Grandfather Paradoxes

Lewis’ Aim and Basic Framework

• Lewis’ paper addresses only the logical (not physical or actual) possibility of time travel.
  • Goal: Show that some backward‐time journeys can be described without contradiction.
  • Distinction emphasized between:
  • Personal time (the traveler’s own sequence of experiences).
  • External time (the timeline measured by clocks “in the world”).
  • Time travel = divergence between the order of events in personal time and in external time.

The Classic Grandfather Paradox Argument

• Standard syllogism employed by opponents:
  • If backward time travel were possible, contradictions would be possible.
  • Contradictions are impossible.
  • Therefore, backward time travel is impossible.
• Lewis concedes the middle premise (contradictions cannot occur) but rejects the first premise.
• Typical illustration:
  • Traveler returns to the past and eliminates a grandparent before parenthood.
  • Result: Traveler’s own existence is removed, making the journey both happen and not happen.
  • Produces the appearance of A \wedge \neg A (a formal contradiction).

Lewis’ Strategy: Preserving Consistency

• Key claim: Backward time travel need not supply the power to bring about logically inconsistent states of affairs.
• Each moment in external time happens once and once only; history is self‐consistent.
  • There is no second, altered running of 1908 with the traveler’s new actions.
  • Whatever the traveler does in the past was already part of the history she departs from.
• Result: Apparent paradoxes dissolve when we track all events within a single, consistent timeline.

Illustrative Case Study: “Assassinate Hitler” Mission

• Setup
  • Time machine launched \text{January }2013.
  • Destination chosen: Vienna, late 1908 (Hitler’s “hunger years”).
• Logical barrier
  • Historical record: Hitler dies in 1945.
  • Death is a one‐shot event ➔ same person cannot die in both 1908 and 1945.
• Possible outcomes consistent with history (all entail mission failure without paradox):
  • Gun jams.
  • Sneezes; shot misses.
  • Hitler bends to tie a shoelace.
  • Traveler is hit by a tram.
  • Shoots the wrong individual.
• Lesson: The traveler’s range of effective actions is restricted, yet action itself is not impossible.

Compossibility: Lewis’ Key Notion of “Possible”

• “Possible” is always relative to a set of facts; call such relative possibility compossibility.
• Example (adapted from Lewis):
  • Question: “Is it possible for me to speak Gaelic?”
  • Relative to anatomical facts (larynx, cognitive capacity, etc.): Yes.
  • Relative to the broader fact that the speaker never learned Gaelic: No.
  • No contradiction, because the two assessments reference different fact sets.
• Application to the Hitler attempt:
  • Relative to local facts about 1908 (gun works, aim true, no body armor): assassination appears possible.
  • Relative to an inclusive fact‐set that contains “Hitler is alive in 1945”: assassination is impossible.
• General principle: \text{Poss}(p\mid F1) does not imply \text{Poss}(p\mid F1 \cup F_2).
  • Hence, saying “If time travel is possible, contradictions are possible” equivocates on the sense of “possible.”

Logical, Ethical, and Philosophical Implications

• Logical:
  • Consistency requires that the traveler’s past actions already feature in the traveler’s history.
  • No act of the traveler can change* the past; it can only realize what was always there.
• Ethical/Practical:
  • Fantasies of “going back and fixing history” (e.g., killing Hitler) are blocked by logical coherence, not merely by chance.
  • Raises moral questions about responsibility: your attempts were always part of history.
• Philosophical:
  • Supports deterministic flavor: the past is fixed, even for those who might revisit it.
  • Undermines scenarios that rely on mutable timelines (many popular science‐fiction plots).

Core Takeaways for Exam Revision

• Time travel’s logical possibility hinges on recognizing the difference between possibility‐simpliciter and compossibility.
• The grandfather paradox only arises if one ignores the self‐consistent nature of a single, unbranching timeline.
• Lewis’ framework does not claim physical feasibility; it targets logical coherence.
• When assessing any purported paradox:
  1. Keep the entire set of relevant facts in view.
  2. Check whether the supposedly paradoxical outcome is actually compossible with that fact‐set.
• Remember formulaic summary:
  • \forall p\,(\neg\,\text{Poss}(p \wedge \neg p)) (No contradictions are possible).
  • But \exists p, F1, F2\,[\text{Poss}(p\mid F1) \wedge \neg \text{Poss}(p\mid F1\cup F_2)] (Different fact‐sets yield different modal verdicts).