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<!DOCTYPE html>
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<title>Equilibrium Mastermind</title>
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### Reality Transurfing: Chapter 1
<br>
<center>
</center>
<center>
Joshua T. Vogelstein, PhD (<img src="assets/img/email-logo.png" align='top' width=25> [[email protected]](mailto:[email protected]),
<!-- <img src="images/Twitter_Logo_Blue.svg"/> -->
<img src="assets/img/twitter-logo.png" align='top' width=25><a href="https://twitter.com/neuro_data" >@neuro_data</a>) <br>
<!-- Jayanta Dey, Ali Geisa, Hayden Helm, Ronak Mehta, Will LeVine, -->
<!-- Carey E. Priebe<br> -->
[Biomedical Engineering](https://www.bme.jhu.edu/) | [Johns Hopkins University](https://www.jhu.edu/)
---
class: middle
Is 1+1=2 true?
---
---
### Page 379
---
### Axiomatic Set Theory
1. Axiom of extensionality
2. Axiom or regularity
3. Axiom schema of specification
4. Axiom of pairing
5. Axion of union
6. Axiom schema of replacement
7. Axiom of Infinity
8. Axiom of power set
9. Well-ordering theorem
---
### Quine: Two Dogmas of Empiricism
1. analytic truths: those truths indpendent of 'matters of fact'
2. synthetic truths: grounded in facts
Turns out, all truths are synthetic truths.
---
### Godel's Incompleteness Proofs
I am lying.
---
### Is .ye[1+1=2] true?
- under certain assumptions, .ye[$1+1 = 2$] is true
- under other assumptions, .ye[$1+1 = 2$] is false
- under other assumptions, .ye[$1+1 = 2$] is true but unprovable
- under other assumptions, .ye[$1+1 = 2$] is false but unprovable
- if that is the case for .ye[$1+1 = 2$], how much more so for any statement we make?
- in each moment, we get to .ye[choose] which system of beliefs we are operating from
---
### Limitations
This logic also applies to this argument itself.
---
### Appendix: Infinities
- how many integers?
- how many numbers between 0 and 1?
---
### .center[Questions]
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