Growth and limitation

Eleven-month-old Daniel, who’d been taking five or six steps at a time, casually walked across the living room two nights ago. He’s learned to climb up our staircases (but not down them). He’s grown tall enough for his head to be whacked by the refrigerator door. Today I caught him playing with the dials on our gas stove.

Samuel received his first YouTube lesson in adding and subtracting. He grinned and squealed and waved his arms. Fireworks of possibility exploded in my brain. Should I buy Samuel an abacus so that he can practice calculating like the Japanese? (Should I buy myself an abacus?) Should I teach Samuel about truth tables? Propositional logic? Quantification? He’d probably get a kick out of seeing “∀” and “∃.”

I’m not even sure I could teach logic to adults. I’ve never tried.

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I spent a couple of hours at the whiteboard with Samuel. He can’t add yet. He won’t even count all the dots unless I do so along with him. He does like to yell out the numbers and the operations, but he gets the sums wrong.

“Five plus three equals FOURTEEN!”

No, son.

He is bitterly disappointed. Not because he’s got the sum wrong – I doubt he understands what it is to get a sum wrong (and he never has minded factual correction as such) – but because he really wants the last term to be fourteen. He is an enthusiastic laissez-faire combinatorialist. If South Africa vs. Mexico is a valid possibility, and if there’s another possibility which is South Africa vs. Finland, and if South Africa vs. North Korea is possible … then surely five plus three equals fourteen is perfectly kosher, perfectly respectable (worth celebrating, even), no matter that dot-counting can establish that five plus three actually (therefore, possibly; therefore, necessarily) equals eight.

I believe this is his first brush with theoretical, as opposed to practical, impossibility. It is baffling to him.

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Philomena Cunk (Cunk on Earth) is coming to Netflix.

I re-train my logical faculty

As the temperature cools, I wonder if I should cut the grass less often. Its growth this week has been negligible.

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Having not studied any formal logic for about fifteen years, I’m working through some very basic textbooks to undo the rust. The funnest one is Logic by Wilfrid Hodges (2nd edition, Penguin, 2001), but not for any reason to do with logic (were I a logician, I’m sure I’d find things to quibble with; indeed, logicians are so finicky, they often assign their own notes when they teach). I just like Hodges’s wry humor and poetical examples. The book makes heavy use of truth trees, which I don’t remember ever having worked with.

I also have the first edition of Barwise & Etchemendy – the book that Cornell undergraduates used to study – but not the software. Oh, look! The second edition is online! All typeset in glorious, drab Computer Modern! Which, incidentally, looks the same as the current font of this blog.

Also online, also typeset in Computer Modern, is the open-source forallx (“for all x”) by a philosopher I once heard speak at Cornell. He praised the grad student who commented on his talk because the student’s notes were nicely typeset (in Computer Modern). It was a genuine compliment, not a Gricean insult.

After I’m happy with my re-mastery of propositional and predicate logic, I’ll read Quine’s Philosophy of Logic, which I meant to do eighteen or nineteen years ago.