- Russell’s Philosophical Puzzles
Russell continues his theory of descriptions by seeing how it resolves three common philosophical puzzles.
Puzzle 1 – Identity
Russell starts by noting the general law of identity: if a is identical to b, whatever is true of the one is true of the other and either may be substituted for the other, without affecting the truth-value of the proposition. However, if we apply the law strictly it results in some paradoxical conclusions, as demonstrated by the following example:
- George IV wishes to know whether Scott was the author of Waverley
- Scott was the author of Waverley
- Therefore, applying the law of identity, George IV wishes to know whether Scott was Scott
Although Russell doesn’t explain exactly how his theory of descriptions resolves this, one possibility could use the notion of scope, as explained further in Puzzle 2 below. In this case, by considering proposition (a), the ‘author of Waverley’ is an example of a definite descriptor that has narrow scope, since it is part of a wider statement of what George IV wishes to know. Because it has narrow scope, the definite description has a ‘secondary occurrence’. So the law of identity does not apply in this case. In other words, the law of identity only allows for substitution where the definite descriptor has primary occurrence.
Puzzle 2 – Law of Excluded Middle
Russell noted the following general principle of classical logic, what is commonly known as the law of excluded middle. It is always the case that P is true, or P is not true, meaning that P v ~P is always true: it is always one or the other. As mentioned above, the statement ‘the present King of France is bald’ seems to infringe this as it is neither true nor false, since the ‘present King of France’ does not exist in either set of ‘bald’ and ‘not bald’. Russell believes that his theory can deal with this situation, by introducing the notion of logical scope.
When we say that ‘the present King of France’ is false, we usually read the negated sentence in the following way: ‘exactly one thing is the present King of France and that thing is not bald’. This is an example of narrow scope where we are negating the specific predicate included in the sentence. However, we can use negation in another way, in wider scope. The negation of the statement now appears as follows: ‘It is not the case that there is exactly one thing that is the present King of France and that thing is bald’. When we use wide scope, the definite descriptor now has a ‘secondary occurrence’ as it fits within the scope of the negation (the entire sentence). This more accurately reflects the nature of ‘false’ that we are assigning to the sentence, plus it also satisfies the law of excluded middle.
Puzzle 3 – Existence
The problem of existence is a common one in regards to logic. How do we deal with objects that don’t exist, such as a statement ‘the largest prime number does not exist’. These non-existent objects provide a paradox. If we say the reference to the ‘object’ refers to nothing at all, then this would result in meaningless statements. However, if we say the reference does mean something, then we are perhaps asserting that the object does exist after all. But this would always result in false statements, as the propositions could never possibly be true.
One solution to the problem – called Meinongian – is to recognise that there is in fact a ‘set’ of non-existent objects. This allows us to reference the object in a proposition, which means it can then be logically evaluated. So ‘the largest prime number does not exist’ would be interpreted as true. Bertrand Russell however is one of many philosophers who disagrees with this approach. For logic to be useful, it must be directly connected to the real, actual world. We should not be introducing concepts that do not exist in the real world. ‘Logic must no more admit a unicorn than zoology can’.
To resolve the issue of the non-existent objects, Russell refers back to his theory of descriptions. Using the idea of wide scope again for a definition description, we can refer to a non-existent object in the following way: ‘it is not the case that the greatest prime number exists’. This allows us to refer to the ‘object’ but does not claim that it exists in any way.
How would Russell deal with the case of a proper noun that does not exist, such as ‘Santa Claus does not exist’? Here, Russell would use his theory of descriptions and replace ‘Santa Claus’ with a possible description: ‘the man who delivers presents at Christmas’. Then, we can go ahead and negate this sentence at wide scope: ‘It is not the case that there is exactly one man who delivers presents at Christmas’.