[FOM] Why inclusive disjunction?

Henrik Nordmark henriknordmark at mac.com
Wed Jan 10 01:57:48 EST 2007

> Can anyone provide a principled reason for why logicians choose to  
> interpret "or" as inclusive disjunction?

I always thought that logicians chose the inclusive or to be the  
default because they were attempting to capture the reasoning process  
of mathematicians speaking Mathematical English, Mathematical-French  
or what have you... Moreover, logicians like Boole were  
mathematicians after all and thus biased towards the way  
mathematicians tend to use the word "or".

But this of course begs the question in some sense. One might then  
ask why did mathematicians choose the inclusive or as the default  
interpretation. Is it actually conceptually easier to think in terms  
of an inclusive or in the context of mathematics? That seems  
doubtful. It seems more  likely that this was a historical accident  
and that sociological pressures keeps the status quo within the  
mathematical community. At some level, the choice is analogous to  
choosing whether to drive on the left side or right side of the road.  
The choice any particular community makes is arbitrary but a choice  
must be made and once you've made your choice you don't really want  
to change it unless there are good enough reasons to do so.

Sociological inertia is a powerful thing. I am still amazed at the  
fact that the U.S.A. has not adopted the metric system even if it is  
clearly a much better system that what they use now. In Sweden,  
people were driving on the left side of the road with cars that had  
the steering wheel on the left and this was causing lots of  
accidents. Despite this, the Swedish people voted against changing  
the side of the road on which they drove in a referendum.  
Fortunately, eventually the Swedish government decided to ignore the  
will of the people and make the change to drive on the right side of  
the road anyway.

Anyways, my point is that I don't think you will find any principled  
reasons as to why logicians choose inclusive disjunction.
Alas, from a pedagogical point of view it would be better if such a  
reason did exist.

Henrik Nordmark
Institute for Logic, Language and Computation
Universiteit van Amsterdam

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