Question

"What does Russell say is the meaning of ‘existence’? What do propositional functions and the theory of descriptions have to do with this?"

** Requires the book of Metaphysics An Antology from Jaegwon Kim and Ernest Sosa from Blackwell publishing**. One page please, will rate**

Answer 1

This question will not classify as Advanced Pysics. It is a part of philosophy. Nonetheless, please go through the answer below.

According to Russell, existence is a property of not the individual, but what he called as propositional functions. We talk about instantiating the existence of objects with definite description and then we take a look at propositions to qualify the objects.

For a quantity/object which exists already, to instantiate its existion does not make sense for Russell. For Russell, existence is a second order property and is a quantified expression referring to a definite description of singular existensial/negative existensial. A singular entity is equivalent to a general descriptive entity. For example 'your name' is nothing but a general description 'a guy in this class, this college with this course GPA'. If you exist then this guy in that college with the course GPA exists.

The propositional function in Russell's existence qualify the truth, i.e. true, sometimes true or never true. If propositional functions are true, it is a necessary propositional function. If it is sometimes true, it is a possible propositional function and if it is never true, it is an impossible propositional function. Lets say this is x, x has to submit an assignment. i.e It is a necessary function for you to be x, but for x is to be a man is is sometimes true. x can be a Woman. So the proposition that x is a man is a possible propostion but for x to be a dog is an impossible proposition to submit the assignment. Now you can use definite description for this x as 'guy in this college, this course with this GPA' or some other description. It is the variability in x that makes the propositional functions.

For the propositional functions which are always true, or sometimes true, imply that the quatity exists. i.e. if x is sometimes true, means that there is at least one instance of x which exists. Existence goes with the propositional function. And this x is a description of what/whom x is, and the description may be always true, sometimes true or impossible giving the propositional function. The existence is only determined by the propositional function & the definite description of x.

For further reading, please go through chapter 3 of the mentioned textbook.