1. Logical Reasoning
2. Induction and Deduction
Induction is the process of deriving universal rules from multiple individual things. For example: black horses and white horses can be induced into the category "horse." Deduction is the opposite of induction; it derives individual rules from universal rules. For example: "horse" can be deduced into black horse, white horse, and so on.
2. Analysis and Synthesis
Analysis is the breaking down of a thing into its various parts, aspects, and attributes, which are then studied separately. It is a necessary stage in understanding a thing as a whole. Synthesis is the organic unification of the various parts, aspects, and attributes of a thing into a whole according to their intrinsic connections, so as to grasp the essence and laws of the thing. Analysis and synthesis mutually permeate and transform into each other: synthesis is carried out on the basis of analysis, and analysis is conducted under the guidance of synthesis. Analysis and synthesis, cycling back and forth, drive the deepening and development of understanding.
For example, in the study of light, people analyzed the straight-line propagation, reflection, and refraction of light, and concluded that light consists of particles. People then analyzed and studied the phenomena of interference and diffraction of light, along with other phenomena that the corpuscular theory could not explain, and concluded that light is a wave. When people measured the wavelengths of various kinds of light and proposed the electromagnetic theory of light, it seemed that light was simply a wave, an electromagnetic wave. However, the discovery of the photoelectric effect could not be explained by the wave theory, and so the photon theory was proposed. When people synthesized these aspects, a new understanding emerged: light possesses wave-particle duality.
3. Abstraction and Generalization
Abstraction is the extraction of common, essential features from a multitude of things, while discarding their non-essential features. Specifically, scientific abstraction is the process by which people, on the basis of practice, work over abundant sensory materials through "discarding the dross and selecting the essential, eliminating the false and retaining the true, proceeding from one to the other, and going from the exterior to the interior," thereby forming thought forms such as concepts, judgments, and inferences to reflect the essence and laws of things.
Generalization is a thought process and method for forming concepts. That is, the essential attributes extracted in the mind from certain things that share some identical attributes are extended to all things possessing these attributes, thereby forming a universal concept about this class of things. Generalization is an important method of scientific discovery, because generalization is the ascent from understanding within a smaller scope to understanding within a larger scope; it is the extension of understanding from one domain to another domain.
4. Comparative thinking: by object, comparison is divided into comparison among things of the same kind and comparison among things of different kinds. By form, comparison is divided into comparison seeking similarities and comparison seeking differences—seeking differences amid similarities, and seeking similarities or commonalities amid differences.
5. Causal thinking: simply put, the logic of causality is: because of A, therefore B; or, if phenomenon A appears, phenomenon B will necessarily appear (a sufficient relationship). This is a relationship of causing and being caused, with cause A preceding and effect B following.
6. Sequential inference: sequential inference is reasoning step by step according to causal relationships, hierarchical relationships, and the like. When a certain cause produces a result, and that result in turn serves as a cause producing the next result, a causal chain is formed. The causal chain is a form of sequential-inference thinking, such as the twelve links of dependent origination.
7. Reverse thinking: reverse thinking is the opposite of causal thinking; it infers causes from results. For example, tracing the twelve links of dependent origination in reverse.
Reprinted from online sources
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