Math Flashcards

1
Q

Analytic proposition

A

statement that is true by defnition

ie transitive property

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2
Q

A posteriori

A

a proposition cannot be known to be true independent of experience

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3
Q

A priori

A

if a proposition can be known true independently of experience

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4
Q

Axioms

A

starting points or basic assumptions in a formal system

4 requirements: consistent, independent, simple, fruitful

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5
Q

conjecture

A

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

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6
Q

Deduction

A

reasoning from general to particular, often using syllogims

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7
Q

empiricism

A

school of thought in which knowledge begins with experience

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8
Q

euclidean geometry

A

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

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9
Q

formal system

A

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

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10
Q

formalism

A

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

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11
Q

godel’s incompleteness theorem

A

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

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12
Q

goldbaach’s conjecture

A

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

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13
Q

idealization

A

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

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14
Q

platonism

A

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

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15
Q

synthetic proposition

A

any proposition that is not analytic

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16
Q

theorem

A

conclusions from a formal system

17
Q

empirical proposition

A

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

18
Q

value judgement

A

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

19
Q

Metaphysical proposition

A

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

20
Q

nominal fallacy

A

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

21
Q

paradigm

A

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

22
Q

master paradigms

A

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
23
Q

knowledge filters

A

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