Lecture 9: Demonstration



Supplementary Text


I.    Introduction: we need tool which gives absolute certainty, demonstration.

II.    Problem of learning.
    A. Problem of learning mentioned.
    B. Problem of learning explained.
    C. Syllogism solves the problem.
        1. Transition to demonstration: the tool that solves the problem.

III.    Demonstration.
    A. Definition of demonstration.
        1. First statement of the definition.
            a. Aristotle's precise meaning: cause and necessary.
                (1)    Example: triangles have 180 degrees is necessary.
        2. Definition of demonstration through matter.
            a. Premisses must be true.
            b. Premisses are first and immediate.
                (1)    Recall what prior in order of knowledge is.
            c. Premisses are prior in order of knowledge to the conclusion.
            d. Premisses state cause of fact which conclusion states.
    B. Demonstration propter quid and quia.
        1. Problem for demonstration.
            a. Recall difference in order of knowledge and being: God. 
            b. Difference in order causes problem for demonstration.
        2. Solution to problem.
            a. Distinction of knowledge of fact and of reasoned fact.
            b. Demonstration propter quid and quia.

IV.    Problem of learning and first principles.
    A. Sensation is pre-existing knowledge for first principles.
    B. Aristotle's comparison: rout in battle.
        1. Application to learning first principles from sensation.
    C. Example in medicine: the herb that cures fever.

V.    Conclusion: need logic of discovery for finding demonstrations and first principles.


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