Logic is the study of the rules which underlie plausible reasoning in mathematics, science, law, and other discliplines.
Symbolic logic is a system for expressing logical rules in an abstract, easily manipulated form.
In algebra, a letter such as x represents a number. Although the symbol gives no clue as to the value of the number, it can be used nevertheless in the formation of sums, products, etc. Similarly P, in geometry, stands for a point and can be used in describing segments, intersections, and the like. In symbolic logic, a letter such as p stands for an entire statement. It may, for example, represent…
Logic deals with statements, and statements vary extensively in the precision with which they may be made. If someone says, "That is a good book," that is a statement. It is far less precise, however, than a statement such as "Albany is the capital of New York." A good book could be good because it is well printed and bound. It could be good because it is written in goo…
Negation is another logical "operation." Unlike conjunction and disjunction, however, it is applied to a single statement. If one were to say, "She is friendly," the negation of that statement would be, "She is not friendly." The symbol for negation is " ~." It is placed in front of the statement to be negated, as in ~ (pΛ…
Another word used in both ordinary English and in logic is "or." Someone who says, "Either he did not hear me, or he is being rude," is saying that at least one of those two possibilities is true. By connecting the two possibilities about which he or she is unsure, the speaker can make a statement of which he or she is sure. In logic, "or" means "an…
Equivalent propositions or statements can be symbolized with the two-headed arrow " ." In the preceeding section we showed the first of De Morgan's rules: Rules such as these are useful for simplifying and clarifying complicated expressions. Other useful rules are Each of these rules can be verified by writing out its truth table. A truth table traces each of the var…
In any discipline one seeks to establish facts and to draw conclusions based on observations and theories. One can do so deductively or inductively. In inductive reasoning, one starts with many observations and formulates an explanation that seems to fit. In deductive reasoning, one starts with premises and, using the rules of logical inference, draws conclusions from them. In disciplines such as …
Please include a link to this page if you have found this material useful for research or writing a related article. Content on this website is from high-quality, licensed material originally published in print form. You can always be sure you're reading unbiased, factual, and accurate information.
Highlight the text below, right-click, and select “copy”. Paste the link into your website, email, or any other HTML document.
User Comments