His examples with the rocks, fingers, and other drawings just seem to represent exactly what the forumla is saying.
Yes, they do. There is a mapping between the mathematics and physical actions. He described the physical actions that some one could do with words. This allows us to confirm that 2+2=4 through experimentation.
Adults have presumably gone through years of education and with little effort recognize a mapping between a math problem and a set of actions. We also learn how to map sentences to math equations through word problems. By the time some one has finished high school they have enough experience with equations of this type to be able to do them with little effort.
To make more sense of this if you have a young child or relative that has just started with their education in school. If that child has already learned numbers and counting and is starting to learn math then the child may be able to demonstrate this for you. I have a young relative that is learning math and as an aid he is given a collection of objects (usually coins) that he can use to test whether or not his math is right.
When he writes down an answer to a question like 6 + 7 then he count perform a task similar to what evid3nce to experiment and see whether or not his result is correct. When I was in elementary school when we started with multiplication we did similar operations. How did we know what 3 * 4 was? We would draw 3 coliniar series of 4 dots and then count them.
In effect, what I saw was akin to this:
Me: Prove this proposition: “All t-shirts are blue”
Evid3nc3: writes All t-shirts are blue in 5 different languages and shows them to me
I could be mistaken, but that seems to be the way he implements his verification style epistemology.
I think he labeled it as “evidential rationalism”. But that example is different entirely. (I’m going to look past the fact that you could evaluate such a proposition as false by producing a non-blue shirt). In your example you are providing 5 different equivalent expressions. It would be like writing “2 + 3 = 5”, “3 + 2 = 5”, “5 = 2 + 3”, “5 = 3+2” Those all evaluate to the same thing, but are different expressions, but that isn’t an experiment. I pulled a few definitions of experiment from a few sources. Some relevant definitions:
The process of testing (
Merriam Websters, def 3)
An operation employed to resolve an uncertainty(
Answers.com)
If I count out two objects and set them aside, and then count out two more objects and set them aside, and then count out all the objects that I have set aside and they add up to 4 then I have done an experiment, or a test, demonstrating that 2+2 is 4.
There are some unspoken assumptions I’ve made in writing this that I will summarize by saying that I’m assuming we are talking about the type of math that is usually taught to children. I can formally define the rules of such mathematics in terms of set theory and cardinalities, defining integers, the base 10 number system, and so on. But I’m trying to keep the discussion in grasp of the general public and avoid concepts that may be esoteric when ever possible. (it may sound unnecessary to qualify this but I’ve been in discussion where some one will throw out something like “what if we are not using a base 10 number system!”).
As you move into more abstract forms of mathematics that are further removed from having relationships to reality then you may start to approach a point where physical experiments may not be an appropriate form of verification. But 2+2=4 is something that is in the realm of being confirmable through an experiment.
had.