Analysis and Science in Aristotle
Presents a new interpretation of Aristotle's Analytics (the Prior and Posterior Analytics) as a unified whole, and argues that to "loose up"or solve -- rather than to reduce or break up -- is the principle meaning which best characterizes the Analytics.
Offering a new interpretation of Aristotle's Analytics (the Prior and Posterior Analytics) as a unified whole, Patrick H. Byrne argues that a non-deductive form of ancient mathematical analysis influenced Aristotle's thinking. Reading the Analytics with this perspective in mind sheds new light on Aristotle's theories of the syllogism, demonstration, and the principles of science.
The book begins with a brief survey of ancient geometrical analysis and an investigation of Aristotle's uses of the Greek term, analuein. Byrne argues that "to loose up" or solve -- rather than to reduce or break up -- is the principal meaning which best characterizes Aristotle's Analytics. Extending this line of reasoning, he argues that for Aristotle scientific analysis commonly begins with knowledge of a "mere fact" (a conclusion) and seeks a rigorous demonstration which expresses knowledge of the "reasoned fact". Moreover, genuine analysis of a fact into a reasoned fact cannot be accomplished unless the premises of demonstrations are themselves reasoned facts. Hence the processes which yield the immediate principles (especially definitions) are next investigated through detailed examinations of key examples which Aristotle provides.
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The Several Senses of Analysis in Aristotle
B Analysis in Plato?
C Simple References to the Analytics
F Analysis and the Formula
G Analysis of Geometrical Figures
H Analysis of Sorites
B Prior Knowledge
B1 The Angle in a Semicircle
B2 Corresponding Diminution Antanairesin
C Hitting on the Middle
D Thickening the Middle
Hunting for Principles
B Immediate Premises and Defining
I To Reduce or to Elevate Anagein?
Analysis of the Problem of Constructing a Square Equal to a Given Rectangle
Analysis of Syllogisms Foundations
A Analysis and the Definition of Syllogism
B Meaning Belonging and Being
C The SoCalled Immediate Inferences
D Figures and Moods
E Complete Syllogisms and NonSyllogisms in the First Figure
F Completing Potential Syllogisms
G Modal Syllogisms
Analysis of Problematic Syllogisms
Finding Intermediate Terms
Finding Obscured Premises
D Book II and Arguments Per Impossibile
Logic Dialectic and Analysis in the Posterior Analytics 11922
Analysis and Episteme
A Aristotles Clarification of the Word Episteme
B Clarification Through Epistemic Questions
C Analysis and Scientific Demonstration
D The Criteria for Demonstrative Premises
Finding the Middle
C The Two Senses of Whatitis
D Defining and the Preconceptual Grasp of Whatitis
E Whatitis Images and the Qua Locution
F The Genus for Which There Is No Name
G How Many Principles?
H Hunting for Whatitis
Can to ti esti Be Demonstrated?
The Principle of Science Is Nous
A Understanding as Movement
B The Movers and the Perfections of Intellect
C Is There Episteme of Immediate Principles? The Problem of 1119
D Aristotles Several Senses of Episteme and Nous
E Habits of the Mind
F Nous as the Principle of Science
A The Analytic Character if the NonDemonstrative Sciences
B The Four Causes and the Analysis of Nature
C Analysis and the Soul
D Science and Necessity
E The Sophistic Aberration of Thought and the Control of Meaning