Truth and Validity
Chapter Eleven
Syllabus topic 1.4, "Some basic logical concepts - Truth, Validity, Inference, Implication."
Pages 53 to 57 of 334
In one line
Truth is a property of propositions; validity is a property of arguments; and neither one implies the other.
In the wording a student can write in an examination: a proposition is true when what it asserts is so, and false otherwise. An argument is valid when its conclusion follows necessarily from its premises, that is, when it is impossible for the premises to be true and the conclusion false. The two notions apply to different things and must never be interchanged.
Why this is the most examined distinction in the paper
Because the words are used loosely in ordinary speech and precisely in logic, and the gap between the two is where students lose marks. In everyday English "that is not a valid argument" often means "I do not accept your premises", and "that is true" often means "that is a good point". In logic neither usage is available.
The safest habit is a verbal one. Never say a proposition is valid. Never say an argument is true. Those two sentences are not merely wrong; they are meaningless, in the way that "a green idea" is meaningless, and an examiner reading either of them knows immediately that the distinction has not been understood.
Truth
A proposition is true if what it asserts is the case, and false if it is not. "The Indian Contract Act was passed in 1872" is true because the Act was passed in 1872. Nothing else is required and nothing else is relevant: not whether anybody believes it, not whether anybody can prove it, not whether it is useful to say so.
Three consequences are worth stating because each is asked.
Truth is not belief. A proposition believed by everyone may be false, and one believed by nobody may be true. Belief is a fact about people; truth is not.
Truth is not proof. A proposition may be true and unproved, which is the ordinary position of a fact in a case before the evidence is led. Proof is what persuades a tribunal; truth is what is so.
Only propositions have truth values. Questions, commands, requests and exclamations are none of them true or false. "Serve the notice" is neither true nor false, which is why it can be neither a premise nor a conclusion.
Validity
An argument is valid when it is impossible for its premises all to be true and its conclusion false at the same time. That is the whole definition, and every property of validity follows from it.
Validity is about the connection, never about the contents. It says what would happen if the premises were true. It does not say they are true, and it is not disturbed by their being false.
Truth and Validity
Validity depends on form alone. Two arguments with the same arrangement of terms and propositions are both valid or both invalid, whatever they are about. This is why symbols work and why one rule covers every subject.
Validity has no degrees. An argument is valid or invalid. "Fairly valid" and "more valid" are not expressions in this subject.
The eight combinations, and the one that cannot happen
Take a deductive argument. Its premises are all true or not, its conclusion is true or not, and it is valid or not. That is eight cases. Seven of them occur, and one is impossible, and knowing which is the examinable point.
| Premises | Conclusion | Valid | Possible? |
|---|---|---|---|
| All true | True | Valid | Yes; this is a sound argument |
| All true | True | Invalid | Yes; true conclusion reached by a bad route |
| All true | False | Valid | No. This is the one impossible case |
| All true | False | Invalid | Yes |
| Some false | True | Valid | Yes |
| Some false | True | Invalid | Yes |
| Some false | False | Valid | Yes |
| Some false | False | Invalid | Yes |
The third line is the definition of validity, stated as an impossibility. Everything a student needs about truth and validity is contained in the fact that exactly one of these eight rows is empty.
Examples of the ones people find hard to believe:
True premises, true conclusion, invalid. "All lawyers are graduates; she is a graduate; therefore she is a lawyer." Both premises may be true and the conclusion may be true, and the argument is still worthless, because being a graduate does not put her among the lawyers. Had she been a doctor, the same argument with the same true premises would have produced a false conclusion.
False premises, true conclusion, valid. "All Acts of Parliament are printed in green ink; the Contract Act is an Act of Parliament; therefore the Contract Act is printed in green ink." Change the conclusion to something true and adjust: "All statutes have sections; the Contract Act is a statute; therefore the Contract Act has sections", where the first premise is not quite true of every statute, is valid and reaches a true conclusion.
False premises, false conclusion, valid. "All contracts are in writing; this contract is a contract; therefore this contract is in writing." Valid, false throughout.
What validity is worth
If a valid argument can have false premises and a false conclusion, what is validity for?
It is worth exactly this: a valid argument transmits truth. It guarantees that you will never move from truth to falsehood. Put true premises in and you must get a true conclusion out. Put anything else in and the guarantee is off, but the machine is not at fault.
That is why the two questions of the evaluation chapter are asked in the order they are. Test validity first, because it is a question logic can answer on its own. Then test the premises, which is a question for evidence and for law. An argument that passes both is sound, and a sound argument's conclusion is established.
Truth and Validity
A worked example
In cross-examination, counsel puts the following to a witness.
"You said you were at the shop at six o'clock. The shop closes at five thirty. So you were not there at all."
Set it out.
1. The witness says he was at the shop at six o'clock.
2. The shop closes at five thirty.
Therefore the witness was not at the shop at all.
Is it valid? No, and the invalidity is gross. Even granting both premises, all that follows is that he was not there at six, or that the shop was open late, or that he was mistaken about the time. That he was never there at all does not follow from anything.
Are the premises true? Quite possibly both.
What is the verdict? True premises, invalid argument, and a conclusion that may be true or false for reasons this argument has not touched. The witness may indeed have been lying about everything. This question does not show it, and if the point is left there the record contains an unanswered assertion rather than a proved contradiction.
Why it matters practically. Counsel who understands the distinction asks the next question, which is what the witness was doing at five thirty. Counsel who does not sits down satisfied.
Distinctions that carry marks
| Truth | Validity | |
|---|---|---|
| Belongs to | Propositions | Arguments |
| Definition | What is asserted is the case | Premises cannot be true with the conclusion false |
| Established by | Evidence, observation, law | Logic alone |
| Depends on subject matter | Yes | No, on form alone |
| Degrees | No | No |
| Opposite | Falsity | Invalidity |
| Valid | Sound | |
|---|---|---|
| Requires | The right form | The right form and true premises |
| Guarantees | Nothing about the conclusion by itself | That the conclusion is true |
| Applies to | Deductive arguments | Deductive arguments |
What this does not mean
An invalid argument is not one with false premises. That is unsoundness. Invalidity is a defect in the connection, and it is present or absent whatever the premises are.
A valid argument is not necessarily a good argument. It may be valid and start from premises nobody accepts, in which case it establishes nothing and wastes everybody's time.
Truth is not "what the court finds". What the court finds is what is proved. The two usually coincide and sometimes do not, which is why appeals and reviews exist.
Quick revision
Truth belongs to propositions, validity to arguments. Never say a proposition is valid or an argument is true.
Truth and Validity
Valid: impossible for the premises to be true and the conclusion false.
Sound: valid and all premises true. Only a sound argument establishes its conclusion.
Of the eight combinations, only true premises with a false conclusion in a valid argument is impossible. That single impossibility is the definition of validity.
Validity transmits truth: true in, true out. Nothing else is guaranteed.
Validity depends on form alone and has no degrees.
Test yourself
1. Define truth and validity and state what each belongs to.
A proposition is true when what it asserts is the case and false when it is not; truth belongs to propositions. An argument is valid when it is impossible for all its premises to be true while its conclusion is false; validity belongs to arguments. The two notions apply to different kinds of thing, so calling a proposition valid or an argument true is not a mistake of fact but a misuse of the words.
2. Which combination of premise truth, conclusion truth and validity is impossible, and why?
An argument cannot be valid, have all true premises, and have a false conclusion. That combination is impossible because it is precisely what validity is defined to exclude: to say an argument is valid is to say that this situation cannot arise. Every other combination of the three can and does occur.
3. Give an example of a valid argument with false premises and a true conclusion, and say what it shows.
"Every statute is divided into sections; the Bharatiya Nyaya Sanhita is a statute; therefore the Bharatiya Nyaya Sanhita is divided into sections." The first premise is not true of every statute, so the argument is unsound, yet it is valid and its conclusion is true. It shows that validity concerns the connection alone, and that a true conclusion is no evidence that the argument which produced it was any good.
4. Why must validity be tested before the truth of the premises?
Because validity is a question logic can settle by itself, needing no facts, while the truth of the premises requires evidence, investigation or research into the law. If the argument is invalid the enquiry stops there and the premises need not be examined at all, since even true premises would establish nothing. Testing in the other order can waste all the work.
5. What does a valid argument guarantee?
That it will never carry you from truth to falsehood. If the premises are all true the conclusion must be true. It guarantees nothing when the premises are false: the conclusion may then be true or false, and the argument gives no indication which. This is what is meant by saying that validity is truth preserving.
Truth and Validity
6. Counsel says: "That is not a valid argument, because I do not accept your second premise." What is wrong with the sentence?
It confuses unsoundness with invalidity. Refusing to accept a premise is a challenge to the truth of the premise, which if made out shows the argument to be unsound while leaving it perfectly valid. Validity concerns whether the conclusion would follow if the premises were granted, and that question is untouched by whether anyone grants them.
The rest of this subject
These notes are cut from the University's printed syllabus. Open the syllabus itself, or the past papers, for the same subject.