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1.44 MB
Extraction Summary
5
People
1
Organizations
0
Locations
0
Events
1
Relationships
3
Quotes
Document Information
Type:
Book page / evidentiary document
File Size:
1.44 MB
Summary
This document is page 206 from a book or paper titled 'Are the Androids Dreaming Yet?'. The text discusses the philosophy of mind, specifically the arguments of Lucas and Penrose regarding Gödel's incompleteness theorems and whether human thought is limited by formal systems like machines are. It features a photograph of Albert Einstein and Kurt Gödel walking together, captioned 'Two Giants'. The document bears a Bates stamp 'HOUSE_OVERSIGHT_015896', indicating it was part of a production to the US House Oversight Committee, likely related to investigations into Jeffrey Epstein's connections with the scientific community.
People (5)
| Name | Role | Context |
|---|---|---|
| Lucas | Philosopher/Mathematician |
Cited in the text regarding arguments about formal systems and human minds (likely John Lucas).
|
| Penrose | Physicist/Mathematician |
Cited in the text regarding arguments about formal systems and human minds (likely Roger Penrose).
|
| Peano | Mathematician |
Mentioned in the context of Peano arithmetic and mathematical discovery.
|
| Gödel | Logician/Mathematician |
Kurt Gödel. Mentioned in text regarding his theorems; appears in the photograph on the right.
|
| Albert Einstein | Physicist |
Appears in the photograph on the left (not named in text, but visually identifiable as one of the 'Two Giants').
|
Organizations (1)
| Name | Type | Context |
|---|---|---|
| House Oversight Committee |
Implied by the Bates stamp 'HOUSE_OVERSIGHT_015896'.
|
Relationships (1)
Pictured walking together in the photograph captioned 'Two Giants'.
Key Quotes (3)
"If humans used a formal system to think, they would be limited by the incompleteness theorem and unable to discover new theorems that required them to extend the formal rules."Source
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Quote #1
"Why should we assume human minds are constrained in the same way as the mathematical systems they discover?"Source
HOUSE_OVERSIGHT_015896.jpg
Quote #2
"The critics of Lucas and Penrose have one big problem to deal with."Source
HOUSE_OVERSIGHT_015896.jpg
Quote #3
Full Extracted Text
Complete text extracted from the document (1,633 characters)
206
Are the Androids Dreaming Yet?
Are the Androids Dreaming Yet?
If humans used a formal system to think, they would be limited by the incompleteness theorem and unable to discover new theorems that required them to extend the formal rules. Humans do not appear to have such a limitation and regularly extend their appreciation of mathematics by expanding the rules, and seeing through the truth.
Many scientists dislike this argument and think it farfetched, saying there is no evidence to show people see past the limitation. Our brains could be following a formal system capable of discovering everything we have discovered to date or, indeed, might encounter in the future. Why should we assume human minds are constrained in the same way as the mathematical systems they discover? There is no evidence to suggest a human thinking about Peano arithmetic is running a Peano based model in their head. When Peano discovered his theorem he was certainly extending our mathematical knowledge, but this does not imply he was extending the capability of his brain.
The critics of Lucas and Penrose have one big problem to deal with. The formal system in our head would need to be able to see the truth in everything we could ever encounter. But, our formal system appears to be small. As infants, it is almost nonexistent. Where does this enormous system come from? It can’t come from our parents because they have the same problem; they were once children. You might argue that the capability of the human brain is huge and we can learn from all the other humans on earth, but let me remind you what Gödel said. However large
Two Giants
HOUSE_OVERSIGHT_015896
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