Deduction
from 350 BCE Aristotle gives the first systematic account; the practice is older
Reasoning where the conclusion is already contained in the premises, so that granting them and denying it is a contradiction rather than a mistake.
- Active
- from 350 BCE
- Where
- Athens
- Status
- In use
- Tradition
- Forms of inference
What it is
Deduction is the family of inferences in which the truth of the premises guarantees the truth of the conclusion. Not makes it likely, not supports it — guarantees it. If the premises are true and the form is valid, the conclusion cannot be false.
This is a much stronger claim than it first appears, and it comes at a price. A deductive argument never tells you anything that was not already present in what you put in. Its whole work is to make explicit what you had committed yourself to without noticing.
How it works
State the premises. Check that the form is one where the conclusion cannot fail if the premises hold. Draw the conclusion.
The second step is where the discipline lies, and it is the only step that logic proper is concerned with. Whether the premises are actually true is somebody else's problem — the historian's, the engineer's, the witness's. Logicians call an argument *valid* when the form is right and *sound* when the premises are true as well, and the gap between those two words is where most bad arguments live.
The form of the inference
- The premises are granted
- The form is one in which true premises cannot yield a false conclusion
- Therefore the conclusion is granted, on pain of contradiction
The argument
Proposition The tenant is entitled to the bond back in full.
- Under the residential tenancies act, a bond must be returned in full unless the landlord lodges a claim within fourteen days of the tenancy ending.
- This tenancy ended on the third of March.
- The landlord lodged no claim before the seventeenth of March.
- So no claim was lodged within fourteen days of the tenancy ending.
Therefore The bond must be returned in full.
Nothing has been discovered here. Everything in the conclusion was already sitting in the act and the calendar. What the deduction does is make it undeniable, which in a dispute is worth a great deal more than discovery.
What it is good for
Anywhere a rule has to be applied to a case and the result must hold rather than merely seem reasonable. Law, engineering, accounting and mathematics all run on it. It is also the only kind of reasoning that can show an opponent that they are already committed to a conclusion they are resisting.
Where it fails
It fails by being asked to do work it cannot do. Deduction cannot establish its own premises, and a valid argument from a false premise produces a confident, well-formed falsehood — one that is harder to dislodge than a sloppy argument, because everything downstream of the premise is beyond reproach.
Its second failure is subtler. Because the conclusion adds nothing, a deductive argument can feel like progress while being a very expensive way of restating what you began with. Long formal derivations sometimes conceal that nothing was learned.
Common misconceptions
That it means reasoning from the general to the particular. That describes some deductions and not others, and there are perfectly good deductions running the other way.
Also the detective's usage. What Holmes does is almost entirely abduction — reasoning to the best explanation of the evidence — which is not deduction and carries none of its guarantees.
Where it came from
Aristotle's Prior Analytics is the first systematic treatment, built around the syllogism. The Stoics developed a parallel and in some ways more powerful propositional system that was largely lost until the nineteenth century rediscovered the same ground.
What became of it
Absorbed and vastly extended by mathematical logic from Frege onward, to the point where Aristotle's syllogistic is now a small fragment of a much larger system.
Lasting influence
It is the model against which every other kind of reasoning has been measured, usually to that other kind's disadvantage. A great deal of philosophy consists of trying to make some other form of argument look more like this one.
Why it still matters
Unchanged. Every proof, every legal application of a statute and every line of correct code is deduction at work.
Put another way
An unpacking rather than a journey. Everything you take out was in the case when you closed it.
Texts
Aristotle, Prior Analytics
The founding treatment, and still readable, though the syllogistic apparatus it builds has been superseded by more general systems.
Where to start
Any first logic course. The rules take a fortnight; telling a valid argument from a sound one is the work of a lifetime.
The surprising bit
Its greatest strength and its greatest limitation are the same fact. Because nothing new can appear in the conclusion, deduction can never tell you anything about the world that your premises did not already contain.
In their own words
A deduction is an argument in which, certain things being stated, something other than what is stated follows of necessity
Who held it
Bertrand Russell
Connections
- Set against
- Induction
The verdict
The only form of inference that comes with a guarantee, and the guarantee covers less than people want it to.