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 xx. 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=xx from Wolfram Alpha |
Of course, all of you who have taken Calculus know that the answer is y' = xx(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.
Your post is extremely practical and very clear except, probably for the second Collatz example.
ReplyDeleteI think it is right to say that the Toulmin model cannot be used to solve specific and accurate scientific and mathematical problems.
The first example, however, I think can be solved easily by the Toulmin Model.
The ground are well written. The Warrant for it could be the basic differentiation formulae that we use to solve calculus problems.
The Backing could be where we got the formulae from, graphs of the function and the differentials.
From that, we can conclude and calculate the differential of x^x.
The second example, I am not very clear about the concept.
But you are right when you say that that the Toulmin Model cannot be extended to everything.
I like the way you used the Toulmin Model in the end.
Overall, a good post where you have expressed yourself strongly.
You have a really different interpretation on Toulmin Model than others usually do, and you made some good points. As long as it is a model, there must be something that doesn't fit. Model is not omnipotent, and it just represent the majority. We still need to solve different problems according to the different situations. Since this is a common drawback of models, it doesn't make Toulmin Model look bad I think.
ReplyDeleteYou said that the model doesn't work when we don't have a claim. But I think claim is served as a question you ask in this model. As long as you have something to work on, you should definitely have a claim, or what's the point for solving problems?
You can probably think about a problem that the Model can help work out and that may fit our homework assignment better. But you still have a good try on thinking back to the Model itself instead of just using it without doubt.
I understand your frustration with the Toulmin model. When you first look at it from an engineering stand point, it is not very useful for solving technical problems. However, I think it is very clear as well that this model isn't meant for such problems. It is good for what you said it was good for human argument. This makes me question why you tried to use it for a calculus problem in the first place. What was your motivation behind that?
ReplyDeleteI feel that the reason this model is useful is simply to know that behind every conjecture there is backing. We often forget the importance in the backing behind all of our decisions. In order to have a strong claim the backing behind it must be strong as well. My friend and I talked about how it would be really helpful to use in preparation for a debate so that the debater can check if the have good support for what they want to prove.
So although the Toulmin model isn't totally universal it can still be very helpful? Although I do wonder if there is a type of model that would fit calc well? I think it could be very beneficial for all persons talking math.
“You cannot build a bridge without land on the other side, right?” I like that quote, especially since it supports what you are saying. I definitely see the problem you are talking about with this process. It already assumes you know the answer to your problem. This is definitely not the strong suit of the Toulmin model. It may get you to analyze a problem, but it’s not necessarily going to get you to a solution. Like you said though, it’s good when you want to argue something, which is why it’s called the Toulmin Argument Process. I think it works better for human arguments, as opposed to engineering processes. In my opinion, I think we should use whatever modeling/question asking technique works best for us. It’s nice for us to be introduced to methods like this, but I probably won’t use this in my normal, everyday life.
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