What Happens When a Sentence Says, "I'm False"? Albert of Saxony Knew
A Riddle That Loops Back on Itself
Imagine you write a short sentence on a slip of paper: This sentence is false. If the sentence is true, then things are exactly the way it says — which means it’s false. If it’s false, then it’s not the way it says — but it says it’s false, so it must be true. Either way, logic seems to crash.
This puzzle, called the liar paradox, has annoyed and delighted thinkers for more than two thousand years. In the middle of the 1300s, one of the cleverest attempts to sort it out came from a man who spent his days in the lecture halls of Paris: Albert of Saxony (c. 1320–1390).
Albert was not a grand system-builder who invented a whole new philosophy from scratch. He was a master of arts, a teacher, and eventually the first rector of the University of Vienna. He wrote a logic textbook whose title means “Very Useful Logic,” and it really was. He also wrote stacks of works on Aristotle’s physics, on motion, on the heavens, and on delicate puzzles about language. His job was to make the best tools of his time sharper and easier to use — and his ideas rippled across Europe for centuries.
Albert’s “Very Useful” Logic Book
Albert’s masterwork, the Perutilis Logica, was finished around 1360. It tackles logic in six big chunks: the building blocks of sentences, the properties of terms, truth conditions of different kinds of sentences, and then three hot topics that were shaking up the 14th-century universities — theories of consequences, fallacies, and insolubles (the technical name for self-referential paradoxes like the liar).
Albert borrowed freely from the great English logician William of Ockham (c. 1287–1347) and from William Heytesbury, but he often arranged their insights in a clearer, more systematic way. He also disagreed with his Parisian rival John Buridan (c. 1300–c. 1358) on several points.
His most talked-about move concerns the liar paradox. Albert held that every sentence, just by being a sentence, silently carries a little claim about itself: it signifies “that it is true”. So when a sentence actually says “I am false,” it ends up signifying two things at once — that it is true and that it is false. Since it claims a contradiction, Albert concluded, the sentence is simply false. It is not a mysterious third kind of beast; it is a normal falsehood that says too much. By treating an insoluble as a piece of language that overloads its own meaning, Albert kept logic from melting down.
He was also a trailblazer in the theory of consequences. A consequence is a logical “if … then” link: from one or more statements (the antecedent), another statement (the consequent) must follow. Albert defined it crisply: a consequence is valid when it is impossible for the antecedent to be true while the consequent is false. He then sorted consequences into formal ones — which hold no matter what particular words you plug in, like “if it’s raining and not raining, then I’m a frog” — and material ones, which depend on facts about the world, like “if this is copper, it conducts electricity.” Within material consequences he further distinguished those that hold in all situations (simpliciter) from those that hold only right now (ut nunc). For example, “if Socrates is sitting, he is not running” holds simpliciter, whereas “if Socrates is in Athens, it is sunny” might hold only at this moment. This tidy system made logical deduction much more precise, and it paved the way for later thinkers to build formal systems of inference.
Relations: Are They Real, or Just in Your Head?
When you say “Sara is taller than Zoe,” it feels as if there is a thing called “taller-than-ness” floating between them. Many philosophers in Albert’s day wondered whether such relations are real items in the world, or just our way of talking.
Albert took a radical line. Like Ockham, he denied that relations are extra little things glued onto ordinary objects. But he went further: he described a relation as an act of the referring soul. Your mind does the work of lining up two things and comparing them. The relation does not exist on its own. So the sentence “Socrates is a relation” would be, for Albert, complete nonsense — whereas Ockham had been willing to let it squeak through in a roundabout way.
This idea fits neatly with Albert’s broader nominalism — the view that only individual things exist, and general words are just signs we use to group them. For Albert, quantity, like “three apples,” is not a mysterious extra layer of reality; it is a disposition of substance and quality, a way the apples are arranged. This outlook helped him trim away invisible furniture from the world, both in logic and in physics.
Vacuums, Cannonballs, and Mighty Impetus
Albert did not keep his logical scalpel in a drawer — he used it on nature. He drew a sharp line between what is absolutely impossible (a square circle) and what is impossible in the common course of nature, even if God could bring it about. A vacuum — perfectly empty space — fell into the second category. You can picture a jar with every atom sucked out, and Albert agreed that God could make one if he wanted. But in the natural world, no vacuum can happen. Physics, Albert insisted, should explain the order of nature, not spend all its time chasing supernatural make-believe.
That didn’t stop him from modernizing the physics of motion. Like Buridan, he pushed the theory of impetus: when you throw a stone, you impress a force inside it — a virtus impressa — that keeps it moving after it leaves your hand. He didn’t claim to know exactly what that force was (that, he said, was a question for the metaphysician), but he used the idea to explain projectiles, falling bodies, and even the motion of planets without needing angels to push them. He also worked with the mean speed theorem — a rule for figuring out the total velocity of something that speeds up or slows down steadily — which was a big step toward modern dynamics.
Where he parted ways with Buridan was on what motion itself is. Buridan thought of motion as a flowing thing, a fluxus, distinct from the object that moves. Albert said no: moving is just being in different places at different times, like an alteration in quality. You don’t need a ghostly “motion-stuff.” Once again, he kept the world lean.
From Paris to the World
Albert of Saxony was not a dramatic rebel. He sharpened Ockham’s tools, argued with Buridan, and folded English logical techniques into Parisian teaching. But his influence was enormous precisely because he was so clear and so systematic.
His Physics commentary — even more than Buridan’s or Nicole Oresme’s — became the go-to textbook in Italy and central Europe. In Bologna, Blasius of Parma studied it in the 1380s. In Vienna, where Albert had helped build the university, his ideas found a natural home. His Very Useful Logic, with its six tidy treatises, kept being copied and taught. Manuscripts traveled to Erfurt, Prague, and far beyond. Thanks to Albert, Parisian discoveries about consequences, insolubles, and impetus didn’t stay in Paris — they became common knowledge across the continent.
Why does a 14th-century logic handbook matter to you? Every time you trace a chain of if‑then reasoning, every time you spot a self‑contradictory claim and think “that can’t be right,” you are walking paths Albert helped clear. Computer programs run on rules of consequence that are distant grandchildren of his formal‑and‑material distinction. And the liar paradox? It’s still a hot topic in philosophy, linguistics, and even artificial intelligence. Albert didn’t slay the riddle — nobody has — but he showed that careful analysis of language can keep logic standing, even when a sentence tries to pull the rug out from under itself. That’s very useful indeed.
Think about it
- If a sentence says “This sentence is false” and you can’t decide whether it’s true or false, is there a third option? Try to explain what it might be.
- Albert said a vacuum can’t happen naturally, but you can imagine one perfectly well. Can you think of something else that seems possible in your imagination but would break the laws of nature? Does that change what you think “real” means?
- Albert sorted consequences into formal and material ones. Come up with your own example of a “formal consequence” that holds no matter what words you plug in, and then a “material consequence” that depends on how the world actually is. Why might that difference matter?
