Tag: Russell’s Paradox

Russell’s Paradox proves Rand wrong and falsifies her philosophy with objective evidence.

http://plato.stanford.edu is my immediate source for the explanation of Russell’s Paradox, but any error in paraphrasing is my own.

(This post, intended to show that Rand’s epistemology is not logical, seems to be perceived as an attempt to show logic to be false since it contradicts Rand’s epistemology! Judging by the comments, anyway.)

Part B: Russell’s Paradox vs Rand’s Objectivist Epistemology.

In Rand’s Introduction to Objectivist Epistemology, mental concepts are “classifications of observed existents according to their relationships to other observed existents”ⁱ. Rand’s philosophy taught that to have mental concepts require us to observe fundamentalⁱⁱ essential distinguishing characteristicsⁱⁱⁱ in real life which share a “Conceptual Common Denominator”^iv. In Rand’s philosophy, logic is “the art of non-contradictory identification”^v of those observations; the result of that process is a mental concept.

Russell’s Paradox proved you shouldn’t just describe a “set” and apply logic to it, because you can get contradiction. Until Russell, “it was initially assumed that any well-defined condition (or precisely specified property) could be used to determine a set.”^vi. Rand’s ideal of a mental concept is that old-fashioned kind of set theory.

Russell’s Paradox logically proves Rand Rand’s logical epistemology is false in three simple steps:

1: Some concepts contain themselves. For example, the concept “things which are not a table” (called a “contrary” in Rand’s philosophy^vii), is itself not a table so it describes itself. You could say, “this concept is not a table” and write it down on a list of things which are not tables.

Another example of a concept that contained itself would be that on a list of everything in the universe, the first thing would be “this list”.

Both of those concepts would be contained in a big list labeled “concepts which contain themselves”. Let’s call this big list concept “A”, and we can write “concept A” in the list first thing; because it contains itself, too.

2: Other concepts do not contain themselves. A list of teacups doesn’t include the list as part of the set of teacups. The concept of a foot is not a foot. Mankind is not a man.

Those three examples are contained in a big list titled “concepts which do not contain themselves”. This list must be concept “not-A”, but…

3: Does that last concept contain itself or not? Can we write “this concept” on the list? Is it “A” or “not-A”? If the concept does not contain itself, we should write it down – which means it does contain itself (there it is on the list), but then it cannot fit it’s own definition as a concept which does not contain itself, so it shouldn’t be on the list and there is contradiction.

By proving the objective definition of sets can lead to logical contradiction, Russell’s Paradox proves Rand’s objective definitions of concepts can result in contradiction. Rand’s Objectivist Epistemology is proved false.

Rand vs Bertrand Russell Part C:

Rand vs Bertrand Russell Part C (Revised):

Russell’s Paradox demonstrates Objectivism is false with real world examples. We can look at actual lists like above and see that A is not-A if it is A, and can be A only if it is not-A. Rand’s assertion that all real things can be logically categorized as A or not-A is demonstrated to be false by objective evidence. Try it at home! Get some pieces of paper and make the actual lists and put labels on them. The last list can’t get a label.

The solution to the riddle is that there are rules we have to make up for logic to work right (axioms), and one of them is that sets can’t contain themselves. Even though we can make a list with the words “this list” on it, we can’t use it for logic. The concept we can see right in front of us can’t be used in a logical system, which falsifies Rand’s Objectivist philosophy of logic.

Stanford Encyclopedia of Philosophy http://plato.stanford.edu is my immediate source for the explanation of Russell’s Paradox, but any error in paraphrasing is my own.