|
Page 2 of 5 In symbolic logic one uses letters and symbols to stand for sentences and the words that connect them. In the above example the "P" and the "Q" stand for any two different sentences, and the arrow stands for the connecting words, "if ..., then...." To read this premise (line 1) you would say, "If P, then Q." Another way of reading P º Q is to say, "P implies Q." To read the second premise (line 2) we just say, "P."The reason letters and symbols are used is because sentences that are very different grammatically may still have the same logical form. For example, the sentences "I’ll go if you go" and "If you go, then I’ll go," though different gram-matically, obviously have the same logical form. By using symbols and letters instead of the sentences themselves we can make the logical form of a sentence clear without being distracted by its grammatical form. As for the rule modus ponens, it tells us that from the two premises P º Q and P, we may validly conclude Q. This rule of inference is one that we use almost unconsciously all the time. A simple example of it can written out this way: If John studies hard, then he will get a good grade in logic. John studies hard. John will get a good grade in logic.
Although there are overlaps, this is not quite the same as Socratic, Aristotelian, or informal logic. This kind of logic assumes the existence of essences and our ability to know them. Modern symbolic logic often does not assume such a metaphysical realism (that essences are real). Rather, symbolic logic tends to assume that essences are only names or "human labels," no doubt because the basic units of symbolic logic are not terms but propositions. Then, as shown above, it relates these propositions in argumentative or syllogistic structures not unlike a computer does: if p, then q; p; therefore q. Today a more popular phrase for Socratic logic or Socratic thinking is "critical thinking." Unlike formal logic, Socratic logic or critical thinking is more practical for most people, although it should not be thought of as simply a watered-down version of formal logic. By this I mean that most people we talk with and engage in dialogue with (such as sharing Christ or talking about the existence of God) do not resort to presenting an argument in symbolic logic. Socratic logic is more practical in the sense that it focuses on understanding and interpreting ordinary language, and not only analyzing an argument, but also constructing an effective or sound argument and smoking out hidden assumptions. Our minds are indeed computers - our brains compute all the time and much faster than any computer. But our minds are also much more than simply a computer. We can also "see" or understand. One’s purpose in using Socratic logic is becase an argument or discussion should begin and end with understanding, with insight. I mentioned Peter Kreeft’s new text, Socratic Logic (St. Augustine’s Press, 2004). In it he introduces students to many classical quotations and great philosophical issues in the hope of preparing them for "reading Great Books [of the Western World] rather than Dick and Jane" literature. In other words, the student trained in logic should easily be able to "critically" read and evaluate any article or book, whether fiction or non-fiction, not to mention speeches, sermons, and even television sitcoms. In an age such as ours when there are so many messages being sent through so many different communication mediums there is great need for skills in logic. This is true both in the world and in the church. Sharon Schwarze and Harvey Lape have much the same purpose in their popular text on Socratic logic, now in its 2nd edition (2001): Thinking Socratically: Critical Thinking About Everyday Issues (Prentice Hall). Like Kreeft, Schwarze and Lape seek to teach critical thinking skills in the context of ordinary life issues. The situations they use range from the problem of evidence at a trial to the absence of an explana-tion of why two children died in the same daycare center on the same day.
|
