What Are Paradoxes?
A paradox (plural: paradoxes) is a seemingly contradictory statement or situation that, despite logically correct reasoning, leads to a contradiction or an absurd conclusion. The term comes from the Greek "para" (against) and "doxa" (opinion) and denotes something that contradicts general expectation or common sense.
Characteristics of Paradoxes
- Contradiction: Paradoxes contain or lead to a contradiction, in which a statement appears to be both true and false.
- Apparent correctness: The reasoning that leads to the paradox appears logically correct at first glance.
- Bewilderment: Paradoxes produce a feeling of surprise or confusion, since they challenge our habitual patterns of thought.
- Deeper meaning: Behind many paradoxes lie deeper insights into the limits of our concepts, language or logic.
Types of Paradoxes
Paradoxes can be classified according to various criteria. One useful classification is:
- Logical paradoxes: These arise within formal logical systems and point to inconsistencies or limits of these systems.
- Semantic paradoxes: These arise from self-reference or circular definitions in language.
- Epistemic paradoxes: These concern our knowledge and our beliefs.
- Decision paradoxes: These occur in decision situations in which every option leads to contradictory or undesirable results.
- Temporal paradoxes: These concern contradictions related to time, in particular to time travel.
- Sorites paradoxes (paradoxes of the heap): These arise from vague concepts and the question of when small, incremental changes lead to a qualitative change.