Final Exam: Russell

Question 1

What is the substitution puzzle?

Answer 1

Consider “George III wondered whether the author of Waverly is Scott” and “George III wondered whether Scott is Scott.” How do we go from true to false just by replacing one denoting phrase with another identical denoting phrase?

Question 2

What is Russell’s solution to the substitution puzzle?

Answer 2

The logical form of “Scott is Scott” is x=x. The logical form of “the author of Waverly is Scott” is “some author of Waverly is identical to Scott, and there is at most one author of Waverly.” Since the substitution changes the logical form, the substitution puzzle does not violate Leibniz’s Law of the Indiscriminability of Identicals.

Question 3

What is the law of the excluded middle puzzle?

Answer 3

Consider “the present King of France is bald” and “the present King of France is not bald.” These are both false because there is no present King of France. How can a claim and its negation both be false?

Question 4

What is Russell’s solution to the law of the excluded middle puzzle?

Answer 4

The logical form of “the present King of France is bald” is “some present King of France is bald, and there is at most one present King of France.”
The logical form of “the present King of France is not bald” is “it is not the case that there is a present King of France who is bald, and that there is at most one present King of France.”
So there is no violation of the law of the excluded middle because the claim and its negation have opposite truth-values.

Question 5

What is the existentials puzzle?

Answer 5

Consider “conscious cows do not exist.” How can one attribute a property to something which does not exist?

Question 6

What is Russell’s solution to the existentials puzzle?

Answer 6

The logical form of “conscious cows do not exist” is “for each and every thing, if it is a thing, then it is not a conscious cow.” Rather than attributing a property to a non-existent thing, the sentence says every existing thing lacks a property.

Question 7

What is Russell’s view on knowledge?

Answer 7

People first acquire knowledge of things by acquaintance with all the ultimate constituents of a description’s logical form. They then acquire “knowledge that” (propositional knowledge) through perception or inference.

Question 8

How is Russell’s logicism similar to Frege’s?

Answer 8

Russell wants to reduce arithmetic to logic and definitions and is interested in explaining mathematical knowledge and its a priori status.

Question 9

How is Russell’s logicism dissimilar to Frege’s?

Answer 9

Russell wants to reduce all math to logic, does not distinguish between objects and concepts, and aims to unify ontology of math as an ontology of sets.

Question 10

What is Russell’s paradox?

Answer 10

Two sets are identical if they have the same members, and every predicate has an extension. Define R as the set of all sets that don’t contain themselves. This set both contains itself and does not contain itself.

Question 11

What is the vicious circle principle?

Answer 11

Vicious circle principle holds that you cannot define a thing either in terms of itself or in terms of any set containing that thing. Because Russell’s set is defined in terms of all sets its definition is illegitimate.

Question 12

What is problematic with the vicious circle principle?

Answer 12

Define the shortest spy as the shortest spy in the set of all spies. According to vicious circle principle, this definition is illegitimate even though it is actually fine.

Question 13

What is type theory?

Answer 13

Metaphysics is stratified into types. So “every” or “some” is restricted to a type, X=Y only if X and Y are in same type, and X is a member of Y only if X is a type below Y. The definition of Russell’s set violates these rules.

Question 14

What is problematic with type theory?

Answer 14

Type theory is meaningless because one cannot say everything has a type. One can only say “everything in type n has a type” which is trivial and does not exclude that there is something outside a type.

Question 15

What is the axiom of infinity?

Answer 15

If there is a finite number of individuals, then the Peano axioms are violated. Therefore, Russell supposes there are infinitely many individuals and justifies it by saying it’s necessary for math to work.

Question 16

What is ramified type theory?

Answer 16

The set of natural numbers is a type 3 class defined in terms of type 3 classes. This violates the vicious circle principle, so Russell adds levels to types (e.g. type 3, level 0).

Question 17

What is problematic with ramified type theory?

Answer 17

It is practically unusable and rules out mathematical induction because it violates level restrictions.

Question 18

What is the axiom of reducability?

Answer 18

For every class that is type n, level m—where n>0—there is a class of type n, level 0 with the same members. This is justified because it is necessary for mathematical induction to work.

Question 19

What is Russell’s view on material objects?

Answer 19

If evidence about something comes from a certain fact, then that something must be constructed out of that fact. Because we only have sense-data, claims about material objects must be constructed from claims about sense-data. So the analysis of “I see a table” is a series of claims about sense-data one would have in various counterfactual situtations.

Question 20

What is problematic with Russell’s view on material objects?

Answer 20

Russell’s epistemic principle is false. It is unclear how one would have knowledge of hypothetical claims. Cannot explain “there is a table” because that is a public object while sense-data are private.

Question 21

What is Russell’s view on the problem of other minds?

Answer 21

The argument from analogy is invalid because it analogizes to all cases from one case, and it is a weak analogy even in that one case. Therefore, Russell views the existence of other minds as a useful hypothesis that we can’t really know.

Question 22

What is Russell’s philosophical method?

Answer 22

Russell believes philosophy should use the scientific method. Philosophy like science is piecemeal, tentative, and fruitful while applying to everything in the universe, investigating essential natures, and being a priori. The two parts of philosophy are general statements and analysis of logical forms.

Question 23

What is Russell’s logical atomism?

Answer 23

The world is fundamentally made up of facts either atomic or complex. Atomic facts are either (entity + property) or (entities + relation).
Sentences are either atomic or complex. Atomic propositions are either (name + predicate) or (names + relational predicate). Atomic proposition is true iff there is a corresponding atomic facts.

Question 24

What is Russell’s view on non-atomic facts?

Answer 24

Conjunctive and disjunctive facts are redundant. Negative facts are necessary because the mere absence of fact A is not enough to know A is false.
General facts are also needed to rule out alternative possibilities.

Question 25

What is problematic with Russell’s view on non-atomic facts?

Answer 25

Consider ~(AvB). For this to be true, ~A&~B must be true; however, it is not clear that the truth of ~A&~B can only be explained through negative facts.