I have personally witnessed a room of people nod their heads in agreement with a definition of a particular term in software testing. Then when we discussed examples of that term in action, we discovered that many of us having agreed with the words in the definition, had a very different interpretation of those words. To my great discouragement, I learned that agreeing on a sign is not the same as agreeing on the interpretant or the object. (sign, object, and interpretant are the three parts of Peirce’s semiotic triangle)
In the case of 2+2=4, I think I know what that means, but when Euclid, Euler, or Laplace thought of 2+2=4, were they thinking the same thing I am? Maybe they were, but I’m not confident of that. And when someday a artificial intelligence ponders 2+2=4, will it be thinking what I’m thinking?
I feel 100% positive that 2+2=4 is true, and 100% positive that I don’t entirely know what I mean by “2+2=4”. I am also not entirely sure what other people mean by it. Maybe they mean “any two objects, combined with two objects, always results in four objects”, which is obviously not true.
In thinking about certainty, it helps me to consider the history of the number zero. That something so obvious could be unknown (or unrecognized as important) for so long is sobering. The Greeks would also have sworn that the square root of negative one has no meaning and certainly no use in mathematics. 100% certain! The Pythagoreans would have sworn it just before stoning you to death for math heresy.
Thanks, Eliezer. Helpful post.
I have personally witnessed a room of people nod their heads in agreement with a definition of a particular term in software testing. Then when we discussed examples of that term in action, we discovered that many of us having agreed with the words in the definition, had a very different interpretation of those words. To my great discouragement, I learned that agreeing on a sign is not the same as agreeing on the interpretant or the object. (sign, object, and interpretant are the three parts of Peirce’s semiotic triangle)
In the case of 2+2=4, I think I know what that means, but when Euclid, Euler, or Laplace thought of 2+2=4, were they thinking the same thing I am? Maybe they were, but I’m not confident of that. And when someday a artificial intelligence ponders 2+2=4, will it be thinking what I’m thinking?
I feel 100% positive that 2+2=4 is true, and 100% positive that I don’t entirely know what I mean by “2+2=4”. I am also not entirely sure what other people mean by it. Maybe they mean “any two objects, combined with two objects, always results in four objects”, which is obviously not true.
In thinking about certainty, it helps me to consider the history of the number zero. That something so obvious could be unknown (or unrecognized as important) for so long is sobering. The Greeks would also have sworn that the square root of negative one has no meaning and certainly no use in mathematics. 100% certain! The Pythagoreans would have sworn it just before stoning you to death for math heresy.