From impossible choices to questions that defy logic, medieval thinkers devised paradoxes that challenged how people understood the world. Here are 15 fascinating puzzles from across the Middle Ages that might leave you questioning what you thought you knew.
Paradoxes have puzzled philosophers for thousands of years. In ancient Greece, thinkers developed problems that seemed to defy logic, including the famous Liar Paradox, traditionally associated with Eubulides of Miletus in the fourth century BC. Its central question is deceptively simple: if someone declares that they are lying, are they telling the truth or not? Such puzzles exposed contradictions in seemingly straightforward statements and raised fundamental questions about truth, knowledge and the limits of human reasoning.
During the Middle Ages, scholars across Europe, the Islamic world and Asia continued to investigate these problems while developing new paradoxes of their own. Medieval logicians examined the peculiarities of language, philosophers questioned the nature of infinity and consciousness, and religious thinkers wrestled with contradictions involving free will, divine love and spiritual enlightenment. Some of their puzzles emerged from university classrooms, while others appeared in theological writings, poetry and storytelling. Together, they reveal a medieval intellectual world fascinated by questions that did not always have easy answers.
1. Buridan’s Ass
Imagine a hungry donkey standing exactly halfway between two identical piles of hay. Both are equally appetising, equally distant and equally easy to reach. Since the donkey has no reason to prefer one pile over the other, it cannot decide which way to move. If every decision requires a reason to favour one option, the donkey will remain motionless and eventually starve, despite having plenty of food available. Can having two equally good choices make it impossible to choose at all?
This paradox is traditionally associated with Jean Buridan (c. 1300–1358), a French philosopher and logician who taught at the University of Paris. Buridan investigated questions of free will, rational decision-making and competing motivations. However, the famous donkey scenario does not appear in his surviving writings, and similar problems had been discussed by ancient philosophers, including Aristotle.
Possible solutions: The donkey could simply make an arbitrary choice, perhaps selecting a pile at random. Even a tiny difference in perception, hunger or movement could also break the symmetry. More fundamentally, the paradox challenges the assumption that every rational decision requires one option to be demonstrably better than another. When two choices are equally good, choosing either may be perfectly reasonable.
2. The Man Hanging from a Tree
Imagine a man hanging high above the ground, gripping a tree branch with his teeth. His hands cannot reach the branch, and his feet have nothing to stand on. Another person approaches and asks him a question about Buddhism. If he opens his mouth to answer, he will fall from the tree. But if he remains silent, he fails to respond to the question. How can he give an answer without risking his life, and how can he remain silent without failing the challenge?
This puzzle is associated with Xiangyan Zhixian (d. 898), a Chinese Chan Buddhist master who lived during the Tang dynasty. The story appears in The Gateless Gate (Wumenguan), a collection of Buddhist kōans compiled by Wumen Huikai in 1228. These puzzles were intended to challenge conventional reasoning and encourage students to question their assumptions about knowledge, language and enlightenment. Although attributed to Xiangyan, the surviving written formulation dates from several centuries after his lifetime.
Possible solutions: Unlike a conventional logical puzzle, this kōan does not have a universally accepted answer. One interpretation is that genuine understanding cannot always be communicated through words. Another is that the dilemma itself is misleading, since it assumes that responding must mean speaking and that remaining silent necessarily constitutes failure. Within Chan Buddhism, the purpose of such questions was often to challenge habitual patterns of thought rather than produce a straightforward verbal solution.
3. Bridge Paradox
A traveller approaches a bridge guarded by a man who allows people to cross only if they speak the truth. Anyone who lies will be thrown into the river. The traveller announces that he will be thrown into the river. The guard now faces an impossible decision. If he throws the traveller into the river, the statement becomes true, so the traveller should have been allowed to cross. But if the guard allows him to cross, the statement becomes false, meaning that he should have been thrown into the river. Whatever the guard decides, he appears to violate his own rules.
This paradox is also associated with Jean Buridan. It belongs to the medieval tradition of insolubilia, or seemingly insoluble propositions, which became an important subject of study at medieval universities. The underlying problem has older antecedents, so its precise origins remain uncertain.
Possible solutions: The guard could refuse to apply the rule, recognising that it cannot consistently govern this particular statement. Another approach is to distinguish between a prediction about the future and the action that determines whether the prediction comes true. The paradox illustrates how a seemingly straightforward rule can become impossible to enforce when the consequences of applying it determine whether the rule has been broken.
4. The Flying Man
Imagine a man who comes into existence fully formed, suspended in mid-air, with his arms and legs spread apart so that no part of his body touches another. He cannot see, hear, smell or feel anything, including his own body. He has never experienced the physical world and has no memories of it. Would he nevertheless be aware of his own existence? The paradox suggests that even without any sensory information, the man would still know that he exists. But if he can recognise his own existence without being aware of his body, does this mean that the soul is something separate from the physical body?
This thought experiment was developed by Avicenna (Ibn Sina, c. 980–1037), the Persian philosopher and physician whose writings profoundly influenced medieval Islamic and European philosophy. He presented the Flying Man argument in The Book of Healing (Kitāb al-Shifāʾ), particularly its section on the soul. Avicenna used the scenario to argue that human self-awareness does not depend upon sensory experience or conscious awareness of the body. His argument became an important contribution to medieval discussions about the nature of the soul and its relationship with the physical world.
Possible solutions: Avicenna believed that the flying man’s awareness of his own existence demonstrated that the self could be understood independently of the physical body. However, critics might argue that imagining consciousness without sensory experience does not prove that consciousness can actually exist without a body. Others might question whether someone who had never experienced anything could possess the concepts necessary to recognise their own existence. The thought experiment remains relevant to philosophical debates about consciousness and personal identity.
5. The Paradox of Women’s Intellectual Inferiority
Christine de Pizan teaching a group of men, from an illuminated manuscript of her collected works produced in Paris around 1413. British Library, Harley MS 4431, fol. 259v.
If women are naturally less intelligent than men, why have so many women demonstrated remarkable wisdom, learning and ability? And if women appear less educated, does this prove that they are intellectually inferior, or simply that they have been denied the same opportunities as men? The apparent contradiction becomes particularly striking when women who supposedly lack intellectual ability successfully challenge the arguments used to justify their exclusion from education. The paradox questions whether women’s alleged inferiority is a natural condition or the result of the social restrictions imposed upon them.
This argument was developed by Christine de Pizan (c. 1364–c. 1430), an Italian-born writer who spent much of her life at the French royal court. In The Book of the City of Ladies, completed in 1405, Christine challenged the misogynistic claims found in many medieval literary and scholarly works. She argued that women possessed the intellectual capacity to excel in learning, government and other fields traditionally dominated by men. By presenting examples of accomplished women from history, literature and religious tradition, she sought to demonstrate the weaknesses in arguments about women’s supposed natural inferiority.
Possible solutions: Christine argued that differences in education and achievement could not be used as evidence of innate intellectual inequality when women had been systematically denied opportunities to learn. If girls received the same education as boys, she maintained, they would be capable of developing comparable intellectual abilities. The contradiction therefore disappears when unequal social circumstances, rather than natural differences in intelligence, are recognised as an explanation for women’s restricted participation in intellectual life.
6. The Liar Cycle Paradox
A man announces on Monday that everything he will say on Tuesday will be false. On Tuesday, he announces that everything he said on Monday was true. These are the only statements he makes on either day. But which statement is correct? If Monday’s statement is true, Tuesday’s statement must be false, meaning Monday’s statement was not true after all. If Monday’s statement is false, Tuesday’s statement must be true, which makes Monday’s statement true. The two statements create a circle in which neither can consistently be assigned a truth value.
This medieval variation of the ancient Liar Paradox was developed by Sa’d al-Din al-Taftazani (c. 1322–1390), a prominent scholar of logic and theology who wrote in Arabic and Persian. Al-Taftazani examined problems involving self-reference and contradictory statements, contributing to a sophisticated tradition of logical investigation in the medieval Islamic world. His Liar Cycle formulation demonstrated how a contradiction could arise between two statements referring to one another, without either statement directly declaring itself false.
Possible solutions: One approach is to argue that the two statements cannot both receive ordinary truth values because each depends upon the other. Another is to reject the assumption that every meaningful statement must be either true or false, allowing some statements to remain without a definite truth value. The paradox demonstrates how seemingly straightforward claims about truth and falsehood can become contradictory when their meanings depend upon one another.
7. The Broken Oath Paradox
A man swears an oath to travel to Athens. He then swears a second oath promising to break his first oath. What should he do? If he travels to Athens, he fulfils his original promise but breaks his second oath. If he stays home, he fulfils his second promise but violates the first. Either way, he becomes an oath-breaker. The puzzle raises a troubling question about whether someone can fulfil a moral obligation by deliberately violating another.
This paradox was examined by Giles of Rome (c. 1243–1316), an Italian philosopher and theologian who studied and taught at the University of Paris. Giles drew upon an older problem discussed by Aristotle, who had considered the apparent contradiction created when someone swears to break an oath. Medieval philosophers were particularly interested in such questions because oaths carried serious religious and moral obligations. Giles investigated whether a person could be required to fulfil a promise that involved committing another wrong.
Possible solutions: Giles concluded that the man should not fulfil the second oath. Although swearing to do something wrong is itself objectionable, deliberately carrying out that wrongdoing would be worse. The two promises are therefore not morally equivalent. The paradox illustrates how moral obligations can conflict and why fulfilling a promise is not necessarily the right thing to do when the promise itself requires an immoral action.
8. The Paradox of the Infinite Universe
Illustration of an excerpt of Pliny’s Natural History on the positions and movements of seven planets, with earth in the centre, and around it the moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn
Imagine that the universe has existed forever, with the planets and stars moving through the heavens for an infinite amount of time. Some celestial bodies complete their revolutions much faster than others. If the universe has no beginning, Saturn would have completed infinitely many revolutions, but the Sun would have completed roughly thirty times as many. How can one infinite number be thirty times larger than another? Furthermore, if the universe has already existed for an infinite amount of time, every new revolution would add to an infinity that supposedly cannot be increased. Does this mean that the universe cannot have existed forever?
This paradox was developed by John Philoponus (c. 490–570), a Christian philosopher working in Alexandria when the city formed part of the Byzantine Empire. Philoponus challenged Aristotle’s belief that the universe had existed eternally, arguing that an infinite sequence of past events would produce mathematical contradictions. His arguments against the eternity of the world became influential in later medieval Islamic, Jewish and Christian philosophy, particularly in debates about whether the universe had a beginning.
Possible solutions: Modern mathematics distinguishes between finite quantities and different ways of comparing infinite quantities. For example, there are infinitely many whole numbers and infinitely many even numbers, yet both sets have the same mathematical cardinality because their members can be paired one-to-one. Similarly, different rates of celestial revolutions do not necessarily produce infinities of different sizes when considered as sets. This challenges Philoponus’s mathematical objection, although it does not settle the broader philosophical question of whether an infinite past is possible.
9. Albert of Saxony’s Donkey Paradox
A child with a donkey, depicted in a fifth-century Byzantine floor mosaic from the Great Palace of Constantinople. Wikimedia Commons
Consider the statement: All men are donkeys or men and donkeys are donkeys. At first, it seems nonsensical, but its truth depends on how the words are grouped. Read one way, it says that all men are either donkeys or men, and that donkeys are donkeys. Both claims are true. Read another way, it says that either all men are donkeys, or that men and donkeys are all donkeys. Both claims are false. How can the same sentence be both true and false?
This paradox was presented by Albert of Saxony (c. 1320–1390), a German philosopher and logician who taught at the University of Paris and later became Bishop of Halberstadt. It appears as the eleventh sophism in his Sophismata, a collection of logical puzzles designed to investigate the meaning and structure of statements. Such exercises were an important part of medieval university education, where students learned to identify ambiguities and defend their interpretations through formal argument.
Possible solutions: Albert explained that the statement is ambiguous. Its meaning changes depending on whether and or or is treated as the principal logical connection. Once the sentence is divided into its intended components, the apparent contradiction disappears. The paradox demonstrates how ordinary language can produce misleading conclusions when its grammatical structure is unclear.
10. The First and Last Instant Paradox
Imagine a piece of wood being heated until it becomes hot. At first, it is cold, and eventually, it is hot. But is there a precise instant when the wood stops being cold and starts being hot? If there is a final instant when it is cold, what happens immediately afterwards? And if there is a first instant when it is hot, must there also be a final instant when it was cold? The puzzle becomes even more complicated when we consider that time can be divided into ever-smaller intervals. How can a change have a definite beginning or ending if there is no instant immediately before or after another?
This problem was investigated by William Heytesbury (c. 1313–1372/73), an English philosopher and logician associated with Merton College, Oxford. Heytesbury belonged to a group of fourteenth-century scholars who developed sophisticated approaches to motion, change and the measurement of time. In his Rules for Solving Sophisms, written in 1335, he examined problems involving the first and last instants of changing states. These discussions formed part of a broader medieval effort to understand how continuous processes could be described through precise logical statements.
Possible solutions: Medieval logicians distinguished between the first instant at which a new condition exists and the last instant at which the previous condition existed. If time is continuous, a condition can have a first instant without the preceding condition having a final instant. For example, if a change occurs at noon, noon can be the first instant of the new state, while there is no single last instant before noon. This distinction allows a change to have a precise boundary without requiring two consecutive instants of time.
11. The Invalid Argument Paradox
Consider an argument that begins with a proposition assumed to be necessarily true, such as the existence of God, and concludes that the argument itself is invalid. If the argument is valid, then its conclusion must be true, making the argument invalid. But if the argument is invalid, its conclusion is true, and, given the necessarily true premise, the argument appears to be valid after all. The argument seems to defeat itself regardless of whether we accept or reject its validity.
This paradox appears in a medieval commentary on Aristotle’s Prior Analytics attributed to Pseudo-Scotus, an unidentified medieval logician whose writings were once mistakenly associated with the Scottish philosopher John Duns Scotus (c. 1265–1308). Medieval scholars frequently examined arguments that appeared to undermine their own validity, using them to investigate the relationship between truth, logical inference and self-reference. The Pseudo-Scotus example is particularly interesting because it creates a contradiction not simply through a statement about truth, but through an argument about its own logical status.
Possible solutions: One approach is to distinguish between the truth of an argument’s conclusion and the logical relationship between its premises and conclusion. Another is to question whether arguments can meaningfully make claims about their own validity without creating a circular dependency. Modern approaches to self-referential paradoxes sometimes restrict the ways statements can refer to their own logical properties. The puzzle demonstrates that even the rules used to determine whether an argument is valid can become problematic when applied to themselves.
12. The Paradox of Divine Love
How can someone become truly free by surrendering their own will? And how can a soul achieve spiritual perfection by abandoning the deliberate pursuit of virtue? These apparent contradictions lie at the heart of a medieval mystical argument about the relationship between human freedom and divine love. A soul that has completely surrendered itself to God no longer needs to seek spiritual rewards or consciously strive to perform good deeds. What appears to be a rejection of morality is instead presented as the highest form of spiritual perfection. But if freedom normally means being able to choose, how can giving up one’s will make a person more free?
This paradox was developed by Marguerite Porete (d. 1310), a French-speaking mystical writer best known for The Mirror of Simple Souls. In this work, Porete described the spiritual journey of the soul through different stages of love and understanding, culminating in a condition in which the individual will is entirely transformed by divine love. Her teachings challenged conventional religious expectations about obedience, virtue and spiritual authority. Her book was condemned by ecclesiastical authorities, and Porete was executed for heresy in Paris in 1310.
Possible solutions: Porete distinguished between a soul governed by personal desires and one whose will has become completely aligned with divine love. In her understanding, surrendering individual will does not eliminate freedom but transforms its meaning. Similarly, abandoning the deliberate pursuit of virtue does not mean embracing wrongdoing. Rather, the perfected soul acts through love without needing external rules or the promise of rewards. The paradox suggests that spiritual freedom may involve liberation from the very desires and choices that ordinarily define human independence.
13. The Two Liars Paradox
A medieval depiction of the French philosopher Jean Buridan, from a manuscript produced in Paris around 1370. Jagiellonian Library, Kraków, MS BJ 1771, fol. 142v.
Two philosophers, Plato and Socrates, make statements about one another. Plato says that Socrates is telling the truth, while Socrates says that Plato is lying. If Plato is telling the truth, then Socrates must also be telling the truth, which means Plato is lying. But if Plato is lying, Socrates’s accusation is true, which means Plato was telling the truth after all. Neither statement can be consistently classified as true or false. How can two apparently simple statements create a contradiction when neither refers directly to itself?
Jean Buridan makes our list for the third time. His paradox appears as the ninth sophism in his investigations into insolubilia, the seemingly insoluble propositions that fascinated medieval logicians. Although the underlying Liar Paradox originated in ancient Greece, Buridan developed more elaborate variations that demonstrated how contradictions could arise through statements referring to one another. His work became an important contribution to medieval theories of truth and language.
Possible solutions: One approach is to reject the assumption that every meaningful statement must be either true or false. Another is to distinguish between different levels of language, preventing statements from making unrestricted claims about the truth of other statements within the same logical system. A further possibility is to recognise that the two statements form a circular dependency that prevents either from receiving a consistent truth value. The paradox demonstrates that self-reference does not always require a statement to refer explicitly to itself.
14. The Paradox of Unequal Infinities
Can one infinity be larger than another? Imagine two roads that stretch endlessly into the distance. One road is ten metres wide, while the other is only one metre wide. Both extend infinitely, yet the wider road appears to cover ten times as much space. If both are infinite, how can one be larger than the other? And if we add another kilometre to an infinitely long road, have we made it longer, or does infinity remain unchanged? The paradox challenges our ordinary understanding of size, measurement and the meaning of infinity.
This problem was examined by Hasdai Crescas (c. 1340–1410/11), a Jewish philosopher and rabbi from medieval Spain. In his major philosophical work, Or Hashem (Light of the Lord), Crescas challenged Aristotle’s arguments against the existence of actual infinity. He questioned whether infinite magnitudes were necessarily impossible and whether different infinite quantities could be compared using ordinary mathematical assumptions. His arguments formed part of a broader medieval debate about space, mathematics and the possibility of an infinite universe.
Possible solutions: Crescas challenged the assumption that the apparent difficulties of comparing infinite magnitudes proved that infinity could not exist. Modern mathematics offers another perspective by distinguishing between different ways of measuring infinite quantities. For example, there are infinitely many whole numbers and infinitely many even numbers, yet the two sets have the same cardinality because their members can be paired one-to-one. Infinite spaces can also differ in width or other dimensions without possessing finite total lengths. The apparent contradiction therefore depends partly on what we mean when we say that one infinity is larger than another.
15. Odin’s Impossible Question
Odin and sons depicted in Libellus de primo Saxonum uel Normannorum adventu, dating from the 12th century. – Wikimedia Commons
Odin, disguised as a traveller, challenges the wise giant Vafþrúðnir to a contest of knowledge. The two exchange questions about the origins of the universe, the gods and the fate of the world. Eventually, Odin asks what he whispered into the ear of his dead son Baldr before Baldr was placed on his funeral pyre. Since only Odin knows the answer, Vafþrúðnir cannot respond. The giant realises that his opponent must be Odin himself and acknowledges his defeat. But was this really a fair contest of wisdom if the winning question was one that nobody else could possibly answer?
This puzzle appears in Vafþrúðnismál, an Old Norse mythological poem preserved in the thirteenth-century Poetic Edda. Its author is unknown, and the poem likely draws upon older oral traditions. The contest between Odin and Vafþrúðnir reflects the importance of wisdom, memory and secret knowledge in Norse mythology. Odin’s final question is particularly striking because it transforms a competition based on shared mythological knowledge into one that can only be won through personal experience.
Possible solutions: There is no answer that Vafþrúðnir can reasonably be expected to provide. Odin wins by asking a question whose answer is known only to himself, making the contest impossible for his opponent to win. One interpretation is that the episode distinguishes between knowledge that can be learned and knowledge that belongs exclusively to an individual. Another is that Odin’s victory demonstrates the limits of even the greatest wisdom. The puzzle leaves readers with an intriguing question: can someone truly be considered wiser simply because they know something that nobody else could possibly know?
From impossible choices and contradictory statements to questions about infinity, consciousness and divine love, these paradoxes reveal the remarkable range of medieval intellectual thought. Although some have possible solutions and others remain open to interpretation, they remind us that medieval thinkers were not simply preserving ancient knowledge. They were also challenging established ideas, questioning assumptions and developing new ways of understanding the world.
Further Readings:
Erickson, Glenn W., and John A. Fossa. Dictionary of Paradox. University Press of America, 1998.
From impossible choices to questions that defy logic, medieval thinkers devised paradoxes that challenged how people understood the world. Here are 15 fascinating puzzles from across the Middle Ages that might leave you questioning what you thought you knew.
Paradoxes have puzzled philosophers for thousands of years. In ancient Greece, thinkers developed problems that seemed to defy logic, including the famous Liar Paradox, traditionally associated with Eubulides of Miletus in the fourth century BC. Its central question is deceptively simple: if someone declares that they are lying, are they telling the truth or not? Such puzzles exposed contradictions in seemingly straightforward statements and raised fundamental questions about truth, knowledge and the limits of human reasoning.
During the Middle Ages, scholars across Europe, the Islamic world and Asia continued to investigate these problems while developing new paradoxes of their own. Medieval logicians examined the peculiarities of language, philosophers questioned the nature of infinity and consciousness, and religious thinkers wrestled with contradictions involving free will, divine love and spiritual enlightenment. Some of their puzzles emerged from university classrooms, while others appeared in theological writings, poetry and storytelling. Together, they reveal a medieval intellectual world fascinated by questions that did not always have easy answers.
1. Buridan’s Ass
Imagine a hungry donkey standing exactly halfway between two identical piles of hay. Both are equally appetising, equally distant and equally easy to reach. Since the donkey has no reason to prefer one pile over the other, it cannot decide which way to move. If every decision requires a reason to favour one option, the donkey will remain motionless and eventually starve, despite having plenty of food available. Can having two equally good choices make it impossible to choose at all?
This paradox is traditionally associated with Jean Buridan (c. 1300–1358), a French philosopher and logician who taught at the University of Paris. Buridan investigated questions of free will, rational decision-making and competing motivations. However, the famous donkey scenario does not appear in his surviving writings, and similar problems had been discussed by ancient philosophers, including Aristotle.
Possible solutions: The donkey could simply make an arbitrary choice, perhaps selecting a pile at random. Even a tiny difference in perception, hunger or movement could also break the symmetry. More fundamentally, the paradox challenges the assumption that every rational decision requires one option to be demonstrably better than another. When two choices are equally good, choosing either may be perfectly reasonable.
2. The Man Hanging from a Tree
Imagine a man hanging high above the ground, gripping a tree branch with his teeth. His hands cannot reach the branch, and his feet have nothing to stand on. Another person approaches and asks him a question about Buddhism. If he opens his mouth to answer, he will fall from the tree. But if he remains silent, he fails to respond to the question. How can he give an answer without risking his life, and how can he remain silent without failing the challenge?
This puzzle is associated with Xiangyan Zhixian (d. 898), a Chinese Chan Buddhist master who lived during the Tang dynasty. The story appears in The Gateless Gate (Wumenguan), a collection of Buddhist kōans compiled by Wumen Huikai in 1228. These puzzles were intended to challenge conventional reasoning and encourage students to question their assumptions about knowledge, language and enlightenment. Although attributed to Xiangyan, the surviving written formulation dates from several centuries after his lifetime.
Possible solutions: Unlike a conventional logical puzzle, this kōan does not have a universally accepted answer. One interpretation is that genuine understanding cannot always be communicated through words. Another is that the dilemma itself is misleading, since it assumes that responding must mean speaking and that remaining silent necessarily constitutes failure. Within Chan Buddhism, the purpose of such questions was often to challenge habitual patterns of thought rather than produce a straightforward verbal solution.
3. Bridge Paradox
A traveller approaches a bridge guarded by a man who allows people to cross only if they speak the truth. Anyone who lies will be thrown into the river. The traveller announces that he will be thrown into the river. The guard now faces an impossible decision. If he throws the traveller into the river, the statement becomes true, so the traveller should have been allowed to cross. But if the guard allows him to cross, the statement becomes false, meaning that he should have been thrown into the river. Whatever the guard decides, he appears to violate his own rules.
This paradox is also associated with Jean Buridan. It belongs to the medieval tradition of insolubilia, or seemingly insoluble propositions, which became an important subject of study at medieval universities. The underlying problem has older antecedents, so its precise origins remain uncertain.
Possible solutions: The guard could refuse to apply the rule, recognising that it cannot consistently govern this particular statement. Another approach is to distinguish between a prediction about the future and the action that determines whether the prediction comes true. The paradox illustrates how a seemingly straightforward rule can become impossible to enforce when the consequences of applying it determine whether the rule has been broken.
4. The Flying Man
Imagine a man who comes into existence fully formed, suspended in mid-air, with his arms and legs spread apart so that no part of his body touches another. He cannot see, hear, smell or feel anything, including his own body. He has never experienced the physical world and has no memories of it. Would he nevertheless be aware of his own existence? The paradox suggests that even without any sensory information, the man would still know that he exists. But if he can recognise his own existence without being aware of his body, does this mean that the soul is something separate from the physical body?
This thought experiment was developed by Avicenna (Ibn Sina, c. 980–1037), the Persian philosopher and physician whose writings profoundly influenced medieval Islamic and European philosophy. He presented the Flying Man argument in The Book of Healing (Kitāb al-Shifāʾ), particularly its section on the soul. Avicenna used the scenario to argue that human self-awareness does not depend upon sensory experience or conscious awareness of the body. His argument became an important contribution to medieval discussions about the nature of the soul and its relationship with the physical world.
Possible solutions: Avicenna believed that the flying man’s awareness of his own existence demonstrated that the self could be understood independently of the physical body. However, critics might argue that imagining consciousness without sensory experience does not prove that consciousness can actually exist without a body. Others might question whether someone who had never experienced anything could possess the concepts necessary to recognise their own existence. The thought experiment remains relevant to philosophical debates about consciousness and personal identity.
5. The Paradox of Women’s Intellectual Inferiority
If women are naturally less intelligent than men, why have so many women demonstrated remarkable wisdom, learning and ability? And if women appear less educated, does this prove that they are intellectually inferior, or simply that they have been denied the same opportunities as men? The apparent contradiction becomes particularly striking when women who supposedly lack intellectual ability successfully challenge the arguments used to justify their exclusion from education. The paradox questions whether women’s alleged inferiority is a natural condition or the result of the social restrictions imposed upon them.
This argument was developed by Christine de Pizan (c. 1364–c. 1430), an Italian-born writer who spent much of her life at the French royal court. In The Book of the City of Ladies, completed in 1405, Christine challenged the misogynistic claims found in many medieval literary and scholarly works. She argued that women possessed the intellectual capacity to excel in learning, government and other fields traditionally dominated by men. By presenting examples of accomplished women from history, literature and religious tradition, she sought to demonstrate the weaknesses in arguments about women’s supposed natural inferiority.
Possible solutions: Christine argued that differences in education and achievement could not be used as evidence of innate intellectual inequality when women had been systematically denied opportunities to learn. If girls received the same education as boys, she maintained, they would be capable of developing comparable intellectual abilities. The contradiction therefore disappears when unequal social circumstances, rather than natural differences in intelligence, are recognised as an explanation for women’s restricted participation in intellectual life.
6. The Liar Cycle Paradox
A man announces on Monday that everything he will say on Tuesday will be false. On Tuesday, he announces that everything he said on Monday was true. These are the only statements he makes on either day. But which statement is correct? If Monday’s statement is true, Tuesday’s statement must be false, meaning Monday’s statement was not true after all. If Monday’s statement is false, Tuesday’s statement must be true, which makes Monday’s statement true. The two statements create a circle in which neither can consistently be assigned a truth value.
This medieval variation of the ancient Liar Paradox was developed by Sa’d al-Din al-Taftazani (c. 1322–1390), a prominent scholar of logic and theology who wrote in Arabic and Persian. Al-Taftazani examined problems involving self-reference and contradictory statements, contributing to a sophisticated tradition of logical investigation in the medieval Islamic world. His Liar Cycle formulation demonstrated how a contradiction could arise between two statements referring to one another, without either statement directly declaring itself false.
Possible solutions: One approach is to argue that the two statements cannot both receive ordinary truth values because each depends upon the other. Another is to reject the assumption that every meaningful statement must be either true or false, allowing some statements to remain without a definite truth value. The paradox demonstrates how seemingly straightforward claims about truth and falsehood can become contradictory when their meanings depend upon one another.
7. The Broken Oath Paradox
A man swears an oath to travel to Athens. He then swears a second oath promising to break his first oath. What should he do? If he travels to Athens, he fulfils his original promise but breaks his second oath. If he stays home, he fulfils his second promise but violates the first. Either way, he becomes an oath-breaker. The puzzle raises a troubling question about whether someone can fulfil a moral obligation by deliberately violating another.
This paradox was examined by Giles of Rome (c. 1243–1316), an Italian philosopher and theologian who studied and taught at the University of Paris. Giles drew upon an older problem discussed by Aristotle, who had considered the apparent contradiction created when someone swears to break an oath. Medieval philosophers were particularly interested in such questions because oaths carried serious religious and moral obligations. Giles investigated whether a person could be required to fulfil a promise that involved committing another wrong.
Possible solutions: Giles concluded that the man should not fulfil the second oath. Although swearing to do something wrong is itself objectionable, deliberately carrying out that wrongdoing would be worse. The two promises are therefore not morally equivalent. The paradox illustrates how moral obligations can conflict and why fulfilling a promise is not necessarily the right thing to do when the promise itself requires an immoral action.
8. The Paradox of the Infinite Universe
Imagine that the universe has existed forever, with the planets and stars moving through the heavens for an infinite amount of time. Some celestial bodies complete their revolutions much faster than others. If the universe has no beginning, Saturn would have completed infinitely many revolutions, but the Sun would have completed roughly thirty times as many. How can one infinite number be thirty times larger than another? Furthermore, if the universe has already existed for an infinite amount of time, every new revolution would add to an infinity that supposedly cannot be increased. Does this mean that the universe cannot have existed forever?
This paradox was developed by John Philoponus (c. 490–570), a Christian philosopher working in Alexandria when the city formed part of the Byzantine Empire. Philoponus challenged Aristotle’s belief that the universe had existed eternally, arguing that an infinite sequence of past events would produce mathematical contradictions. His arguments against the eternity of the world became influential in later medieval Islamic, Jewish and Christian philosophy, particularly in debates about whether the universe had a beginning.
Possible solutions: Modern mathematics distinguishes between finite quantities and different ways of comparing infinite quantities. For example, there are infinitely many whole numbers and infinitely many even numbers, yet both sets have the same mathematical cardinality because their members can be paired one-to-one. Similarly, different rates of celestial revolutions do not necessarily produce infinities of different sizes when considered as sets. This challenges Philoponus’s mathematical objection, although it does not settle the broader philosophical question of whether an infinite past is possible.
9. Albert of Saxony’s Donkey Paradox
Consider the statement: All men are donkeys or men and donkeys are donkeys. At first, it seems nonsensical, but its truth depends on how the words are grouped. Read one way, it says that all men are either donkeys or men, and that donkeys are donkeys. Both claims are true. Read another way, it says that either all men are donkeys, or that men and donkeys are all donkeys. Both claims are false. How can the same sentence be both true and false?
This paradox was presented by Albert of Saxony (c. 1320–1390), a German philosopher and logician who taught at the University of Paris and later became Bishop of Halberstadt. It appears as the eleventh sophism in his Sophismata, a collection of logical puzzles designed to investigate the meaning and structure of statements. Such exercises were an important part of medieval university education, where students learned to identify ambiguities and defend their interpretations through formal argument.
Possible solutions: Albert explained that the statement is ambiguous. Its meaning changes depending on whether and or or is treated as the principal logical connection. Once the sentence is divided into its intended components, the apparent contradiction disappears. The paradox demonstrates how ordinary language can produce misleading conclusions when its grammatical structure is unclear.
10. The First and Last Instant Paradox
Imagine a piece of wood being heated until it becomes hot. At first, it is cold, and eventually, it is hot. But is there a precise instant when the wood stops being cold and starts being hot? If there is a final instant when it is cold, what happens immediately afterwards? And if there is a first instant when it is hot, must there also be a final instant when it was cold? The puzzle becomes even more complicated when we consider that time can be divided into ever-smaller intervals. How can a change have a definite beginning or ending if there is no instant immediately before or after another?
This problem was investigated by William Heytesbury (c. 1313–1372/73), an English philosopher and logician associated with Merton College, Oxford. Heytesbury belonged to a group of fourteenth-century scholars who developed sophisticated approaches to motion, change and the measurement of time. In his Rules for Solving Sophisms, written in 1335, he examined problems involving the first and last instants of changing states. These discussions formed part of a broader medieval effort to understand how continuous processes could be described through precise logical statements.
Possible solutions: Medieval logicians distinguished between the first instant at which a new condition exists and the last instant at which the previous condition existed. If time is continuous, a condition can have a first instant without the preceding condition having a final instant. For example, if a change occurs at noon, noon can be the first instant of the new state, while there is no single last instant before noon. This distinction allows a change to have a precise boundary without requiring two consecutive instants of time.
11. The Invalid Argument Paradox
Consider an argument that begins with a proposition assumed to be necessarily true, such as the existence of God, and concludes that the argument itself is invalid. If the argument is valid, then its conclusion must be true, making the argument invalid. But if the argument is invalid, its conclusion is true, and, given the necessarily true premise, the argument appears to be valid after all. The argument seems to defeat itself regardless of whether we accept or reject its validity.
This paradox appears in a medieval commentary on Aristotle’s Prior Analytics attributed to Pseudo-Scotus, an unidentified medieval logician whose writings were once mistakenly associated with the Scottish philosopher John Duns Scotus (c. 1265–1308). Medieval scholars frequently examined arguments that appeared to undermine their own validity, using them to investigate the relationship between truth, logical inference and self-reference. The Pseudo-Scotus example is particularly interesting because it creates a contradiction not simply through a statement about truth, but through an argument about its own logical status.
Possible solutions: One approach is to distinguish between the truth of an argument’s conclusion and the logical relationship between its premises and conclusion. Another is to question whether arguments can meaningfully make claims about their own validity without creating a circular dependency. Modern approaches to self-referential paradoxes sometimes restrict the ways statements can refer to their own logical properties. The puzzle demonstrates that even the rules used to determine whether an argument is valid can become problematic when applied to themselves.
12. The Paradox of Divine Love
How can someone become truly free by surrendering their own will? And how can a soul achieve spiritual perfection by abandoning the deliberate pursuit of virtue? These apparent contradictions lie at the heart of a medieval mystical argument about the relationship between human freedom and divine love. A soul that has completely surrendered itself to God no longer needs to seek spiritual rewards or consciously strive to perform good deeds. What appears to be a rejection of morality is instead presented as the highest form of spiritual perfection. But if freedom normally means being able to choose, how can giving up one’s will make a person more free?
This paradox was developed by Marguerite Porete (d. 1310), a French-speaking mystical writer best known for The Mirror of Simple Souls. In this work, Porete described the spiritual journey of the soul through different stages of love and understanding, culminating in a condition in which the individual will is entirely transformed by divine love. Her teachings challenged conventional religious expectations about obedience, virtue and spiritual authority. Her book was condemned by ecclesiastical authorities, and Porete was executed for heresy in Paris in 1310.
Possible solutions: Porete distinguished between a soul governed by personal desires and one whose will has become completely aligned with divine love. In her understanding, surrendering individual will does not eliminate freedom but transforms its meaning. Similarly, abandoning the deliberate pursuit of virtue does not mean embracing wrongdoing. Rather, the perfected soul acts through love without needing external rules or the promise of rewards. The paradox suggests that spiritual freedom may involve liberation from the very desires and choices that ordinarily define human independence.
13. The Two Liars Paradox
Two philosophers, Plato and Socrates, make statements about one another. Plato says that Socrates is telling the truth, while Socrates says that Plato is lying. If Plato is telling the truth, then Socrates must also be telling the truth, which means Plato is lying. But if Plato is lying, Socrates’s accusation is true, which means Plato was telling the truth after all. Neither statement can be consistently classified as true or false. How can two apparently simple statements create a contradiction when neither refers directly to itself?
Jean Buridan makes our list for the third time. His paradox appears as the ninth sophism in his investigations into insolubilia, the seemingly insoluble propositions that fascinated medieval logicians. Although the underlying Liar Paradox originated in ancient Greece, Buridan developed more elaborate variations that demonstrated how contradictions could arise through statements referring to one another. His work became an important contribution to medieval theories of truth and language.
Possible solutions: One approach is to reject the assumption that every meaningful statement must be either true or false. Another is to distinguish between different levels of language, preventing statements from making unrestricted claims about the truth of other statements within the same logical system. A further possibility is to recognise that the two statements form a circular dependency that prevents either from receiving a consistent truth value. The paradox demonstrates that self-reference does not always require a statement to refer explicitly to itself.
14. The Paradox of Unequal Infinities
Can one infinity be larger than another? Imagine two roads that stretch endlessly into the distance. One road is ten metres wide, while the other is only one metre wide. Both extend infinitely, yet the wider road appears to cover ten times as much space. If both are infinite, how can one be larger than the other? And if we add another kilometre to an infinitely long road, have we made it longer, or does infinity remain unchanged? The paradox challenges our ordinary understanding of size, measurement and the meaning of infinity.
This problem was examined by Hasdai Crescas (c. 1340–1410/11), a Jewish philosopher and rabbi from medieval Spain. In his major philosophical work, Or Hashem (Light of the Lord), Crescas challenged Aristotle’s arguments against the existence of actual infinity. He questioned whether infinite magnitudes were necessarily impossible and whether different infinite quantities could be compared using ordinary mathematical assumptions. His arguments formed part of a broader medieval debate about space, mathematics and the possibility of an infinite universe.
Possible solutions: Crescas challenged the assumption that the apparent difficulties of comparing infinite magnitudes proved that infinity could not exist. Modern mathematics offers another perspective by distinguishing between different ways of measuring infinite quantities. For example, there are infinitely many whole numbers and infinitely many even numbers, yet the two sets have the same cardinality because their members can be paired one-to-one. Infinite spaces can also differ in width or other dimensions without possessing finite total lengths. The apparent contradiction therefore depends partly on what we mean when we say that one infinity is larger than another.
15. Odin’s Impossible Question
Odin, disguised as a traveller, challenges the wise giant Vafþrúðnir to a contest of knowledge. The two exchange questions about the origins of the universe, the gods and the fate of the world. Eventually, Odin asks what he whispered into the ear of his dead son Baldr before Baldr was placed on his funeral pyre. Since only Odin knows the answer, Vafþrúðnir cannot respond. The giant realises that his opponent must be Odin himself and acknowledges his defeat. But was this really a fair contest of wisdom if the winning question was one that nobody else could possibly answer?
This puzzle appears in Vafþrúðnismál, an Old Norse mythological poem preserved in the thirteenth-century Poetic Edda. Its author is unknown, and the poem likely draws upon older oral traditions. The contest between Odin and Vafþrúðnir reflects the importance of wisdom, memory and secret knowledge in Norse mythology. Odin’s final question is particularly striking because it transforms a competition based on shared mythological knowledge into one that can only be won through personal experience.
Possible solutions: There is no answer that Vafþrúðnir can reasonably be expected to provide. Odin wins by asking a question whose answer is known only to himself, making the contest impossible for his opponent to win. One interpretation is that the episode distinguishes between knowledge that can be learned and knowledge that belongs exclusively to an individual. Another is that Odin’s victory demonstrates the limits of even the greatest wisdom. The puzzle leaves readers with an intriguing question: can someone truly be considered wiser simply because they know something that nobody else could possibly know?
From impossible choices and contradictory statements to questions about infinity, consciousness and divine love, these paradoxes reveal the remarkable range of medieval intellectual thought. Although some have possible solutions and others remain open to interpretation, they remind us that medieval thinkers were not simply preserving ancient knowledge. They were also challenging established ideas, questioning assumptions and developing new ways of understanding the world.
Further Readings:
Erickson, Glenn W., and John A. Fossa. Dictionary of Paradox. University Press of America, 1998.
Sorensen, Roy. A Brief History of the Paradox: Philosophy and the Labyrinths of the Mind. Oxford University Press, 2003.
Top Image: Badische Landesbibliothek, Karlsruhe, Cod. St. Peter perg. 92, fol. 11v.
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