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)



Demonstrative Premises

immediate: no middles
better known (to us/by nature)
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