Making an inference

1. Something must be done.
2. This is something.
3. Therefore we must do it.

I'm fascinated by our ability as humans to reason, argue and debate within the confines of our expressive, yet imprecise, natural language.  We quickly reject nonsense arguments; very few managers would accept the following argument from an employee:

1. Today is Tuesday.
2. In two days' time it will Thursday.
3. I deserve a 2K pay rise.

The problem is that of inference: drawing conclusions from existing knowledge.   Combined with our childhood-learnt knowledge of the calendar step 1. 'obviously' implies step two.  That is, if it is Tuesday then in two days' time it will be Thursday.   Equivalently there exists no Tuesday where in two days' time it will not be Thursday.  

Step 3 is pure speculation (if you are wasting your time reading this I wouldn't hold out for one!), most importantly it doesn't seem to follow from the previous two statements.   It's not always clear that an argument is 'wrong', in the earlier argument at the top of this post (the so-called politician's fallacy) each step seems to follow logically from the previous but the ultimate conclusion is garbage.   

The point of the waffle that has preceded is show that discriminating between reasonable and fallacious logical argument is hard.    To help I'm going to reiterate the fallacy of the undistributed middle.   It is a fallacy that I see committed on almost a daily basis by myself, in direct contact with people and in print, it goes something like this:

1. Assign a property to all people or objects or a certain group.
   
2. Find another object or person that also shares the property.
   
3. Conclude that the person or object is a member of the group.
   

Do you agree with the following (quite convincing) argument?:

1. Terrible programmers write Java
   
2. John writes Java.
   
3. John is a terrible programmer.

How about this (less convincing) one:

1. All dogs smell
   
2. John smells
   
3. John is a dog
   

So, to reiterate, this post is part of my attempt to post one item per day, it has no conclusion.  Well, ok, maybe that you should think about your inferences carefully and don't be led by attractive but specious arguments.