Deduction and induction: the difference(演绎与归纳:差异)-金字塔原理
2024-11-25
Deduction and induction: the difference
As we have demonstrated, clear writing results from a clear exposition of the exact relationships between a group of ideas on the same subject. Properly organized, these ideas will always form a pyramid, with the various levels of abstraction sorted out and related under a single thought.
Ideas in the pyramid relate in three ways — up, down, and sideways. An idea above a grouping summarizes the ideas below, while these ideas in turn explain or defend the point above. At the same time, the ideas in the grouping march sideways in logical order. What constitutes logical order differs depending on whether the pyramided group was formed deductively or inductively.
These two forms of reasoning are the only patterns available for establishing logical relationships between ideas. Consequently, an understanding of how they differ and what their rules are is essential to being able to sort out your thinking and express it clearly in writing.
Briefly, the difference is as shown in Exhibit 17. Deduction presents a line of reasoning that leads to a “therefore” conclusion, and the point above is a summary of that line of reasoning, resting heavily on the final point. Induction defines a group of facts or ideas to be the same kind of thing, and then makes a statement (or inference) about that sameness. The deductive points derive from each other; the inductive points do not. These differences are really quite enormous, as the next two sections will demonstrate. Once you have digested them, you should have little difficulty in recognizing or sorting out either form of reasoning, or in choosing the one that appropriately permits you to say clearly what you mean.
翻译(交叉格式)
演绎与归纳:差异
Deduction and induction: the difference
正如我们所展示的,清晰的写作来自于清楚阐述一组围绕同一主题的思想之间的准确关系。
As we have demonstrated, clear writing results from a clear exposition of the exact relationships between a group of ideas on the same subject.
如果组织得当,这些思想总是会形成一个金字塔结构,其中不同抽象层级的思想归类并统一在一个主旨之下。
Properly organized, these ideas will always form a pyramid, with the various levels of abstraction sorted out and related under a single thought.
金字塔中的思想通过三种方式相互关联——向上、向下以及横向。
Ideas in the pyramid relate in three ways — up, down, and sideways.
一个位于上方的思想总结了其下的思想,而这些下层思想反过来又解释或支持上方的观点。
An idea above a grouping summarizes the ideas below, while these ideas in turn explain or defend the point above.
同时,分组中的思想在逻辑顺序上横向排列。
At the same time, the ideas in the grouping march sideways in logical order.
逻辑顺序的定义因金字塔式思想分组是通过演绎还是归纳形成的而有所不同。
What constitutes logical order differs depending on whether the pyramided group was formed deductively or inductively.
这两种推理方式是建立思想之间逻辑关系的唯一模式。
These two forms of reasoning are the only patterns available for establishing logical relationships between ideas.
因此,了解它们之间的差异及其规则对整理你的思路并清晰表达你的想法至关重要。
Consequently, an understanding of how they differ and what their rules are is essential to being able to sort out your thinking and express it clearly in writing.
简而言之,如图表17所示,演绎推理呈现的是一条通向“因此”结论的推理链条,位于上方的观点总结了这一推理链条,并在很大程度上依赖于最终结论。
Briefly, the difference is as shown in Exhibit 17. Deduction presents a line of reasoning that leads to a “therefore” conclusion, and the point above is a summary of that line of reasoning, resting heavily on the final point.
归纳推理定义了一组事实或观点为同类事物,然后就这种同质性提出声明(或推论)。
Induction defines a group of facts or ideas to be the same kind of thing, and then makes a statement (or inference) about that sameness.
演绎推理中的观点相互衍生,而归纳推理中的观点则没有这种关系。
The deductive points derive from each other; the inductive points do not.
这些差异是非常显著的,接下来的两节将详细说明。
These differences are really quite enormous, as the next two sections will demonstrate.
一旦你消化了这些内容,你就很容易识别或区分这两种推理形式,并选择适合清晰表达你的意思的一种方式。
Once you have digested them, you should have little difficulty in recognizing or sorting out either form of reasoning, or in choosing the one that appropriately permits you to say clearly what you mean.
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