Monday, March 12, 2012

The Humpty-Dumpty Principle in Definitions

In dealing with empty concepts, we came across the issue that if somebody uses a term that potentially has an unintelligible definition, they are likely to defend themselves by quickly making up some kind of definition.   I strongly suspect that in such cases, the usage of the term will be inconsistent with the definition.  Which brings us to Humpty-Dumpty.

Lewis Carroll (Rev. Charles Lutwidge Dodgson) is best known for his children's' books Alice's Adventures in Wonderland and Through the Looking Glass.  It is in the latter that Humpty Dumpty - an argumentative egg perched on a wall has the following exchange with Alice:

'And only one for birthday presents, you know. There's glory for you!'
`I don't know what you mean by "glory",' Alice said.
Humpty Dumpty smiled contemptuously. `Of course you don't -- till I tell you. I meant "there's a nice knock-down argument for you!"'
`But "glory" doesn't mean "a nice knock-down argument",' Alice objected.
`When I use a word,' Humpty Dumpty said, in rather a scornful tone, `it means just what I choose it to mean -- neither more nor less.'
`The question is,' said Alice, `whether you can make words mean so many different things.'
`The question is,' said Humpty Dumpty, `which is to be master -- that's all.'

What Humpty-Dumpty is saying is that he can stipulate what the definition of a term is.  Lewis Carroll was a processor of logic and mathematics at Oxford University (Christ Church College), and wrote extensively on logic.  He elaborated on the theme in Humpty Dumpty in Chapter 2 of Book 10 of his work Symbolic Logic, where he says:

"...I maintain that any writer of a book is fully authorized in attaching any meaning he likes to any word he intends to use.  If I find an author saying at the beginning of his book, 'Let it be understood that by the word white I shall always mean black' I meekly accept his ruling, however injudicious I may think it. " 

[I quote from Lewis Carroll's Symbolic Logic by William Warren Bartley III,  ISBN 0-517-52383-3 - a book I had great difficulty in obtaining].   

Carroll implies that an author must use such a term consistently - that is, without varying the underlying definition.  This appears to be the principle that Humpty Dumpty was getting at.  Varying the definition of a term within an argument is the fallacy of equivocation, but Carroll is going beyond that and demanding consistent usage throughout a universe of discourse.

A second point here is that if a term is to be used in a nonconventional way, then the definition should be explained up front.  Again, Carroll implies this in his example of white.  This is one place where I would agree with the maxim of "starting with definitions".  However, this maxim is often misused.  For instance, in analysis we nearly always aim to arrive at definitions, as we do not understand concepts at the outset.

Thus, I think we now have a reasonable framework for dealing with individuals who use terms that they cannot supply adequate definitions for, particularly in the context of empty concepts.

One quick Lewis Carroll story.  Carroll found it necessary to deny that he had ever presented Queen Victoria with a book.  The story circulated that the Queen has been so charmed by reading Alice in Wonderland that she expressed her desire to receive the author's next work - whereupon he sent her The Condensation of Determinants


  1. Kind of sounds like Donald Trump and his "alternative facts".

  2. Kind of sounds like the left, changing the meaning of words willy-nilly to fit their social constructs and political bias.

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  4. To the bleeding heart liberal luvvies who embrace every human calamity in the world (e.g drought in Africa) and shift the blame on governments, if you are not with them you are a heartless racist, xenophobic, reactionary and you name it, all of these things. Words truly mean what they choose them to mean !