Aristotle's work on scientific method have been assembled into a body of texts known as the Organon, which is composed of six different writings. I will concentrate here on some of the most important ideas in the Analytica Priora and Analytica Posteriora, where Aristotle discusses deduction and induction respectively.
In his Analytica Priora, Aristotle develops from the ground up a system of logic which remained unsurpassed until the late 19th century. The idea was to examine two statements, called major and minor premise, and then to determine whether or not a third, the conclusion, actually follows from these two premises. When the conclusion is a valid logical consequence of the major and minor premise, Aristotle calls this logical structure a syllogism. Syllogism in this sense is entirely Aristotle's invention.
For drawing logical conclusions, Aristotle looks at premises and conclusions with the general form "A is true of B," but including certain modifiers, such as "A is true of all B," "A is true of some B," "A must be true of B," or "A might be true of B." We thus get such syllogisms as this:
A is true of all B B is true of all C A is true of all C
This syllogism is valid, but the order of the terms
makes it somewhat confusing. While I stated above that Aristotle's system of logic "remained unsurpassed" until the
late 19th century,
some genuine improvements were made by Aristotle's successors, and one of these was to improve
upon Aristotle's notation. The canonical medieval representation of the same syllogism is:
All B are A All C are B All C are A
Represented in this way, the validity of the syllogism is obvious. I won't go through Aristotle's entire calculus, but will let it suffice to give two additional examples, one showing another valid conclusion and the other a fallacy. First a valid syllogism (also returning Aristotle's representation of the sentence structure):
A is true of no B B is true of all C A is true of no C
What I hope has become clear is that using the modifiers "all," "some," or "no" prior to the first term of the sentence, we get quite a variety of distinct major and minor premises, some of which will be valid conclusions and others not. The following is an example of a fallacy and hence is not a syllogism:
A is true of some B B is true of some C A is true of some C
There are certainly many facets of both syllogisms and fallacies that I haven't touched on, but my intention is simply to give a basic idea of how this logical calculus works. Given two premises of the requisite types, Aristotle's analysis enables us to distinguish between one group of valid conclusions and another group of fallacious claims that do not follow from the given premises. Aristotle attempts to apply this model in both scientific and argumentative contexts. Here, I will touch only upon how he applies it in the sciences.
We now know how to derive true conclusions from true premises but are left with the question of how to find true premises as the foundational principles of a given science. In his Posterior Analytics, Aristotle addresses this question.
He recognizes that an infinite regress of premises can never provide an adequate foundation for a scientific body of knowledge. Nor, Aristotle argues, can we come to recognize first principles through remembering knowledge already present in our minds. Instead, we must acquire our foundational premises through experiences derived from perceptions and memories of perceptions. Our faculties eventually allow us to comprehend the first principles after we have repeatedly assembled various perceptions into memories and then, processing these memories, appropriately adjust the way in which we define our concepts.
In the subsequent history of science, this methodology worked particularly well for developing a taxonomical framework in biology. But Aristotle's focus essentially on the progressive refinement of a science's basic concepts at some point becomes a limitation in physics and chemistry. In the Renaissance, these sciences began a period of rapid development when their methodologies broke out of the Aristotelian framework and became more oriented toward the quantitative verification of hypotheses and the specification of physical laws. Neither quantitative methods nor the notion of a physical law not derived from definitions fit well into Aristotle's proposed method for deriving first principles in the empirical sciences. While noting the eventual limitations of the methodology Aristotle proposes, we must at the same time give due recognition to the fact that his was the first methodology in the Western World allowing us to ascribe unqualified validity to the empirical sciences.