Deductive Reasoning

7. The premises need not be true. Validity is a relation and not a certificate. "All lawyers can fly; she is a lawyer; therefore she can fly" is perfectly valid and thoroughly absurd, and both of those things are true at once.

Demonstrating feature 1

The claim that denial produces a contradiction is not a slogan and can be shown.

Take: every agreement enforceable by law is a contract; this agreement is enforceable by law; therefore this agreement is a contract.

Now try to deny the conclusion while keeping the premises. You must say: every agreement enforceable by law is a contract, and this agreement is enforceable by law, and this agreement is not a contract. The second and third statements together give you an agreement which is enforceable by law and is not a contract, and the first statement says there is no such thing. You have asserted and denied the same proposition. That is what "necessity" means here, and it is not a claim about how confident anybody feels.

The forms this syllabus will teach

Deductive inference is divided by how many premises it uses, and the division is MU's own, at topic 3.1.

Immediate inference draws a conclusion from a single premise. From "all contracts are agreements" it follows immediately that "some agreements are contracts". The whole of Module III, opposition and eduction, is immediate inference.

Mediate inference draws a conclusion from two or more premises taken together, and its classical form is the syllogism, three propositions and three terms. Every example in this chapter is a syllogism.

Note carefully: the syllogism itself is Logic II's subject and is not on this paper. It appears here only because the basic features of deduction cannot be shown without an example, and the syllogism is the natural one. What this paper examines is immediate inference.

A worked example

Section 11 of the Indian Contract Act 1872 provides that every person is competent to contract who is of the age of majority according to the law to which he is subject, who is of sound mind, and who is not disqualified from contracting by any law to which he is subject.

Ravi, aged seventeen, signs an agreement to sell his motorcycle.

The deduction.

1. Only a person who is of the age of majority is competent to contract.

2. Ravi is not of the age of majority.

Therefore Ravi is not competent to contract.

Test each feature against it. Is it truth preserving? If both premises are true the conclusion cannot be false. Is it ampliative? No: premise 1 already says that non-majors are not competent, and premise 2 puts Ravi among them; nothing new has entered. Does form alone decide? Yes: replace "competent to contract" with any predicate and "Ravi" with any name and the argument stands. Would further facts destroy it? No: learning that Ravi is unusually mature, or that the price was fair, or that he has a bank account, changes nothing whatever, because none of it makes him of the age of majority.

That last point is the one worth dwelling on. In an inductive argument, every one of those additional facts would matter. In a deductive one they are simply irrelevant, and a student who begins arguing about Ravi's maturity has not understood which kind of reasoning is in play.

Distinctions that carry marks

That last row is a tendency and not a definition, and the reason is under "What this does not mean" below.

What this does not mean

Deduction is not "general to particular". This is the definition most students arrive with and it is wrong. "All contracts are agreements; all agreements are promises; therefore all contracts are promises" moves from general to general and is deductive. "Ravi is a minor; Ravi signed this agreement; therefore some minor signed this agreement" moves from particular to particular and is deductive. The definition is necessity, not direction. The direction is only a common pattern.

Deduction does not give certainty about the world. It gives certainty about the connection. The conclusion of a valid argument is only as good as its premises, and the premises come from outside logic.

"Not ampliative" is not a criticism. That deduction adds no information is the price of its reliability, and it is a bargain: a lawyer who can show that a conclusion is already contained in a statute and an admitted fact does not need any further information.

Limits

The great limitation of deduction is that it cannot establish its own premises. Every deductive argument has to be given something to work on, and where the premises come from is not a deductive question. In law they come from statutes, from precedent and from findings of fact, and findings of fact are reached inductively, which is the subject of the next chapter and the reason the two are taught together.

Quick revision

Definition: an argument whose premises are claimed to provide conclusive grounds for its conclusion, so that if they are true it cannot be false.

Seven features: necessity; truth preserving; not ampliative; judged by validity, which has no degrees; validity depends on form alone; adding premises cannot destroy it; premises need not be true.

Necessity means contradiction: asserting the premises and denying the conclusion is self-contradictory.

Two kinds: immediate inference, one premise, which is Module III; mediate inference, the syllogism, which is Logic II.

Not "general to particular", which is the standard student error. General to general and particular to particular deductions both exist.

Its limit: it cannot establish its own premises.

Test yourself

1. Define deductive reasoning and explain the word "necessity" in your definition.

Deductive reasoning is reasoning in which the premises are claimed to provide conclusive grounds for the conclusion, so that if the premises are true the conclusion cannot be false. "Necessity" is not a description of the arguer's confidence. It means that asserting the premises while denying the conclusion produces a contradiction, that is, requires the same proposition to be both asserted and denied.

2. List the basic features of deductive reasoning.

The conclusion follows necessarily; the reasoning is truth preserving, so true premises cannot yield a false conclusion; it is not ampliative, adding no information beyond what the premises already contain; it is judged by validity, which admits of no degrees; validity depends on the form of the argument and not on its subject matter; adding further premises cannot make a valid argument invalid; and the premises need not in fact be true for the argument to be valid.

3. Why is it wrong to define deduction as reasoning from the general to the particular?

Because the direction of movement is a common pattern and not the defining feature. Deductions run from general premises to general conclusions, as in a chain of universal propositions, and from particular premises to particular conclusions. What makes an argument deductive is the claim that the conclusion follows necessarily, and arguments of every direction can make that claim.

4. What does it mean to say that deduction is not ampliative, and is that a defect?

It means the conclusion contains no information that was not already present, at least implicitly, in the premises: deduction makes explicit what was implicit rather than adding to our knowledge of the world. It is not a defect but the reverse side of reliability. The reason deduction can guarantee its conclusion is precisely that it never ventures beyond what it was given.

5. What is meant by saying deduction is monotonic, and why does it matter in litigation?

That adding further premises to a valid argument cannot make it invalid. It matters because it tells a lawyer which additional facts are worth investigating. Where a conclusion rests on a valid deduction from a rule and an admitted fact, no amount of further evidence about surrounding circumstances can touch it, and time spent gathering that evidence is wasted. Where the reasoning is inductive, the position is exactly the opposite.

6. Give a valid deductive argument with false premises and explain what it shows.

"Every document registered under the Registration Act is a contract; this sale deed is registered under that Act; therefore this sale deed is a contract." The first premise is false, since many registered documents are not contracts, so the argument is unsound. It is nevertheless valid, because if the premises were true the conclusion would have to be. It shows that validity concerns the connection between premises and conclusion and says nothing about truth.