Math Flashcards
Analytic proposition
statement that is true by defnition
ie transitive property
A posteriori
a proposition cannot be known to be true independent of experience
A priori
if a proposition can be known true independently of experience
Axioms
starting points or basic assumptions in a formal system
4 requirements: consistent, independent, simple, fruitful
conjecture
a hypothesis that seems to work, but has not been show to be necessarily true (inductively reasoned)
Deduction
reasoning from general to particular, often using syllogims
empiricism
school of thought in which knowledge begins with experience
euclidean geometry
elucid: first person to organize geometry into a rigorous body of knowledge and his ideas have hand an enduring influence on civilization
formal system
model of reasoning developed by elucid; 3 elements: axioms, deductive reasoning, derive theorems
formalism
Math is invented and exists only in our mind, so mathematical truths are true by definition.
godel’s incompleteness theorem
it is impossible to prove that a formal mathematical system is free from contradiction
goldbaach’s conjecture
mathematical conjecture according to which every even number is the sum of two primes
idealization
ideal values that are not attainable because everuthing is created or measured with uncertainty
platonism
school of thouht; argument for the superior reality of mathematical over physical objects; math is more cerptain than perception and is timelessly true
synthetic proposition
any proposition that is not analytic
theorem
conclusions from a formal system
empirical proposition
statement whose truth or falsity can be determined by appeal to evidence based on perception
value judgement
statement which contains a value word, such as “good” or “bad”
-generally appeal to a standard, and is difficult to establish truth or falsity
Metaphysical proposition
statement that is neither analytic, empirical, nor a value judgement
about the nature of all/ultimate reality
nominal fallacy
assuming that we have explained something simply becasue we have put a name on it
paradigm
set of interrelated ideas for making sense of one or more aspects of reality
master paradigms
group of paradigms that can be found in various subject areas
- deductive system- logic and math
- scientific theory- natural and human sciences
- narrative- history and literature
- style-arts
knowledge filters
paradigms have the ability to trap us into a particular way of looking at things and close our minds to other possibilities
