FREGE AND RUSSELL.
'Natural Numbers' - Words used to count. Created from Abstract Categories or Groups. "Plural" - Combination of Numbers/Words - Small Numbers different function to Large Numbers (logically reach up to 6/7 before start to count).
-(8545)- Basic Symbols Organised According to Syntax (inferred system of rules). Can be Analysed Through Division, etc. Addition and Multiplication as "Plurals of Plurals". Technology as innate part of Neurological Syntax. [CHOMSKY] A Basic Logical Language containing Limited Human Intelligence (predictive text, etc).
Three attitudes towards numbers:
1) They are natural and empirical/observed. [RUSSELL]
2) They are intuitive [PYTHAGORAS/PLATO] - Numbers are from a different world. "Supernatural".
3) They are abstract objects [FREGE] that modify meaning. Not something we learn so must be innate [CHOMSKY]
Apes able to distinguish Simple Plurality. 0 (the absence of a thing/"one thing"), 1 (one/enough/"more than one thing") and 2 (a lot/unlimited/more than one/"many things") - All are strong natural numbers.
Showing posts with label Ludwig Wittgenstein. Show all posts
Showing posts with label Ludwig Wittgenstein. Show all posts
Saturday, 16 February 2013
Monday, 19 November 2012
L2: "Empiricism vs. Idealism"
KARL POPPER (1902-1994)
"Logical Positivism" The Vienna Circle (FREUD, WITTGENSTEIN). Attack on Empiricism. Metaphysics as "gibberish" consisting of theories that have not been verified. Rejection of DESCARTES, his Cogito branded a "non-verifiable induction". Something that cannot be proved through aposteriori reasoning.
POPPER was against the scientific process of induction. Like HUME, he saw the process of induction as "unreliable" but necessary in the quest for truth.
"Hume has proved that pure Empiricism is not a basis for science... without the principle of induction, then science is impossible" (page 612)
In "The Open Society and it's Enemies" POPPER explains how the state should leave maximum room for self-correction in order to minimise suffering. Each law should be highly experimental. There is no 100% knowledge, therefore everything is untrue/falsifiable. Otherwise known as "The Theory of Falsification".
"Logical Positivism" The Vienna Circle (FREUD, WITTGENSTEIN). Attack on Empiricism. Metaphysics as "gibberish" consisting of theories that have not been verified. Rejection of DESCARTES, his Cogito branded a "non-verifiable induction". Something that cannot be proved through aposteriori reasoning.
POPPER was against the scientific process of induction. Like HUME, he saw the process of induction as "unreliable" but necessary in the quest for truth.
"Hume has proved that pure Empiricism is not a basis for science... without the principle of induction, then science is impossible" (page 612)
In "The Open Society and it's Enemies" POPPER explains how the state should leave maximum room for self-correction in order to minimise suffering. Each law should be highly experimental. There is no 100% knowledge, therefore everything is untrue/falsifiable. Otherwise known as "The Theory of Falsification".
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