HISTORY OF LOGICHuman beings have certainly been thinking logically since before the dawn of recorded history. But the academic discipline named logic dates back only to the 4th century B.C., to the city of Athens, Greece. For it was there that the ancient Greek philosopher Aristotle (384-322 B.C.) wrote the first known treatises of logical theory and began teaching the first logic classes in history. The subject matter of the new academic subject was not specific reasoning about a particular topic, rather, it was the standards any reasoning must follow if it is to be good reasoning.

In sum, logical thinking has been around as long as human beings have been reasoning, but the academic discipline named “logic” only dates to the 4th century B.C., to the creative genius of one of the greatest of the ancient Greek philosophers, Aristotle. Incidentally, the subject founded by Aristotle was not called “logic” at first and apparently did not have a formal name during his lifetime. Several decades after the death of Aristotle, it was named “Logos” by a school of philosophers who met every day in downtown Athens on a painted porch (Greek: “stoa”), the philosophers known to history as the Stoics.

The founder of logic as an academic subject was born and spent his early years in Macedonia, a state located on the northeastern part of the Greek peninsula. After his father died, Aristotle was sent to Athens, to study philosophy at Plato’s Academy, the first recognizable university in world history. (The name of the school came from its location: the grove of Akademos, a garden of olive trees named after a legendary Greek hero.) Aristotle studied under the great philosopher Plato (429-347 B.C.) for nearly 20 years before leaving to found his own university and research institute, the Lyceum.

It is likely that the seed idea for a subject devoted solely to the study of reasoning occurred to Aristotle while he was studying philosophy at Plato’s Academy. In order to see why the study of philosophy might inspire the birth of logical theory, let us take a brief look at the discipline the Greeks named philosophy (from the Greek words “philo” for love and “sophia” for wisdom, literally, “the love of wisdom”).

At the dawn of the 6th century B.C., ancient people everywhere made sense of the world on the basis of customary myths (stories passed down orally from generation to generation) and by obediently believing what priestly and political authorities told them to believe. Beginning with Thales of Miletus (c. 625- 546 B.C), a group of individuals in ancient Greece began questioning the customary myths and the traditional explanations of the universe. In written works and in discussions recorded in the historical record, these individuals pioneered a radically new way to make sense of the world. Named “philosophers” by the Greeks, Thales and his associates were the first persons in history to do all three of the following:

They rejected the explanations of the world contained in the traditional myths and the claims of religious and political authorities, on the grounds that there was no good reason to believe that unbacked myths and unquestioned claims of authorities are true, that is, in correspondence with reality.

In place of mythical stories and authoritative pronouncements, they sought explanations based on unaided reasoning and on observations that could in principle be made by anyone.

They put their theories and the supporting evidence for their theories into written form and passed this around for critical comments, reasoned discussion, and intellectual debate. Philosophical theories were to be proposed, criticized, defended, revised, and / or rejected on the basis of reasoning and observable evidence, without reference to unbacked myth and authorities whose statements could not be questioned.

In short, the first philosophers sought rational explanations of the world and of things within the world—accounts justified on the basis of evidence and reasoning alone. The birth of the philosophical tradition, in ancient Greece during the 6th century B.C., was one of the first intellectual revolutions in world history.

The Value of LogicThe principles of logic are thus no mere academic exercise. They are guides to correct reasoning just as the principles of accounting are guides to keeping a correct set of books, the principles of arithmetic are guides to correctly adding, subtracting, multiplying and dividing numbers, the principles of photography are guides to taking good pictures, the principles of physics are guides to correctly landing a manned spacecraft on the moon and getting it back home again afterwards, and so on. Not everyone reasons correctly all the time. Everyone makes logical errors at least sometimes. We all need to pay attention to the principles of logic, at least when matters get complicated and things get hard to sort out.(The Worlds of Many Logic, http://www.manyworldsoflogic.com/whatIsLogic.html)

The Significance of Logic for LawProf. Douglas LindEver since Justice Holmes asserted that “[t]he life of the law has not been logic: it has been experience,” lawyers and judges in the United States have minimized the importance of formal logic for understanding law and legal reasoning. Many legal scholars and practitioners have feared that to acknowledge that logic is central to law would risk a return to the rationalistic excesses of the formalistic jurisprudences that dominated nineteenth century legal thought. It was, after all, against that formalist tradition that Holmes wrote. And it was in spirited opposition to that tradition that members of the Legal Realist movement in America, as well as the Free Law movement in Europe, directed much of their energies early in the twentieth century.

There is good reason to remain skeptical of overly rationalistic accounts of law and judicial practice. The weave of historical doctrine, legal principle, and factual nuances that goes into each judicial decision is far too intricate to permit critical appraisal under any single evaluative method, including the principles of logic. So we are rightfully apprehensive when we recollect the formalistic visions of nineteenth century jurists — visions which found the essence of adjudication in the logical derivation of conclusions necessarily required by predetermined legal principles.

Yet it is somewhere between strict formalistic jurisprudence and an outright disregard for logic and argumentative form where the law and judicial practice really find repose. Though all that is typically repeated of Justice Holmes’ view is the pithy remark quoted above, his jurisprudential writings together with his judicial opinions show clearly that he never intended to suggest that logic is not a central aspect of law or judicial decision making. He, as well as the legal realists and other critics of legal formalism, well recognized that evaluating and creating arguments lie at the heart of the crafts of lawyering and judging.

It is thus worthwhile for practitioners and students of the law alike to possess an understanding of the basic principles of logic that are used regularly in legal reasoning and judicial decision making. This understanding requires, in important part, skill in navigating the processes of inductive reasoning — the methods of analogy and inductive generalization — by which inferences are drawn on the basis of past experience and empirical observation. The common law method of case law development, as well as the general prescript often referred to as “the Rule of Law” — that like cases be decided alike — are grounded logically in inductive reasoning.Equally important is a second basic category of argumentation — deductive logic, especially the deductive argument forms known as “syllogisms.” These are the classic forms of deductive argument consisting of a major premise, a minor premise, and a conclusion. It was this aspect of logic that a century ago stirred such virulent opposition to formalism. And it is this aspect of logic which was so severely downplayed throughout the twentieth century. Yet even a rudimentary understanding of deductive logic gives lawyers, judges, and students of the law a valuable tool for determining whether an argument in a legal opinion or brief is valid or fallacious.In essence, the domain of the law and, within that domain, perhaps most especially the practice of judicial decision making are exercises in practical reasoning. Law, to be sure, involves more than logic. Yet the myriad of factors that contribute to good lawyering and fair judging suggest that the “life of the law,” while not logic alone, is a manifold of activities that all use and depend upon reason in specialized ways. The precision of detail required in the drafting of contracts, wills, trusts, and other legal documents is a rational precision; the care in planning and strategizing demanded of trial attorneys in deciding how to present their cases is a rational care; the skill in written and oral argumentation required for appellate practice is, quite obviously, a rational skill; the talent expected of administrative law judges in crafting coherent findings of fact and conclusions of law is a rational talent; and the ability of trial and appellate court judges to separate, dispassionately and without bias, the kernel of argument from the rhetorical and emotive chaff of adversarial presentation, so as to render judgments that are justified under the law, is a rational ability.

While it is true that many other factors — from self-interest to moral values, from psychology to science — enter into the decision making of lawyers and judges, all such factors bear the ever-present tincture of reason and logic. Trial attorneys may appeal to the psychology or sentiments of the jury, but only so far as they reasonably expect to influence the jury to draw rational inferences in their client’s favor. Self-interest may be the sole driving motive for each party in the drafting of a contract, yet the recognition, grounded in reason, that insisting on onerous provisions will likely undermine the entire contractual arrangement has the tendency to hold everyone’s self-interest in check. And while adjudicative practice calls for a good deal of “value judgment” in the choice, interpretation, and application of legal principles, such value judgments are not free of the constraints of reason. As stated by one appellate court, “[E]very legal analysis should begin at the point of reason, continue along a path of logic and arrive at a fundamentally fair result.” (Sunrise Lumber v. Johnson, Appeal No. 165). To criticize, reverse, or overrule an administrative or judicial decision as “arbitrary,” “capricious,” “unsupported by law,” or “contrary to precedent” is to say nothing more, but nothing less, than that the decision is deficient in logic and reason.(THE NATIONAL JUDICIAL COLLEGE, http://www.judges.org/the-significance-of-logic-for-law/)

Induction vs. Deduction

In writing, argument is used in an attempt to convince the reader of the truth or falsity of some proposal or thesis. Two of the methods used are induction and deduction.

Induction:

Example:

A process of reasoning (arguing) which infers a general conclusion based on individual cases, examples, specific bits of evidence, and other specific types of premises.

In Chicago last month, a nine-year-old boy died of an asthma attack while waiting for emergency aid. After their ambulance was pelted by rocks in an earlier incident, city paramedics wouldn’t risk entering the Dearborn Homes Project (where the boy lived) without a police escort.

Thus, based on this example, one could inductively reason that the nine- year-old boy died as a result of having to wait for emergency treatment.

Guidelines for logical and valid induction:1. When a body of evidence is being evaluated, the conclusion about that

Deduction:

Example:

evidence that is the simplest but still covers all the facts is the best conclusion.

2. The evidence needs to be well-known and understood. 3. The evidence needs to be sufficient. When generalizing from a sample to an entire population, make sure the sample is large

enough to show a real pattern. 4. The evidence needs to be representative. It should be typical of the entire population being generalized.

A process of reasoning that starts with a general truth, applies that truth to a specific case (resulting in a second piece of evidence), and from those two pieces of evidence (premises), draws a specific conclusion about the specific case.

Free access to public education is a key factor in the success of industrialized nations like the United States. (major premise)India is working to become a successful, industrialized nation. (specific case)

Therefore, India should provide free access to public education for its citizens. (conclusion)

Thus, deduction is an argument in which the conclusion is said to follow necessarily from the premise.

Guidelines for logical and valid deduction:

1. All premises must be true. 2. All expressions used in the premises must be clearly and consistently defined. 3. The first idea of the major premise must reappear in some form as the second idea in the specific case. 4. No valid deductive argument can have two negative premises. 5. No new idea can be introduced in the conclusion.

PROPOSITIONS AND SENTENCES

Leitgeb distinguishes between statements, which are declarative sentences (he calls them 'descriptive sentences'), from propositions, which, unlike statements, are not linguistic objects. Propositions are the sort of objects that can have truth-values. E.g., [that snow is white] is a true proposition (Lecture 2-1).

Once the distinction is made, the key idea is this: statements express propositions, which are then said to be true or false. E.g. "snow is white" is a statement that itself doesn't have a truth-value, but instead expresses the proposition that snow is white, which happens to be true. That's pretty much it.

Logic is the science that evaluates arguments.An argument is a group of statements including one or more premises and one and only one conclusion.A statement is a sentence that is either true or false, such as "The cat is on the mat." Many sentences are not statements, such as "Close the door, please" , "How old are you?"A premise is a statement in an argument that provides reason or support for the conclusion. There can be one or many premises in a single argument.A conclusion is a statement in an argument that indicates of what the arguer is trying to convince the reader/listener. What is the argument trying to prove? There can be only one conclusion in a single argument.