Video blog - Engineered object

A video is made up of thousands of pictures. A picture is worth a thousand words. 

video > 1,000,000 words :-)

Click here to view the video:

Toulmin's model for arguments

Toulmin's model for arguments divides arguments into five critical components, namely ground, warrant, backing, qualifier and claim. They align in a order similar to the one below.

However, I want to point out that Toulmin's model is designed to analyze human arguments, not for either scientific proof or seeking solutions. This model cannot operate when we don't have a claim, an assumption or a hypothesis to work with in the first place. This is exactly what Toulmin thought about developing an argument, which should be started with a claim and then proving it, as opposed to looking at the grounds we have a extending outwards. 

To prove my point, I will use two examples of problems I faced. 

The first is a problem from my calculus course. (I assume as engineers, everyone here knows about calculus) I want to find out what is the derivative of x^x. If I use the Toulmin's model now, I will start with the claim. But then I have no idea what the derivative is, I cannot claim or hypothesize anything. I tried to looking at the graph, but from what I learnt, I have no idea what the derivative is. Although I do have the grounds, which are the definition of derivative and the rules of differentiation, I won't know what to put in all the other boxes, because the warrant is the bridge between ground and the claim. You cannot build a bridge without land on the other side, right?

Now I am stuck here, essentially helpless. I can try to guess something and use the Toulmin's model to try to prove it, but the probability that I will get the correct answer is very small. This method of trial and error is not very effective and will take me decades to solve a simple question like that. 

Graph of y=x^x from Wolfram Alpha

Of course, all of you who have taken Calculus know that the answer is y' = x^x(ln x + 1). But my point is that the Toulmin's model is not designed for, and not useful in solving problems which we cannot come up with a reasonable hypothesis. 

---

The second one is Collatz conjecture. You who have read my previous post should know what it is, it is an unsolved mathematical problem. The problem is to prove that for any positive integer I put into N below, it will eventually reach 1. 

- if N is odd, give 3N + 1

- if N is even, give N/2

Put the new given value into N and loop

Now that I have a claim: it will reach one eventually, I suppose I can use Toulmin's model to help. Then I created the box below:

I have support from computations to see that the rule applies for each and every positive integer from 1 up to 5.764x10¹⁸ (Wikipedia). Seeing that it still holds up to an integer so large, I would claim that the rule holds for all positive integers. There is when I fall into the trap of this model: scientific research requires a high degree of accuracy and you never know that the number after the last one you tested will break the rule or not until you test it. But then numbers are infinite, so you cannot test all numbers. When I try to support my claim, I have to also be aware of accuracy requirements and generalizations. While human arguments tend to have a reasonable tolerance to uncertainty, science does not. This is where the weakness of Toulmin's model is exposed. When trying to apply the Toulmin's model, especially when outside of its designed scope, we have to be very aware of the limitations and possible failures. 

---

After all, this Toulmin's model is a good model in its originally designed scope: human arguments. Review what I have written in this passage, I am trying to convince a claim that this model cannot be used to find solutions and may fail if the subject is a scientific research requiring high degree of accuracy and generalization. Here is where I can use the Toulmin's model to analyze my arguments.