Lecture 3.3  Demonstration

For Thursday: 300 word synopsis (provide word count) for Posterior Analytics ii.19

true and necessary reasoning
model is mathematics
Plato and mathematics

knowledge comes from knowledge
explanations have to come to an end somewhere
two kinds of knowledge: demonstration, intuition

syllogism and demonstration

three kinds of principles
axioms (Euclid: common notions):
theses:               definitions (Euclid: definitions)
hypotheses (Euclid: postulates; primitives of existence; or assumptions granted by student)

Three Things in a Demonstrative Science (i.7)

-subject
-attributes
-axioms

Demonstrative Premises

true
immediate: no middles
[primary]
better known (to us/by nature)
[prior]
causative: twinkling stars because they are near (fact and cause)

also            universal
necessary = per se (“virtue of itself,” essential, non-accidental attribute)
per se 1: animal is said per se of man
per se 2: male is said per se of animal
per se being: human is a per se being
per se cause: death is said per se of slaughter

also  commensurately universal
2R of triangle, not isosceles
animals – having sensation
mammals – having hair
primates – having hands
man – having reason
arithmetic and geometry
genus and metabasis
subordinate sciences: geometry, optic, iridology

Essence and Property

dark at full moon a earth interposed between moon and sun
earth interposed between moon and sun a eclipse
dark at full moon a eclipse

wings a fliers
fliers a birds
wings a birds

demonstration is of eternal, unchanging things, but

anginoia: ability to grasp the middle

Posterior Analytics II

Main Point  relationship of definition – cause – demonstration

a) chh. 1-3 hunt for the middle
b) chh 4-10 demonstration and definition
c) ch. 11 cause, definition and demonstration
d) ch. 12 demonstration and time
e) chh. 13-18: cause and effect
f) ch. 19: induction

A.                                                FACT                                    REASON
SIMPLE                        does it exist?         -->              what is it?

COMPOUND               is it A?                       -->         why is it A?

is there a middle?            what is the middle?

middle is the definition

B.  Can we demonstrate a definition?
a) not without circularity (begging the question)
b) division: renders definition, but is not demonstration

C. middle = definition = cause

dark at full moon a earth interposed between moon and sun
earth interposed between moon and sun a eclipse
dark at full moon a eclipsed moon

eclipsed moon: term
dark at full moon: nominal definition (or effect)
earth interposed between moon and sun: real definition (or cause)

three kinds of definition: real, nominal, combination

D. Causes as middles and definitions
a. definable form (formal cause, e.g., half of two rights)
b. antecedent necessitating a consequent (material cause?: e.g., half of two rights)
c. efficient cause (e.g., Athenians attacking Sardis)
d. final cause (e.g., walking, health, non-regurgitation?)
final and efficient: lanterns and thunder

E. Discovering definitions
a. by dichotomous division: completeness and order
b. multiple differentiae (e.g. triad: odd, prime (not a product), prime (not a sum))
c. collection: distinguishing kinds of pride; similarity in shape and color;
avoid metaphor
d. collect subjects with their properties
animal – sensation
lunged animals – terrestrial, four points of motion

F. a. single causes of multiple effects
e.g., repercussion is cause of reflection and echo
b. multiple causes of a single effect: yes, but in different subjects
i. alternating proportionals
ii. similarity in color and shape
iii. longevity caused by dryness and bilelessness
problems in Meteorologica