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Joel David Hamkins @joeldavidhamkins.bsky.social · 9h

I am scheduled to be offering my course on Infinity next semester, and I have been a little worried that previously the class may have been a bit too hard, too demanding of the students. To correct this, my wife Barbara has suggested that I lecture instead on the half infinite.

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Joel David Hamkins @joeldavidhamkins.bsky.social · 10h

See the full reading list here. bsky.app/profile/joel...

Joel David Hamkins @joeldavidhamkins.bsky.social · Aug 26

For your enjoyment, here is the reading list for my undergraduate core seminar this semester in Philosophy, Science, and Mathematics. We shall focus on topics in the philosophy of mathematics, philosophy of science, and philosophy of computability and AI.

Joel David Hamkins @joeldavidhamkins.bsky.social · 10h

This week's reading for my undergrad PhilSciMath core seminar. Looking forward to the discussion.

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Joel David Hamkins @joeldavidhamkins.bsky.social · 13h

In the essay, I explain rather that the surreal omega x omega chessboard is equinumerous with the surreals themselves. This can be strictly larger than Ord in ZFC.

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Joel David Hamkins @joeldavidhamkins.bsky.social · 14h

If V is equinumerous with On, then there is a global well order of V, which is the global choice axiom. This implies all proper classes are equinumerous. So when global choice fails, V is not equinumerous with On. (In ZFC, one speaks about definable classes and definable bijections between them.)

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Joel David Hamkins @joeldavidhamkins.bsky.social · 16h

Well, you are definitely on the right track, since the naive answer, which I have heard from many people, is that there should be only countably many squares. But amongst the proper classes, how big is it? In ZFC, for example, not all proper classes have the same size.

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Joel David Hamkins @joeldavidhamkins.bsky.social · 17h

The surreal ω × ω chessboard is bigger—and stranger—than you think!
Enjoy my latest post on #InfinitelyMore.
www.infinitelymore.xyz/p/surreal-ch...

The surreal ω × ω chessboard is bigger—and stranger—than you think

What is the nature of the surreal ω × ω chessboard? How many squares are there? How many chess pieces shall we require to set up the board?

www.infinitelymore.xyz

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Reposted by Joel David Hamkins

Christian Lawson-Perfect @christianp.mathstodon.xyz.ap.brid.gy · 2d

Asked my pal from Somerset if he knew anyone capable of taking the square root of -𝑟².
"I are!" he said.
That's a proof by country diction.

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Joel David Hamkins @joeldavidhamkins.bsky.social · 3d

www.infinitelymore.xyz/p/monkey-mad...

Chaos train and monkey madness—fun with quantifiers

Learn the language of first-order logic by immersion in some fun logic puzzles

www.infinitelymore.xyz

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Joel David Hamkins @joeldavidhamkins.bsky.social · 3d

I answered a question on MathOverflow about the fruitfulness of considering the closeness-to-falsity of a given statement in mathematics. mathoverflow.net/a/501465/1946

Relations between the usefulness of a true statement, its closeness to falsity, and the difficulty of its proof

Let us start with a trivial observation: for any statements $A$ and $B$ (in a standard language), the implication $A\implies B$ is true if $A$ is false. So, if one were able to prove a false statem...

mathoverflow.net

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Reposted by Joel David Hamkins

Joel David Hamkins @joeldavidhamkins.bsky.social · 28d

New post-doctoral position at Notre Dame
Core analytic/logic/phil math. philjobs.org/job/show/29622
2 year position, $75K annual salary plus $15K expense account. Please apply! (I am chairing this search.)

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Joel David Hamkins @joeldavidhamkins.bsky.social · 5d

I think the best topics will be mathematically interesting and surprising. Should be accessible at first (since undergraduates) but grow in sophistication (since Caltech). I have several ideas, but would be interested to hear people's requests and suggestions.

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Joel David Hamkins @joeldavidhamkins.bsky.social · 5d

I am deeply honored to be invited to give the De Prima lecture at Caltech this fall, a distinguished annual math lecture aimed primarily at undergraduates. Help me decide on a topic! What would you request, drawing from topics on which you've seen me write or speak?

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Joel David Hamkins @joeldavidhamkins.bsky.social · 7d

I answered a question on MathOverflow about the Boolean ultrapower, regarding the algebraic approach to the ultrapower versus the names-based approach. mathoverflow.net/a/501257/1946

Boolean ultrapower - set-theoretic vs algebraic/model-theoretic

I've been looking through the Hamkins/Seabold paper "Well-founded Boolean ultrapowers as large cardinal embeddings". The Boolean ultrapowers are defined there in two different ways: in

mathoverflow.net

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Joel David Hamkins @joeldavidhamkins.bsky.social · 8d

I deleted an earlier version of this post, since I had screwed up the quotation marks! I hope it is right now.

Joel David Hamkins @joeldavidhamkins.bsky.social · 8d

And the author reply to critics:

"On 'On "On"' and 'On "On 'on'"'".

(Note: CMS nested quote rule.)

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Joel David Hamkins @joeldavidhamkins.bsky.social · 8d

"On 'On'"

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Joel David Hamkins @joeldavidhamkins.bsky.social · 9d

What is the view you are pointing out? We are to think of Lotks-Volterra in a Kuhnian light?

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Joel David Hamkins @joeldavidhamkins.bsky.social · 9d

Full reading list here. bsky.app/profile/joel...

Joel David Hamkins @joeldavidhamkins.bsky.social · Aug 26

For your enjoyment, here is the reading list for my undergraduate core seminar this semester in Philosophy, Science, and Mathematics. We shall focus on topics in the philosophy of mathematics, philosophy of science, and philosophy of computability and AI.

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Joel David Hamkins @joeldavidhamkins.bsky.social · 9d

This week's reading for my undergrad PhilSciMath core seminar. Looking forward to the discussion.

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Joel David Hamkins @joeldavidhamkins.bsky.social · 10d

If I were a musician...
youtu.be/fjesu41f1mY?...

Artist Chalon dans la rue, l’homme orchestre, festival 2021

YouTube video by Svenleboubou

youtu.be

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Joel David Hamkins @joeldavidhamkins.bsky.social · 10d

Attending team summit STOP Boss and colleagues have now boarded the hot-air balloon STOP Ready to cut them loose STOP

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Joel David Hamkins @joeldavidhamkins.bsky.social · 10d

Detail from student quiz on Lakatos, Proofs and Refutations.

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Joel David Hamkins @joeldavidhamkins.bsky.social · 10d

Overheard: the wife says "You're always wrong" and the husband replies "You're right".

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Joel David Hamkins @joeldavidhamkins.bsky.social · 15d

I have made a post on Substack Notes substack.com/@joeldavidha...
to the effect that we should have a Mathematics category on Substack. If you support math on Substack, please like and restack there.

Joel David Hamkins (@joeldavidhamkins)

Substack @Substack, when do we get a Mathematics category for bestsellers? We have many great math stacks with huge engagement and audiences.

substack.com

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