Theories as Vector Spaces of Valid Statements - Revision history

George Barouxis: 6 revisions imported

2021-10-29T20:24:54Z

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George Barouxis: 5 revisions imported

2015-10-11T21:23:45Z

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George Barouxis at 15:47, 11 November 2007

2007-11-11T15:47:10Z

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George Barouxis at 20:59, 14 January 2007

2007-01-14T20:59:46Z

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	Consider the set of all symbols used in a theory. Take the subset of well-formed combinations of these symbols, or theorems. Take a space whose points represent these ~~theorem~~, theorem space. Usually there is a category of symbols such as =, `=>` and `<=>` that act as "vectors", in the sense that they allow as to move from one point of the theorem space to another. Axioms act as starting points or points of entry to the theorem space. From these, we contruct more complex vectors (for instance, `(a+b)^2=a^2+b^2+2ab`), and so on). Using these, we expand the area of "true" theorems within the theorem space, that is, the theorems to which we can arrive to starting from the axiom entry points and using the vectors that the rules of the theory allow us.		Consider the set of all symbols used in a theory. Take the subset of well-formed combinations of these symbols, or theorems. Take a space whose points represent these theorems, the theorem space. Usually there is a category of symbols such as =, `=>` and `<=>` that act as "vectors", in the sense that they allow as to move from one point of the theorem space to another. Axioms act as starting points or points of entry to the theorem space. From these, we contruct more complex vectors (for instance, `(a+b)^2=a^2+b^2+2ab`), and so on). Using these, we expand the area of "true" theorems within the theorem space, that is, the theorems to which we can arrive to starting from the axiom entry points and using the vectors that the rules of the theory allow us.

George Barouxis at 20:47, 12 January 2007

2007-01-12T20:47:33Z

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George Barouxis: 1 revision(s)

2006-12-31T14:36:14Z

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George Barouxis at 15:54, 23 December 2006

2006-12-23T15:54:16Z

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Consider the set of all symbols used in a theory. Take the subset of well-formed combinations of these symbols, or theorems. Take a space whose points represent these theorem, theorem space. Usually there is a category of symbols such as =, `=>` and `<=>` that act as "vectors", in the sense that they allow as to move from one point of the theorem space to another. Axioms act as starting points or points of entry to the theorem space. From these, we contruct more complex vectors (for instance, `(a+b)^2=a^2+b^2+2ab`), and so on). Using these, we expand the area of "true" theorems within the theorem space, that is, the theorems to which we can arrive to starting from the axiom entry points and using the vectors that the rules of the theory allow us.

[[Category:Metatheoretical Considerations]]