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
circular reasoning: bad
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