The Research Methods Knowledge Base: Deductive and Inductive Reasoning
"In logic, we often refer to the two broad methods of reasoning as the deductive and inductive approaches.
Deductive reasoning works from the more general to the more specific. Sometimes this is informally called a 'top-down' approach. We might begin with thinking up a theory about our topic of interest. We then narrow that down into more specific hypotheses that we can test. We narrow down even further when we collect observations to address the hypotheses. This ultimately leads us to be able to test the hypotheses with specific data -- a confirmation (or not) of our original theories.
Inductive reasoning works the other way, moving from specific observations to broader generalizations and theories. Informally, we sometimes call this a 'bottom up' approach ... In inductive reasoning, we begin with specific observations and measures, begin to detect patterns and regularities, formulate some tentative hypotheses that we can explore, and finally end up developing some general conclusions or theories.
These two methods of reasoning have a very different 'feel' to them when you're conducting research. Inductive reasoning, by its very nature, is more open-ended and exploratory, especially at the beginning. Deductive reasoning is more narrow in nature and is concerned with testing or confirming hypotheses. Even though a particular study may look like it's purely deductive (e.g., an experiment designed to test the hypothesized effects of some treatment on some outcome), most social research involves both inductive and deductive reasoning processes at some time in the project. In fact, it doesn't take a rocket scientist to see that we could assemble the two graphs above into a single circular one that continually cycles from theories down to observations and back up again to theories. Even in the most constrained experiment, the researchers may observe patterns in the data that lead them to develop new theories."
(William M.K. Trochim)
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Simon PerkinsSHARE
Kantian Euclidean Space and Husserlian Material Ontologies
"When considering the relevance of Kant's transcendental position on Euclidean space, one widespread complaint goes something like this: In what concerns the transcendental validity of mathematics in experience, Kant failed to distinguish between pure and applied geometry the way we do today. Pure geometry, as Hilbert showed, is a mere mathematical multiplicity, an axiomatic system interwoven by means of formal relationships where a priori intuition plays no role at all. Its claims have no empirical content whatsoever. Applied geometry, on the other hand, as exemplified by the use of non-Euclidean geometries by Einstein, has to do with the application of a formal geometrical structure as a means of depicting the empirical world. This application is done under certain theoretical assumptions and the postulation of an empirical spatial congruence. Once the coordination of the geometrical structure with the empirical phenomena is established, it can be empirically tested. There is no place for the idea that Euclidean geometry is a priori and synthetic, a transcendental constitutive of experience. Euclidean geometry is just a possible 'mathematical multiplicity', a formal structure whose correspondence with the physical world is not imposed. Thus, the transcendental a priori validity of geometry for all possible experience as implicitly ascertained in the mathematical principles of the pure understanding appears to have been refuted."
(José Ruiz Fernández, 2003)
Essays in Celebration of the Founding of the Organization of Phenomenological Organizations. Ed. CHEUNG, Chan-Fai, Ivan Chvatik, Ion Copoeru, Lester Embree, Julia Iribarne, & Hans Rainer Sepp. Web- Published at www.o-p-o.net, 2003
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Simon PerkinsSHARE
