Developing the Ability to Use the Tools of Epistemic Semantics
Developing the Ability to Use the Tools of Epistemic Semantics
In the course of a discussion of a physics problem involving gravity, one of my young friends — call him/her ‘Zeno’ said:
"...normally we think of tunnels as horizontal and not vertical entities. I think most people would agree that the attached image is a vertical tunnel (citation missing) so if you agree with that, then the earth diameter hole should also be a tunnel. "
My response was:
Questions of Epistemic Semantics
1) What do the words 'vertical' and 'horizontal' mean? ( = How do you define them?)
2) How do you define 'perpendicular'?
3) How are the concepts in (1) and (2) related?
4) What is the difference between the concept of distance on the one hand, and the concepts of height and depth on the other?
5) How are the concepts of distance on the one hand and length and breadth/width on the other related?
6) How would you generalise the concepts of length and breadth in rectangles to squares, ellipses, circles, triangles, and polygons... and to any two dimensional shape?
7) What did you learn by engaging with questions (1)-(6) above?
Mo
And Zeno’s response (mildly edited) to my email was:
From: Zeno
Date: Thu, Apr 6, 2023 at 11:43 PM
Subject: Re: About your tunnel through the earth question
To: Mohanan K P <mohanan.kp@gmail.com>
About the last question first... to what level should we go to while doing epistemic semantics? Surely after a point a reasonable person can justifiably use the catchphrase "come on man, that's just semantics now!"
I think one should do epistemic semantics till the point that I am getting some insight into the problem by carefully trying to understand the meaning behind the words being used. In this case then, I casually used the term vertical and horizontal because I have a very strong intuitive idea about these concepts, but then you asked me to further clarify them. When attempting to do so I didn't have anything better than "earth is a circle, tangents to a circle at a point are horizontal" and the conceptual basis of my explanation doesn't seem as rigorous to me as I had originally thought.
But so what? I don't immediately see how trying to define these terms will help me make progress, perhaps like the professor you mentioned who when asked by you what meaning does the arrow that he has written on the board is implying just said "it's just an arrow!". I ask this because a one layer deep epistemic semantic analysis of the words used might surely be beneficial, but what about the Nth layer? And how to know that the Nth layer that I exhaust myself at is sufficient for my problem? One can say "grow up and develop experience and you will know" but that seems like a risky business - because you are relying on a subjective feeling of satisfaction to determine if your epistemic understanding is rigorous enough (like I did, for better or for worse, when using the terms horizontal and vertical).
From: Mohanan K P <mohanan.kp@gmail.com>
Date: Fri, Apr 7, 2023 at 7:09 AM
Subject: Re: About your tunnel through the earth question
To: Zeno
Those who shirk hard work using the catchphrase "come on man, that's just semantics now!" need to understand that there is an important difference between
a) the semantics of ordinary words, and
b) epistemic semantics of terms used in academic communication crucial for critical thinking, rational justification, and debate.
And there is a further distinction between (b) and (c):
c) conceptual clarification and engagement with concepts as part of inquiry/research and critical thinking.
Folks in the so called Humanities and the Social Sciences throw words like academic terms like ideology, positivism and reductionism in their research and teaching without understanding the concepts these technical terms denote. And folks in STEM disciplines through notations like '--> ' and terms like 'force' , 'field' and 'energy' without bothering about the concepts. Both groups exhibit a certain form of laziness, and in refusing to do some work to engage with the problem, they are being irresponsible.
Needless to say, perfection is impossible as a target. All that is needed is the willingness to travel in that direction.
The following quora posting by Jeff Suzuki might be useful in helping someone appreciate the value of conceptual rigour, conceptual clarity, and the ability to use the tools of epistemic semantics.
Mathematician and math historian 7mo
Why are mathematicians so obsessed with proofs? Many theorems are just intuitive.
Here’s the example I usually give: “The square of an odd number is an odd number.”
Obvious and intuitive, right?
Now try to prove it. The process goes something like this:
“What’s a odd number?”
“It’s a number that isn’t divisible by 2.”
“Wait, aren’t all numbers divisible by 2? Like 5 divided by 2 is 2.5.”
“No, it’s an integer not divisible by 2.”
“What do you mean by that?”
“When you divide it, you have a remainder.”
“How can you tell?”
[some thought, ending with]
“OK, if an integer is not divisible by k, then it has the form pk + r, where k is an integer and r is a whole number less than k.
“So an odd number is a number of the form 2k + 1, where k is an integer.”
Now at this point, notice you have to define what you mean by an odd number, and have to clarify notions like “not divisible by.” In other words, proof CREATES mathematics.