Math

Question 1

Analytic proposition

Answer 1

statement that is true by defnition

ie transitive property

Question 2

A posteriori

Answer 2

a proposition cannot be known to be true independent of experience

Question 3

A priori

Answer 3

if a proposition can be known true independently of experience

Question 4

Axioms

Answer 4

starting points or basic assumptions in a formal system

4 requirements: consistent, independent, simple, fruitful

Question 5

conjecture

Answer 5

a hypothesis that seems to work, but has not been show to be necessarily true (inductively reasoned)

Question 6

Deduction

Answer 6

reasoning from general to particular, often using syllogims

Question 7

empiricism

Answer 7

school of thought in which knowledge begins with experience

Question 8

euclidean geometry

Answer 8

elucid: first person to organize geometry into a rigorous body of knowledge and his ideas have hand an enduring influence on civilization

Question 9

formal system

Answer 9

model of reasoning developed by elucid; 3 elements: axioms, deductive reasoning, derive theorems

Question 10

formalism

Answer 10

Math is invented and exists only in our mind, so mathematical truths are true by definition.

Question 11

godel’s incompleteness theorem

Answer 11

it is impossible to prove that a formal mathematical system is free from contradiction

Question 12

goldbaach’s conjecture

Answer 12

mathematical conjecture according to which every even number is the sum of two primes

Question 13

idealization

Answer 13

ideal values that are not attainable because everuthing is created or measured with uncertainty

Question 14

platonism

Answer 14

school of thouht; argument for the superior reality of mathematical over physical objects; math is more cerptain than perception and is timelessly true

Question 15

synthetic proposition

Answer 15

any proposition that is not analytic

Question 16

theorem

Answer 16

conclusions from a formal system

Question 17

empirical proposition

Answer 17

statement whose truth or falsity can be determined by appeal to evidence based on perception

Question 18

value judgement

Answer 18

statement which contains a value word, such as “good” or “bad”
-generally appeal to a standard, and is difficult to establish truth or falsity

Question 19

Metaphysical proposition

Answer 19

statement that is neither analytic, empirical, nor a value judgement
about the nature of all/ultimate reality

Question 20

nominal fallacy

Answer 20

assuming that we have explained something simply becasue we have put a name on it

Question 21

paradigm

Answer 21

set of interrelated ideas for making sense of one or more aspects of reality

Question 22

master paradigms

Answer 22

group of paradigms that can be found in various subject areas

1. deductive system- logic and math
2. scientific theory- natural and human sciences
3. narrative- history and literature
4. style-arts

Question 23

knowledge filters

Answer 23

paradigms have the ability to trap us into a particular way of looking at things and close our minds to other possibilities