# What did Turing mean when saying that “machines cannot give rise to surprises” is due to a fallacy?

I encountered below statement by Alan M. Turing here:

“The view that machines cannot give rise to surprises is due, I
believe, to a fallacy to which philosophers and mathematicians are
particularly subject. This is the assumption that as soon as a fact is
presented to a mind all consequences of that fact spring into the mind
simultaneously with it. It is a very useful assumption under many
circumstances, but one too easily forgets that it is false.”

I am not a native English speaker. Could anyone explain it in plain English?

He’s saying that systems with simple, finite descriptions (e.g., Turing machines) can exhibit very complicated behaviour and that this surprises some people. We can easily understand the concept of Turing machines but then we realise that they have complicated consequences, such as the undecidability of the halting problem and so on. The technical term here is that “knowledge is not closed under deduction”. That is, we can know some fact $$AA$$, but not know $$BB$$, even though $$AA$$ implies $$BB$$.