皮尔士存在图。
Let us briefly look at the graphs to get a better idea of what Peirce’s graphical logic looks like. The first element is the paper on which the graphs are drawn. Peirce calls this the sheet of assertion. An assertion is made whenever someone claims something is true. Consequently, any assertion written on the sheet of assertion is claimed to be true. For convenience we abbreviate assertions with capital letters. Since all assertions on the sheet of assertion are claimed to be true, we can only deny an assertion by removing it from the sheet of assertion. This we do by quite literally cutting it out, a process that can be visualized by drawing a closed line around the letter. If we adhere to material implication—where “if P then Q” is taken to be logically equivalent with “not (P and not-Q)”—all common logical operators can be easily expressed in graphs (Figure 4.6). This allows us to build a functionally complete propositional logic in any medium that is sufficiently static (paper, computer, imagination) using only variables and cuts.
让我们简要地看看这些图表,以便更好地了解皮尔士的图表逻辑是什么样的。第一个元素是绘图用的纸。皮尔士称之为断言纸。每当有人声称某事是真实的,就产生了一个断言。因此,断言纸上的任何断言都被认为是真实的。为了方便起见,我们用大写字母来表示断言。由于断言纸上的所有断言都被认为是真实的,我们只能通过把它从断言纸上剪下来来否认一个断言。我们通过在字母周围画一条封闭的线来形象地表示这个过程。如果我们坚持实质蕴涵,即“如果P则Q”在逻辑上等价于“非(P和非Q)”,那么所有常见的逻辑运算符都可以很容易地用图表表示(图4.6)。这使我们能够在任何足够静态的介质(纸、计算机、想象)上,使用变量和剪切,构建一个功能完备的命题逻辑。
FIGURE 4.6 Existential Graphs. The left figure represents material implication; the right figure disjunction. Both combined represent (P→Q) & (P v Q).
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