Logic
From CreationWiki, the encyclopedia of creation science
Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) encompasses the guiding principles of reasoning.
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What Logic Is
There are a number of views regarding what logic actually is:
- Logical objectivism: Logic encompasses the guiding principles that organize the universe itself; they exist whether we believe in them or not.
- Logical subjectivism: Logic encompasses a set of abstractions designed by humans to explain what we see in the universe; they only exist because we invented them, and are not fundamental principles of the universe itself.
One's opinion on this issue has a substantial impact on one's approach to science and the universe. If one believes that logic is objective and real, then logical argument, debate, and science become our means of learning how the universe actually is: it brings empowerment, and ultimately joy. If, on the other hand, one believes that logic is only an artificial abstraction humans have invented to explain what we experience, then logical argument becomes nothing more than one person forcing his feelings on another.
History's greatest scientists, from Aristotle to Galileo to Newton, all held to the former view. They viewed the universe as having objective, logical principles which exist whether we understand them or not, and viewed philosophy and science as man's effort to grasp the true nature of the universe. Great scientists who were also creationists, they all further believed that God endowed the universe with logic, so that logic is nothing less than the mind of God.
Branches of Logic
Branches of logic include:
- Informal logic: The reasoning that occurs in daily life, in the course of decision-making and debate;
- Formal logic: A set of formal "rules of logic;"
- Symbolic logic: A system of symbols reducing formal logic to formulae similar to mathematics;
Informal logic
Informal logic is the form of logic people use in everyday life. It is primarily concerned with making effective arguments, making good decisions, and avoiding logical fallacy. While it is extremely important, it is also extremely difficult to boil down to a set of hard and fast rules, because it operates in the uncertain realm of daily life, when many things are unknown to us. For example, juries must seek to use logic to determine whether they believe, "beyond a reasonable doubt," that a person committed a particular crime. However, in most cases, because they cannot actually observe the events surrounding the crime, they cannot know for certain whether or not a crime was committed. To compensate for their uncertainty, they must apply their common sense, their knowledge of human nature, and the evidence presented to them, in order to make a logical decision as to what they think occurred.
Formal logic
Formal logic is a set of formal "rules of logic" that have themselves been given names. For example, one "rule of logic" is the syllogism: "Major premise: All humans are mortal; Minor premise: Socrates is a human; Conclusion: Therefore Socrates is mortal." Formal logic states the "law of logic" that if both the major premise and minor premise are true, then the conclusion is true.
The laws of formal logic can be named and listed, and are reliable. Indeed, if Socrates is a human and all humans are mortal, then we know that Socrates must be mortal. But what if we doubt that Socrates was a human? What if we doubt that all humans are mortals? Then the argument holds no force. Formal logic is only as good as its premises. In this case, the premises are that all humans are mortal and Socrates is a human. But formal logic cannot question its premises. If someone counters the argument by saying, "I don't believe all men are mortal. Enoch didn't die," the formal logician has to resort to informal logic if he wants to continue the argument. He has to argue that it's not reasonable to believe that Socrates was immortal.
Consequently, formal logic is a powerful tool, but is powerful only within a very limited realm: arguments in which both parties agree on the premises. And unfortunately, the parties to an argument rarely agree on their premises.
Symbolic logic
Symbolic logic is a system of variables and symbols, much like those used in mathematics, that allows logicians to quickly sort through complex problems in formal logic. It is useless, however, in solving problems in informal logic, because just like formal logic, it only functions in arguments where the parties agree on their premises.
Relationship between the branches of logic
Informal logic is the broadest of all the forms: it encompasses all the issues of reasonableness, of evidence, and of logical fallacy that we address in daily life. It also knows by "common sense" the things that formal logic only knows by rules. One doesn't need to know what the word "syllogism" means to know that if all humans are mortal and Socrates is a human, then Socrates is mortal. It's common sense.
Formal logic and its symbolic counterpart are more secure and certain than informal logic. Their rules can be named, tested, and verified. However, they only operate within a limited realm: the realm in which the parties agree on their premises. They have nothing to say when it comes to questions of whether premises are reasonable or not. Further, they are, for the most part, simply a codification of informal logic: putting names on things we all know by common sense.
Disciplines Within Logic
Traditionally, logic is studied as a branch of philosophy. Since the mid-nineteenth century logic has been commonly studied in mathematics, and, even more recently, in computer science. As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialist analyses of reasoning such as probably correct reasoning and arguments involving causality.
Formal logic encompasses a wide variety of logical systems. Various systems of logic we will discuss later can be captured in this framework, such as term logic, predicate logic and modal logic, and formal systems are indispensable in all branches of mathematical logic. The table of logic symbols describes various widely used notations in symbolic logic.
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