Arguments Drawn on Napkins

The napkin snatcher strikes again.

Feb 15, 2026

Issue No. 51

Quite a bit of what we’ve covered since the very start has touched on the idea of categorical thinking. Something we lean into when we quickly want to make sense of the world around us, and something that can blind us to the nuance and detail of the individual parts we lump into categories.

When I’m at a cafe on some mornings unable to put pen to paper, gazing out the window at passers-by, I’ll look up early sources for ideas we take for granted. And on the topic of putting things into boxes and connecting them together, an early surviving work on categorical inference is Aristotle’s1 writings from 350 B.C. where he introduces this thing called a syllogism.2

A syllogism is an argument in three statements. The first two statements set up the third, and take the form “All … are …”, “No … are …”, or “Some … are/aren’t …” A twist on the canonical example being:

All people are mortal.
Jane is a person.
Therefore, Jane is mortal.

The pattern is meant to produce compelling arguments by combining existing statements about categories of things into necessary conclusions. Are all people mortal? They are. Is Jane a person? Looks like it. Then it must follow that she’s mortal.

The line of reasoning works irrespective of who Jane is as a person, so long as she remains a member of this category we call people. And it works even if someone were to dispute that all people are mortal. We’d counter by saying, “For the sake of argument, let’s assume all people are mortal.”

When we use that phrase, we might not even realize that we’re actually separating two forms of thinking: determining whether or not something is true, and determining whether or not we’ve arranged a set of statements in such a way that the conclusion then necessarily follows from earlier statements.

There’s more to say on this topic, but for this Sunday morning, here are two more syllogisms drawn on napkins.

Can we have syllogism imposters? Arguments that look like syllogisms, but aren’t ones? For instance, this argument has three statements, and looks like a syllogism.

All planets are round.
A head is round.
Therefore, a head is a planet.

The first statement tells us something about planets; that they’re round (granted, nearly round). The second statement tells us something about heads; that they’re round (nearly round, at least mine is.)

But neither statement tells us anything about round things as a whole. The category of round things is doing all the heavy lifting, but we never examine it. We assume overlap where none is guaranteed.

We might call this pattern a categorical fallacy, or more broadly, a logical fallacy. And this particular pattern is nowadays called the fallacy of the undistributed middle.

The fallacy of the undistributed middle.

The fact that an argument can seem logical at first glance is precisely why it’s useful (and fun) to learn about patterns like these. They’re not just errors, they’re illusions. Optical illusions exploit the way our visual system works, logical fallacies exploit how our reasoning works. And in both cases, we can either fall for them, unwittingly, or someone might exploit them to maneuver us in a certain direction or get us feeling a certain way.3

Something interesting about something else

I was reading about pangrams the other day. A pangram is a sentence using every letter of a given alphabet at least once. For instance, in English, the following sentence would be a pangram:

The quick brown fox jumps over the lazy dog.

I was curious if other languages had them. Here are a few:

Azeri: Zafar, jaketini da papagini da götür, bu axsam hava çox soyuq olacaq.
Zafar, take your jacket and cap, it will be very cold tonight.
Polish: Pchnac w te lódé jeza lub osm skrzyn fig.
Push into this boat a hedgehog or eight boxes of figs.
Finish: Wieniläinen sioux’ ta puhuva ökyzombie diggaa Asan roquefort-tacoja.
The Sioux-speaking filthy rich zombie from Vienna digs Ása’s Roquefort tacos.
Irish: D’ith cat mór dubh na héisc lofa go pras .
A large black cat ate the rotten fish promptly.

Some are too hot or Substack, so look into them if you’re curious.