How Far Can Logic Take Us? The Strange World of Albert of Saxony

Imagine someone throws a ball across a room. You watch it arc through the air, then drop. That seems simple enough. But now imagine someone asks you: What keeps the ball moving after it leaves the hand? In Aristotle’s physics, which people believed for nearly 2,000 years, the answer was that the air itself somehow pushes the ball along. But a 14th-century philosopher named Albert of Saxony found this deeply unsatisfying. He thought the ball carried something inside it—a kind of force that the thrower had impressed upon it, which gradually wore out until gravity took over. He called this impetus.

This might sound like a small, technical disagreement. But it opens up a much bigger question: How do you figure out what’s really going on when you can’t see the mechanism? And once you start thinking that way, you quickly end up in stranger territory. What if there are other worlds besides ours? What if space could be empty—a vacuum—even though nature never seems to produce one? What if you could say something that is true about a thing, yet also false about the same thing, depending on how you look at it?

Albert of Saxony spent his life thinking about these puzzles. He was part of a group of philosophers at the University of Paris in the 1300s who believed that the best way to understand the world was to first get really, really clear about language. Because if you’re not careful, the words you use can trick you into thinking things exist that don’t.

Who Was Albert of Saxony?

Not much is known about Albert’s early life. He was born around 1320 in what is now Germany, in a village called Rickensdorf. He made his way to the University of Paris, which was the intellectual capital of Europe at the time. He became a master of arts (basically a professor) in 1351, served as rector of the university in 1353, and stayed in Paris for more than a decade.

At the time, the Faculty of Arts in Paris was buzzing with new ideas. A philosopher named John Buridan (yes, the guy with the donkey thought experiment) was developing a whole new way of thinking about motion, logic, and the nature of reality. Albert was right in the middle of this conversation. He wrote books on logic, physics, and mathematics that were read across Europe for centuries. Some people have dismissed him as just an imitator of more famous thinkers, but recent scholarship shows he was genuinely original—often disagreeing with his teachers and proposing his own solutions to difficult problems.

In 1365, he was put in charge of founding the University of Vienna. He later became a bishop and died in 1390.

The Problem of Language: How Words Can Fool Us

Here’s a puzzle Albert cared about a lot. Suppose I say: “A unicorn does not exist.” The sentence seems perfectly fine. But look closely at what it does. The word “unicorn” is supposed to refer to something. But if unicorns don’t exist, what does “unicorn” refer to? You might say it refers to the idea of a unicorn. But that idea is something real—it’s in your mind. So does “A unicorn does not exist” mean the same thing as “The idea of a unicorn does not exist”? That can’t be right, because the idea does exist.

This is the kind of thing that kept medieval logicians up at night. And Albert had a specific way of handling it. He believed that words should ultimately point back to real, individual things in the world. When you say “human,” you’re not naming some mysterious abstract thing called “humanness” that floats around in a different dimension. You’re using a word that can apply to any individual human—Socrates, your mom, the person next to you on the bus. The word works as a kind of mental shortcut. It signifies many individuals at once.

This position is called nominalism, and Albert was one of its defenders. The basic idea is that general categories (like “justice,” “humanity,” “blueness”) don’t have their own separate reality. They’re just ways of grouping things that actually exist. The only things that really exist are individual, particular things: this stone, that tree, that person.

This might seem obvious to you. But in Albert’s time, plenty of philosophers disagreed. They thought that “humanity” was a real thing—more real than any particular human, actually. Albert thought that was a mistake caused by letting language trick you. Just because we have a word for something doesn’t mean that thing exists out there in the world.

The Logic of “If… Then…” — Consequences

One of Albert’s major contributions was in the theory of consequences—basically, the logic of “if… then…” statements. Think about all the times you use if-then reasoning. “If it’s raining, then the ground is wet.” “If I study for this test, then I’ll do better.” “If all humans are mortal, and Socrates is human, then Socrates is mortal.”

Albert wanted to figure out exactly what makes a valid consequence. His definition is simple and elegant: A consequence is valid when it’s impossible for the “if” part to be true without the “then” part also being true.

So take: “If you are my brother, then you are male.” Is it possible for “you are my brother” to be true without “you are male” also being true? No. So it’s a valid consequence.

Take: “If you are my brother, then you are older than me.” Is it possible for “you are my brother” to be true without “you are older than me” being true? Yes—you could have a younger brother. So it’s invalid.

Albert distinguished between different kinds of consequences. Some are formal: they’re valid just because of their logical shape, like “If A is B, and B is C, then A is C.” Others are material: they depend on the actual meanings of the words, like “If you are a human, you are an animal.” He also distinguished between consequences that hold absolutely (all the time, in every possible situation) and ones that hold only “for now” (given how things actually are at this moment—like “If it’s daytime, the sun is above the horizon”).

This might sound dry, but it’s the foundation of all logical reasoning. Every time you argue with someone, you’re relying on the idea that some consequences are valid and others aren’t. Albert was one of the first people to work out a systematic theory of how that works.

The Strange Case of Self-Referential Sentences

Albert also tackled what he called insolubles—sentences that seem to undermine themselves. The most famous one is the Liar Paradox: “This sentence is false.” If the sentence is true, then it’s false. If it’s false, then it’s true. Either way, you get a contradiction.

Albert’s solution was clever. He argued that every proposition, by its very form, signifies that it is true. So when you say “This sentence is false,” you’re actually saying two things at once: (1) that the sentence is false, and (2) that the sentence is true (because all sentences carry that built-in claim). Since those two things can’t both be true, the sentence is simply false. Problem solved—or at least, Albert thought so. Philosophers still argue about whether this really works.

Physics: What’s Really Going On When Things Move?

Now back to the thrown ball. Albert developed the idea of impetus alongside his contemporary John Buridan. The theory says that when you throw a ball, you transfer a force into it—a “motive force” that keeps it going until it’s used up by air resistance or gravity. This is much closer to our modern concept of inertia and momentum than Aristotle’s theory was.

But Albert pushed these ideas further. He asked: could there be other worlds besides ours, each with their own physics? His answer was yes—at least, it’s not impossible. God could create other worlds if he wanted to. But Albert was careful: just because you can imagine something doesn’t mean it actually happens in nature. Nature follows regular patterns, and physics is about describing those patterns, not every possible thing God could do.

He also considered the vacuum. Can empty space exist? Aristotle had said no: “nature abhors a vacuum.” Albert agreed that in the normal course of nature, vacuums don’t occur. But he thought they were logically possible. If God wanted to create a vacuum, he could. This kind of thinking—distinguishing between what’s naturally impossible and what’s absolutely impossible—was a major step toward modern physics. It let philosophers ask “what if” questions without being accused of contradicting established science.

Why Does Any of This Matter?

Albert of Saxony is not a household name. But his work helped shape the way we think about logic, language, and physics. He was part of a generation of philosophers who realized that before you can understand the world, you have to understand how your own mind and language work. What are words actually doing? When is an argument valid? What does it mean for something to be “true”?

These aren’t just academic questions. Every time you say “That doesn’t follow” during an argument, you’re making a judgment about the validity of a consequence. Every time you wonder whether a category really exists or is just a convenient label, you’re thinking about nominalism. Every time you notice that a sentence seems to contradict itself, you’re dealing with an insoluble.

The questions Albert wrestled with are still alive today. Scientists argue about whether the laws of physics could be different in other universes. Philosophers still debate the Liar Paradox. And nobody has fully settled whether general categories are real or just useful fictions.

So the next time you throw a ball, or argue with a friend, or read a sentence that seems to twist back on itself, you’re walking the same ground Albert walked—700 years ago, in a room full of candles and manuscripts, trying to figure out how far logic can take you.

Appendices

Key Terms

Term	What it does in this debate
Nominalism	The view that only individual things really exist; general categories are just names or mental shortcuts
Signification	The relationship between a word and the thing or things it points to in the world
Consequence	An “if-then” relationship between statements; the study of what makes one statement follow from another
Impetus	A force impressed into a moving object that keeps it going until it wears out
Insolubles	Self-referential sentences that seem to create contradictions (like “This sentence is false”)
Vacuum	Empty space with nothing in it; considered naturally impossible but logically possible by Albert

Key People

Albert of Saxony (c. 1320–1390): German philosopher and physicist who helped develop the theory of impetus and made original contributions to logic; later became a bishop and helped found the University of Vienna.
John Buridan (c. 1300–1360): French philosopher famous for the “Buridan’s donkey” thought experiment; developed the theory of impetus alongside Albert and was a major influence on Parisian philosophy.
William of Ockham (c. 1287–1347): English philosopher known for “Ockham’s razor” (the simplest explanation is usually best); his views on language and reality heavily influenced Albert’s nominalism.

Things to Think About

If nominalism is right, and general categories aren’t real, what does that mean for things like “justice” or “fairness”? Are they just useful labels, or is there something real they point to?
Albert thought that every sentence carries a hidden claim that it’s true. If that’s the case, does the sentence “This sentence is false” really get solved by saying it’s simply false? Or does the problem just move somewhere else?
The distinction between what’s “naturally impossible” and what’s “absolutely impossible” is a powerful tool. Can you think of something that’s impossible in the ordinary course of life but isn’t logically contradictory? What does that distinction let you do that you couldn’t do otherwise?
If you could throw a ball in a vacuum (empty space) with no gravity, what would happen according to impetus theory? How is that different from what modern physics says?

Where This Shows Up

Computer programming: The study of logical consequences is the foundation of how computers process “if-then” statements and make decisions.
Law and argument: Lawyers and judges constantly rely on whether one claim validly follows from another—exactly the kind of reasoning Albert systematized.
Physics: The concept of inertia, which is central to how we understand motion today, developed directly out of the medieval impetus theory.
Social media and self-reference: Memes, jokes, and arguments that play with self-reference (like “This statement is false” memes) are modern versions of the insolubles Albert studied.