Lecture Notes
- counting is to create a group or category
- one thing, more than one thing, many things - all you need
- small numbers are functionally different from large numbers
- plurality = more than one
- 0-1 is very different from 6000-6001 - number is not solid
- 0-1 you have doubled it
- predicate = result of the operation
- you cannot analyse 0 or 1 - not complex enough
- language is a system - vocab of fixed symbols, a syntax and a grammar
- Analytic philosophy - breaking down to find logical basis - logical atoms
- Russell = logical atomist
- fuzzy logic = neat logic
- hieroglyphics - first example of symbolism and recording information - writing things down
- zero is not an actual number - the idea of "nothing" is impossible
- first manipulative number was 2
- Greeks believed the number 3 was a magic number - worshiped it
- Numerology
- zero = nothing = something
- therefore zero must be something
- something cannot be here and not here at the same time
- zero is not nothing, but it is a natural number meaning for example there are no people in the room
- 0+1=1
BUT 0*1=0
- Russell wrote
Principia Mathematica - trying to replace numbers with logic
- no number in his system can be understood except with reference to another number
- Peano - first before Russell to define numbers as logical - problem of infinity
- Tool Russell uses - a class or a category
-
The class of classes similar to a given class.