On the Existence of Numbers
| dc.contributor | Harold, James | |
| dc.contributor | Shepardson, Dylan | |
| dc.contributor.advisor | Mitchell, Samuel | |
| dc.contributor.author | Cazeault, Ellamae | |
| dc.date.accessioned | 2025-07-08T17:50:48Z | |
| dc.date.available | 2025-07-08T17:50:48Z | |
| dc.date.gradyear | 2025 | |
| dc.date.issued | 2025-07-08 | |
| dc.description.abstract | This thesis will argue that numbers are real objects and that we ought to admit them into our ontology. Results in logic, particularly Gödel’s incompleteness proofs make it impossible to avoid doing so. I will argue that to give up the fact that numbers are real is to give up math as we currently understand it and practice it. I will argue this by explaining how David Hilbert has the best method of utilizing math without committing numbers to our ontology. I will then go through Gödel’s incompleteness proofs and show why Hilbert’s methods will never work. This means that in order to do math, we must admit numbers into ontology. I will then further argue that it is very difficult to give up math. I will show this through Quine’s indispensability argument. Thus, we must admit numbers into our ontology. | |
| dc.description.sponsorship | Philosophy | |
| dc.identifier.uri | https://hdl.handle.net/10166/6753 | |
| dc.language.iso | en | |
| dc.rights.restricted | restricted | |
| dc.subject | Philosophy of Mathematics | |
| dc.subject | Gödel's Proof | |
| dc.subject | Mathematical Realism | |
| dc.subject | Platonism | |
| dc.subject | Quine | |
| dc.subject | Hilbert | |
| dc.title | On the Existence of Numbers | |
| dc.type | Thesis | |
| mhc.degree | Undergraduate | |
| mhc.institution | Mount Holyoke College |