Bertrand Russell once famously made the following proposition: ‘The present King of France is bald’. Given that there is no present King of France, what truth-value do we assign to this sentence?
Under classical logic, the choice will be between ‘true’ and ‘false’, so the process of analysis will go something like this. In the category of ‘true’, we will put in all bald people, while in the category of ‘false’ we will put in all non-bald people. Then we see which category the King of France – the ‘referring expression’– falls within. However, we have the troubling result that the King of France does not fall into either set of results. So what does this mean for the proposition? While it might seem patently false, this is not easily demonstrated by classical logic. Do we perhaps need to use some further status, such as ‘indeterminate’?
In the philosophy of logic, we can describe the problem more formally as follows. If we have a logical proposition that uses a constant or variable – such as the example below – how do map the use of the variable ‘x’ to an actual ‘object’ in the real world? Which expressions in normal language can be used to satisfy the logical variable?
Vx (Fx -> Gx)
In the case of names that refer to actual people, eg ‘Queen Elizabeth II’, there is generally no problem. However difficulties arise when we attempt to use an expression such as ‘the current monarch of England’. This uses a ‘definite descriptor’: it describes the sort of person we are after but doesn’t actually name any one person in particular. Can this definite descriptor be used to substitute for the variable in the logical statement?
In the context of naming and descriptions, philosophers such as Bertrand Russell have made a further distinction between de dicto knowledge and de re knowledge. As was discussed in modal logic, these two concepts can be used to define the way in which the knowledge is held – by description / by words (de dicto) or by acquaintance / experience (de re).
- Russell’s Theory of Descriptions
One of Russell’s objectives – as part of his theory of descriptions – was to clarify exactly what we mean when we use a noun with a definite article (‘the so-and-so’). Russell was less concerned with the indefinite article (‘a so-and-so’), although that would be explored by later philosophers. In terms of the definite article, Russell proposed the following definition (known as ‘contextual definition’): ‘the F is G’ is true if and only if one thing exists that is ‘F’ and this is also ‘G’. More generally, if we say ‘F exists’, this is true if and only one thing exists that is F. If these definitions are not satisfied, then the statement must be false.
Another way of looking at Russell’s theory is that the use of ‘the so-and-so’ is a kind of logical quantifier, similar to ‘some’ and ‘all’. ‘The so-and-so’ acts as a logical quantifier for only one item, with the rest of the description providing the conditions that have to be met.
Applying this principle to the original statement, ‘the present King of France is bald’, we can now see that this is false since it is not the case that there is ‘one and only one’ subject that matches the description. Nothing matches the description at all. Having now defined his general theory of descriptions, Russell next applies the theory to three philosophical ‘puzzles’.