Category: Mathematics
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Topics in Current Technical Threads
1) Potential versus actual infinity. 2) Are there mathematical sets? 3) Does mathematics need a foundation in set theory? 4) Is there irreducibly plural reference, predication, and quantification? If yes, does plural quantification allow us to avoid ontological commitment to sets? 5) Discreteness, density, and continuity at the level of number theory, geometry, and nature…
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Weyl’s Tiles: An Argument against Discrete Space
Is physical space, the space of the natural world, continuous or discrete? If composed of space atoms, then discrete. The Weyl Tile argument (WTA), however, seems to show that physical space cannot be discrete or 'quantized' and therefore must be continuous. This is relevant to our ongoing debate about potential versus actual infinities. For if…
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Notes on Infinite Series
The resident nominalist writes, Your post generated a lot of interest. What I have to say now is better put as a separate post, rather than a long comment. Feel free to post. 1) Plural reference provides a means of dealing with numbers-of-things without introducing extra unwanted entities such as sets. Even realists agree that…
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Spherical Triangles as Incongruent Counterparts?
Over the last 24 hours I have been obsessing over Kant's spherical triangles. He claims that they are incongruent counterparts. Now I understand how a hand and its mirror image are incongruent counterparts. (A right hand's mirror image is a left hand.) But it is not clear to me how Kant's spherical triangles are incongruent…
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Kant, Spherical Triangles, and Incongruent Counterparts
Buckner demands an argument from incongruent counterparts to the ideality of space. But before we get to that, I am having trouble understanding how the 'spherical triangles' Kant mentions in the Prolegomena to Any Future Metaphysics, sec. 13, are incongruent counterparts. Perhaps my powers of visualization are weak. Maybe someone can help me. I understand…
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For the Left, the Subject is not the Subject: Why Math is ‘Racist’
It has often been noted that for the Left, the issue is not the issue. David Horowitz: As President Obama’s political mentor, Saul Alinsky, put it in Rules for Radicals: “One acts decisively only in the conviction that all of the angels are on one side and the devils are on the other.” Here is another…
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“But it’s exponential!”
Peggy Noonan advertises her ignorance in this opening sentence: This coronavirus is new to our species—it is “novel.” It spreads more easily than the flu—“exponentially,” as we now say—and is estimated to be at least 10 times as lethal. Why is it "novel"? It is a form of flu, and it is not unique in…
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Beware of Cranks
It starts like this: The four impossible “problems of antiquity”—trisecting an angle, doubling the cube, constructing every regular polygon, and squaring the circle—are catnip for mathematical cranks. Every mathematician who has email has received letters from crackpots claiming to have solved these problems. They are so elementary to state that nonmathematicians are unable to resist.…
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Jerking Towards Social Collapse
Thanks to 'progressives,' our 'progress' toward social and cultural collapse seems not be proceeding at a constant speed, but to be accelerating. But perhaps a better metaphor from the lexicon of physics is jerking. After all, our 'progress' is jerkwad-driven. No need to name names. You know who they are. From your college physics you may recall…
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3/14 is π Day
My best π day post
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Infinity and Mathematics Education
Time for a re-post. This first appeared in these pages on 18 August 2010. ……………………. A reader writes, Regarding your post about Cantor, Morris Kline, and potentially vs. actually infinite sets: I was a math major in college, so I do know a little about math (unlike philosophy where I'm a rank newbie); on the other hand, I…
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Math is Racist!
Here There is nothing so stupid, destructive, and inane that a 'liberal' won't embrace it.
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Super π Day Approximately
π day is 3/14. March 14th last year was called super π day: 3/14/15. Years ago, as a student of electrical engineering, I memorized π this far out: 3.14159. So isn't today better called super π day? I mean, 3.1416 is closer to the value of π than 3.1415. Am I right? Of course…
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Social Utility and the Value of Pure Inquiry: The Example of Complex Numbers
Much as I disagree with Daniel Dennett on most matters, I agree entirely with what he says in the following passage: I deplore the narrow pragmatism that demands immediate social utility for any intellectual exercise. Theoretical physicists and cosmologists, for instance, may have more prestige than ontologists, but not because there is any more social utility…