Abstract

1. Transmission Jim’s teacher has just given him his marked maths exam. Jim knows that his mark is 7.25 out of 22. He also knows that the pass mark is 35%. Does Jim know he has failed? No, he doesn’t. Not yet. As you would expect from his mark, Jim is not very good with numbers. He’ll need a few minutes with pencil and paper to work out that 7.25 is less than 35% of 22. Only then will he know that he has failed. This case exemplifies a common and important phenomenon: someone recognises the validity of an inference from a set of premises that he knows, and in so doing he acquires knowledge of the conclusion. Jim knows that his mark is 7.25 out of 22 and that the passmark is 35%. Then, by virtue of his calculation, he comes to recognise the validity of the inference from these premises to the conclusion that he has failed, thereby coming to know the sad truth. It is undeniable that there are many cases, like Jim’s, in which recognising the validity of an inference from known premises brings about knowledge of the conclusion, as this is the most natural characterisation of what goes on when we acquire knowledge by deductive inference. But can knowledge always be acquired in this way? Does recognition of the validity of an inference from known premises always bring about knowledge of the conclusion?