Missives from a fly bottle
barang dot sg
Last revised 31 August 2017
1. Introduction

If someone presents you with a certain line of reasoning, would you be able to discern its exact “shape”?

There are many ways to test for logical ability but I especially like this one because it fosters the good habit of clarifying someone’s argument before trying to criticize it.

Two examples are given below and the rest are tests!

The first example is given by this casual remark:
If every word were a name, then ‘nothing’ would name something, which is absurd.
This remark is extremely swift, but the speaker is clearly arguing for something, i.e., presenting us with a certain line of reasoning. But what is her main conclusion (or bottom line) and how is she proposing to get there?

In other words, what is the “shape” of her reasoning?

A question of this sort can be quite challenging especially if one is new to this and not quite sure of what is being asked – but let’s just jump in and pick things up as we go along.

The question was to discern the exact shape of the reasoning found in the casual remark above. Here’s one possible answer, expressed in a simple diagram:

‘Nothing’ is a word  
  
If every word were a name, ‘nothing’ would be a name A name must name something
 
 
If every word were a name, ‘nothing’ would name something ‘Nothing’ does not name anything
 
 
 Not every word is a name 

A diagram like this may seem intimidating when compared with the original casual remark, so let’s point a few things out.

The diagram is meant to clarify the reasoning found in the remark. Notice that the speaker’s main conclusion (or bottom line) is placed at the bottom of the diagram. According to the diagram, that is, the speaker is ultimately trying to persuade us that not every word is a name. (If this was not obvious, pause and reflect on her words a little more?) We may think of her as starting at the top of the diagram and gradually descending to the bottom, where her argument eventually terminates.

Notice also the arrows in the diagram. Each arrow marks a stage of the argument where the speaker infers a certain conclusion from a certain bunch of premises (or from just a single premise). This act of inferring a conclusion from a bunch of premises is central to the business of reasoning and three such stages are identified in the diagram above. (The argument moves through three stages.) In each case, the arrow points to the conclusion being inferred at that particular stage of the argument. And the premise(s) from which the conclusion is inferred are found at the tail of the arrow. (If more than one premise is used, a horizontal line groups them together.)

More slowly, and using the same diagram, the bit shown here in red highlights the opening stage of the argument:

‘Nothing’ is a word  
  
If every word were a name, ‘nothing’ would be a name A name must name something
 
 
If every word were a name, ‘nothing’ would name something ‘Nothing’ does not name anything
 
 
 Not every word is a name 

The following bit in blue now highlights the second stage of the argument:

‘Nothing’ is a word  
  
If every word were a name, ‘nothing’ would be a name A name must name something
 
 
If every word were a name, ‘nothing’ would name something ‘Nothing’ does not name anything
 
 
 Not every word is a name 

Finally, this bit in green highlights the third and final stage of the argument:

‘Nothing’ is a word  
  
If every word were a name, ‘nothing’ would be a name A name must name something
 
 
If every word were a name, ‘nothing’ would name something ‘Nothing’ does not name anything
 
 
 Not every word is a name 

And so we arrive at the speaker’s bottom line, or main conclusion, which is that not every word is a name. The job of the diagram is to make it clear exactly how she got there.

Two final things are worth mentioning.

First, the diagram shows how a conclusion already inferred may be used as a premise in a subsequent inference, which is a common feature of argument. For example, the statement:
If every word were a name, ‘nothing’ would be a name
figures as a conclusion of a certain inference in the red stage of the argument, but as a premise of a new inference in the subsequent blue stage.

Second, the diagram contains various statements not found in the original casual remark. This is normal since various things are often left unspoken and part of the challenge is to bring them out. For example, the statement:
‘Nothing’ is a word
is not found in the original remark at all but is obviously intended by the speaker, and the diagram reveals the exact place where it is used.

So the challenge is to reveal the logical structure of the original remark (often a short passage) by producing the diagram. More than one answer is possible so long as the structure is more or less captured but all acceptable answers will look essentially the same.

If you have little acquaintance with logic, you can pick up many central concepts just by studying these diagrams and grasping their point!