This rule was well known to the Stoics , but they expressed it this way: " If , if the first then the second and if the second then the third, then, if the first then the third. We begin with the simplest part of propositional logic: combining simple propositions into compound propositions and determining the truth value of the resulting compounds. Propositions or statements can be thought of as the "atoms" of propositional logic. Simple propositions are statements which cannot be broken down without a loss in meaning.
Note the change in meaning with "John is a brother" and "Charles is a brother. Conventionally, capital letters usually towards the beginning of the alphabet may be used as abbreviations for specific propositions. The logical operator "and," as we will see, will be symbolized as " ".
With precise sentences it is much clearer whether the conclusion does or doesn't follow from the premises. If the conclusion doesn't follow, then it will be clearer just what else must be assumed to make the conclusion follow.
Then the philosophers can concentrate on discussing whether these additional assumptions are acceptable. Therefore, the use of symbolic logic can help and has helped direct the philosophers' discussions toward the crucial points in their disputes. Some philosophers believe that symbolic logic can reveal the structure of all possible good inference, and so reveal the common skeletal structure that underlies all reasonable thought processes.
Bertrand Russell, Ludwig Wittgenstein, and other 20th century philosophers have argued that there is an intimate connection among these three things: logic, our mind, and the deep structure of the physical world. This issue is discussed in Phil. The symbolic analysis of our natural language can reveal exciting new information about the character of language itself.
For example, can all the grammatical sentences of English, but none of the ungrammatical ones, be generated mechanically by using a small number of symbolic rules? Can all the meaningful sentences of English, but none of the nonsensical ones, be generated mechanically by using a small number of symbolic rules?
The attempt to answer these questions is an active area of contemporary philosophical research begun by Noam Chomsky at M. This topic is taken up in Phil.
Logic also impacts philosophy in other ways. Consider this seemingly good inference that has, unfortunately, an unacceptable conclusion. This paradox about substitution is an unsolved problem in philosophy. Finally, symbolic logic is a very useful tool for clarifying the philosophically important concepts of meaning, truth, and proof.
If our car won't start, we reason that the battery may be dead—so we test the battery. If the battery isn't dead, then we deduce the problem must lie elsewhere, perhaps with the starter motor—so we check the starter motor, and so on. The reasoning here is simple, but sometimes chains of reasoning can become quite complex.
Training ourselves to construct effective arguments and to spot weak ones is a skill that is useful in just about every field of endeavor, as well as in everyday life.
It helps steer us in the direction of truth and away from falsehood. The art of persuasion is called rhetoric. Rhetoric, like logic, used to be an essential part of the liberal arts curriculum. Sadly, neither is generally required any longer, and rhetoric has given way to Composition Rhetoric can encompass just about any means of persuasion—short of bribery, blackmail, or physical violence.
It includes, for instance, appeals to emotion, provocative images, or clever wordplay. There's no doubt that all of these can be persuasive; however, so can cogent reasoning. We're not saying that a good argument will always win the day over clever rhetoric. After all, human beings are not Vulcans like Mr. In the long run, though, good arguments usually come out on top.
Logic is foundational to any field that makes use of arguments. It has especially close connections to mathematics, computer science, and philosophy. Both Aristotelian logic and modern symbolic logic are impressive bodies of knowledge that constitute major intellectual achievements.
Fallacious thinking—in the form of propaganda, exaggeration, misdirection, and even outright lies—abounds in our culture.
Politicians, pundits, advertisers, and corporate spokespersons attack straw men, appeal to the majority opinion, promote red herrings, or oppose a view simply because they dislike the person who holds it. Familiarity with common fallacies of this sort helps make you a more critical reader, listener, and thinker. Dubious techniques of persuasion, such as "criticizing" a candidate's views by showing an unflattering image of them, once used most often during election campaigns have become the norm of news and social media.
These tactics are no doubt sometimes effective, however, that's no reason for preferring them to a sound clear argument. On the contrary, this trend toward believing everything you hear is why the need for logical thinking is more crucial than ever.
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