What Logic Is: the Traditional Definitions

Logic is the science of reasoning. This is the definition most Indian textbooks put first, and it is the narrowest of the three. It says that logic is concerned with one particular mental operation, inference, the passage from something known to something not yet known.

Logic is the science and art of reasoning. This third form, associated with Archbishop Whately, adds a word deliberately. A science is a systematic body of knowledge about something. An art is a practical skill, a set of rules for doing something well. Whately's point was that logic is both: it studies inference and it also trains you to infer better, in the way that grammar both describes a language and teaches you to write it.

Science, art, or normative science

Examiners ask this as a short note, so it is worth having the answer ready in three sentences.

Logic is a science because it is a systematic and reasoned body of knowledge about a definite subject matter, namely the forms of correct inference. It is an art because its rules can be applied, and applying them is a skill that improves with practice. It is called a normative science because it does not merely record how people in fact think, which is what a purely positive science would do; it lays down a standard which thinking ought to satisfy.

The contrast that makes this clear is with psychology. Both logic and psychology study thinking. Psychology asks how people actually think, including all the ways they think badly, and it treats a fallacy as a fact to be explained. Logic asks how people ought to think if their conclusions are to be worth anything, and it treats a fallacy as an error to be corrected. Ethics and aesthetics are normative in the same way: ethics sets a standard for conduct, aesthetics for beauty, logic for thought.

"Logic is the science of sciences"

Added after the past-paper check. MU sets this exact phrase as an essay, usually joined to the questions whether logic is an art and whether deductive logic is purely formal while inductive is purely material. All three are answered here.

What the phrase claims. That logic is not one science among others but the science every other science depends on, because every science reasons and none of them studies reasoning. Chemistry tells you what happens when two substances meet; it does not tell you whether a conclusion follows from what it has found. Logic supplies that to all of them and takes nothing from any of them.

It is Aristotle's point in later words. He called his logical works the Organon, the instrument, for the same reason: an instrument is used by every craft and is the property of none.

How far the claim is fair. Fair, in that no science can dispense with logic and logic borrows nothing from any of them. Overstated, in that logic supplies only the form of reasoning: it can tell a chemist that his conclusion follows and can never tell him that his premises are true, which is the limit already stated at sequence 110.

Is logic an art as well? Yes, on Whately's answer above: a science because it is an organised body of knowledge about the forms of valid inference, and an art because its rules can be applied and applying them is a skill that improves with practice.

Is deductive logic purely formal and inductive purely material? The claim is half right and the half that is wrong is the examinable half.

Deductive logic is purely formal, and this part is correct. Validity depends on the arrangement of terms and propositions alone, so any two arguments of the same form stand or fall together whatever they are about. That is why the whole of Modules II and III can be conducted without a single real fact.

Inductive logic is NOT purely material. It certainly depends on matter in a way deduction does not: whether a sample is varied, whether an analogy's resemblances are relevant, whether a cause is plausible, are all questions about the subject and not about the shape. But induction also has form. Simple enumeration has a form, analogy has a form, and the tests of strength at sequence 90 are general rules that apply whatever the instances are about.

So the accurate answer is that deduction is formal and induction is both formal and material, its form supplying the pattern and its matter supplying the strength. A student who agrees with the proposition as put has conceded more than the evidence allows.

The three parts of traditional logic, which are also this syllabus

Traditional logic divided its own subject into three, following the three operations the mind was thought to perform.

Simple apprehension, the grasping of a single idea, expressed in language by a term. "Contract" is a term.

Judgment, the putting of two ideas together and asserting or denying one of the other, expressed in language by a proposition. "Every contract is an agreement" is a proposition.

Reasoning, the passing from one or more judgments to another, expressed in language by an inference or argument. "Every contract is an agreement; this is a contract; therefore this is an agreement" is an inference.

Now look at the syllabus. Module I ends with terms. Module II is propositions. Module III is inference. MU's Modules I to III are the three parts of traditional logic in their traditional order, and the reason the order cannot be rearranged is that each part is built out of the one before it: an inference is made of propositions, and a proposition is made of terms.

A worked example

Two neighbours, Anil and Bharat, are arguing. Anil says the boundary wall belongs to him because his grandfather built it. Bharat says it belongs to him because the municipal record shows the plot boundary running on the other side of it.

Nothing about that dispute is a matter of logic yet. Whether the grandfather built the wall is a question of fact, to be answered by evidence. Whether a municipal record proves ownership is a question of law, to be answered out of the statutes and the cases.

Logic enters at the third stage, and only there. Suppose the court accepts that the grandfather built the wall, and accepts a legal rule that a person who builds a wall on their own land owns it. Then "Anil's grandfather built the wall on his own land; a person who builds a wall on their own land owns it; therefore Anil's family owns the wall" is an inference, and logic can say whether the conclusion follows. It cannot say whether the grandfather built anything.

That is the whole division of labour. Evidence supplies the facts, law supplies the rules, and logic supplies the guarantee that the conclusion drawn from them is the conclusion they actually support.

Distinctions that carry marks

What this does not mean

Logic is not about being clever in an argument. Winning a quarrel by shouting, by ridicule or by appealing to sympathy is exactly what logic exists to expose. Those are studied later as fallacies, and they are studied as faults.

Logic does not tell you whether a statement is true. It tells you whether a statement follows from other statements. Whether those other statements are themselves true is a question for evidence, for science, or for the law of the land.

"Logical" does not mean "sensible". An argument can be perfectly valid and lead to a conclusion nobody would accept, because it started from a premise nobody should have accepted. Validity is about the connection, never about the starting point.

Limits of the traditional definitions

Each of the three traditional definitions has been criticised, and the criticism is what produced the modern definition in the next chapter.

"Science of the laws of thought" is too wide and too narrow at once. Too wide, because psychology also studies the laws of thought and is not logic. Too narrow, because a great deal of thinking, remembering a face, imagining a scene, feeling regret, involves no inference at all and logic has nothing to say about it.

"Science of reasoning" is criticised for the opposite reason: it names only the third of the three operations, when traditional logic in fact studies terms and propositions as well. The answer usually given is that terms and propositions are studied only because inference is made of them, which is fair, but it makes the definition depend on a qualification that the definition itself does not state.

Quick revision

Definition to write: logic is the science which investigates the general principles of valid thought, that is, of the distinction between correct and incorrect reasoning.

Etymology: Greek logos, meaning word, thought or reason. Aristotle called his logical works the Organon, the instrument.

Three traditional definitions: science of the laws of thought (Hamilton); science of reasoning; science and art of reasoning (Whately).

Logic is a normative science: it prescribes a standard, it does not merely describe. Compare ethics for conduct and aesthetics for beauty.

Logic against psychology: ought against is; product against process; error against fact.

Three parts of traditional logic: terms, propositions, inference. They are MU's Modules I, II and III.

"Logic is the science of sciences": every science reasons and none studies reasoning, so logic serves all of them and borrows from none. Aristotle's Organon makes the same point. Overstated only in that logic supplies form and never the truth of the premises.

Deduction is purely formal; induction is NOT purely material, since it has form as well, the tests of strength being general rules. Agreeing with the proposition as put concedes too much.

Main criticisms: "laws of thought" is both too wide (psychology) and too narrow (non-inferential thinking); "science of reasoning" ignores terms and propositions.

Test yourself

1. Define logic and explain each part of your definition.

Logic is the science which investigates the general principles of valid thought. "Science" means a systematic body of reasoned knowledge, not a collection of tips. "General principles" means that logic studies the form of reasoning and not the subject matter, so one principle covers arguments about contracts and arguments about chemistry alike. "Valid" means that logic asks whether the conclusion follows from the premises, not whether the premises are true.

2. Why is logic called a normative science?

Because it lays down a norm or standard which thinking ought to satisfy, instead of merely recording how people in fact think. A positive science such as physics describes what happens. Logic tells us what ought to follow from what, and treats a piece of reasoning that departs from it as wrong rather than as merely unusual. Ethics and aesthetics are normative in the same sense, for conduct and for beauty.

3. Distinguish logic from psychology.

Both study thought, but they ask different questions. Psychology asks how the mind actually works and includes bad reasoning among the facts it explains; it studies thought as a process going on in a particular person at a particular time. Logic asks how one ought to reason if the conclusion is to be worth anything, and studies thought as a product, judged by its form and independently of who thought it. A fallacy is a fact for the psychologist and an error for the logician.

4. Is logic a science or an art?

Both, and the traditional answer is Whately's. It is a science because it is an organised body of knowledge about a definite subject, the forms of valid inference. It is an art because its principles can be applied and the application is a skill that improves with practice. The comparison usually drawn is with grammar, which both describes a language and teaches its correct use.

5. State two criticisms of the definition "logic is the science of the laws of thought".

First, it is too wide: psychology also investigates the laws of thought, and psychology is not logic, so the definition fails to mark logic off from a neighbouring subject. Second, it is too narrow: a great deal of thinking, such as remembering, imagining or wishing, involves no inference, and logic says nothing whatever about it, so the definition claims more territory than logic actually occupies.

7. Explain "logic is the science of sciences".

The phrase claims that logic is not one science beside the others but the one every other science depends on, since every science reasons and none of them studies reasoning. Chemistry can tell you what two substances do and cannot tell you whether a conclusion follows from that. Aristotle made the same point by calling his logical works the Organon, the instrument, which every craft uses and none owns. The claim is fair as far as it goes and overstated in one respect: logic supplies the form of reasoning and never the truth of the premises.

8. Is it correct to say that deductive logic is purely formal and inductive logic purely material?

Half correct. Deductive logic is purely formal, since validity depends on the arrangement of terms and propositions alone and any two arguments of the same form stand or fall together. Inductive logic is not purely material: it does depend on the matter in a way deduction does not, since the variety of a sample and the relevance of a resemblance are questions about the subject, but it also has form, simple enumeration and analogy each having a pattern and the tests of strength being general rules. Deduction is formal; induction is both formal and material.

6. What are the three parts of traditional logic and how do they relate to each other?

Terms, propositions and inference, corresponding to simple apprehension, judgment and reasoning. They are studied in that order because each is built out of the one before: a term is the smallest unit, a proposition is made by joining two terms, and an inference is made by putting propositions together. This is also the order of Modules I, II and III of this syllabus, which is why the modules cannot be read out of sequence.