‘Conspiracy Theory’ as a Tonkish Term: Some Runabout Inference-Tickets from Truth to Falsehood
January 3, 2026 | 925 words | 5min read
Paper Title: ‘Conspiracy Theory’ as a Tonkish Term: Some Runabout Inference-Tickets from Truth to Falsehood
Link to Paper: https://philpapers.org/rec/PIGCTA-3
Deate: 15 June 2023
Paper Type: Philosophy, Philosophy of Politics, ideology, Political Epistemology
Short Abstract This paper argues that conspiracy theories employ what can be called tonkish terms, a logical construct that allows inferences from truths to falsehoods. This means conspiracy theories do not have determinate truth-values. As a result, investigating the psychology of conspiracy theories is akin to studying “bastards” and trying to determine what makes them mean, the category itself is unstable and context-dependent.
1. ‘And’, ‘Not’, ‘Or’, and ‘If-Then’
Truth Conditionals
To understand logical connectives like and, or, not, and if-then, one need to understand first the conditions under which a sentence containing the connective is true:
- And (conjunction): “A and B” is true if and only if both A and B are true.
- Or (inclusive disjunction): “A or B” is true if at least one of A or B is true (possibly both).
- Not (negation): “Not-A” is true if and only if A is false.
- If-then (material conditional, classical version): “If A then B” is true unless A is true and B is false; equivalently, “Not-A or B.”
This is standard and generally uncontroversial in philosophy.
Logical Consequences
A logical inference is valid when the premises cannot all be true while the conclusion is false. Validity depends solely on the meanings of the logical connectives, not the specific content of the statements.
Elimination and Introduction Rules
Truth-preserving rules explain why standard logical inferences work:
- And-introduction: From A and B, infer “A and B.”
- And-elimination: From “A and B,” infer A; infer B.
- Modus Ponens: From “If A then B” and A, infer B.
- Modus Tollens: From “If A then B” and “Not-B,” infer “Not-A.”
These rules work because, given the truth-conditions, it is impossible for the premises to be true while the conclusion is false. This explanation is known as the truth-conditional semantics of logical connectives.
2. Inferentialism and Inference-Tickets
Not all philosophers agree that truth-conditions fully explain how logical connectives work. Inferentialism proposes that the meaning of logical connectives is determined entirely by the introduction and elimination rules, the inferences they license, rather than by truth conditions.
Thus, inferentialists reverse the classical order of explanation:
| Classical | Inferentialist |
|---|---|
| Truth-conditions → valid inference rules | Inference rules → meaning → truth (if at all) |
Example:
- In truth-conditional semantics, the meaning of “and” can be represented with a truth table.
- In inferentialism, the meaning of “and” is determined by:
- Introduction: From A and B, infer A & B
- Elimination: From A & B, infer A; infer B
Notice that nowhere in inferentialism we appeal to truth or falsity.
3. Problems with Inferentialism: Tonk
Inferentialism faces a challenge. If meaning is determined solely by inference rules, we could define arbitrary connectives. Arthur Prior proposed “tonk”:
- Tonk-Introduction: From A, infer A tonk B (like “or”).
- Tonk-Elimination: From A tonk B, infer B (like “and”).
The result is absurd: one can infer anything from anything, including false or nonsensical statements.
Example:
- From “Biden is old,” infer “Biden is old tonk Putin has no designs on Ukraine.”
- From “Biden is old tonk Putin has no designs on Ukraine,” infer “Putin has no designs on Ukraine.”
This shows that logical connectives cannot be defined solely by their inferential roles.
4. ‘Conspiracy Theory’ as a Tonkish Term
The same concept helps us understand the term “conspiracy theory.” It is not just tonkish, but mega-tonkish: multiple conflicting rules allow moves from truths to falsehoods.
Tonkish Rules 1
- Introduction: From “This is a theory positing a conspiracy,” infer “This is a conspiracy theory.”
- Elimination: From “This is a conspiracy theory,” infer “This theory is false, crazy, or unbelievable.”
Problem: Many conspiracy-positing theories are true, plausible, or rational to investigate. These rules license inferences from truth to falsehood.
Tonkish Rules 2
- Introduction: From “This theory posits a conspiracy that I (or authorities I respect) do not subscribe to,” infer “This is a conspiracy theory.”
- Elimination: From “This is a conspiracy theory,” infer “This theory is false, crazy, or unbelievable.”
Problem: These rules are indexical (dependent on the speaker’s stance) but produce non-indexical conclusions, often false.
Tonkish Rules 5 & 6: Negation
- Conspiracy Theory Negation (Rules 5):
- Introduction: From “This theory I or authorities I respect DO believe,” infer “This is NOT a conspiracy theory.”
- Elimination: Infer the theory is not false, crazy, or unbelievable.
- Conspiracy Theorist Negation (Rules 6):
- Introduction: From “This person subscribes to a theory I respect,” infer “This person is NOT a conspiracy theorist.”
- Elimination: Infer the person is not irrational.
Problem: These rules move from indexical truths (what the speaker believes) to general claims about rationality, which are often false. They generate inconsistent definitions of conspiracy theories and theorists across groups.
5. Why This Matters
Social science and psychology studies often try to investigate “conspiracy theorists,” claiming, for example:
“Research shows conspiracy theorists think X or have characteristic Y.”
Such claims are problematic because the category itself is tonkish: its rules of inference are inconsistent, context-dependent, and often move from truth to falsehood.
An analogy: the term “bastard” works similarly:
- Introduction: From “This is a man I disapprove of,” infer “This man is a bastard.”
- Elimination: From “This man is a bastard,” infer “This man is arrogant, vindictive, or mean.”
Both cases license inferences from personal judgments to general claims about character, which are often false. Scientificly studying questions like
“Why are so many men such utter bastards?”
is therefore nonsensical, just as claims about conspiracy theorists are methodologically unsound.
reply via email