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Ideas for 'Mahaprajnaparamitashastra', 'Intro to Gdel's Theorems' and 'Moral Dilemmas Revisited'

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7 ideas

5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic

10076	The 'range' of a function is the set of elements in the output set created by the function [Smith,P]
	Full Idea: The 'range' of a function is the set of elements in the output set that are values of the function for elements in the original set.
	From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1)
	A reaction: In other words, the range is the set of values that were created by the function.

10605	Two functions are the same if they have the same extension [Smith,P]
	Full Idea: We count two functions as being the same if they have the same extension, i.e. if they pair up arguments with values in the same way.
	From: Peter Smith (Intro to Gödel's Theorems [2007], 11.3)
	A reaction: So there's only one way to skin a cat in mathematical logic.

10075	A 'partial function' maps only some elements to another set [Smith,P]
	Full Idea: A 'partial function' is one which maps only some elements of a domain to elements in another set. For example, the reciprocal function 1/x is not defined for x=0.
	From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1 n1)

10074	A 'total function' maps every element to one element in another set [Smith,P]
	Full Idea: A 'total function' is one which maps every element of a domain to exactly one corresponding value in another set.
	From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1)

10612	An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P]
	Full Idea: If a function f maps the argument a back to a itself, so that f(a) = a, then a is said to be a 'fixed point' for f.
	From: Peter Smith (Intro to Gödel's Theorems [2007], 20.5)

5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic

10615	The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P]
	Full Idea: The so-called Comprehension Schema ∃X∀x(Xx ↔ φ(x)) says that there is a property which is had by just those things which satisfy the condition φ.
	From: Peter Smith (Intro to Gödel's Theorems [2007], 22.3)

5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic

10595	A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P]
	Full Idea: 'Theorem': given a derivation of the sentence φ from the axioms of the theory T using the background logical proof system, we will say that φ is a 'theorem' of the theory. Standard abbreviation is T |- φ.
	From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4)