Questions: Rule-Following and Meaning Constitution

Question 1

A person has correctly solved every addition problem they've ever encountered. Asked for 68 + 57, they answer 5. According to Kripke's skeptical argument, what does their long history of correct answers demonstrate?

• A. That they have always genuinely understood addition, and answering 5 is simply an isolated computational error
• B. That all their past correct performances are consistent with infinitely many deviant rules — including 'quus' — that agree with ordinary addition for all previously computed cases but give different outputs for new ones
• C. That they were using a different operation the whole time and never actually understood standard addition
• D. That community standards for mathematical correctness are inherently unstable and subject to revision

Answer: (B)

Kripke's point is not that the person made an error, but that no fact about their past behavior uniquely determines which rule they were following. The 'quus' function agrees with addition for all cases computed before some threshold but outputs 5 for inputs above that threshold. Since 68+57 was never computed before, the past performance history is equally consistent with following addition or following quus. This is not skepticism about the correct answer (125) — it is a challenge about what fact makes 125 the answer they *meant*.

Question 2

Why does appealing to a mental rule or an introspective report of one's intentions fail to resolve the rule-following regress?

• A. Because Wittgenstein argued that mental states are philosophical fictions with no genuine existence
• B. Because introspective access to the mind is unreliable and prone to motivated self-deception
• C. Because any introspective report of a rule is itself a piece of behavior subject to the same skeptical challenge — interpreting that report requires further rules, regenerating the infinite regress
• D. Because only community consensus, not individual mental states, can ground facts about mathematical operations

Answer: (C)

The regress problem is structural. If you try to fix meaning by citing a mental rule ('I had addition in mind'), the skeptic applies the same challenge to that mental state: what makes your mental representation mean addition rather than quaddition? Any attempt to interpret a rule requires a further rule for doing the interpreting, which itself requires a further rule, and so on. Wittgenstein's diagnosis is that meaning cannot *consist* in any interpretation. What stops the regress is not a bedrock interpretation but unreflective participation in a shared practice.

Question 3

Kripke's skeptical argument is fundamentally about the ambiguity of rules — that words and symbols are often unclear and can be interpreted in multiple plausible ways.

• T. True
• F. False

Answer: False

The problem is deeper than ambiguity. Ambiguity implies a rule could mean one of a few plausible things. The rule-following problem applies even to perfectly clear, unambiguous rules: no matter how precisely '+' is defined, any finite record of past applications is logically consistent with infinitely many deviant rules that agree on all past cases but diverge on new ones. The challenge is not to remove unclarity but to explain what *fact* — about behavior, mental states, or physical constitution — makes any particular rule the one that was meant.

Question 4

According to Wittgenstein, what stops the rule-following regress is not a final self-interpreting bedrock interpretation, but brute participation in shared practices and forms of life.

• T. True
• F. False

Answer: True

Wittgenstein's key move is to show that demanding a foundational interpretation generates an infinite regress and must therefore be abandoned. There is no interpretation that interprets itself. What actually grounds rule-following is something non-interpretive: trained capacities, natural responses, and shared participation in practices that are already in place. When someone 'just sees' that 125 is the right answer, this reflects mastery of an embodied practice, not the application of a private mental rule.

Question 5

What does Kripke's 'quus/quaddition' thought experiment show about the relationship between past behavior and the meaning of a rule? Why is this result philosophically troubling?

Model answer: The quus thought experiment shows that no finite record of past behavior uniquely determines which rule was being followed. 'Quus' is defined to agree with addition for all previously computed cases but to give a different answer for new inputs. Since any history of computation is finite, it is always consistent with some deviant rule. This means past behavior alone cannot constitute the fact that someone meant addition rather than quaddition — there is no behavioral fact that fixes meaning.

The deeper implication is that the traditional picture of meaning — where a symbol is tied to a rule by some inner mental act — cannot be sustained. The skeptical argument rules out mental facts, behavioral facts, and dispositional facts as candidates for what constitutes meaning. Wittgenstein's response is not to find a better candidate fact but to reconceive where normativity lives: not in any single person's mind or history, but in shared practices and forms of life that we are trained into and participate in without further justification.