List of paradoxes

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This list of paradoxes includes numerous paradoxes , many of which have an article of their own and which are referred to as paradoxes in the literature. It is sorted thematically, but this sorting is only approximate, since some paradoxes can also be assigned to several categories or topics, and does not claim to be complete. Some of the so-called paradoxes here are merely correct answers to a problem that contradict intuition, prevailing opinion or expectation, or they are based on fallacies . However, some fall under the common usage of an antinomial or self- contradicting result of inference based on (hidden) inconsistent definitions that brings up problems in the assumed definitions or accepted rules.

Logic, philosophy and theology

mathematics

physics

  • astronomy
    • Olbersian paradox : In an eternal, infinite, unchanging and evenly filled with stars universe the sky would be as bright as the surface of the sun.
    • Fermi paradox : possibility of encountering extraterrestrial life forms.

Medicine and biology

  • Large harlequin frog ( Pseudis paradoxa ): In this type of frog, also known as the paradoxical frog, the tadpole is up to 25 cm tall, while the adult frog is only 7.5 cm tall.
  • Paradox of the plankton : When different species live together, an ecological divergence ( ecological niche ) must exist. This is obviously largely absent in phytoplankton .
  • Reef paradox : The high biomass production of coral reefs with a relative lack of nutrients in the environment.
  • Gray's paradox : The flow characteristics of a fast whale are better than the pure body shape of the animals allows. Improvements occur through various optimizations of the skin structure.
  • Levinthal paradox : problem from molecular biology how an amino acid chain finds its correctly folded state as a protein in a short time.
  • Paradoxical effect with drugs and stimulants : Exactly the opposite effect is observed to the intended effect (e.g. sleeping pills cause insomnia).
  • Obesity paradox : Obese patients have a longer life expectancy than those of normal weight with many chronic diseases.
  • Peto's paradox : As the number of body cells increases, the likelihood of malignant degeneration should increase proportionally, which means that large mammals should develop cancer much more frequently than small mammals. In fact, mammalian cancer incidences differ only slightly.
  • Hormesis : The paradox that a small dose of harmful or toxic substances can have a positive effect under certain circumstances.

psychology

Game and decision theory, statistics

  • The solution to the goat problem
  • Braess paradox : Increasing the capacity of a network can reduce its performance.
  • Jevons' paradox : The more efficient use of a raw material ultimately leads to an increased use of this raw material instead of reducing it.
  • Saint Petersburg paradox : the profit to be expected is infinite and yet you are only willing to make a small stake.
  • Simpson paradox : In a survey that is carried out in several sub-surveys, it can happen that a comparison group achieves a higher value per group size in the majority or all of the sub-surveys and still has a poorer rate overall.
  • Voting procedure
    • Condorcet paradox : the majority prefers option A over B, and B over C. Nevertheless, the majority would prefer C to A (see also Arrow theorem )
    • Alabama Paradox : The increase in the number of parliamentary seats can lead to certain proportional distributions that parties lose seats in absolute terms.
    • Negative voting weight : Additional voters of a party reduce their seats in parliament.
    • Ostrogorski's paradox : election results depend crucially on the election process.
  • Allais paradox
  • Ellsberg paradox
  • Prisoner's Dilemma

earth sciences

Schwanenstein , the fifth largest boulder off the Baltic Sea island of Rügen

A multitude of historical and current paradoxes in the geosciences and resulting scientific controversies are believed to be a major driving force in scientific knowledge in the field. Some examples:

  • Until the middle of the 19th century, the origin and the transport of erratic blocks to their place of discovery was a scientific paradox.
  • Paradox of the weak young sun : A radiation output of the young sun that was 25% lower 3.8 billion years ago is actually incompatible with evidence of liquid water and life at the time.
  • Snowball Earth : Apparently incompatible deposits of ice age and tropical sediments on many continents suggest widespread and abruptly disappeared global glaciation.
  • Messinian salinity crisis : The origin of difficult-to-interpret shallow water sediments on the ocean floor of the Mediterranean Sea was only clarified in the 20th century.
  • Münchberger Gneissasse The origin of a highly metamorphic rock island in a completely different environment has not been conclusively clarified.
  • The quasicrystals Dan Shechtman is the extent paradoxical, but as they aperiodic structure are arranged in a seemingly regular, in truth. Shechtman's crystallographic work was initially fundamentally attacked by greats like Linus Pauling and received the Nobel Prize in 2011.

Demography, Market and Macroeconomics

  • Demographic-economic paradox : the population in industrialized nations (and the middle class in developing and emerging countries) have fewer children the more they could actually afford them due to the increased real income.
  • Laffer Paradox : Falling tax rates lead to higher tax revenues
  • Savings paradox : Individual economic operators in a closed economy can "save" (increase their net financial wealth through income surpluses). All economic operators can never increase their net financial wealth through income surpluses, since every financial claim (credit) of the creditor (saver) is matched by an equal debt of a debtor, with which it is netted to zero in the aggregate total balance sheet of the closed economy. The net financial wealth of a closed economy is therefore always zero. Individuals or groups can only increase their net financial wealth to the extent that the complementary group reduces theirs (achieves or accepts a spending surplus). If all economic operators seek to increase their net financial wealth, they must seek to sell more goods and services than they buy. This means that the total supply is greater than the total demand, the total demand determines the actual strength of the purchasing flow, buyer markets are subject to downward pressure on costs and prices (negative price trend - deflation ), and the pressure on suppliers of goods and services to perform increases.
  • Spending paradox: Individual economic operators in a closed economy can reduce their net financial wealth through excess spending. All economic operators as a whole can never decrease or increase their financial wealth, since this is always netted to zero in the aggregated total balance sheet. If all economic agents strive to reduce their financial wealth, they must try to buy more than they sell. The total demand thus exceeds the total supply. There are sellers' markets and a tendency towards rising prices ( inflation ). The pressure to perform on the providers of goods and services is declining.
  • Stage migration : A person who moves from one place to another increases the average income in both places.
  • Giffen paradox : the more expensive the bread, the more people buy.
  • Bertrand paradox : two competing providers cannot make a profit.
  • Catch-22 (Dilemma) : "How should I gain experience for a job if I am constantly rejected for this job because of a lack of experience?"

aesthetics

Computer science

Paradoxical platitudes

Fried quote on a remnant of the Berlin Wall

In colloquial language , the contradicting effect of paradoxes is often used as a rhetorical stylistic device (cf. also Oxymoron ).

  • Stronger than the strongest
  • Dumber than the dumbest
  • This is so true that it can only be false.
  • Life is death and death is life.
  • Man is created free, is free and would he be born in chains!
  • The more it changes, the more it stays the same.
  • Progress lies in regression.
  • If someone explained the meaning of life, life would have lost its meaning!
  • Eternity is long, especially towards the end!
  • ... with without ketchup / mustard
  • The only constant is change.
  • Sometimes, if you want to be clear, you have to contradict yourself.
  • Death is free and it costs life.
  • The grain of wheat has to die to live.
  • The more cheese, the more holes; The more holes, the less cheese. → The more cheese, the less cheese
  • The more you learn, the more you know. The more you know, the more you forget. The more you forget, the less you know. → The more you learn, the less you know
  • We learn from experience that man does not learn from experience.
  • Whoever wants the world to stay the way it is does not want it to stay the way it is. ( Erich Fried )
  • I know that I know nothing . ( Socrates )
  • Illusion of reality ( Thomas Mann )
  • That sentence is a lie.
  • After all, we agree that we disagree.
  • Paid gift
  • No rule without exception

Individual evidence

  1. ↑ Ueli Briegel, Wenjiao Xiao (Ed.): Paradoxes in Geology. Elsevier, Amsterdam a. a. 2001, ISBN 0-444-50560-1 .
  2. ^ David AD Evans: Stratigraphic, geochronological, and paleomagnetic constraints upon the Neoproterozoic climatic paradox. In: American Journal of Science. Vol. 300, No. 5, ISSN  0002-9599 , pp. 347-433, doi : 10.2475 / ajs.300.5.347 .