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Exercise: Analysing and Discussing Paradoxes

Analyse the following paradoxical situations. Identify the type of paradox, the hidden assumptions and possible approaches to a solution.

1. The Grandfather Paradox​

"Suppose time travel were possible, and someone travels into the past and kills their own grandfather before he could father any children. Then the time traveller would never be born and could therefore not travel into the past to kill their grandfather. But if they do not kill their grandfather, then they would be born and could travel into the past to kill their grandfather."

2. The Paradox of Tolerance​

"A perfectly tolerant society would also have to tolerate intolerance. But if it tolerates intolerance, intolerance could gain the upper hand and destroy tolerance. If, on the other hand, the society does not tolerate intolerance, it is itself intolerant and therefore not perfectly tolerant."

3. The Omniscience Paradox​

"Can an omniscient being know what it is like to be ignorant? If yes, how can it really know what ignorance feels like if it was never ignorant itself? If no, then there is something it does not know, and it is therefore not omniscient."

4. The Paradox of the Heap (Sorites)​

"A heap of sand remains a heap if you remove a single grain of sand. If you continue this process, even a single grain of sand would still have to be a 'heap', which is obviously false."

5. The Bootstrap Paradox​

"A time traveller brings a book from the future into the past. This book is then published and eventually becomes exactly the book that the time traveller brought into the past. Where does the original content of the book come from?"

Approaches to Solutions​

  1. The Grandfather Paradox
    • Type of paradox: Temporal paradox
    • Hidden assumptions: Linear temporal causality; uniqueness of the timeline
    • Possible solutions:
      • Many-worlds interpretation: The time traveller creates an alternative timeline in which his grandfather dies, but this does not affect his own original timeline.
      • Consistency principle: Time travel can only take place in a way that does not create contradictions (the attempt to kill the grandfather would always fail in some way).
      • Time travel might be fundamentally impossible, precisely because of such paradoxes.
  1. The Paradox of Tolerance
    • Type of paradox: Self-referential paradox, ethical paradox
    • Hidden assumptions: Tolerance is an absolute value; tolerance means accepting everything
    • Possible solutions:
      • Differentiating the concept of tolerance: Tolerance does not mean accepting everything, but respecting differences that do not themselves undermine the foundations of tolerance.
      • Karl Popper's solution: A tolerant society should have the right not to tolerate intolerance when it threatens tolerance itself.
      • Contextual application: Tolerance as a regulative principle that is applied differently depending on the context.
  1. The Omniscience Paradox
    • Type of paradox: Epistemic paradox
    • Hidden assumptions: Knowledge requires experience; omniscience means having all experiences
    • Possible solutions:
      • Distinguishing between propositional knowledge (knowing that) and experiential knowledge (knowing how): An omniscient being could know everything about ignorance without experiencing it.
      • Omniscience could include the ability to simulate or understand experiences without having them directly.
      • The paradox could point to the limits of human concepts of omniscience.
  1. The Paradox of the Heap (Sorites)
    • Type of paradox: Sorites paradox (paradox of vagueness)
    • Hidden assumptions: Vague concepts have sharp boundaries; small changes cannot bring about qualitative differences
    • Possible solutions:
      • Fuzzy logic: The concept "heap" has degrees of membership, not sharp boundaries.
      • Supervaluationism: There is a range in which the application of the concept "heap" is indeterminate.
      • Contextualism: The meaning of "heap" depends on the context.
      • Epistemicism: There is a sharp boundary, but we cannot know where it lies.
  1. The Bootstrap Paradox
    • Type of paradox: Temporal paradox, causality paradox
    • Hidden assumptions: Information must have an origin; causality is linear
    • Possible solutions:
      • Closed time loops: Information can exist in a causal loop without having a definable origin.
      • Many-worlds interpretation: The book originally comes from another timeline.
      • Time travel might be fundamentally impossible, precisely because of such paradoxes.
      • The information could gradually change within the loop, which would lead to inconsistencies in the long run.