a daily practice of logical thinking — one watercolor page at a time
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day 001 · modus ponens
The first form. P → Q. P. ∴ Q. A door swings open the moment you accept its hinge. To say "if rain, then wet" is to promise: should rain arrive, wetness must follow. Today I noticed how often I forget to ask whether the antecedent has actually happened — I race to the conclusion before the rain has fallen.
day 002 · modus tollens
The mirror of the first. P → Q. ¬Q. ∴ ¬P. Denying the conclusion denies the cause. I find this one harder. It asks me to look at the absence of an effect and walk backwards through the implication. To refuse a proposition because its consequence is missing — this is the logician's quiet form of skepticism.
day 003 · disjunctive syllogism
P ∨ Q. ¬P. ∴ Q. Two doors, one closed. The other must be the way. I keep finding small versions of this in the kitchen, in conversations: either I left it here, or I left it in the car. Logic, before it becomes formal, is the everyday relief of narrowing down what remains.
day 004 · hypothetical syllogism
P → Q. Q → R. ∴ P → R. A long thought is a chain of small thoughts that hold each other up. If I water the seed, it sprouts; if it sprouts, it grows; therefore, if I water the seed, it grows. The rule lets us skip middles — but I am trying to remember the middles today, because the middles are where the practice lives.
day 005 · the fallacy I keep making
P → Q. Q. ∴ P — and I would believe it, every time, if I were not careful. "The ground is wet, therefore it rained" — but the sprinklers run on Tuesdays. Most of my errors in thinking are this shape: a true conclusion, mistaken for a proof of its cause. Today I noticed it in three different conversations.
day 006 · contraposition
"If P, then Q" is the same statement as "if not Q, then not P." Walking around a tree, you see different branches but the same trunk. I find I trust contraposition more than the original sometimes — looking at where a claim fails tells me more than looking at where it works.
the root system
Every day's logic grows from somewhere older. Below — a botanical sketch of the foundations this journal returns to: the soil of identity, non-contradiction, and excluded middle; the trunk of inference; the canopy of conclusions reached and conclusions still to come.