This thinker formalized a statement of equinumerosity that George Boolos later identified as Hume’s principle. This thinker wrote two essays criticizing David Hilbert’s lecture on geometry for relying on the demonstration of consistency. This thinker introduced the turnstile symbol to logic in a book that criticizes Kant’s claim that 2 + 3 = 5 was unprovable. Michael Dummett attributes the beginning of the linguistic turn to this thinker’s use of the context principle while discussing the origin of numbers. This thinker’s Basic Law V (“five”) was shown to be flawed when considering sets through Russell’s paradox. A puzzle at the start of a paper by this thinker notes “Hesperus is Hesperus. Hesperus is Phosphorus.” For 10 points, name this German philosopher who wrote The Foundations of Arithmetic and On Sense and Reference. ■END■
| California (North) | Main Site | Y | 3 | 100% | 0% | 0% | 61.33 |
| California (South) | Main Site | Y | 4 | 75% | 0% | 75% | 121.33 |
| Canada | Main Site | Y | 12 | 58% | 0% | 25% | 101.86 |
| Florida | Main Site | Y | 3 | 33% | 0% | 0% | 112.00 |
| Great Lakes | Main Site | Y | 5 | 60% | 0% | 0% | 102.00 |
| Lower Mid-Atlantic | Main Site | Y | 8 | 50% | 0% | 25% | 105.00 |
| Midwest | Main Site | Y | 8 | 50% | 0% | 25% | 86.50 |
| Northeast | Main Site | Y | 5 | 80% | 0% | 40% | 103.75 |
| Overflow | Main Site | Y | 3 | 67% | 0% | 0% | 107.00 |
| South Central | Main Site | Y | 2 | 50% | 0% | 0% | 87.00 |
| Southeast | Main Site | Y | 7 | 43% | 0% | 14% | 107.33 |
| UK | Main Site | Y | 6 | 83% | 0% | 33% | 87.60 |
| Upper Mid-Atlantic | Main Site | Y | 9 | 78% | 0% | 44% | 103.57 |
| Upstate NY | Main Site | Y | 4 | 50% | 0% | 0% | 88.00 |
| Player | Team | Opponent | Buzz Position | Value |
|---|---|---|---|---|
| Asha Basu | McGill A | Waterloo B | 14 | 10 |
| John Marvin | Chicago A | Chicago E | 14 | 10 |
| Eveline Ong | Oxford A | Imperial C | 14 | 10 |
| Zaid Asif | NYU C | Vassar | 16 | -5 |
| Anuttam Ramji | Berkeley B | Berkeley A | 18 | 10 |
| Walter Carson | NC State B | Wake Forest | 53 | -5 |
| Ian Theysmeyer | Queen's | McMaster A | 55 | -5 |
| Jack Lewis | Bruin | WashU A | 60 | 10 |
| Moses Kitakule | Columbia A | Johns Hopkins A | 63 | -5 |
| Mitch McCullar | Penn State | RIT | 64 | 10 |
| Matthew Sumanen | Georgia Tech C | Georgia Tech B | 65 | -5 |
| Gus Vanskike | Maryland C | Rutgers A | 66 | -5 |
| Kevin Ye | Simon Fraser | Toronto C | 67 | -5 |
| Matt Sheldon | Oxford B | Durham | 67 | -5 |
| Kerry Xu | UCSD B | UCSD A | 68 | -5 |
| Ryan Rosenberg | NYU A | Maryland A | 69 | -5 |
| Alex Jiang | Brown | Dartmouth B | 70 | 10 |
| Karthik Jayaram | UCLA A | UC Irvine | 72 | -5 |
| Matthew Wang | UBC A | Waterloo A | 72 | 10 |
| Artem Borisov | Bristol | Edinburgh B | 74 | -5 |
| Jerry Vinokurov | John Jay | Johns Hopkins B | 74 | 10 |
| Michał Gerasimiuk | Stanford A | Stanford B | 78 | 10 |
| Ben Hellman | Swarthmore | Georgetown | 78 | 10 |
| Faraz Foroughi | NC State A | Liberty B | 80 | -5 |
| Akshar Goyal | Illinois A | Chicago B | 83 | 10 |
| Yrwin Batan | MIT | Yale | 83 | 10 |
| Joel Miles | Minnesota A | Georgia Tech A | 83 | 10 |
| Oscar O'Flanagan | Imperial A | UCL | 83 | 10 |
| Albert Nyang | LSE | Cambridge C | 83 | 10 |
| Kevin Zheng | Michigan A | Ohio State B | 87 | 10 |
| Jisoo Yoo | Texas A | Texas B | 87 | 10 |
| Nathaniel Hull | Berkeley C | Berkeley D | 88 | 10 |
| Ariel Faeder | Pittsburgh | CWRU B | 88 | 10 |
| Noah Chin | Virginia Tech A | North Carolina C | 88 | 10 |
| Kevin Liu | Maryland B | Catholic | 88 | 10 |
| Mats Miller | Chicago D | Northwestern D | 94 | -5 |
| Chris Yoo | William and Mary | VCU | 95 | 10 |
| Dmitri Anh-Minh Tran | UC Santa Barbara | UCSD C | 102 | 10 |
| Joseph Chambers | Virginia | James Madison A | 107 | 10 |
| Amir Dolansky | Toronto E | Guelph | 109 | 10 |
| Emmanuel Alayande | Florida B | Central Florida C | 112 | 10 |
| Omkar Marathe | Columbia B | NYU B | 112 | 10 |
| Chauncey Lo | Columbia C | Rutgers B | 112 | 10 |
| Robert Chen | Rochester | Cornell C | 112 | 10 |
| Evan Gniadek | Purdue B | Chicago C | 118 | 10 |
| Stefan Stealey-Euchner | Arizona State | UCLA B | 119 | -5 |
| Owen Riviere | Western B | Western A | 119 | -5 |
| Christopher Bradley | Southern Connecticut State | Harvard A | 123 | -5 |
| Sriram Susarla | UBC B | Carleton University | 125 | 10 |
| Chris Dech | Brandeis A | Dartmouth A | 125 | -5 |
| Arvin Boraghi | Cambridge B | City St. George's | 127 | 10 |
| Zachary Bornstein | Virginia Tech B | South Carolina A | 130 | 10 |
| Stephen Walsh | Northwestern B | Indiana B | 130 | -5 |
| Sinecio Morales | Johns Hopkins A | Columbia A | 130 | 10 |
| Jaskaran Singh | UCLA B | Arizona State | 131 | 10 |
| Scott Sibley | UC Irvine | UCLA A | 131 | 0 |
| Nolan Dannels | UCSD A | UCSD B | 131 | 10 |
| Luke Sloan | McGill B | Brock | 131 | 0 |
| Yihong Chen | Toronto C | Simon Fraser | 131 | 10 |
| Milan Fernandez | Brock | McGill B | 131 | 0 |
| Jay Misuk | Western C | Toronto G | 131 | 0 |
| Jesse Chusing | Ottawa | Toronto B | 131 | 10 |
| Yusuf Baig | McMaster B | Toronto F | 131 | 0 |
| Sonia Zhang | Western A | Western B | 131 | 0 |
| Saju Ramraj | Toronto F | McMaster B | 131 | 0 |
| Seth Allen | McMaster A | Queen's | 131 | 10 |
| Ishan Joshi | Toronto Metropolitan | Toronto D | 131 | 0 |
| Khanh Nguyen | Florida C | Central Florida B | 131 | 0 |
| AnnaMaria Donnelly | Central Florida B | Florida C | 131 | 0 |
| June Miller | Florida A | Central Florida A | 131 | 0 |
| Andrew Amygdalos | CWRU A | Michigan C | 131 | 0 |
| Maddie Baldwin | Michigan State | Michigan B | 131 | 0 |
| Roxanne Tang | Ohio State A | Ohio State C | 131 | 10 |
| Aryan Desarapu | Michigan B | Michigan State | 131 | 0 |
| Thomas Jenkins | Michigan C | CWRU A | 131 | 0 |
| Kabir Zaman | South Carolina B | James Madison B | 131 | 0 |
| James Watson | Wake Forest | NC State B | 131 | 0 |
| Laila Peterson | James Madison B | South Carolina B | 131 | 0 |
| Owen Banks | Duke | North Carolina A | 131 | 0 |
| Joseph Cole | North Carolina A | Duke | 131 | 0 |
| Faith Magiera | Northwestern D | Chicago D | 131 | 0 |
| Ethan Ma | Illinois C | Indiana C | 131 | 0 |
| Jacob Finley | Notre Dame A | Northwestern C | 131 | 10 |
| Nolan Jones | Purdue A | Notre Dame B | 131 | 0 |
| John Augustyn | Notre Dame B | Purdue A | 131 | 0 |
| Emily Justak | Indiana C | Illinois C | 131 | 0 |
| Max Neal | Harvard B | Brandeis B | 131 | 10 |
| Elliott Gomes | Dartmouth A | Brandeis A | 131 | 0 |
| Joy An | Harvard A | Southern Connecticut State | 131 | 10 |
| Isaac Studley | Carleton College | Missouri B | 131 | 10 |
| Annika Larson | Claremont | Washington B | 131 | 0 |
| Carson Kessler | Washington B | Claremont | 131 | 0 |
| Dwight Solano | Texas A&M A | Murray State A | 131 | 0 |
| Kanyon Beck | Murray State A | Texas A&M A | 131 | 0 |
| Sawyer Smith | Mississipi State | Alabama B | 131 | 0 |
| Olivia Kiser | Kentucky | WashU B | 131 | 0 |
| Arhith Dharanendra | Georgia Tech B | Georgia Tech C | 131 | 10 |
| Parker McCoig | Tennessee A | Georgia Tech D | 131 | 10 |
| Britton Webster | Alabama A | Louisville B | 131 | 0 |
| Camden Walker | WashU B | Kentucky | 131 | 0 |
| Davin Sivertson | Alabama B | Mississipi State | 131 | 0 |
| Danny Tran | Tennessee B | Sewanee | 131 | 0 |
| Joseph Strom | Louisville B | Alabama A | 131 | 0 |
| Daniel Bloom | Edinburgh B | Bristol | 131 | 10 |
| Mattias Ehatamm | Maryland A | NYU A | 131 | 10 |
| Aiden Dartley | Rutgers A | Maryland C | 131 | 0 |
| Eli O'Sick Johnson | Binghamton B | Binghamton A | 131 | 0 |
| Peter Smith | Binghamton A | Binghamton B | 131 | 0 |
| Julian Bushlow | Cornell A | Cornell B | 131 | 0 |
| Brian Hoff | Cornell B | Cornell A | 131 | 0 |