THEORY OF KNOWLEDGE MATHEMATICS FINAL
EXAM SOLVED #13
Definition of Math - Hempel - correct answer Axiomatized - made up of axioms that are
made from primitive terms
Deductive - a process in math is to deduce all conclusions (ultimately from the axioms)
System - self contained as axioms serve as boundaries
Definition of Math - Halmos - correct answer Logical dovetailing of a carefully selected
sparse set of assumptions with its surprising conclusions via a conceptually elegant
proof (same explanation as the other one except this emphasizes that what
mathematicians care about is surprising/elegant they don't just study anything)
Conjecture - correct answer conclusion in math that is believed to be true but not yet
proven
Theorem - correct answer a conclusion in math that is believed to be true and has been
proven
Primitive - correct answer terms that are not defined that can combine to make a set of
axioms
A priori - correct answer knowledge prior to or independent of evidence (logically
known)
A posteriori - correct answer knowledge after or dependent on evidence (scientifically
known)
Postulate/axiom - correct answer a set of assumptions that are self-evident and
combine to create a system of math
Theoretically new - correct answer a new creation and you can just make up whatever
you want in math for example
Psychologically new - correct answer it already existed but only now are we aware it
exists
Pure math - correct answer -abstract and does not exist in reality (applied)
-exists when the primitives have no real-world definition
-ALL CONCLUSIONS ARE CERTAIN
(Mathology - the study fo pure math and mathematicians are interested in ideas of
math)
Physical math - correct answer -applied to the real world
-primitive terms are given physical definitions
EXAM SOLVED #13
Definition of Math - Hempel - correct answer Axiomatized - made up of axioms that are
made from primitive terms
Deductive - a process in math is to deduce all conclusions (ultimately from the axioms)
System - self contained as axioms serve as boundaries
Definition of Math - Halmos - correct answer Logical dovetailing of a carefully selected
sparse set of assumptions with its surprising conclusions via a conceptually elegant
proof (same explanation as the other one except this emphasizes that what
mathematicians care about is surprising/elegant they don't just study anything)
Conjecture - correct answer conclusion in math that is believed to be true but not yet
proven
Theorem - correct answer a conclusion in math that is believed to be true and has been
proven
Primitive - correct answer terms that are not defined that can combine to make a set of
axioms
A priori - correct answer knowledge prior to or independent of evidence (logically
known)
A posteriori - correct answer knowledge after or dependent on evidence (scientifically
known)
Postulate/axiom - correct answer a set of assumptions that are self-evident and
combine to create a system of math
Theoretically new - correct answer a new creation and you can just make up whatever
you want in math for example
Psychologically new - correct answer it already existed but only now are we aware it
exists
Pure math - correct answer -abstract and does not exist in reality (applied)
-exists when the primitives have no real-world definition
-ALL CONCLUSIONS ARE CERTAIN
(Mathology - the study fo pure math and mathematicians are interested in ideas of
math)
Physical math - correct answer -applied to the real world
-primitive terms are given physical definitions
