes a leap of imagination to see all of those things as instantiating the same kind of abstract truth.

There is another problem, which is that the notation 1+1 = 2 is an ingenious invention. Before that notation came along, many people would use roman numerals, which made mathematical operations like multiplication very difficult. Try multiplying together 231 and 659 in roman numerals without using our current number system. Before that, there were even worse number systems like tying knots in pieces of rope. Our current notation for arithmetic makes many problems much easier.

Ideas that people think of as obvious are inventions that were created with great difficulty after many worse ideas were tried. To say that these inventions are trivial is to underrate the importance and difficulty of the problems they solve. Nor should we expect “obvious” ideas necessarily to survive because many of them will turn out to be false. Only a few decades ago, many people considered it obvious that homosexuals should be persecuted, a position that fewer people hold now. Today, most people think that children should be forced to go to school: they are wrong.

Einstein said something about “the gift of wonder” which is partly the capacity to ask questions about the obvious. Of course children do that all the time (the little pests)!

This is relevant to some more paras from Simon Blackburn, following some of the paras quoted in a previous post. He wants to argue that our perception of regualrities is not conjectural. Actually confuding subjective and objective knowledge.

In the chapter Why Do Things Keep On Keeping On? Problems of constancy and chaos.

Our lives are premised on the supposition that the immediate future will indeed resemble the immediate past…Anyone thinking these regularities are about to break in his favour (or his harm) is deluded. Karl Popper was famour for asserting that all science could give us are ‘bold conjectures’ as to what might happen next (see What Do We Know?). But if the right attitude to a bold conjecture falls short of actually believing it, the comparison must be wrong. Our empirical science, our discoveries about the way the world works, give us more than mere hypotheses or mere conjectures. They give us our certainties, the beliefs that our whole lives presuppose. In fact, the philosophical sceptic arguing that we should not place any confidence in these continuities is wasting his breath. Nature forces us to expect things as we do. p. 128.

The problem we have been looking at is a philosophers problem…It does not affect our natural confidence in ongoing order as we conduct our daily lives. But in some contexts, when emotions run high, the inevitable confidence in regularity can falter, and here Popper’s description of us as merely making bold conjectures can do real damage. Consdider that the standard timeline for cosmology and geology, the age of the earth…the evolution of animals, is premised on regularities…But if we say that all of this is, nevertheless, merely bold conjectures we open the way for biblical fundamentalists and creationists to say thier ‘bold conjecture’ that the earth is in fact only six thousand years old is just as good a ‘hypothesis’ as that which science gives us. Careful philosophy of science thus seems to open the door to the most unscientific nonsense, and strips us of any rational weapon with which to counteract the nonsense. pp 130-31.

Actually, many people do not understand the statement “1 + 1 = 2”. They know to put “2” on the right side of an equation when “1 + 1” is on the left side, but the action is reflexive. In my experience, few people realise that “2 x 1” would also be a correct answer, because they do not understand that “=” expresses a relation of equality. The “=” sign is instead interpreted as merely indicating where to write an answer, rather than expressing an abstract relation between two formulae. What is obvious about “1 + 1 = 2” is not always so obvious.

With regard to Blackburn.

Although Popper argued that knowledge is conjectural, he did not argue that “we should not place any confidence” in our conjectures. Popper merely noted that our confidence offers no protection from error, and, with that in mind, he cautioned against absolute certainty. Blackburn claims that “our empirical science, our discoveries about the way the world works … give us our certainties,” but they do no such thing. Although Blackburn may satisfy his craving for certainty by such means, others do so in other ways. Then again, some of us, like Popper, do not even believe that absolute certainty is a worthy end, and are suspicious of a feeling that may set us permanently on the wrong path.